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Efficient analysis of OFDM channels. (English) Zbl 1397.94029
Rohling, Hermann (ed.), OFDM. Concepts for future communication systems. Berlin: Springer (ISBN 978-3-642-17495-7/hbk; 978-3-642-17496-4/ebook). Signals and Communication Technology, 109-114 (2011).
For the entire collection see [Zbl 1214.94004].
94A14 Modulation and demodulation in information and communication theory
Full Text: DOI
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[12] T.Strohmer,“PseudodifferentialoperatorsandBanachalgebrasinmobilecommunications,”Appl.Comput.Harmon.Anal.,20(2):237–249,March2006,WWW: http:///www.math.ucdavis.edu/∼strohmer/papers/2005/pseudodiff.pdf. 4.2 Generic Description of a MIMO-OFDM-Radio-Transmission-Link R. Amling, V. Kühn, University of Rostock, Germany 4.2.1 Introduction As more and more mobile devices are supporting multiple air interfaces it is necessary to choose the best radio access system for a requested service. Therefore, several quality parameters are needed to accomplish an automatic selection of the optimal access network. In order to prevent mobile devices from complex calculations a generic model is regarded to be useful. This model should allow the prediction of important parameters like error rate, data rate and latency as reliably as possible based on a usually imperfect channel estimation and related system parameters. The focus of this project is the analysis of a multiple-input multiple-output (MIMO) link in combination with orthogonal frequency-division multiplexing (OFDM). Channel coding, interleaving and further system parameters have been taken from the LTE-specifications. As the first half of the project time has elapsed, this summary presents only the results of a coded single-input single-output (SISO) OFDM system. 4.2.2 System Model dbax ENCΠMODOFDM TransmitterH dˆb˜˜ay DECΠ−1DEMODOFDM−1n ReceiverChannel Figure 4.1: System model of MIMO-OFDM link A typical OFDM link as depicted in Fig. 4.1 is considered. The binary information sequence d 0, 1Nd×1is encoded using one of the following three forward error correction schemes [1–3]. Code 1: convolutional code, constraint length Lc= 3, code rate Rc=1, generators 2 G = [7; 5]8 Code 2: convolutional code, constraint length Lc= 9, code rate Rc=1, generators 2 G = [561; 715]8 Code 3: parallel turbo code, constraint length Lc= 4, code rate Rc=1, generators 3 G = [13; 15]8 After encoding, a random bit interleaver is employed. The encoded and interleaved binary sequence b 0, 1Nb×1is mapped onto M -QAM symbols a with constellation sizes M =4, 16, 64, using binary reflected Gray mapping [4,5]. According to the LTE specifications [6], the OFDM symbol can consist of Nc= 256 subcarriers and a guard interval whose length NGis 20% of the core OFDM symbol. The corresponding sequence x is transmitted over a block fading channel whose impulse response has a length Nh∈ 2, 10, 20. Its coefficients are i.i.d. complex Gaussian distributed random variables with zero mean and variance 1/Nh. The additive noise is assumed to be white and Gaussian with n∼ N (0, σ2N). A major advantage of OFDM is the very efficient equalization of the received signal y due to frequency nonselective conditions on each subcarrier. The demodulation block provides LLRs ˜b of each code bit which are de-interleaved and decoded by a conventional Viterbi algorithm. As no iterative turbo detection is performed, this approach is termed bit-interleaved coded modulation with parallel decoding (BICM-PD) [5]. The estimated information word is denoted by ˆd 0, 1Nd×1. For channel estimation, a typical OFDM pilot symbol based approach is applied. In the simulations, NP= 2 OFDM pilot symbols with unit power are inserted in front of each OFDM frame. At the receiver, the estimation of the channel transfer function is improved by a noise reduction approach exploiting the fact that the channel impulse response does not exceed the guard interval [7, 8]. This leads to the estimated channel coefficient ˆHk= Hk+ ΔHkon subcarrier k with a variance of σ2N σH2=·NG.(4.3) NPNc 4.2.3 Performance Analysis In order to develop a feasible generic model, the achievable bit error rate (BER) for a fixed channel and a given signal to noise ratio (SNR) have been determined by simulations for different channel models, modulation and coding schemes. The channel capacity was chosen as an intermediate parameter representing the channel transfer function and the SNR by a single value. As will be shown later, this mapping is not bijective but allows a tight prediction of the BER. For subcarrier k and a perfectly known channel coefficient Hkat the receiver, the link capacity for a discrete input alphabetX and a continuous output set Y is  Ck= I(X; Y| Hk) =Prxp(y| x, Hk)· log2p(y| x, Hk) x∈XYp(y| Hk)dy .(4.4) Since BICM-PD is employed, the capacity Ckin (4.4) cannot be achieved. Instead, the bit-level capacities Ck,μblfor bit-level μ, μ = 0, 1, . . . , m− 1, with m = log2M as introduced in [5] have to be determined. This can be accomplished by applying the chain rule of mutual information Ck= I(b0, b1, . . . , bm−1; Y| Hk) = I(b0; Y| Hk) + I(b1; Y| b0, Hk) + . . . +(4.5) + I(bm−1; Y| b0, b1, . . . , bm−2, Hk) . Neglecting the constraint of known bit-levels leads to a reduction of the mutual information in (4.4) and the capacity for parallel decoding becomes m−1 Ckpd= I(b0; Y| Hk) + I(b1; Y| Hk) + . . . + I(bm−1; Y| Hk) =Ck,μbl< Ck. (4.6) μ=0 Finally, the average parallel-decoding capacity for an OFDM symbol with Nc subcarriers and m bit-levels becomes Cpd=1NcCpd1Ncm−1 Nck=NCk,μbl.(4.7) k=1ck=1μ=0 In order to infer from the bit-level capacities to the BER, simulations have been performed for different channel realizations, codes and modulation schemes. As an example, Fig. 4.2 illustrates the obtained results for a 16-QAM and all considered channel impulse response lengths with uniform power delay profile. a)Code 1b)Code 2c)Code 3 000 101010 −1−1−1 101010 →10→10→10 −3−3−3 101010 BERBERBER −4−4−4 1010simulated10simulated simulatedx1C + y1x1C + y1 xCy+ zx2C + y2x2C + y2 rateraterate 012340123401234 Cpdin bit/s/Hz→Cpdin bit/s/Hz→Cpdin bit/s/Hz→ Figure 4.2: Simulation results (gray), generated models (black) and for different FEC codes and 16-QAM In Fig. 4.2a), the error rates for the simple convolution code show an exponential slope with an increasing variance at higher capacities. For the convolution code with Lc= 9 and the turbo code in the diagrams b) and c), a waterfall-like behavior can be observed. Moreover, the turbo code’s BER can be predicted quite accurately as the variations are very small even at high capacities. The largest capacities required for a reference BER of 10−5are 3.4 bit/s/Hz, 2.6 bit/s/Hz and 1.7 bit/s/Hz for code 1, 2, and 3, respectively. Comparing these values with the spectral efficiencies R = m· Rcindicated by the dashed vertical lines, gaps ΔR(BER) = Cpd(BER)− R can be defined. They take the values 1.4 bit/s/Hz, 0.6 bit/s/Hz and 0.3 bit/s/Hz, respectively. As expected, the turbo code’s efficiency R approaches the capacity most closely. Further simulations have been performed for different modulation schemes and channels which cannot be shown in this survey. The modulation schemes 4QAM and 64-QAM show a similar behavior as 16-QAM. The 4-QAM reaches a BER of 10−5at 1.8 bit/s/Hz with code 1, 1.4 bit/s/Hz with code 2 and 1 bit/s/Hz with code 3 and has smaller variations at low error rates. For 64-QAM, the BER variations increase at higher capacities especially for the weak code 1. A BER of 10−5can be reached at capacities from 4 bit/s/Hz to 5 bit/s/Hz. Figure 4.3 illustrates that the relationship between bit error rate and bit-level capacity does not depend on the length of the channel impulse response. For different lengths Nh, the same quantitative behavior can be observed. a)Nh= 2b)Nh= 10c)Nh= 20 100100100 −1−1−1 101010 →→→ −3−3−3 101010 BERBERBER −4−4−4 101010 012340123401234 Cpdin bit/s/Hz→Cpdin bit/s/Hz→Cpdin bit/s/Hz→ Figure 4.3: Simulation results comparison for 16-QAM, Code 2 and different channel impulse response lengths Nh 4.2.4 Generic Model The aim of the project is to describe the dependency between the capacity Cpd and the BER by a generic model. This is accomplished by applying curve fitting algorithms to the results shown in Fig. 4.2. They provide results with a confidence level of 95%. For the code 1 with memory 2, an exponential function of the form log10( BER(C) ) = x· Cy+ z(4.8) emerged as the best description. The function is depicted in Fig. 4.2a). The parameters x, y and z are provided in Table 4.1 for 16-QAM modulation. For the other two codes, the curves were separated into two regions. The first region covers low capacities and high error rates, the second is the one of interest and includes the waterfall region. In both of them, the logarithm of the BER can be approximated by a straight line. We obtain log10( BER1(C) ) = x1C + y1for0 < C < CP(4.9a) log10( BER2(C) ) = x2C + y2forCP< C < log2(M ) ,(4.9b) where CPdenotes the capacity where both lines intersect. Figures 4.2b) and c) illustrate the results, the corresponding model parameters are summarized in Table 4.1. It also contains the gaps between the spectral efficiency R and the required capacity Cpdpredicted by the model. Table 4.1: Generic model parameters for 16-QAM Code 1Code 2Code 3 generic model log10(BER(C))x· Cy+ zx1,2· C + y1,2x1,2· C + y1,2 parameters region 1x =−0.3689 x1=−0.1085 x1=−0.2340 y = +2.1666y1=−0.2427y1=−0.3291 z =−0.2958-parameters region 2-x2=−4.4219 x2=−17.1307 -y2= +5.7116y2= +22.9040 ΔR at 10−51.240.420.3 In order to use these models, the capacity Cpdneeds to be computed using estimated channel coefficients ˆHkincluding errors ΔHkwith a variance determined in (4.3)2. For codes whose BER curves exhibit a very high slope, capacity estimation errors lead to dramatic prediction errors of the achievable error rate. This effect shall be investigated now. The channel estimation errors ΔHkare assumed to be independent and complex Gaussian distributed. Including ˆHkinto (4.6) leads to the final estimate ˆCpd=1NcCˆpd. Nck=1k An example for the distribution of ˆCpdat a target bit error rate 10−5for FEC code 2 is illustrated in Fig. 4.4a) which corresponds to an average Es/N0of 12.2 dB. Two OFDM pilot symbols are used for channel estimation with subsequent noise reduction. It can be observed that ˆCpdis nearly Gaussian distributed which could be expected since it stems from averaging over 256 subcarriers. The estimates’ mean depends on the specific channel realization and is generally close to the true capacity Cpdwhile the variance only depends on the signal to noise ratio of the operating point of the specific BICM scheme. Hence, ˆCpd> Cpdholds in most cases, i.e., the estimate is too optimistic and its application to resource allocation strategies would lead to error rates larger than 10−5. Further investigations revealed that the difference ΔCpd= ˆCpd− Cpdbecomes not larger than 0.027 bit/s/Hz for 95% of all estimated channels at the specific operating point of code 1, not larger than 0.04 bit/s/Hz for the operating point of code 2 and 0.053 bit/s/Hz for code 3. The distance ΔCpdis getting smaller at high SNRs as can be seen from Fig. 4.4b) illustrating the maximum relative deviation of 95% of all channels. Considering a worst case scenario, an offset reducing ˆCpdby max95(Δ ˆCpd) guarantees that 95% of all estimated capacities are not larger than Cpd. Otherwise, the model causes an outage. A second influence on the model quality is the variation of the required capacity 2It is assumed that the signal to noise ratio is perfectly known although this is a rather optimistic assumption. a)histogram of ˆCpdb)ΔCpdover SNR 0.040.16 p( ˆˆCpd) 0.035Cpd0.14 max95( ˆCpd) 0.03ΔCpd)0.12 pd 0.025/C0.1 pd 0.020.08 (ΔC 0.015950.06 x 0.01ma0.04 0.0050.02 00 Cˆpdin bit/s/Hz→10 log10(Es/N0) in dB→ Figure 4.4: a): probability density of ˆCpdand true Cpdfor operating point of code 2, dashed red line indicates maximum of 95% of all ˆCpd, b): maximum of 95% of all ΔCpd/Cpd Cpdat the target error rate. With respect to Fig. 4.2 the capacity varies at a BER of 10−5by±0.25 bit/s/Hz for code 1 and by ±0.2 bit/s/Hz for code 2. The turbo code shows nearly no variations. Again, a worst case consideration extracts the maximum required capacity to ensure the target BER. Moreover, channel estimation errors at the receiver cause an additional loss which can be modeled by a complementary noise term. This error causes small SNR degradations between 0.2 dB and 0.5 dB and, consequently, a small shift of the curves in Fig. 4.2 towards higher capacities. 4.2.5 Summary and Further Work Simple generic models have been developed for a BICM-PD OFDM link describing the dependency between the bit-level capacity and the error probability. These models include different coding and modulation schemes related to LTE-specifications but can be easily generalized. Uncertainties due to estimation errors have been analyzed and allow worst case scenarios with which the target error rate can be achieved in a predefined percentage of channels. In a next step, the OFDM system shall be extended to a MIMO-OFDM system enabling spatial multiplexing and different diversity methods like cyclic delay diversity. This extension requires the analysis of additional spatial parameters characterizing the MIMO channel that have to be integrated into the generic models. Furthermore, automatic-repeat-and-request procedures shall be included into the investigations. Bibliography
[13] 3GPP, 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Multiplexing and channel coding (FDD) (Release 9), December 2009, available: http://www.3gpp.org/ftp/Specs/html-info/25212.htm.
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[16] C. Stierstorfer and R.F.H. Fischer, “(gray) mappings for bit-interleaved coded modulation,” April 2007.
[17] C. Stierstorfer, A Bit-Level-Based Approach to Coded Multicarrier Transmission, PhD thesis, University of Erlangen-Nürnberg, Germany, Aug 2009.
[18] 3GPP, 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA), Physical Channels and Modulation (Release 9), December 2009,available: http://www.3gpp.org/ftp/Specs/html-info/36211.htm.
[19] K.-D. Kammeyer and H. Schmidt, “OFDM: An old idea solves new problems,” in International Symposium on Theoretical Electrical Engineering (ISTET 01), Linz, Austria, Aug 2001.
[20] H. Zamiri-Jafarian, M.J. Omidi, and S. Pasupathy, “Improved channel estimation using noise reduction for ofdm systems,” volume 2, pages 1308 – 1312 vol.2, April 2003.
[21] G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Transactions on Information Theory, 44(3):927–946, 1998. · Zbl 0912.94019
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[23] C. Stierstorfer and R.F.H. Fischer, “Adaptive interleaving for bit-interleaved coded modulation,” January 2008. 4.3 Resource Allocation Using Broadcast Techniques M. Bossert, C. Huppert, J.G. Klotz, University of Ulm, Germany 4.3.1 Motivation In the following we consider the downlink of a multi user communication system. For transmission in such a system the available resources, e.g., bandwidth and power, has to be allocated to the single users. This is often done by means of orthogonal access techniques, e.g., OFDMA, as in the uplink channel. However, the downlink channel is equivalent to the information theoretic broadcast channel since there is only one sender transmitting messages to several receivers. In contrast to the uplink channel which can only be modeled as multiple access channel there is perfect synchronization and coordination for transmitting messages in the downlink channel. Thus, using broadcast techniques as multiple access technique is superior in terms of the achievable rates. This was first shown by Cover in 1972 in [18]. He investigated the achievable rate region in the degraded broadcast channel and showed that all points of this region can be reached by means of superposition techniques. 4.3.2 Resource Allocation Algorithms In multi-user OFDM systems the available subcarriers and the transmit-power must be allocated to the individual users in a way that certain service requirements are fulfilled. Motivated by the information theoretic superiority of broadcast techniques over orthogonal access techniques, we consider resource allocation schemes for different requirements taking into account the broadcast gain in the following. Furthermore, we do not only consider nodes equipped with a single antenna (SISO), but also multi antenna systems (MIMO). The optimal resource allocation schemes are known for all considered scenarios, however compared to the orthogonal methods it is more complex to determine their solutions and a larger signaling overhead is required to inform the users about the determined allocation. Thus, we propose strategies which achieve a near optimum performance while requiring only a reasonable complexity. These strategies are based on one or more of the following techniques: • Restriction to at most two users per carrier in order to keep the overhead low. • Introduction of a new metric to predict interference caused by broadcast techniques (e.g. Eigenvalue Update). • Usage of hybrid allocation strategies combining orthogonal access with broadcast techniques. In the following some of the proposed algorithms a briefly described and some simulation results are presented. Sum-Rate Maximization First, we consider a scenario where the overall system throughput, defined by the sum over all achievable user rates, is maximized under a transmit power constraint. The proposed algorithm uses eigen-beamforming and dirty paper coding, cf. [13]. The inter-user interference is estimated and the eigenvalues of the affected beams are updated (so-called ). Then the optimal power allocation is retrieved by perform water-filling over the adapted eigenvalues, cf. [19, 20]. In Fig. 4.5 the results of the algorithm are compared with the optimal solution. It can be seen that the heuristic algorithm achieves a sum rate of up to 99% of the optimal algorithm for low SNRs. For higher SNRs it still reaches 91%. Sum-Rate Maximization with Minimum Rate Requirements Like in the above considered scenario we maximize the sum rate of the system. However an individual minimum rate requirement for each user has to be fulfilled. Such a scheme may be needed in systems where delay critical as well as non-delay critical data should be sent to each user. Minimum Rate Requirements in SISO-OFDM systems The proposed algorithm, cf. [12], mainly works in two steps. First, a simple scheduler allocates one user to each carrier aiming in assigning the minimum rates. This scheduler performs the “worst selects” algorithm, i.e., always the instantaneous worst user chooses its best carrier. In the second step, an additional user is added to each suitable carrier by means of broadcast techniques. A modified version of this algorithm avoids irresolvable decoding dependencies in order to make it applicable to code words stretching over several blocks. Some simulation results of these two algorithms, named BC and DEP, are compared to the optimum solution, cf. [21,22], as well as to a pure scheduling strategy in Fig. 4.6. It can be seen that the proposed algorithm achieves a performance near to the optimum and is clearly superior to the pure scheduler. Furthermore, the results reveal that the modified version still exploit a big part of the possible broadcast gain. Minimum Rate Requirements in MIMO-OFDM systems For this problem two different heuristic resource allocation algorithms are proposed, cf. [14], which have a much lower complexity than the existing optimal solution, cf. [23]. The first strategy, extended eigenvalue update (EEU) algorithm, is based on the previously discussed heuristic sum rate maximization algorithm using eigenvalue updates. The second algorithm, the rate based coding (RBC) algorithm, makes use of the duality of uplink and downlink, which allows us to determine the allocation in the dual uplink. The performance of these algorithms for different minimum rates compared to the optimal algorithm is depicted in Fig. 4.7. It can be seen, that the EEU algorithm clearly outperforms the “simple scheduler”. The RBC algorithm achieves a better performance than the first algorithm at the cost of more complexity. Actually, it gets very close to the optimal solution for low required minimum rates. 40 Optimal Algorithm (Algorithm 1) 35Eigenvalue Update (Algorithm 2) 30 25 20 15 Sum Rate in bit/s/Hz10 5 0 −5051015202530 SNR [dB] Figure 4.5:Sum-RateMaximizationinMIMO-OFDM (8 tx-antennas,up to 4 rx-antennas,blockfading channels,64carriers,40 users, average SNR values are uniformly distributed in a range from 0dB to 20 dB) 48 46 av 44 42 average user rate ROPT SISO 40BC SISO DEP SISO SCH SISO 38 2468101214 minimum rate Rmin Figure 4.6:Minimum rate requirements in SISO-OFDM (block fading channels, 256 carriers, 40 users, average SNR values are uniformly distributed in a range from 0dB to 20 dB) Maximization of the Number of Users While in the upper two scenarios the number of users, which are served in the system, is constant and the rate of the users is maximized, we maximize in this scenario the number of users which can be served in the system. Each user is provided a fixed rate. In the following we propose an hybrid algorithm, cf. [11], aiming in maximization of the number of served users. This algorithm works iteratively. In each iteration step it increases the number of users successively until the rate requirements can not be fulfilled anymore. The idea behind this iterative method is that based on a stable system new users should be added. In each iteration all carriers are exclusively assigned to users by the “worst selects” algorithm in a first step. Then, always the instantaneous worst user is added as second user to its best suitable carrier as long as the rate requirements are not fulfilled. Finally, the fraction for the power distribution is determined individually for each carrier. The performance of this algorithms is displayed in Fig. 4.8 and compared to the optimum solution based on [24] as well as to a simple scheduler. It can be seen that for high required rates all algorithms achieve nearly the same performance whereas for lower rate requirements the proposed algorithm clearly outperforms the scheduler by exploiting parts of the broadcast gain. 90 80 av 70 60 optimal solution average user rate R50EEU (B=30)RBC simple scheduler 40 010203040 minimum rate Rmin Figure 4.7:Minimum rate requirements in MIMO-OFDM (block fading channels, 64 carriers, 20 users, average SNR values are uniformly distributed in a range from 0dB to 20 dB) 1 SCH high BC high 0.8 OPT high SCH low 0.6BC low OPT low 0.4 Outage probability 0.2 0 050100150200 Number of served users Figure 4.8:User maximization in SISOOFDM (block fading channels, 256 carriers, average SNR values are uniformly distributed in a range from 0dB to 20 dB) Bibliography Publications Emerged from the Projects:
[24] C. Huppert and M. Bossert, “Delay-limited capacity for broadcast channels,” in 11th European Wireless Conference, pages 829–834, Nicosia, Cyprus, April 2005.
[25] M. Bossert, “Coded modulation for OFDM and the broadcast channel - invited,”in Fifth International Workshop on Multi-Carrier Spread Spectrum, Oberpfaffenhofen, Germany, September 2005.
[26] C. Huppert and M. Bossert, “Downlink transmission and the broadcast channel - invited,” in RadioTecC, Berlin, Germany, October 2005.
[27] M. Bossert,“OFDM-Übertragung und der Broadcast-Kanal - invited,”in Öffentliche Diskussionssitzung “‘Beyond 3G - Zukünftige Entwicklung mobiler Funksysteme”’, ITG, Ulm, Germany, November 2005.
[28] Carolin Huppert and Boris Stender, “Hybrid scheduling and broadcast with minimum rates in OFDM,” in 12th European Wireless Conference, Athens, Greece, April 2006.
[29] Boris Stender and Carolin Huppert, “Power allocation with constraints over parallel gaussian broadcast channels,” in 12th European Wireless Conference, Athens, Greece, April 2006.
[30] Carolin Huppert and Martin Bossert, “Performance evaluation of a low complex broadcast algorithm for OFDM channels,” in 11th International OFDMWorkshop, Hamburg, Germany, August 2006.
[31] Carolin Huppert, Boris Stender, and Axel Hof, “Resource allocation for OFDM broadcast channels allowing user-wise coding,” in 3rd International Symposium on Wireless Communication Systems, Valencia, Spain, September 2006.
[32] Boris Stender, Carolin Huppert, and Gerd Richter, “Fast broadcasting,” In 3rd International Symposium on Wireless Communication Systems, Valencia, Spain, September 2006.
[33] Carolin Huppert and Martin Bossert, “On achievable rates in the two user AWGN broadcast channel with finite input alphabets,” in IEEE International Symposium on Information Theory, Nice, France, June 2007.
[34] C. Huppert and M. Bossert, “Heuristic approach of maximizing the number of served users in an OFDM broadcast channel,” in 12th International OFDMWorkshop, Hamburg, Germany, August 2007.
[35] C. Huppert and B. Stender,“Resource allocation with minimum rates for OFDM broadcast channels,” European Transactions on Telecommunications, 18, No. 6:563–572, October 2007.
[36] J. Klotz, C. Huppert, and M. Bossert, “Heuristic resource allocation for sum rate optimization in MIMO-OFDM systems using eigenvalue updates,”in IEEE International Symposium on Wireless Communication Systems (ISWCS), Reykjavik, Iceland, October 2008.
[37] J. Klotz, F. Knabe, and C. Huppert, “Resource allocation algorithms for minimum rates scheduling in MIMO-OFDM systems,” in 7th International Workshop on Multi-Carrier Systems & Solutions (MC-SS 2009), Herrsching, Germany, May 2009.
[38] C. Huppert, F. Knabe, and J. Klotz,“User assignment for minimum rate requirements in OFDM-MIMO broadcast systems,” IET Electronic Letters, 45, No. 12:621–623, June 2009.
[39] J. G. Klotz, F. Knabe, and C. Huppert, “Resource allocation algorithms for minimum rates scheduling in MIMO-OFDM systems,” European Transactions on Telecommunications, 21, No. 5:449–457, August 2010.
[40] C. Huppert and J. Klotz,“Required transmit power applying TomlinsonHarashima-precoding in scalar and MIMO broadcast systems,” IEEE Transactions on Communications, 2010. Accepted for publication. Other References:
[41] T. M. Cover, “Broadcast channels,” IEEE Transactions on Information Theory, IT-18(1):2–14, January 1972. · Zbl 0228.94008
[42] T. Michel and G. Wunder, “Optimal and low complex suboptimal transmission schemes for MIMO-OFDM broadcast channels,” in IEEE International Conference on Communications, Seoul, Korea, May 2005.
[43] R. Böhnke, V. Kühn, and K.-D. Kammeyer, “Fast sum rate maximization for the downlink of MIMO-OFDM systems,” in Canadian Workshop on Information Theory, Montreal, Canada, June 2005.
[44] T. Michel and G. Wunder, “Minimum rates scheduling for OFDM broadcast channels,” in IEEE International Conference on Acoustics, Speech and Signal Processing, volume 4, pages 41–44, Toulouse, France, May 2006.
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[47] D. N. C. Tse,“Optimal power allocation over parallel Gaussian broadcast channels,” in IEEE International Symposium on Information Theory, Ulm, Germany, June 1997. 4.4 Rate Allocation for the 2-user Multiple Access Channel with MMSE Turbo Equalization M. Grossmann, R. Thomä, Ilmenau University of Technology, Germany 4.4.1 Introduction Recently, iterative (turbo) techniques have been recognized as practical solutions to multi-user detection/equalization problems in coded communication systems. In [1], utilization of the optimal a posteriori probability (APP) equalizer in combination with the APP-based decoder is considered for turbo equalization in frequencyselective fading channels. In [2], the APP detector is replaced by a less computational complex detector that performs soft canceling and minimum mean squared error (SC MMSE) filtering. The turbo equalization technique for block-transmissions over multiple-access channels (MACs) in [3] performs the equivalent signal processing in frequency domain (FD), further reducing the computational complexity. The convergence of turbo systems can be analyzed by extrinsic information transfer (EXIT) charts [4]. Ashikhmin et al. [5] showed that for any code with rate R, the area under its corresponding EXIT function is 1−R. Based on this area property of the EXIT chart, it has been shown in [6]- [8], that the problem of rate allocation in the single-user or equal-rate multi-user turbo case, reduces to a simple curve-fitting problem of the two-dimensional (2D) EXIT curves of the detector and decoder. In this contribution, we consider the problem of rate allocation for the 2-user MAC in the presence of frequency-selective fading employing the low-complexity SC FD-MMSE turbo equalizer [3]. Specifically, we show that for such a turbo system, the equalizer EXIT characteristic is given by multidimensional surfaces, and thus, rate allocation to the users is no longer a simple 2D matching of the EXIT curves. Moreover, we derive an upper bound for the rate region of the turbo system, and study the problem of maximizing the sum rate of both users. 4.4.2 Turbo Equalization Consider the cyclic prefix (CP) assisted U -user uplink system in Fig. 4.9, where a base station having M receive antennas receives signals from U active users, each equipped with K transmit antennas. For the ease of analysis, we assume in the following U = M = 2 and K = 1. However, the extension to more generic cases (U > 2, M > 2, K > 1) is rather straightforward. The transmission scheme of the u-th user (u = 1, 2) is based on bit interleaved coded modulation, where the information bit sequence is independently encoded by a binary encoder, randomly bit-interleaved, binary phase-shift keying (BPSK) modulated, and grouped into several blocks that are transmitted over the frequency-selective multiple-access MIMO fading channel. At the receiver side, iterative processing for joint equalization and decoding is performed. The receiver consists of an SC FD-MMSE equalizer and two singleuser APP decoders. Within the iterative processing, the extrinsic LLR sequences λu(n) and ζu(n) of the coded bit sequences bu(n) are exchanged between the ˆb1(n) b1(n)λ1(n) BPSKDeInterleaverDecoderInterleaver EncoderInterleaverMapperζ1(n) MMSEˆbU(n) Equalizerλ bU(n)BPSKU(n)DeInterleaverDecoderInterleaver EncoderInterleaverMapperζU(n) feedback links Figure 4.9: Structure for a coded multiuser MIMO system with turbo equalization. equalizer and both decoders, each separated by the interleaver and deinterleaver in their iteration loop, following the turbo principle [2]. The receiver also selects the code to be used for each user, for the channel realization given, from an available code set, where the users are notified of the codes selected through separated feedback links. We assume zero-delay and error-free feedback links. 4.4.3 Rate Allocation using EXIT Charts In the 2-user case the convergence characteristic of the equalizer is defined by two EXIT functions [3], fe: Id→ fe≡fe,1(Id), fe,2(Id)∈ [0, 1]2, which depend on the mutual information (MI) Id≡ (Id,1, Id,2)∈ [0, 1]2with Id,u being the MI between the transmitted bits bu(n) and the LLRs ζu(n). Similarly, the convergence characteristics of the two decoders are defined by two EXIT functions3 fd,k: Id,k→ fd,k(Id,k)∈ [0, 1]. An example of the equalizer EXIT vector-functions feand the decoder EXIT function fd,1is shown in Fig. 4.10 (a). Also shown is a possible decoding trajectory (plotted as a projection onto the plane regionU ≡ Id: Id∈ [0, 1]2) of the MI exchange over the iterations, and a region D, which is referred to as the feasible region of the EXIT functions fe, fd,1, and fd,2. Note that fd,2(not shown) is drawn in the Id,2-coordinate. For the computation of the decoding trajectory, the codes of both users were in this case assumed to be identical, and hence the shapes of their EXIT functions are exactly the same. The monotonicity of the EXIT functions imply that the decoding trajectory converges monotonically to a unique limit point [9]. Convergence of turbo equalization is achieved, when the decoding trajectory attains the maximum point a2≡ (1, 1). This is possible for the number of turbo iterations being sufficiently large, if the following two constraints hold:D is pathwise connected and a2∈ D. Let AD≡DdIdbe the area ofD. Assume now that each decoder EXIT function fd,kis matched to the corresponding equalizer EXIT function fe,kso that only an infinitesimally small open tube between the four EXIT surfaces remains. Note that such decoder EXIT functions imply 1) an ideally designed code for each user of infinite block length to achieve a nearly zero BER and 2) an infinite number of 3Note thatf d,k, denoted here as the decoder EXIT function, corresponds to the inverse decoder EXIT characteristic defined in [4]. fe,20.95 0.8fe,1 V1 ,20.9 0.6 =1 ,kc] Ike,fd,1[bp0.85 decodingR2 0.2 a2trajectory 0.8V2 a11Da3Rmax= 1.62 bpc 0.40.750.60.650.70.750.80.85 Id,2a0Id,1R1[bpc] (a)(b) Figure 4.10: (a) Equalizer EXIT functions fe,1and fe,2for a single random Rayleigh channel realization having L = 10 taps and decoder EXIT function fd,1 for a rate-1/2 convolutional code. (b) Rate region of the 2-user MAC with SC FD-MMSE turbo equalization for a single random channel realization at Es/N0= 5 dB, numerically computed by generating a large number of different admissible convergence curves (a gray dot corresponds to one curve). turbo iterations. Under this assumption, the size of the area ADis close to zero and the feasible regionD can be characterized by a single curve, which is referred to as convergence curve. LetP be the set of admissible convergence curves in the plane region U, as defined in [10]. With the the area property of EXIT functions [5], we derive in a straightforward manner an upper bound for the rate region of both users, as  R ≡(R1, R2) : Rk<fe,l(Id)dId,k, k = 1, 2.(4.10) p∈Pp Figure 4.10 (b) illustrates an example of the rate region in (4.10), where fe,1and fe,2have been computed for a random channel realization using the algorithm in [3]. Note that the rate region in (4.10) is non-convex, in general, where the dominant face of this region strongly depends on the particular realization of the equalizer EXIT vector-function fe. Using the rate bound in (4.10), the problem of maximizing the sum rate of both users can be formulated as Rmax≡ maxp∈P2k=1pfe,k(Id)dId,k. Specifically, we show in [10] that this optimization problem can be efficiently solved by using the Euler-Lagrange formalism [11]. As a result, the optimal decoder EXIT curves for both users with respect to the maximum sum rate of the turbo system, are obtained. For practical reasons, however, each transmitter is restricted to have only a finite number of codes with fixed rates. For this scenario assumption, we propose in [10] a simple code selection algorithm for the rate allocation that maximizes the coding rate of each user, given the optimal decoder EXIT curve obtained from (4.10), while satisfying the constraints for successful decoding. Figure 4.11 shows the average total throughput of the 2-user turbo system with the proposed code selection approach for frequency-selective Rayleigh fading channels having L = 32 taps. We assume sufficient long CP for inter-block interference to be negligible. The binary-input sum capacity of the 2-user system is shown as a reference. Also shown is the average total throughput performance for an automatic repeat-request scheme with fixed coding rates of both users. For clarity, the rates shown do not include the fractional rate loss incurred by the CP. As observed in Fig. 4.11, substantial throughput gain is obtained with the proposed code selection algorithm over the fixed rate case. Further, we find that the throughput performance is only 2 dB away (in the high Es/N0region) from the theoretical limit. 2 proposed method 1.8BPSK capacity 1.6 1.4 1.2 1 0.8 0.6 0.4 Average throughput [bpc] 0.2 0 −6−4−2024681012 Es/N0[dB] Figure 4.11: Average total throughput of both users versus Es/N0for the proposed rate allocation scheme using the rate-compatible punctured serial concatenated convolutional codes in [12], and for automatic repeat-request with fixed coding rates r1/2= 0.1· n with n = 1, .., 9 (dashed curves, from bottom to top). 4.4.4 Summary In this contribution, we consider the problem of rate allocation in the frequencyselective 2-user Gaussian multiple-access fading channel employing a low complexity MMSE turbo equalizer. We derive an upper bound on the rate region of the turbo system and study the problem of maximizing the sum rate of both users. In addition, numerical results of a simple code selection algorithm for rate allocation to both users are presented. 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[59] M. Tüchler, “Design of serially concatenated systems depending on the block length,” IEEE Trans. Commun., vol. 52, no. 2, pp. 209-218, Feb. 2004. 4.5 Coexistence of Systems F. K. Jondral, U. Berthold4, Karlsruhe Institute of Technology (KIT), Germany M. Schnell, S. Brandes, DLR, Germany The efficiency of spectrum usage for a radio communications system employing a fixed bandwidth is measured as the average number of bits that are transmitted per second and per Hertz in a certain area. For simplicity reasons we will use the notion spectrum efficiency instead of efficiency of spectrum usage here. The results of measurement campaigns recently accomplished, pointed out that, even in heavily occupied bands, usually not more than fifteen percent of the spectral resource is effectively employed. This leads to the justifiable assumption that dynamic access upon the transmission resource will at least contribute to a reduction of spectrum scarcity. The TAKOKO5project within TakeOFDM dealt with the utilization of resources left idle in the frequency band allocated to a primary system of authorized users (so-called spectrum holes in the time-frequency-plane) by an overlay system of secondary users. A coexistence strategy is investigated that explicitly harnesses the flexibility of the OFDM (orthogonal frequency-division multiplexing) method with respect to spectrum utilization. I.e. an OFDM-based overlay system is installed in order to enhance the spectrum efficiency within the frequency region allocated to an authorized primary user system. As a starting point of our investigations, frequency regions as well as primary user systems appearing capable for additional use by an overlay system were identified. These are essentially systems employing the resource by FDMA (frequency division multiple access) or TDMA (time division multiple access). Table 4.2 provides an overview over the scenarios adopted. Table 4.2: Overviews over scenarios adopted Scenario 1Scenario 2Scenario 3 Frequency regionVHF band960 - 1215 MHz1800 MHz Primary systemAircraft radioDistanceMeasuringGSM Equipment (DME) Overlay systemWLAN for communi-Flexible mobile commu-MetropolitanArea cation at airportsnication systemNetwork (MAN) Special aspectsInterferencesuppres-Detection of spectrumUtilizationofspecsionholes,suppressionoftrum holes jammers Reliable detection of idle resources in the time-frequency-plane, i.e., the detection of primary user signals by the overlay system, as well as the signalization of the results within the overlay systems are of paramount importance for the acceptance of overlay systems by primary users. 4Dr.-Ing. Ulrich Bertold is now an employee of COMSOFT GmbH, Karlsruhe. 5TAKOKO is an acronym for technologies, algorithms, and concepts for OFDM systems coexisting with authorized systems in the same frequency band licensed system spectrum hole time Figure 4.12: Idle resources represented by spectrum holes The impact that the overlay has on the primary system has to be kept minimum. Therefore, detection as well as false alarm probabilities for the detection of primary users’ signals by the overlay system were derived. In the course of the work it became evident that only the application of a detection algorithm distributed over the overlay system’s stations is able to guarantee sufficiently high detection probabilities and at the same time lead to tolerable false alarm rates. Moreover, an efficient signaling within the overlay system of the spectrum utilization by the primary system proves to be important in order to optimally make use of the spectrum holes. Employing OFDM in overlay systems, of course, also implicates some disadvantages. Among these disadvantages are the strong spurious transmissions that may lead to disturbances in the primary system. To reduce them, in addition to well known methods, like windowing of the transmitted signal in the time domain or the introduction of guard bands, subcarrier weighting, the application of cancellation carriers as well as a combination of windowing and cancellation carriers were investigated in TAKOKO. In scenario 1, for example, it was shown that the application of this combination may reduce the energy level contained in a secondary lobe to a value of 50 dB below the OFDM signal energy level. The new techniques for disturbance suppression were integrated into the simulation model of an adaptive OFDM transmitter. At the receiver side of an overlay system’s user the desired signal is superimposed by interferences generated by the primary system. Although the channels occupied by primary system’s users are generally not employed by the overlay system, the overlay system’s performance is influenced by these interferences. In this connection, interference reduction methods concerning narrow band interferers were investigated with respect to scenario 1. Here time domain windowing of the received signal as well as the frequency domain estimation of the interfering signal were applied. High quality results were achieved with a combination of time domain windowing and leakage compensation in the frequency domain. The interference minimization techniques were integrated into the overlay system’s receivers. To facilitate a dynamic adaptation to varying interference situations, the OFDM frame structure had to be modified by introducing observation carriers such that their position may be adjusted to the actual spectrum occupancy. Further essential aspects of the TAKOKO project were the investigation of the requirements on the MAC (medium access control) layer as well as the specification of an adequate MAC protocol. Here the essential assumption was that the overlay system operates as an ad-hoc network, i.e., without central coordination. Therefore, all individual stations are equal and the MAC protocol has to incorporate the system’s distributed character. In order to be able to initiate a data transmission the stations essentially need a) knowledge about the frequency occupation by the primary system (overlay feature) and b) information about those stations in their environment to which it is possible to establish a connection (ad hoc feature). For determination of the primary system’s frequency occupation measurements are performed periodically. The measurement periods for the overlay system’s stations have to be coordinated because no overlay system’s stations should radiate signals then to guarantee a reliable detection of primary system signals. Exactly this coordination is assumed by the AHO-MAC (ad hoc overlay MAC) protocol developed in the TAKOKO project. Similar to PRMA (packet reservation multiple-access), as many time slots for data transmission as mini slots for acknowledgments are provided. Moreover, special time slots for occupancy measurements and for the mutual synchronization of the overlay stations are defined. The representation of the frequency utilization by the primary system in form of the occupancy vector plays an important role within the overlay system and affects the PHY (physical) as well as the MAC layer. Therefore, an approach of cross layer optimization was chosen. Here the layered model was kept but the interfaces between the layers were extended by the definition of more detailed as well as more specific parameters. In summary promising methods were developed in TAKOKO which show that in principle OFDM based overlay systems may be implemented.Although the TAKOKO approaches were considered with respect to preferably realistic overlay scenarios (Table 4.2), further investigations have to be performed before OFDM based overlay systems may be practically implemented. Those investigations could not be accomplished within the project because of the given time and effort constraints and because they were beyond the project’s objectives. Moreover, the real implementation of OFDM based overlay systems requires fundamental decisions in the political as well as in the regulatory area in order to define the principle framework. The scientific results acquired in the TAKOKO project are essentially summarized in the doctoral dissertations [1] and [2]6. 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[61] S. Brandes. Suppression of Mutual Interference in OFDM Based Overlay Systems, Dissertation, Forschungsberichte aus dem Institut für Nachrichtentechnik der Universität Karlsruhe (TH), Band 22, Karlsruhe, 2009. 6Both dissertations may be downloaded from www.cel.kit.edu 4.6 System Design for Time-Variant Channels P. Klenner, S. Vogeler, K.-D. Kammeyer, University of Bremen, Germany L. Reichardt, S. Knörzer, J. Maurer, W. Wiesbeck, University of Karlsruhe, Germany The following two subsections summarize the cooperation between the Arbeitsbereich Nachrichtentechnik (ANT) at the University of Bremen and the Institut für Hochfrequenztechnik und Elektronik (IHE) at the University Karlsruhe. Both partners were engaged in two projects within the DFG program ”TakeOFDM”. The project titles coincide with the names of the following sections. The focus is in Section 4.6.1 on SIMO (Single-Input-Multiple-Output)-OFDM and in Section 4.6.2 on MIMO (Multiple-Input-Multiple-Output)-OFDM in rapidly fading channels, which are modeled by ray-optic methods to include realistic propagation effects. 4.6.1 Multicarrier Systems for Rapidly Moving Receivers In this section, the use of multicarrier systems and, in particular, OFDM for highrate wireless data transmission and for fast moving receivers mounted on high-speed trains, cars, or airplanes is considered. Realizing high data rates at simultaneously high mobility is a difficult feat for any communication system. If broadband signaling for a high data rate causes the sample duration to become smaller than the channel’s maximal echo duration, then OFDM can simplify the resulting equalization effort. But a frequency-selective channel is only separated into orthogonal parallel subcarriers in the case of a time-invariant channel, i.e., if the channel remains unchanged during one OFDM symbol. High mobility environments, however, are characterized by time-invariant channels, which leads to a loss of the subcarriers’ orthogonality. Intercarrier interference (ICI) occurs, the equivalent to intersymbol interference in time-domain. In the simplest case, ICI can be modeled as a source of noise in addition to the thermal noise. Neglecting it results in a degradation of the achievable bit-error rate. More dramatic is the impact, if the channel is changing so fast, that the violation of the sampling theorem prevents a reliable channel estimation. This case does not necessarily occur due to extreme speed, but also due to a large pilot symbol spacing. The observations conducted here refer to a system for a high-speed train in a single frequency network. The channel model described in Section 2.2.2 is applicable to different frequencies and is transferable to other types of mobiles. Similarly, the considerations apply to the Doppler effect for other types of fast moving receivers. For an extensive investigation under realistic channel conditions, the project is based on modeling the propagation conditions via ray-tracing methods by which a series of channel impulse response is computed. Subsequently, three main strategies will be discussed with the aim to solve the conflict between the transmission channel’s high time and frequency selectivity: The application of a pre-equalizer to shorten the channel impulse response, the use of soft impulse shaping for a non-orthogonal multicarrier system, and multi-antenna concepts to reduce the Doppler spread. During the project, parameters of an OFDM system were defined taking into account the main characteristics of the channel that was determined by ray-tracing simulations. The system’s performance limits were established through Monte Carlo simulations. The system parameters have been dimensioned such that the timebandwidth conflict caused by the interference is completely focused on the frequency domain, while time domain intersymbol interference is avoided. Thus, the procedures to counter the Doppler effect can be performed after the DFT in the receiver. By consolidating the effects of multipath and Doppler spread in the form of a channel matrix, a linear equalization of both effects according to the MMSE criterion can be carried out. The disadvantage of this procedure, however, is a relatively high computational effort, while the knowledge of the signal alphabet is not exploited. Therefore, two well-known algorithms for low-complex equalization were implemented: a successive linear MMSE equalizer and a successive equalizer with decision feedback structure, which were modified in accordance to the requirements of the scenario. Both methods, however, did not provide satisfactory simulation results, which in the decision-feedback method is due to the suboptimal detection sequence. This called for the sorted QR decomposition (SQRD) employed in VBLAST to improve the detection sequence.This resulted in the best detection performance, but at the cost of a comparably high computational effort. Through the gradual decomposition of the channel matrix in submatrices the effort can be reduced significantly, yielding a trade-off between high performance and low complexity equalization. This successive SQRD is detailed in [11, 12]. As part of the investigations of alternative multicarrier concepts the subcarrier spectra of OFDM were replaced by soft non-orthogonal pulse shapes, i.e., timelimited Gaussian pulses. In the frequency domain, this leads to a concentration of interference power in the vicinity of the main diagonal of the channel matrix. This in turn has a positive effect on the performance of the aforementioned equalization methods, particularly for the low-complex variants such as the successive SQRD. The soft impulse shaping also allowed for Maximum Likelihood detection with reasonable effort, because the concentration of the interference power allows the use of a timevariant Tailbiting-MaxLogMAP algorithm with a reduced number of states. This procedure resulted in the best compromise between complexity and performance of the transmission system [13]. Shortening the channel impulse response potentially allows for a shorter OFDM symbol, which is beneficial in rapidly time-varying environments. Numerous wellknown non-blind and blind algorithms for computing equalizer coefficients were investigated regarding their applicability in the scenarios. It turned out that these methods produce either ill-conditioned frequency responses or that the convergence speed is not sufficient in case of the blind methods. Multi-antenna concepts open up the spatial domain to procure Doppler spread compensation. Sectorizing antennas exploit the relationship between the impinging waves’ angle of incidence and their resulting Doppler shift. By restricting the range of angles of incidences a sectorizing antenna simultaneously reduces the effective Doppler spread compared to a omnidirectional antenna without any restriction of the incidence angle. One practical implementation is beamforming via a Uniform Linear Array (ULA), and the beams are formed such that the Doppler spread is equally distributed among all beams [2]. Furthermore, a ULA can be used for a method called spatial interpolation, in which the signals of the individual antenna elements are filtered by a time-variant interpolator such that the filter output resembles the output of a time-invariant channel [3]. The two scenarios of a noise barrier and vegetation are considered as typical high speed lines. The radio channel has very different properties, therefore, these scenarios are used as a reference. Details can be found in [6,8,9]. For the simulation of wave propagation, a three dimensional ray-propagation model is employed. It provides characteristic parameters for each multipath, from which the sequence of channel impulse responses and channel characteristics are extracted. The wave propagation model takes into account the propagation phenomena of reflection, diffraction and scattering. The approach to modeling the distribution of vegetation is described in 2.2.2. Figure 4.13 shows the BER performance for a SIMO-OFDM system with receive diversity in a rapidly fading channel (one transmit and two or four receive antennas, Nt= 1, Nr= 2, 4). For omnidirectional reception widely spaced antennas are used, which yield completely uncorrelated channels per antenna. Without any means of Doppler compensation this results in the worst performance. Sectorizing antennas and spatial interpolation based on a ULA with interantenna spacing d/λ yield a better performance. Sectorization is here achieved by forming two beams in and against the direction of the movement. Spatial interpolation is achieved by computing two virtually non-moving antennas, which fix the channel over the middle of the respectively received OFDM signal. The received signals on the resulting virtual antennas are correlated. Taking this correlation into account by means of a whitening matched filter (WMF) improves the performance over the matched filter (MF). 4.6.2 Highly Mobile MIMO-OFDM-Transmission in Realistic Propagation Scenarios Doppler spread compensating antenna structures at the receiver offer an efficient approach to solve the problem of the channel’s time-variance already in time-domain. The focus now is on the two antenna configuration discussed in Section 4.6.1, whose function ultimately is to affect a less rapidly fading channel prior to the DFT. Unlike the previous discussion, where a single transmit antenna was employed, in the following the focus is shifted to the transmitter side. The MIMO philosophy is based on two pillars: Spatial transmit diversity is provided by Space-Time codes, and spatial multiplexing allows to increase the data rate by transmitting independent data streams. The development of these techniques is shaped by the assumption of a time-invariant channel, and most methods even demand that. In the following, the mutual benefit of MIMO-signaling and Doppler spread compensation measures is described. If the Doppler spread is small, then the loss of time diversity can be made up by spatial diversity, and if the Doppler spread is large, then the Doppler compensating antennas can effect a less time-invariant channel such that the MIMO-signal processing upholds its validity [1, 4]. Rapid channel fluctuations in conjunction with multiple transmit antennas pose the a)Nt= 1, Nr= 2b)Nt= 1, Nr= 4 100100 10−110−1 R10−2R10−2 BEBE omni,MFomni,MF sec,MFsec,MF 10−3sec,WMF10−3sec,WMF SI,MFSI,MF SI,WMFSI,WMF 10−410−4 0510 15 20 25 30 35 400510 15 20 25 30 35 40 Eb/N0in dBEb/N0in dB Figure 4.13: BER-performance for SIMO-OFDM with a single transmit antenna and different receiver configurations: omnidirectional antennas with widely spaced antennas, sectorizing antennas and spatial interpolation based on a ULA, parameters: 256 subcarriers, 16QAM, exp. power delay profile, antenna spacing d/λ = 0.25, Doppler spread fDTs= 0.2, raised cosine filters (r = 0.18), zero forcing channel est. possible disadvantage of decreased bandwidth efficiency, in that frequent training becomes necessary. However, since the channel is forced to become less rapidly fading by Doppler compensating measures the pilot spacing in time direction can become larger. Similarly, noncoherent ST codes can profit from a channel that does not change too much during a signaling interval. During the course of the project it is investigated how the functions of Doppler compensation and the separation of data streams using multiple receiving antennas can be combined. One possibility is the use of multiple spatially separated antenna arrays, each used for Doppler compensation, followed by the recovery of the transmitted data streams. Parameter estimation is a further important issue. In particular, the channel’s autocorrelation function needs to be estimated, since the receiver requires it in order to perform the spatial interpolation. The idealized assumption of the Bessel function as autocorrelation holds only in isotropic scattering environments. Other scattering conditions and mutual antenna coupling lead to different correlations. Realistic channels already studied lead to an SNR loss. It is possible to find an estimate of the ACF based on the cyclic OFDM signal structure without spending extra training data [5]. Furthermore, the optimization of antenna structures for the purpose of minimizing the mutual antenna coupling is considered. The algorithms used for data processing in the baseband yield a better performance if the individual antennas for sectorization or spatial interpolation are decoupled. This condition is violated in practical systems, since the individual antenna elements are positioned very close to each other, so that inevitably crosstalk of the antennas occurs. The effect of mutual coupling and its minimization and compensation are investigated, so that the idealized assumptions of the baseband processing can be maintained. The consideration of realistic channel models as a benchmark of these approaches represents a further focus of the project. Two scenarios are considered, a highspeed train and vehicle-to-vehicle environments. In the former, the propagation conditions are dominated by a major incident direction (by the base stations along the railroad tracks), while in the latter, in principle, all incidence directions are possible. Regarding the car-to-car scenario, a further challenge is to find Doppler compensating antenna structures, which are not impaired by the car structure. Figure 4.14 shows the BER performance for a (2×2)-MIMO OFDM systems with the receiver configurations known from Fig. 4.13. In Fig. 4.14a transmit diversity is provided by the Alamouti Space-Time code, whereas in Fig. 4.14b the V-BLAST is employed, i.e., independent data streams are transmitted from both transmit antennas.For a fair comparison identical data-rates are used, i.e., 16QAM for the Alamouti scheme, and QPSK for V-BLAST. Comparing the two-fold transmit diversity scheme in Fig. 4.14a with the single transmit diversity case in Fig. 4.13a shows that except for spatial interpolation the gains promised by two-fold transmit diversity are small. This can be attributed to the channel estimation which needs to determine twice as many channel parameters. On the other hand, the gains for VBLAST in employing Doppler compensating antenna structure are more impressive. a)Nt= 2, Nr= 2, Alamoutib)Nt= 2, Nr= 2, VBLAST 100100 10−110−1 BEomni,ZFRBE10−2omni,ZF omni,MLomni,ML 10−3sec,ZFsec,ML10−3sec,ZFsec,ML SI,ZFSI,ZF SI,MLSI,ML 10−410−4 0510 15 20 25 30 35 400510 15 20 25 30 35 40 Eb/N0in dBEb/N0in dB Figure 4.14: BER-performance for (2× 2)-OFDM and different receiver configurations: omnidirectional antennas with widely spaced antennas, sectorizing antennas and spatial interpolation based on a ULA, parameters: 256 subcarriers, 16QAM (a) and QPSK (b), exp. PDP, d/λ = 0.25, fDTs= 0.2, RC-filters (r = 0.18), ZF channel est. Bibliography
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[64] P. Klenner and K.-D. Kammeyer, “Spatially Interpolated OFDM with Channel Estimation for Fast Fading Channels,” in IEEE Vehicular Technology Conference 2007 (VTC2007-Spring), Dublin, Ireland, April 2007.
[65] P. Klenner and K.-D. Kammeyer, “Performance of Space-Time-Coded OFDM with Sectorized Antenna Reception,” in International ITG/IEEE Workshop on Smart Antennas (WSA 08), Darmstadt, Germany, Feb. 2008.
[66] P. Klenner and K.-D. Kammeyer, “Temporal Autocorrelation Estimation for OFDM with Application to Spatial Interpolation,” in Asilomar Conf. on Signals, Systems and Computers, Monterey, CA, Oct. 2008.
[67] S. Knörzer,Funkkanalmodellierung für OFDM-Kommunikationssysteme bei Hochgeschwindigkeitszügen, PhD thesis, University Karlsruhe, Germany, 2009.
[68] S. Knörzer, J. Maurer, T. Fügen, and W. Wiesbeck, “Wave Propagation Modeling for Communication between Moving Vehicles,” in National Radio Science Meeting, Boulder, USA, Jan 2005.
[69] S. Knörzer, J. Maurer, S. Vogeler, K.-D. Kammeyer, and W. Wiesbeck, “Channel Modeling and Characterization for High-Speed Train OFDM Systems,” in COST 273 TD(05)086, Leuven, Belgium, June 2005.
[70] S. Knörzer, J. Maurer, S. Vogeler, K.-D. Kammeyer, and W. Wiesbeck, “Channel modeling for a high-speed train ofdm communication link supporting high data rates,” in Proc. 5th Int. Conf. on ITS Telecomm. 2005, pages 333–336, Brest, France, June 2005. Best Student Paper Award.
[71] J. Maurer, S. Knörzer, and W. Wiesbeck, “Ray Tracing in Rich Scattering Environments for Mobile-to-Mobile Links,” in Proc. of the Int. Conf. on Electromagnetics in Advanced Applications, Italy, Sept. 2005.
[72] S. Vogeler, Verfahren zur Kompensation von Doppler-Einflüssen in MehrträgerÜbertragungssystemen, PhD thesis, University of Bremen, Germany, 2006.
[73] S. Vogeler, L. Brötje, P. Klenner, V. Kühn, and K.-D. Kammeyer, “Intercarrier Interference Suppression for OFDM Transmission at Very High Velocities,” in 9th International OFDM-Workshop (InOWo 2004), Dresden, Germany, Sept. 2004.
[74] S. Vogeler, P. Klenner, and K.-D. Kammeyer, “Multicarrier Transmission for Scenarios with High Doppler Influence,” in 10th International OFDM-Workshop (InOWo 2005), Hamburg, Germany, Aug. 2005. 4.7 Combination of Adaptive and Non-Adaptive Multi-User OFDMA Schemes in the Presence of User-Dependent Imperfect CSI A. Kühne, A. Klein, Technische Universität Darmstadt, Germany 4.7.1 Introduction The Orthogonal Frequency-Division Multiple Access (OFDMA) transmission scheme is a promising candidate for future mobile networks. It offers an efficient adaptation to the channel conditions by performing a time-frequency scheduling of the different subcarriers to the different users. However, Channel State Information (CSI) is required at the transmitter in order to perform such an adaptive scheduling in an optimal way. Having perfect CSI for all users at the Base Station (BS), the use of frequency adaptive OFDMA schemes achieves very good performances by exploiting multiuser diversity . Having no CSI at all at the BS, the use of frequency non-adaptive OFDMA schemes exploiting frequency diversity independently from any CSI is the best strategy, however, not achieving the performance of adaptive schemes with perfect CSI . For the case of imperfect CSI, only pure adaptive OFDMbased systems have been studied in the literature but not a combination of adaptive and non-adaptive transmission modes. A comparison of adaptive and non-adaptive multiuser OFDMA schemes in the presence of imperfect channel knowledge has been investigated assuming the same degree of CSI imperfectness for each user [1]- [5]. It appears that at a certain level of CSI imperfectness, it is beneficial to switch from adaptive to non-adaptive transmission, i.e., depending on the quality of the channel knowledge, either all users apply the adaptive or non-adaptive transmission mode. In a realistic scenario however, the level of CSI imperfectness differs from user to user, i.e., for some users, the CSI is only slightly corrupted, whereas for other users, the CSI is totally inaccurate. Hence, we propose a hybrid OFDMA scheme where both adaptive and non-adaptive transmission schemes co-exist at the same time and show how to optimally combine these transmission schemes in the presence of user-dependent imperfect CSI [6]. 4.7.2 Combining Transmission Schemes In the considered hybrid OFDMA scheme, different users are served either adaptively or non-adaptively sharing the available bandwidth. Applying the non-adaptive OFDMA transmission scheme, a fixed modulation and subcarrier allocation is performed. This scheme does not rely on instantaneous CSI but exploits frequency diversity. Applying the adaptive OFDMA transmission scheme, an adaptive subcarrier allocation together with an adaptive modulation based on the instantaneous CSI is performed. The goal is to achieve a maximum system data rate under the constraint of a minimum user data rate and target Bit Error Rate (BER). Hence, the question arises, which user shall be served adaptively or non-adaptively taking into account user-dependent imperfect CSI and furthermore how to choose the signal-to-noise-ratio (SNR) thresholds for the applied modulation schemes in order to maximize the system data rate while guaranteeing a certain minimum user data rate and target BER. Since the performance of an adaptive users strongly depends on the total number of adaptive users in the system due to the selection process and the multi-user diversity involved, the decision whether a user is served adaptively or non-adaptively cannot be made userwise independently from the other users but has to be done jointly considering all users, resulting in a combinatorial problem. For the order of allocating the available subcarriers to the adaptive and nonadaptive users, two possibilities are considered.Firstly, the subcarriers of nonadaptive users are allocated in a first step and the remaining subcarriers are then allocated to the adaptive users in a second step referred to as Non-Adaptive First (NAF). Secondly, first the subcarriers of the adaptive users are allocated followed by the allocation of the subcarriers of the non-adaptive users referred to as Adaptive First (AF). To solve the described optimization problem, it is split up into two subproblems without losing optimality, namely the SNR threshold problem and the user serving problem. The SNR threshold problem can be solved applying a Lagrange multiplier approach leading to the optimized user data rate for each possible combination of serving the different users. In order to do so, analytical expressions for user data rate and BER have been derived taking into account user-dependent imperfect CSI. Solving the combinatorial user serving problem, it appears that it is not necessary to check all 2Upossible user serving combinations with U denoting the number of users in order to find the optimal combination maximizing the system performance subject to the mentioned data rate and BER constraints. Utilizing the fact that the data rate of an adaptive user does not depend on which users are adaptively served but only on the total number of adaptive users, the order of complexity can be reduced toO(U3) without loosing optimality. Taking into account the characteristics of the user data rate as a function of the number UAof adaptive users, the complexity can be further reduced toO(U2). 4.7.3 Numerical Results In Fig. 4.15a, the system data rate of a single cell OFDMA system with N = 125 subcarriers and U = 25 users in the downlink is depicted as a function of the average Mobile Station velocity ¯v in the cell for the different transmission schemes. The target BER is set to 10−3while each user shall achieve at least the data rate achievable applying the Pure Non-adaptive Transmission Scheme (PNTS). As one can see, PNTS achieves a constant system data rate since it does not depend on the reliability of the CSI. In case of ¯v = 0 km/h, the Pure Adaptive Transmission Scheme (PATS) and the hybrid transmission schemes achieve the same system data rate and outperform PNTS. However, when increasing ¯v in the cell and, thus, the unreliability of the CSI, the performances of PATS dramatically decrease, especially for the naive approach, where the SNR thresholds are calculated assuming perfect CSI for all users, since now, due to the imperfect CSI, wrong users and modulation schemes are selected for transmission. This results in a BER which no longer fulfills the target BER requirements. For PATS which is aware of the imperfect CSI, the 4.5 4 3.5 3 2.5 2 1.5 1 system data rate in bps/Hz 0.5 0 0510 15 20 25 30 35 40 45 50 55 average MS velocity in km/h 25 PATS (naive)AF PATS (aware)NAF NAF20 AF PNTS 15 of adaptive users A 10 5 average number U0 0510 15 20 25 30 35 40 45 50 55 average MS velocity in km/h (a)(b) Figure 4.15: (a) System data rate and (b) Number UAof adaptive users vs. ¯v decrease is less dramatical. However, at some point the system performance is worse than using PNTS. Applying the hybrid schemes NAF and AF for an increasing ¯v in the cell, the system performance is always equal or better than both PNTS and PATS, where AF outperforms NAF due to the more exclusive resource selection. For large velocities, the performances of the hybrid schemes converge to the one of PNTS, since now all users in the hybrid scheme are served non-adaptively due to the totally outdated CSI. This effect is also shown in Fig. 4.15b, where the number UAof adaptively served users is depicted as a function of ¯v. It can be seen that for low velocities, almost all users are served adaptively. When increasing ¯v, more and more users are served non-adaptively. Bibliography
[75] A. Kühne and A. Klein, “An analytical consideration of imperfect CQI feedback on the performance of a Multi-user OFDM-system,” in Proc. 12th International OFDM-Workshop (InOWo’07), Hamburg, Germany, August 2007.
[76] A. Kühne and A. Klein, “Adaptive subcarrier allocation with imperfect channel knowledge versus diversity techniques in a multi-user OFDM-system,” in Proc. Proc. International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07), Athens, Greece, September 2007.
[77] A. Kühne and A. Klein, “Throughput analysis of Multi-user OFDMA-Systems using imperfect CQI feedback and diversity techniques,” IEEE Journal of Selected Areas in Communications, vol. 26, no. 8, pp. 1440-1451, October 2008.
[78] A. Kühne and A. Klein, “Adaptive MIMO-OFDM using OSTBC with imperfect CQI feedback,” in Proc. International ITG Workshop on Smart Antennas (WSA’08), Darmstadt, Germany, February 2008.
[79] A. Kühne, A. Klein, X. Wei, and T. Weber, “Transmit Antenna Selection with imperfect CQI feedback in Multi-user OFDMA systems,” in Proc. Proc. 13-th International OFDM-Workshop (InOWo’08), Hamburg, August 2008.
[80] A. Kühne and A. Klein,“Combining adaptive and non-adaptive Multi-user OFDMA schemes in the presence of user-dependent imperfect channel knowledge,” IEEE Transactions on Wireless Communications. (submitted) 4.8 Integration of COFDM Systems with Multiple Antennas and Design of Adaptive Medium Access Protocols D. Martini, B. Wolz, B. Rembold, B. Walke, RWTH Aachen University, Germany 4.8.1 Abstract Besides medium access in time and frequency domain, the space and polarization domain can be exploited using multiple antenna (MIMO) systems for space division multiple access. SDMA combined with OFDM are the key technologies for future wireless and mobile communication systems as specified in standards such as IEEE 802.16d, IEEE 802.11n and 3GPP LTE. This work focuses on the development and prototype implementation of Medium Access Control (MAC) protocols of a demonstration system that uses multiple antennas. The goal is to serve all user terminals (UT) best by taking their instantaneous channel condition into account. A number of candidate channel-adaptive MAC protocols were designed to be implemented in a stochastic event driven simulator based on the openWNS tool. The protocol stack under study operates in between a multi-media load generator and an interference engine that calculates the current SINR at the receiver dependent on the direction of arrival (DoA). The contribution of a IEEE 802.16 specific transceiver chain is fed-in from link-level simulation results providing DoA specific bit-error characteristics. The openWNS tool is mainly employed to compare the performance of the MAC protocols, the usefulness of the interface between MAC and PHY and the constraints of an SDMA enabled scheduler. Besides simulation studies to understand the performance critical parameters, an analytical validation of the used simulator and a complexity analysis of a number of SDMA based service disciplines was performed. The demonstration system was completely implemented using a modular FPGA system and two high-performance power PCs that to perform MAC in real time. The contribution of MIMO technologies to improve the system capacity was evaluated by means of the SINR values that results from the studied antenna configurations. While the FPGA hardware was taken from a former project, the bidirectional transceiver chains including multiport antennas were new designed and implemented, resulting in a realtime 4x4 bidirectional MIMO testbed. 4.8.2 MAC Frame for SDMA Operation and Spatial Grouping A multi-cellular scenario served by 120◦antennas each serving 15 UTs was chosen operated with re-use one. Transmit power is 1 W and UTs control their power between 200 mW and 1 W. The scheduler decides based on data volume in MACand PHY layer, signaling overhead per UT and SINR of an UT, estimated based on the beamforming algorithm information. Figure 4.16 shows an example twodimensinal MAC frame to serve two spatially separated data streams. Above the MAC frame the transmit situation is shown using abstract antenna diagrams. The first part of the frame is transmitted omnidirectional to implement broadcast mode. DL-MAP (blue) and UL-MAP (green) and arrows are shown pointing to the time instants contained in the MAPs, where up to four radio bursts can be transmitted, spatially separated. Similar applies to the UL-MAP. UTs cannot be arbitrarily scheduled for concurrent SDMA transmissions since their spatial separability by the beam-forming antenna array depends on their relative spatial positions. Spatially separated concurrent transmissions cannot be assumed to be orthogonal. Therefore, a hierarchical scheduling algorithm is introduced that first computes a spatial grouping of UTs that can be well separated by the base station’s (BS) beamforming antenna. The result of this grouping is a set of groups of UTs. Users of the same spatial group can be separated and thus be served at the same time. Users in different groups must be separated in the time domain. Structuring of the scheduling process into two hierarchical steps adds flexibility and simplicity to the scheduling process. The grouping process is independent from the TDMA scheduling and vice versa. Thus, spatial grouping and group scheduling procedures can be freely combined and interchanged according to the specific needs of the system. Spatial grouping of UTs has been proposed earlier [2] and hierarchical grouping and scheduling in an SDMA enhanced IEEE 802.16 systems is proposed first in [4]. Since an optimal grouping is far too complex to be applied, a greedy algorithm to sort spatial groups according to achievable throughput was used resulting in grouping gain slightly below the optimal grouper’s gain. A tree-based heuristic algorithm only estimating the most promising spatial groups appear well suited to reduce run-time complexity to be applicable in real-time condition, with a grouping gain comparable to that of the greedy algorithm. Simulation Results Figure 4.17 shows the aggregate DL cell throughput versus offered traffic. Saturation is reached where the throughput deviates to grow linearly with offered traffic. Clearly, with omnidirectional it is lower than with SFIR or SDMA transmission. Under SDMA with up to 4 parallel transmissions, the throughput curve climbs from a value of about 22 MBit/s, where the first UTs reach saturation, to a final maximum of 30 MBit/s. SDMA transmission with up to 4 beams achieves about 440% gain compared to omnidirectional transmission. Most of the results on MIMO based MAC protocols, grouping etc. gained in this project are available from [3]. The scheduler algorithms developed for multiple antenna systems were implemented on a real-time hardware platform. 4.8.3 Hardware Implementation of COFDM Systems with Multiple Antennas A realtime testbed was developed and used to validate the scheduler algorithms in “real world” scenario. The demonstrator architecture had to be adapted resulting in redesign of the analog frontend as well as the digital transceiver. The testbed is based on OFDM transmission with 256 subcarriers for each UT. A WLAN transceiver chip Figure 4.17: DL throughput vs. total offered DL traffic for Figure 4.16: AMACframesupportingomnidirectional, SFIR, SDMA operationand SDMA transmission modes is used for the analog frontend operating at a radio frequency of 5.6 GHz with an RF bandwidth of 25 MHz. The modulation of the radio link is adaptive and is BPSK, QPSK, 16- or 64-QAM, and can be defined independently for each user. In total the system can serve four BS antennas and four UTs resulting in a 4x4 MIMO system. Each antenna combination between 1x1 (SISO) and 4x4 (MIMO) with or without diversity can be operated. Up- and downlink are separated in time division duplex (TDD). Digital signal processing performs the linear equalization algorithms ZF and MMSE in real time [1]. Furthermore, pre-equalization at the transmitter is possible using channel information from uplink transmission. diversity gain in SIMO configuration − LOS uplink scenariodiversity gain in SIMO configuration − LOS uplink scenario − 16 QAM 2525 1 X 1 − 16 QAMuser 1 −− 4X2 MIMO 1 X 2 − 16 QAMuser 2 −− 4X2 MIMO 1 X 3 − 16 QAMuser 1 −− 4X4 MIMO 20 1 X 4 − 16 QAM20user 2 −− 4X4 MIMO user 3 −− 4X4 MIMO user 4 −− 4X4 MIMO 15 15 10 10 5 SNR of user at the receiver in dBSNR of user at the receiver in dB 5 0 −50 0−2−4−6−8−10−12−14−16−180−2−4−6−8−10−12−14−16−18 attenuation of the transmit power in dBattenuation of the transmit power in dB Figure 4.18: Diversity gain under SIMOFigure 4.19: SNR per user with 4x2 and with different number of4x4 MIMO antennas As an example Fig. 4.18 presents the measured diversity gain that is obtained using more than one antenna. Regarding MIMO scenarios diversity also plays an important role as shown in Fig. 4.19. All user can be served with smaller SNR. Regarding two users the SNR and therefore the data rate is much higher. The measurements were taken at the entrance hall of the IHF building. The BS was equipped with a compact four-port-inverted-F antenna and the UT was fit with another compact four-port antenna using four orthogonal radiation modes [5]. Bibliography
[81] L. Bruehl, Parallele Prozessorarchitektur fuer die Raum-Zeit-Entzerrung in breitbandigen Funksystemen mit adaptiven Gruppenantennen, PhD thesis, RWTH Aachen, 2005, Shaker ISBN 3-8322-4523-5.
[82] M. Fuchs, G. Del Galdo, and M. Haardt, “A Novel Tree-based Scheduling Algorithm for the Downlink of Multi-user MIMO Systems with ZF Beamforming,” in Proc. IEEE Internat. Conf. on Acoustics, Speech, and Signal Proc.(ICASSP, 2005.
[83] C. Hoymann, IEEE 802.16 Metropolitan Area Network with SDMA Enhancement, PhD thesis, RWTH Aachen University, Department of Communication Networks, Faculty 6, July 2008, http://www.comnets.rwth-aachen.de.
[84] C. Hoymann, H. Meng, and J. Ellenbeck,“Influence of SDMA-Specific MAC Scheduling on the Performance of IEEE 802.16 Networks,” in Proceedings of 12th European Wireless Conference 2006, Athens, Greece, April 2006, http://www.comnets.rwth-aachen.de.
[85] C. Oikonomopoulos-Zachos and B. Rembold, “A 4-Port Antenna for MIMO Channels,” in IEEE Conf. of Antennas and Propagartion (EUCAP), pages 1–4, 2007. 4.9 Large System Analysis of Nearly Optimum Low Complex Beamforming in Multicarrier Multiuser Multiantenna Systems C. Guthy, W. Utschick, Technische Universität München, Germany 4.9.1 Introduction In general, analytical expressions for the average sum rate in the Multiple-Input Multiple-Output (MIMO) Broadcast Channel (BC), resulting from signal processing algorithms requiring perfect channel state information at the transmitter, are difficult to obtain. That is true for the optimum sum capacity [11] as well as near optimum algorithms such as the Successive Encoding Successive Allocation Method (SESAM) [9] and its variant with Minimum Mean Square Error (MMSE) transmit filters [8, Ch. 4.2]. Thus, performance evaluation of these algorithms is only possible via simulation results. In the large system limit however, i.e., when at least two system parameters go to infinity at a fixed and finite ratio [6, 10], the performance of many algorithms becomes deterministic, although random variables are used. That is because the eigenvalues of random matrices often converge to an asymptotic limit, which can be obtained from the asymptotic eigenvalue distribution (a.e.d.) and which is independent of the current realization of the random matrix. The most prominent example is the Marčenko-Pastur distribution [5] for Wishart matrices. Furthermore the analytical expressions in the large system limit often serve as a good approximation of the system performance also with finite system parameters, which makes large system analysis an interesting tool for the analysis of signal processing algorithms. In this chapter we will present analytical approximations of the ergodic sum rates achievable with SESAM with MMSE transmit filters [8] and zero-forcing transmit filters [9] based on large system results with Gaussian i.i.d. channel matrices and an infinite number of transmit and receive antennas. It will be shown that the results also serve as good approximations for the average sum rate in systems with finite parameters. 4.9.2 System Model We consider a multi-user multi-carrier MIMO system with C carriers, one base station with N antennas and K non-cooperative users with R antennas. The k-th user’s channel matrix on carrier c, denoted asHk,c∈ CR×N, consists of uncorrelated Gaussian entries with zero mean and variance 1/R. Perfect knowledge of the matricesHk,cat the transmitter is assumed. The additive noise at each receiver is assumed to be white Gaussian with zero mean and unit covariance matrix. 4.9.3 Description of Algorithms As the optimum solution, both variants of SESAM rely on the principle of Dirty Paper Coding (DPC). Furthermore they successively allocate data streams to users, where in each step filters and user allocation of previously allocated data streams are kept fixed and the next data stream is allocated to that user such that the increase in the objective function becomes maximum. The allocation stops, if no increase in the objective function is possible with a new allocation. Denoting the number of totally allocated subchannels on carrier c with Mc, the achievable sum rate computes according to CMc Rsum=log2(1 + pi,cλi,c). c=1i=1 In the following we will shortly describe how the subchannel powers pi,cand the channel gains λi,ccompute for the two algorithms. For notational convenience, we assume that the user allocation is given in the following, where πc(i) denotes the user to which the data stream encoded at i-th place has been allocated to on carrier c. Certainly, when the algorithm is run, potential subchannel gains have to be computed for every user and carrier to select the most suitable user and carrier for each data stream. SESAM with MMSE Filters With MMSE filters, the problem of maximizing sum rate under a total power constraint can be solved almost optimally at drastically reduced computational complexity. In this case a simplified power allocation is assumed such that pi,c=PTx7, CMc where PTxdenotes the available transmit power. The subchannel gains λi,cthen compute according to ⎛⎛⎞−1⎞ ⎜⎝Hi−1 λi,c= ρ1πc(i),c⎝I +PTxHHt CMcπc(j),cj,ctHj,cHπc(j),c⎠HπHc(i),c⎟⎠,(4.11) j=1 where ρ1(A) denotes the principal eigenvalue of the matrix A. tj,cdenotes the transmit filter in the dual uplink for the j-th data stream on carrier c and is equal to the unit-norm eigenvector belonging to the principal eigenvalue of the matrix ⎛⎞−1 i−1 Hπc(i),c⎝I +PTxHHt j=1CMcπc(j),cj,ctHj,cHπc(j),c⎠HπHc(i),c(4.12) 7For SESAM with MMSE filter thep i,ccorrespond to the powers in the dual uplink. As the rates in the broadcast and the dual uplink are the same [8], we consider the uplink rates for the SESAM MMSE algorithm in this chapter. SESAM with Zero-Forcing Filters With zero-forcing filters the subchannel gains λi,care given by ⎛⎛⎞⎞ i−1 λi,c= ρ1⎝Hπc(i),c⎝I −tj,ctHj,c⎠HπH⎠,(4.13) c(i) j=1 where here thetj,care the downlink transmit filters for the j-th data stream on carrier c and equal to the unit-norm eigenvectors corresponding to the principal eigenvalues of the matrices ⎛⎞⎛⎞ j−1j−1 ,cπc(j),cπc(j),c ,ctH ,c⎠. =1 =1 Each matrixI −j =1−1t ,ctH ,cprojects into the nullspace of the beamformers of the previously allocated data streams on carrier c and therefore assures that thetj,cto do not interfere with the previously allocated subchannels on carrier c. Interference on later allocated subchannels is suppressed by DPC. With this kind of zero-forcing, several Quality-of-Service (QoS) constrained optimization problems can be solved at reduced computational complexity, where the optimum can be achieved quite closely. Such optimization problems can be the weighted sum rate maximization under minimum and maximum rate requirements with a transmit power constraint or the transmit power minimization for the fulfillment of minimum rate requirements. As zero-forcing filters are applied together with DPC, the subchannels are interference-free and the optimum powers pi,ccan be determined by water-filling alike solutions. For the details of the power and user allocation the reader is referred to [9] for the pure sum rate maximization, to [4] for the weighted sum rate maximization under a power constraint and [1] for QoS constrained optimization problems. 4.9.4 Approximation of the Ergodic Sum Rate with Large System Analysis In this section we will present approximations for the subchannel gains λi,cwith results from large system analysis. For the large system analysis the number transmit antennas and receive antennas go to infinity at a finite fixed ratio β, i.e., N→ ∞, R → ∞, β =NR, finite. Then the empirical eigenvalue distributions of the matrices in (4.13) and (4.11) converge almost surely to an asymptotic limit. For finite systems, we propose to use the a.e.d. fA(x) of a matrixA to find an approximation for the i-th strongest eigenvalue as follows. LetA be a L × L matrix with finite L, then the i-th eigenvalue of this matrix is approximated by these two implicit equations. mm ρi(A) = LixfA(x)d x,whereifA(x)d x =L− i + 1. mi−10L Hence the x domain is divided into L intervals, where in each interval [mi−1; mi] the integralmmifA(x)d xis equal to 1/L. The centroid of each interval then reprei−1 sents one eigenvalue. Using these approximations for the computation of eigenvalues in (4.11) and (4.13), the user and power allocation is afterwards done as originally proposed for finite systems. The a.e.d.s fA(x) can be computed from the Stieltjes transformation SA(z) as described for example in [10]. In the following we will therefore present equations for the Stieltjes transforms. SESAM with MMSE Filters As a direct computation of the Stieltjes transforms of the matrices in (4.11) seams to be difficult, we first introduce the following approximation of the subchannel gains. −1 λi,c≈ ρni,c+1Hπc(i),cI +PTxVnVHHH,(4.14) CMci,cni,cπc(i),c where ni,cdenotes the number of subchannels assigned to the user πc(i) in previous steps on carrier c.Vni,c∈ CN×i−1−ni,cis a matrix with orthonormal columns, i.e., VnHi,cVni,c=I, independent of Hπc(i),c. Hence the effect of the interfering subchannels allocated to other users is taken into account by the matrixVni,c, which consists of as many orthonormal columns as subchannels assigned to other users than user πc(i) interfere with the i-th subchannel on carrier c.The effect of interference of subchannels allocated to the same user is considered by taking the ni,c+ 1-th largest eigenvalue in (4.14), denoted as ρni,c+1. Due to the independence between the matricesHπc(i),candVn, the Stieltjes transform SA˜(z) of the matrix ˜Ai,c= i,ci,c Hπc(i),cI +CMPTxcVni,cVnHi,c−1HπHc(i),c∈ CR×Rcan be derived from [10, Theorem 2.39] and is given by the implicit equation 1 + zSA˜(z) β =i,c. 1−1N−(i−1−ni,c)−1+CMcPTxi−1−ni,c Ai,c(z)N1+CMcPTx+SAi,c˜(z)N For details the reader is referred to [3]. SESAM with ZF Filters As the matrixHπc(i),cI −ij=1−1tj,ctHj,cHπHhas the same nonzero eigenvalues as c(i),c Ai,c=ViH−1,cHπHc(i),cHπc(i),cVi−1,c, whereVi−1,ccontains the N− i − 1 orthonormal basis vectors of the projectorI −ij=1−1tj,ctHj,c, we derive an implicit equation for the Stieltjes transform SAi,c(z) of the latter matrix in the following. The computation of SAi,c(z) works recursively, as it requires the a.e.d. fA(x), where i,cdenotes i,c,c the last step before step i, in which a subchannel has been assigned to the user πc(i) on carrier c. SAi,c(z) is given implicitly by n1f 01− ˜β + (x − z) ˜βSA(z)d x =N− i,ci,c− 1, i,c where fA(x)d x =i,c− 1. 0i,c,cN− i,c For details the reader is referred to [2]. 4.9.5 Numerical Results Figure 4.20 exhibits the sum rate averaged over 1000 channel realizations versus the number of transmit antennas, where the sum rate maximization under a transmit power constraint is considered. The ratio β has been fixed to β = 2. Each cross for the SESAM approaches corresponds to the sum rate achieved with one channel realization and the line goes through the average sum rates. Figure 4.20 (a) com12040 Asymptotic Computation 100Average Gain35 30 80 25 6020 15 Sum rate (bpcu)40Sum rate (bpcu)Sum Capacity SESAM 10 SESAM large system 20 5BD DPC large system BD large system 00 01020304050600102030405060 Number of transmit antennasNumber of transmit antennas (a) Sum rate averaged over 1000 channel re-(b) Large system approximation of sum alizations compared to asymptotic sumrates for different algorithms withK = rate in a system withK = 2 users,5,PTx= 10,β = 2 β = N/R = 2 Figure 4.20: Numerical Results pares the approximated sum rate with the average sum rate for SESAM with MMSE filters in a system with 2 users, one carrier, and at a transmit power of PTx= 100, which corresponds to a transmit SNR of 20dB. In Fig. 4.20 (b) the same comparison is made with SESAM and ZF filters at 10 dB and in a system with 5 users. Additionally, Fig. 4.20 (b) exhibits the average sum capacities and the large system approximations of Block Diagonalization [7] with and without DPC, which have also been derived in [2]. From both figures we can conclude that the presented approximations match the average sum rate quite well, already with reasonable numbers of transmit and receive antennas. Bibliography
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[96] H. Viswanathan, S. Venkatesan, and H. Huang, “Downlink Capacity Evaluation of Cellular Networks With Known-Interference Cancellation,” IEEE Journal on Selected Areas in Communications, 21(6):802–811, June 2003. 4.10 Combined Radar and Communication Systems Using OFDM M. Braun, C. Sturm, F. Jondral, T. Zwick, Karlsruhe Institute of Technology (KIT), Germany 4.10.1 Introduction In the current technological development, the radio frequency front-end architectures used in radar and digital communication technology are becoming more and more similar. In both applications more and more functions that have traditionally been accomplished by hardware components are now being replaced by digital signal processing algorithms. Moreover, today’s digital communication systems use frequencies in the microwave regime for transmission, which are close to the frequency bands traditionally used for radar applications. This technological advancement opens the possibility for the implementation of joint radar and communication systems that are able to support both applications with one single platform and even with a common transmit signal. A typical application area for such systems would be intelligent transportation networks, which require the ability for inter-vehicle communications as well as the need for reliable environment sensing. First concepts of joint radar and communication systems have been primarily based on spread spectrum techniques. Recently, OFDM signals have gained a lot of attraction for this purpose. This is motivated by two facts: First, most currently released communications standards, e.g., IEEE 802.11p, employ OFDM signals. Second, in the radar community OFDM signals recently have attracted general interest and their suitability for radar applications has been proven. Hence, OFDM signals currently seem to be the ideal basis for joint radar and communication implementations. A possible application scenario of an OFDM based joint radar and communication system is illustrated in Fig. 4.21. The OFDM signal (colored in green) is transmitted from the car on the left side and transports information to distant receivers. At the same time this signal is reflected at objects, also cars, in the neighborhood (reflected signal depicted in gray). The OFDM system observes the echoes of its own transmit signal and calculates a radar image by applying suitable processing algorithms. Also, communication with base stations could be included in this concept. In the following, detailed considerations regarding an optimum parametrization of the OFDM signals for simultaneous radar and communication operation as well as optimum radar processing strategies will be discussed. Moreover, a fully operational system demonstrator and verification measurement results will be presented. 4.10.2 Signal Design A major challenge is the design of the OFDM signals. It must be guaranteed that the communication link is reliable over mobile communication channels with severe fading, and that the radar imaging algorithm is not negatively affected by the signal Table 4.3: Channel limitations for the OFDM parameters PropertyUrbanAutobahn RMS excess delay0.102 μs0.122 μs Maximum Doppler spread7.24 kHz5.23 kHz Coherence bandwidth2246.1 kHz1269.53 kHz RMS Coherence time0.401 ms0.46 ms design. A large variety of parameters can be changed, ranging from sub-carrier distance to channel coding. This section will explain the most important parameters. A more detailed description can be found in [1, 2]. Physical Parameters Physical parameters of an OFDM frame are sub-carrier distance, guard interval duration, total bandwidth and the frame duration. Their choice depends on the required radar accuracy and the quality of the mobile propagation channels. In [1] and [2], we analyzed the effects of the mobile propagation channels. Basis for the analysis were RayTracing channels, i.e., simulations of real traffic scenarios where the channels between transmitter and receiver were obtained by optical methods [3]. A database of 10567 channels from a total of eight urban traffic and two highway (“Autobahn”) scenarios was used to test and evaluate parameterizations. These channels were analyzed for time and frequency variance to obtain limits for the physical OFDM parameters. In particular, the sub-carrier spacing is limited by the coherence time and the Doppler spread; the guard length duration depends on the excess delay [1]. Table 4.3 shows the results of the analysis. The requirements of the radar accuracy also impose constraints on the parametrization of the signal. In particular, the resolution in range and Doppler domain set minimum limits on bandwidth B and frame duration TF, which can be estimated Figure 4.21: Application scenario for a combined radar and communication system by the following equations: c0c0 B≥, TF≥(4.15) 2Δdmax2Δvmaxfc For a range resolution of 1.5 m, the bandwidth must therefore be on the order of 100 MHz. This in turn has other side effects, such as a low power density. A less obvious design criterion is the effect of the parametrization on the OFDM radar processing algorithm. The maximum likelihood estimator presented in the following section is prone to threshold effects. In [4], we present a method to test the range in which a given set of parameters works without threshold effects. Channel Coding A suitable channel coding is an important choice in the frame design process. Vehicular applications in particular have high demands regarding reliability of the data transmission. At the same time, the signal’s low power density and the highly frequency- and time-variant channels make error-free data transmission very difficult. On the other hand, the large bandwidth allows for high data rates, which might not be necessary. It therefore makes sense to sacrifice raw data rate for lower bit error rates by using robust codes with low coding rates. Although several types of codes can satisfy these requirements, Reed-Muller codes appear particularly suitable. Their big advantage is the possibility to use sub-sets of codes which exhibit a low peak-to-average power ratio (PAPR) [5, 6]. This is gives the whole system a new degree of freedom, since the low PAPR values exhibit fewer requirements towards the amplifiers. Simulations have shown the codes to perform well under adverse channel effects with a fixed PAPR of 3 dB [5]. 4.10.3 The Radar Subsystem The radar subsystem deals with the task of estimating range and relative speed of other objects in the vicinity. When transmitting, it receives and analyses the backscattered signal and processes it to gain information about the surrounding objects. In order to identify a suitable estimation algorithm we must first analyze the effects the backscattering has on OFDM frames. In the following, one OFDM frame shall be described by an N× M-matrix FTx∈ CN×M, where every element (FTx)k,l) =±1 is a modulation symbol from the BPSK modulation alphabet. Every row in FTxcorresponds to an OFDM sub-carrier; every column corresponds to an OFDM symbol. s(t) denotes the transmitted time domain signal and is created from FTxby the usual OFDM modulation process of calculating an IFFT of every column and prepending the result with a cyclic prefix. During transmission, a receiver is active. The received signal r(t) consists of the Doppler shifted and time-delayed reflected signals. In the case of H reflecting targets, the relation between transmitted and received signals is H−1 r(t) =bhs(t− τh)ej2πfD,ht+ wσ2(t).(4.16) h=0 The Doppler shift and roundtrip propagation time of the h-th target are denoted fD,hand τh, respectively. bh=|bh|ej ˜ϕhis the corresponding complex attenuation factor. The received signal is a linear superposition of reflected signals from every target, plus complex white Gaussian noise wσ2(t) with variance σ2. For the development of the estimation algorithm it is useful to analyze the effects of Doppler shift and time delay on FTx. For simplicity, we will analyze the effect of a single reflecting target with Doppler shift of fDand a roundtrip delay of τ . In this case, the Doppler shift causes an oscillation of the matrix rows by ej2πlTOfD. This assumes a constant Doppler shift over all frequencies, which is a valid approximation if the bandwidth is much smaller than the signal’s center frequency. The delay causes a phase shift on every sub-carrier of e−j2π(f0+kΔf )τ0. Without loss of generality,|b0| can be assumed to be of unit value. Representing the received signal in the same matrix notation as FTxcan thus be done as (FRx)k,l= (FTx)k,l· ej2πlTOfD,0e−j2πkτ0Δfejϕ0+ (W)k,l.(4.17) W is a matrix representation of the additive white Gaussian noise (AWGN); its entries are i.i.d. random values from a circular, complex, zero-mean normal distribution with variance σ2. All phase shifts which are constant for the entire frame are summarized into the phase term ϕ. Before estimation, the known modulation symbols inside FTxcan be eliminated from FRxby simple element-wise division. The resulting matrix is thus (F)k,l== ej(2π(lTOfD,0−kτ0Δf )+ϕ0)+(W)k,l.(4.18) (FTx)k,l(FTx)k,l All estimation is now performed on F, which consists of two orthogonal oscillations and AWGN. It must be noted that the statistics of the noise are not affected by the division if the BPSK symbols are not correlated, since in this case, the division is nothing but a random phase rotation by either π or zero of the rotationally invariant noise. Therefore, the estimation of fDand τ is equivalent to estimating the frequencies of the two orthogonal oscillations within the matrix F and is therefore very similar to an identification of spectral components. Finally, the target parameters must be estimated from F. We have chosen a maximum likelihood estimate (MLE) approach, which was originally introduced in [7] and [8]. The MLE is obtained by calculating [4] ⎧⎫ ⎪⎨⎪⎬ ⎪⎩FFT(m)!“#F\(⎪⎭(4.19) FFT over every row ofF !''#\) IFFT over all columns of the FFT result and finding the values ˆm, ˆn which maximize C(m, n). The MLE for Doppler shift and propagation time is then τ =ˆ,fˆD=mˆ,(4.20) NIFFTΔfMFFTTO where NIFFTand MFFTare the lengths of the IFFT and the FFT, respectively. It must be noted that the complexity of such an approach is smaller than the classical approach of correlating in frequency and time domain. Moreover, additional investigations have been conducted regarding the estimation of the direction of arrival (DoA) with a multiple antenna receiver. It has been shown that standard DoA estimation techniques can be applied directly to the output of the range and velocity estimators in Eq. (6). Detailed results have been published in [9]. 4.10.4 Measurements Demonstrator Setup The demonstrator system consists of three main hardware components: a Rohde & Schwarz (R&S) SMJ100A vector signal generator, a R&S FSQ26 signal analyzer, and optionally a R&S SMR40 microwave signal generator. The SMJ100A is limited to a maximum carrier frequency of 6 GHz but offers higher output power than the SMR40. Therefore it has been decided to implement two different configurations, one with the SMJ100A only in order to achieve high output power at 6 GHz and another one with both SMJ100A and SMR40 in order to generate a signal at the intended carrier frequency of 24 GHz but with reduced transmit power. All instruments are connected through an Ethernet link and controlled from a computer via the MatLab Instrument Control Toolbox. All signals are generated and processed in MatLab. The OFDM system parameters that have been applied for the measurements are summarized in Table 4.4. These parameters have been obtained through a theoretical study described in [10] and verified with ray tracing simulations in [1]. Table 4.4: OFDM system parameters SymbolQuantityValue fcCarrier frequency6 GHz / 24 GHz NcNumber of subcarriers1024 ΔfSubcarrier spacing90.909 kHz TElementary OFDM symbol duration11 μs TpCyclic prefix length1.375 μs BTotal signal bandwidth93.1 MHz The first configuration of the system setup is shown in Fig. 4.22. The transmit signal is generated in MatLab, transferred to the signal generator, converted to the carrier frequency and radiated. The signal analyzer is synchronized in phase through a 10 MHz reference signal and in time through a trigger signal. The signal analyzer samples the I and Q components of the received signal after conversion Figure 4.22: OFDM system setup for a maximum carrier frequency of 6 GHz to the baseband and transfers them back to the computer. The signal generator provides a maximum carrier frequency of 6 GHz and a maximum peak power of 20 dBm. Since with the chosen parameters the OFDM signal shows a relatively stable PAPR of approx. 10 dB, a maximum mean transmit power of 10 dBm is available for uncoded transmission. The employed horn antennas at the transmitter and at the receiver have a gain of 18.5 dBi each. In order to carry out measurements with a carrier frequency of 24 GHz an additional mixer is required. In that case a slightly different second setup is used, in which the output signal of the SMJ100A signal generator is fed to the external modulation signal input of the SMR40 signal generator. With an intermediate frequency of 200 MHz at the input of the SMR40 and a local oscillator frequency of 23.85 GHz, the center frequency of the upper sideband occurs at 24.05 GHz. The radiation of a lower sideband cannot be suppressed in this configuration, however the receiver is tuned only to the upper sideband, which spans from 24.0 GHz to 24.1 GHz. The external modulation input of the SMR40 does not allow for output power control. When driving the SMR40 with an average input signal power of 0 dBm a total average output power of only -12 dBm is available in the upper sideband. With an additional medium power amplifier the output power can be increased to 10 dBm. Also in this setup horn antennas are employed, which have a gain of 22 dBi each. Measurement Results In order to verify the developed algorithms a dynamic scenario with at least one moving object is required. Therefore in the scenario shown in Fig. 4.23a measurements have been taken with the system demonstrator. The scenario consists of a corner reflector with a radar cross section of σRCS= 16.3 dBm2at 24 GHz and a car moving towards the radar with a velocity of approximately 25 km/h. The measurement was taken at the instant when the car was at the same distance of R = 20 m as the reflector. The result obtained from the Doppler estimation algorithm is shown in Fig. 4.23b. In the FFT processing a Hamming window has been applied for both Doppler and range processing. It can be observed that in the distance of (a) Investigated scenario(b) Measured radar image (normalized, in dB) Figure 4.23: Verification measurement in a dynamic scenario 20 m both a high peak from the reflector at zero velocity and an additional peak at approximately 7 m/s corresponding to the speed of the car appear in the image. The reflection from the car is around 15 dB weaker than the signal scattered from the reflector. In the radar image additional reflections from ground clutter and objects in the background appear at zero velocity. The measurement result proves that both objects can be clearly identified and separated with the proposed processing algorithm. In order to completely characterize the system performance also the SNR of the radar image after the processing has to be analyzed. The estimator described in Eq. (4.20) provides an SNR gain equivalent to the product of the number of subcarriers N and the number of evaluated OFDM symbols M . The expected radar image SNR amounts to PT xN M GT xGRxλ2σRCS SNRimage=(4.21) PN(4π3)r4 with PT xbeing the transmitted signal power, GT xand GRxbeing the transmit and receive antenna gain, λ being the wavelength, and σRCSdenoting the radar cross section of the reflector. In order to verify that this relation applies for practical OFDM radar measurements with the proposed estimator, additional measurements have been carried out with the system setup for the 24 GHz ISM band. In these measurements radar images of the trihedral reflector have been taken for three different distances of r = 4, 10, 20 m without using the amplifier. For each measurement result the ratio between the peak caused by the reflector and the average background noise level has been determined, assuming that this value represents SN Rimagefrom (4.21). The measured values have been compared to the theoretically expected values, taking into account the receiver noise power level specified by the manufacturer to -143 dBm/Hz corresponding to a total noise power of -64 dBm. The results are reported in Table 4.5. With increasing distance the measured SNR values approach the expected ones. Table 4.5: Radar image SNR for PT x= -12 dBm Distance to the reflector in m41020 Measured SNR in dB49.841.430.8 Expected SNR in dB60.744.532.8 For the distance of 4 m the discrepancy is caused by the fact that the reflector is not yet in the far field. For higher distances of the reflector there is only a minor discrepancy between the measured and the expected SNR, which results form the SNR degradation caused by the Hamming window. From the measurement results it is evident that the proposed estimator provides the gain claimed in (4.21). A detailed report on the measurements can be found in [11]. 4.10.5 Summary In this project a detailed concept for a combined radar and communication system based on OFDM signals has been elaborated and evaluated. A suitable estimator has been developed that allows for performing range and Doppler measurements with OFDM signals without any negative impact of the simultaneously transmitted user information. Both measurements and simulations show that OFDM radar is an interesting and feasible new technology with some interesting qualities. Acknowledgement We would like to thank Rohde & Schwarz for providing the measurement equipment. Bibliography
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