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Coon, J., Siew, J., Beach, MA., Nix, AR., Armour, SMD., & McGeehan, JP. (3). A comparison of MIMO-OFDM and MIMO-SCFDE in WLAN environments. In Goba Teecommunications Conference, 3 (Gobecom 3) (Vo.

1 Coon, J., Siew, J., Beach, MA., Nix, AR., Armour, SMD., & McGeehan, JP. (3). A comparison of MIMO-OFDM and MIMO-SCFDE in WLAN environments. In Goba Teecommunications Conference, 3 (Gobecom 3) (Vo. 6, pp ). Institute of Eectrica and Eectronics Engineers (IEEE). DOI:.19/GLOCOM Peer reviewed version Link to pubished version (if avaiabe):.19/glocom Link to pubication record in Expore Bristo Research PDF-document University of Bristo - Expore Bristo Research Genera rights This document is made avaiabe in accordance with pubisher poicies. Pease cite ony the pubished version using the reference above. Fu terms of use are avaiabe:

2 A Comparison of MIMO-OFDM and MIMO-SCFDE in WLAN Environments J. Coon, J. Siew, M. Beach, A. Nix, S. Armour, and J. McGeehan Centre for Communications Research, University of Bristo Merchant Venturers Buiding, Woodand Road, Bristo BS8 1UB, UK Emai: {Justin.Coon, Abstract Recent deveopments in orthogona frequency division mutipexing (OFDM) and singe-carrier frequency-domain equaization (SCFDE) have sparked debate about the superiority of one method over the other. In this paper, we further this debate by comparing the theoretica performance of OFDM and SCFDE when each is impemented in one of two different mutipe-input mutipe-output (MIMO) architectures: spatia mutipexing and space-time bock codes. This study focuses on the use of MIMO-OFDM and MIMO-SCFDE in wireess oca area network (WLAN) appications. Performance is given in terms of the packet error rate (PER) and the throughput of the systems. I. INTRODUCTION Latey, much attention has been focused on physica ayer (PHY) techniques that are suitabe for high-data-rate mutipeinput mutipe-output (MIMO) wireess communications systems. Of specia interest are techniques that minimize the compexity of the muti-dimensiona equaization process that is required in a wideband MIMO system. In this paper, we present arguments both for and against the use of two techniques, namey orthogona frequency division mutipexing (OFDM) and singe-carrier frequency-domain equaization (SCFDE). These arguments are presented in the form of a theoretica performance comparison. In singe-antenna systems, OFDM is we-documented and is favored among many in academia as we as in industry [1]. SCFDE, a PHY technique of simiar compexity, has received much attention of ate and has recenty stimuated much singe-carrier vs muti-carrier debate [2]. Both of these techniques utiize signa processing in the frequency domain to provide reativey ow-compexity soutions to the probem of equaization. In [2], a comparison of these two technoogies was conducted with a focus on singe-antenna systems empoyed in fixed broadband wireess appications (IEEE 82.16) where the mutipath spread of the channe is ony a few non-zero discrete taps. However, to the best of our knowedge, an OFDM/SCFDE performance comparison has not been conducted for MIMO systems empoyed in wireess oca area network (WLAN) appications where the effects of mutipath propagation in the channe can be much greater. In this paper, we present an investigation of the performance of severa different MIMO-OFDM and MIMO-SCFDE systems in WLAN environments. In section II, an overview of the chosen MIMO-OFDM and MIMO-SCFDE systems is presented. In section III, the seected wireess channe modes are discussed. The resuts that were obtained in this investigation are iustrated in section IV. Finay, concusions are given in section V. II. SYSTEM DESCRIPTION OFDM and SCFDE were appied to two MIMO baseband architectures: spatia mutipexing (SM) and space-time bock coding (STBC). Two transmit antennas and two receive antennas were used in a systems. A generaized bock diagram of the systems under investigation is shown in Figure 1. The key architectura difference between a MIMO-OFDM system and a MIMO-SCFDE system, namey the order in which the operation is executed, is depicted in Figure 1. Other differences between the SCFDE and OFDM architectures incude the impementation of the Viterbi decoder, the designs of the transmit and receive fiters, and the structure of the frequency-domain equaizers. We address these dissimiarities beow. A. Viterbi Decoder Impementation A MIMO architectures were simuated with and without a haf-rate convoutiona code with random bit intereaving foowing the encoder as depicted in Figure 1. The convoutiona code used in this study is specified in [3], [4]. At the receiver, ½-rate conv. enc. AWGN AWGN Π RX Fiter RX Fiter remova remova Space-Time Processing (SM, STBC) FFT FFT OFDM ony Space-Time Processing (Decoupe, Equaize) SCFDE ony Viterbi decoder Π -1 TX Fiter TX Fiter P/S Fig. 1. Generaized bock diagram of MIMO-OFDM and MIMO-SCFDE systems. GLOBECOM /3/$17. 3 IEEE

3 the equaized symbos were mapped to soft bits that were then passed through a soft-input hard-output Viterbi decoder as iustrated in Figure 1. The OFDM systems utiize channe state information (CSI) to weight the branch metrics, thus enhancing the performance of the Viterbi decoder. However, singe-carrier systems are generay unabe to utiize CSI in this fashion because the energy in each transmitted bit is spread across the entire bandwidth of the system. As a resut, a standard soft-input hard-output Viterbi decoder was used in the SCFDE systems. B. TX and RX Fiter Design In genera, the transmit and receive fiters in OFDM systems can be much tighter than those used in singe-carrier systems. Consequenty, we impemented root-raised-cosine fiters with a ro-off factor of.4 at the transmitter and the receiver of each SCFDE system studied and root-raised-cosine fiters with a ro-off factor of.25 at the transmitter and the receiver of each OFDM system [5]. Additionay, the bandwidth used by the simuated systems was kept as cose to MHz as possibe. Therefore, to avoid the introduction of intersymbo interference (ISI) by the fiters, the symbo periods for the OFDM and SCFDE systems were set equa to ns and 7 ns, respectivey. The fu specifications of these fiters are presented in Tabe I. C. Equaizer Design In each MIMO system, two factors affect the design of the frequency-domain equaizer: the PHY technique (i.e. OFDM or SCFDE) and the MIMO architecture (i.e. SM or STBC). Throughout this study, zero forcing (ZF) equaizers were impemented in the OFDM systems whereas minimum meansquared error (MMSE) equaizers were empoyed in the SCFDE systems. Both of these common inear equaization techniques have simiar compexity in the context of MIMO appications. Before discussing each system in turn, some notation is defined. The matrix I q is the q q identity matrix, q is the q q zero matrix, denotes the Kronecker product, and ( ) K, ( ), ( ) T, ( ) H, and E{ } denote the moduo- K, compex conjugate, transpose, conjugate transpose, and expectation operations, respectivey. 1) SM-OFDM: The SM-OFDM equaized symbo vector x is given by x = W SM (Λx + η) (1) where Λ 1,1... Λ1,nt Λ =..... (2) Λ nr,1... Λnr,n t is the overa channe matrix of a system with n t transmit antennas and n r receive antennas and W SM is the ZF equaizer matrix. As previousy mentioned, n t = n r =2in this study. The sub-matrix Λ i,j is a diagona matrix defining the frequency response of a K subcarriers between the jth transmit antenna and the ith receive antenna. The vector x is a 2K 1 vector of transmitted symbos and η is a 2K 1 vector of white Gaussian noise sampes. The ZF equaizer W SM = Λ 1 removes the channe distortion from the received symbos at the expense of possiby enhancing the noise as seen in (1). 2) STBC-OFDM: For STBC-OFDM systems, equaization is performed after the received signas are combined [6]. If s is the stacked 2K 1 vector of symbos after maximum ratio combining (MRC), the equaized symbo vector x is given by x = W STBC (s + η). (3) In (3), W STBC = Λ 1 is the ZF equaizer matrix where ( ) 2 ( 2 Λ = diag h (1) i,j,1,..., h (p) i,j,k) i,j is a diagona matrix and h (p) i,j,k is the channe gain between the jth transmit antenna and the ith receive antenna on subcarrier k for the pth MRC signa. The vector η is the noise after MRC. 3) SM-SCFDE: For SM-SCFDE systems, the vector x of equaized symbos at both receive antennas is given by x = D 1 F W (ΛD SM Fx + D F η) (4) where D F = I 2 F. The matrix F is the K K FFT matrix where K is the ength of each transmitted bock in the SCFDE system. In (4), W SM is the MMSE equaizer matrix defined in [7] and reproduced beow for convenience. ( ) 1 W SM = Λ H ΛΛ H + σ2 η σx 2 I 2K. (5) The quantity ση 2 is the tota variance of the compex Gaussian noise process at one receive antenna, σx 2 is the tota power of the compex transmitted signa from one transmit antenna, and Λ is defined in (2). As observed in (4), the equaizer spans both receiver branches to separate the transmitted symbo streams and equaize the received symbos simutaneousy. 4) STBC-SCFDE: The MMSE equaizer used in the STBC- SCFDE systems, first discussed in [8], is different from that empoyed in the SM-SCFDE systems in that the decouping and equaization processes are performed separatey. To iustrate, et x (1) and x (2) be the two K 1 symbo vectors transmitted from the first and second antennas respectivey at time. Then the two vectors transmitted at time +1, directy after the first two vectors, are defined by x (1) +1 (k) = x (2) (( k) K ) x (2) +1 (k) = x (1) (( k) K ) for k =, 1,..., K 1. At the receiver, the vectors corresponding to those transmitted during the (+1)th time sot are conjugated, after which each received vector is transformed into the frequency domain and MRC is impemented to decoupe the transmitted sequences. The resuting ength-2k vector of symbos prior to equaization is given by Y = Λ ( H (i) Λ(i) D F x + D F η (i)) (6) i=1 i,j GLOBECOM /3/$17. 3 IEEE

4 where Λ (i) = ( Λi,1 Λi,2 Λ i,2 Λ i,1 Λ i,j is defined in (2), x =(x T(1), x T(2) ) T, and η (i) represents the noise contribution from the ith receive antenna. The sequence Y is then passed through an MMSE equaizer. The equaizer matrix W STBC for this system is obtained by soving the equation { W STBC = arg min E x x 2} (7) W where x = D 1 F WY represents the equaized symbos in the time domain. It can be shown that the soution to (7) is [6], [8] ( ) 1 W STBC = Λ + σ2 η σx 2 I 2K (8) where Λ = i=1 j=1 Λ 2 i,j K K i=1 j=1 ), 2 Λ i,j III. CHANNEL DESCRIPTION. (9) In [9], five different indoor WLAN channe modes are described. For this study, the channe modes with the shortest and the ongest RMS deay spreads were chosen. The ETSI A mode corresponds to a typica office environment and has an RMS deay spread of ns, whereas the ETSI E mode corresponds to a typica arge open space environment with an RMS deay spread of 2 ns. Both of these channes represent non-ine-of-sight (NLOS) conditions in their respective environments. In the simuations, statisticay independent Rayeigh fading channe reaizations were generated, and the receiver was assumed to have compete knowedge of the channe. Athough these modes are specified for MHz bandwidth, the fiters discussed in section II-B were empoyed to give an RF bandwidth of MHz. IV. SIMULATION RESULTS To provide a fair comparison, severa system parameters were hed constant in the simuations. A compete ist of the simuation parameters is given in Tabe I. It is important to note that the number of bits in a packet specified in Tabe I incudes six tai bits used to return the encoder to the zero state for the systems impementing the convoutiona code. As metrics of performance, packet error rate (PER) and throughput were used. To simuate the PER of a system, one packet was transmitted for each independent channe reaization. The transmission of one packet was assumed to be we within the coherence time of the channe. The PERs of systems empoying QPSK and 16-QAM in the ETSI A channe are shown in Figure 2. Likewise, the PERs of systems empoying QPSK and 16-QAM in the ETSI E channe are shown in Figure 3. Figures 4 and 5 show the throughputs of TABLE I SIMULATION PARAMETERS. SCFDE Parameters OFDM Parameters Bandwidth MHz.5 MHz Moduation QPSK & 16-QAM QPSK & 16-QAM Channes simuated ETSI A & E ETSI A & E Convoutiona (2,1,6) [3], [4] (2,1,6) [3], [4] encoder Viterbi decoder soft-input hard-output soft-input hard-output (standard) (weighted metrics) Equaization MMSE ZF Bits per packet No. of subcarriers (symbos per bock) TX fiter RRC RRC Sampe rate 7 sampes/symbo 5 sampes/symbo Fiter span symbos symbos Ro-off factor.4.25 [5] RX fiter RRC RRC Sampe rate 7 sampes/symbo 5 sampes/symbo Fiter span symbos symbos Ro-off factor.4.25 [5] Symbo period 7 ns ns Cycic prefix 12 sym. 84 ns 17 sym. 8 ns the simuated systems in the ETSI A and ETSI E channes, respectivey. In Figures 2 through 5, cd signifies a system in which the convoutiona code is empoyed, uncd signifies a system that does not utiize the code; curves reated to SCFDE systems are soid ines, and curves reated to OFDM systems are dot-dashed ines. A. PER Anaysis The graphs presented in Figures 2 and 3 show a number of interesting trends. Firsty, as expected, the uncoded SM- OFDM systems perform extremey poory and are, in genera, outperformed by the SM-SCFDE systems. This is most obvious in Figure 2(a) where the SNR gain of the uncoded SM- SCFDE system is about db at a PER of.3. Secondy, the best PER performance is achieved by concatenating a channe code with STBC. This is aso expected since this arrangement expoits spatia diversity and coding. Furthermore, the performance difference between the OFDM and SCFDE system with this particuar architecture is at most.5 db. It is interesting to note that resuts pubished in [2] for singe-input singe-output (SISO) systems with inear equaization show that for a sufficienty strong channe code, OFDM systems outperform SCFDE systems. In the MIMO case, however, this trend appears to be reversed as shown by the coded SM and uncoded STBC curves in Figures 2 and 3. An exception to the trend is seen in Figure 2(b), where it is shown that the SM-SCFDE system performs approximatey 2 db worse than the SM-OFDM system in the ETSI A channe when a 16-QAM consteation is used. This behavior is most ikey due to the imitations of MMSE equaization when dense signa consteations are used. Identica behavior is not observed for transmissions in the ETSI E channe GLOBECOM /3/$17. 3 IEEE

5 Probabiity of Packet Error 2 Probabiity of Packet Error (a) QPSK (b) 16-QAM Fig. 2. Packet error rates for STBC and SM systems in the ETSI A channe (n t = n r =2). Probabiity of Packet Error 2 Probabiity of Packet Error (a) QPSK (b) 16-QAM Fig. 3. Packet error rates for STBC and SM systems in the ETSI E channe (n t = n r =2). due to SCFDE s efficient utiization of frequency diversity and OFDM s sensitivity to the oss of orthogonaity between subcarriers, which is caused by an insufficient cycic prefix. The resuts aso show the trade-off between SM and STBC schemes for wideband systems. For exampe, in the ETSI A channe, the coded SM and uncoded STBC-OFDM systems perform amost identicay as shown in Figure 2(a). However, in the ETSI E channe, the SM-OFDM system outperforms the STBC-OFDM system in Figure 3(a) by approximatey 3 db at a PER of.1. A simiar trend can be seen for the same systems with 16-QAM moduation in Figures 2(b) and 3(b). These trends impy that the expoitation of frequency diversity can potentiay provide better performance gains for MIMO-OFDM systems than the utiization of spatia diversity aone. In practica terms this means that importance shoud be paced on the type of channe code empoyed over the type of diversity scheme used. Frequency diversity can be expoited further by increasing the number of subcarriers used in the system, which decreases the subcarrier spacing thus causing sma perturbations in the channe to become significant. The practica trade-off here is that the OFDM system becomes more sensitive to synchronization errors and imperfect channe knowedge as the number of subcarriers increase. In the SCFDE systems, the trade-off between SM and STBC is most obvious in the ETSI A channe where the coded SM-SCFDE systems perform better at ow SNR whie the STBC-SCFDE systems perform better at high SNR as shown in Figures 2(a) and 2(b). The crossover occurs at an SNR of approximatey 12 db (PER =.25) for the QPSK moduation and at an SNR of 15 db (PER =.5) for 16-QAM, which suggests that spatia diversity expoited through the STBC significanty aids the detection process in a channe with ow frequency seectivity such as the ETSI A channe. Additionay, in rich scattering environments, SCFDE GLOBECOM /3/$17. 3 IEEE

6 (a) SM (b) STBC Fig. 4. Throughput for systems in ETSI A channe (a) SM (b) STBC Fig. 5. Throughput for systems in ETSI E channe. efficienty expoits frequency diversity, which eads to better overa performance. This is ceary depicted in Figures 3(a) and 3(b), where the coded SM-SCFDE systems perform better than the uncoded STBC-SCFDE systems. B. Throughput Anaysis The throughput for each simuated system was cacuated as a function of the SNR from the foowing equation. 2mKR (N v) D(SNR) = (1 (SNR)) () NT s (K + Q)(1+µ) where m is the number of bits per symbo, R is the code rate, N is the tota number of bits in a packet prior to encoding, v is the number of tai bits in a packet, T s is the symbo period, Q is the number of symbos used for a cycic prefix in each bock, µ is equa to one if the system utiizes STBC and zero otherwise, and (γ) is the PER as a function of SNR. Figures 4 and 5 iustrate the effect the high fiter ro-off factor has on the singe-carrier systems. Indeed, the OFDM systems generay provide higher throughput than the SCFDE systems. It is interesting to note, however, that advantages can be gained through the use of a hybrid SCFDE-OFDM ink adaptive system, especiay for SM architectures. As shown in Figures 4(a) and 5(a), coded SCFDE systems provide the highest throughput at ow SNR for SM architectures. Furthermore, uncoded SCFDE systems empoying 16-QAM give the highest throughput at high SNR for SM systems in the ETSI A channe as iustrated in Figure 4(a). It is aso important to note that for mid-range SNR, the singecarrier STBC system is capabe of a higher throughput than the OFDM system in the ETSI E channe as iustrated in 5(b). GLOBECOM /3/$17. 3 IEEE

7 V. CONCLUSIONS In this study, severa different MIMO-SCFDE and MIMO- OFDM systems were compared in terms of PER and throughput. The resuts obtained in this investigation suggest that designing a MIMO-OFDM system to expoit frequency diversity through the use of a channe code and intereaving tends to give better performance than optimizing for spatia diversity through the use of STBC. Simiary, SM-SCFDE systems empoying inear MMSE equaization and a channe code perform reativey we in rich scattering environments; however, optimizing for spatia diversity via STBC can improve the performance of SCFDE systems in channes with ow frequency seectivity. Additionay, unike in the SISO case, MIMO-SCFDE generay performs better than MIMO- OFDM in terms of PER. It was aso shown that the throughput of MIMO-SCFDE systems wi inevitaby suffer from the tight constraints paced on the transmit and receive fiters uness bandwidth restrictions are reaxed. ACKNOWLEDGMENT The authors woud ike to thank Toshiba TRL Bristo for financiay supporting this work and are particuary gratefu for the insight provided by Dr. M. Sande, Dr. M. Yee, Dr. S. Parker, and Dr. Y. Sun. The authors are aso indebted to Dr. R. Piechocki for his participation in numerous technica discussions. REFERENCES [1] Z. Wang and G. B. Giannakis, Wireess muticarrier communications: where Fourier meets Shannon, IEEE Signa Processing Magazine, pp , May. [2] D. Faconer, S. L. Ariyavisitaku, A. Benyamin-Seeyar, and B. Eidson, Frequency domain equaization for singe-carrier broadband wireess systems, IEEE Communications Magazine, pp , Apri 2. [3] Broadband Radio Access Networks (BRAN); HIPERLAN Type 2; Physica (PHY) ayer, European Teecommunications Standards Institute,. [4] Suppement to IEEE standard for information technoogy - teecommunications and information exchange between systems - oca and metropoitan area networks - specific requirements. Part 11: wireess LAN Medium Access Contro (MAC) and Physica Layer (PHY), IEEE Std 82.11a, [5] R. van Nee and R. Prasad, OFDM for Wireess Mutimedia Communications, 1st ed. Boston: Artech House,. [6] S. M. Aamouti, A simpe transmit diversity technique for wireess communications, IEEE Journa on Seected Areas in Communications, vo. 16, no. 8, pp , October [7] J. P. Coon and M. A. Beach, An investigation of MIMO singecarrier frequency-domain MMSE equaization, London Communications Symposium, pp , 2. [8] N. A-Dhahir, Singe-carrier frequency-domain equaization for spacetime bock-coded transmissions over frequency-seective fading channes, IEEE Communications Letters, vo. 5, no. 7, pp. 4 6, Juy 1. [9] Channe Modes for HIPERLAN/2 in Different Indoor Scenarios, European Teecommunications Standards Institute, GLOBECOM /3/$17. 3 IEEE

Rate-Allocation Strategies for Closed-Loop MIMO-OFDM

Rate-Allocation Strategies for Closed-Loop MIMO-OFDM Rate-Aocation Strategies for Cosed-Loop MIMO-OFDM Joon Hyun Sung and John R. Barry Schoo of Eectrica and Computer Engineering Georgia Institute of Technoogy, Atanta, Georgia 30332 0250, USA Emai: {jhsung,barry}@ece.gatech.edu