ANTENNA SELIECTION FOR MIMO-OFDM WLAN SYSTEMS Manel Collados', Alexei Gorokhov2 Philips Research Laboratories, Prof. I'Iolstlaan 4, 5656 AA Eindhoven, The Netherlands,
[email protected] Qualcomm Inc., 5775 Morehouse Drive, San Diego CA 92121-1714, USA,
[email protected]
Abstract - This paper discusses the packet error rate (PER) performance of multiple-input multiple-output (MIMO) wireless systems. We focus our discussion on communication systems based on the IEEE 802.1 l d g standard. In particular, we study the performance of spatial multiplexing systems with joint encoding at the transmitter and linear detection at the receiver. We show that spatial multiplexing systems based on minimum mean square error (MMSE) or zero forcing (ZF) demultiplexing benefit greatly from antenna subset selection. These results agree with recent analytical results showing the equivalence in diversity order between a full system (all receive antennas) and a system with antenna selection. Keywords - MIMO, WLAN, OFDM, PEEL, MMSE, antenna selection.
I. INTRODUCTION Multi-input multi-output (MIMO) antenna techniques substantially improve wireless link performance by increasing the reliability when using space-time coding [ l ] or by increasing the data rate when implementing spatial multiplexing schemes [2], [3], [4]. A major impediment in deploying multiple antennas is the cost of the hardware associated with each antenna (radio frequency power amplifiers, ADDA converters, etc). Antenna subset selection where transmissiodreception is performed through a selection of the total available antennas is a powerful solution that reduces the need for multiple radio frequency (RF) chains yet retains many diversity benefits. Early work on antenna selection focuses on single-input multi-output (SIMO) and multi-input single-output (MISO) systems [ 5 ] . A well-known result in SIMO systems is that the diversity order achievable with selection xs the same as that achievable with maximum ratio combining (MRC). Recently, there has been increasing interest in applying antenna subset selection techniques to MIMO links (see e.g. [6], [7], [8] and references therein). In [9], the authors demonstrated the effect of antenna subset selection for the error rate performance of a MIMO system. A comprehensive information-theoretic study of the receive antenna subset selection for MIMO systems may be found in [lo], [ l l ] . In this contribution, we study the effect of receive antenna selection for the performance of the overall MIMO WLAN communication system at the link (PHY) level. A MIMO orthogonal frequency division multiplexing (OFDM)
0-7803-8523-3/04/$20.00 02004 IEEE,.
transceiver architecture is analysed. Our goal is to demonstrate that the theoretical conclusions found in [9], [ lo], [ 111 apply for practical MIMO architectures being considered for the new high throughput WLAN standard (IEEE 802.1 In). In Section 11, we present the transceiver architecture. The system under study is based on the 802.1 lalg standard combined with spatial multiplexing. The basics and implementation of MIMO receive antenna selection are explained in Section 111. In Section IV, we present the simulation results with and without antenna selection for different channel root mean squared (RMS) delay spread values. Finally, a comparison between MMSE and ZF receivers is also presented. 11. TRANSCEIVER ARCHITECTURE
The discussed MIMO-OFDM transmitter and receiver are shown in Fig. 1 and Fig. 2 respectively. Such a transceiver performs spatial multiplexing over MT transmit antennas in order to increase the data rate by a factor of MT compared to the standard 802.1 lalg. At the receiver, the original data stream is reconstructed from MR received signals. When antenna subset selection is used, these MR signals are selected out of K R receive antennas (not shown in the picture). Thus, there are MRantenna sets to choose from. More details on antenna selection may be found in Section 111. At the transmitter, data bits are encoded using the standard (1338,17 18) convolutional encoder. The coding rate can be adjusted to 112, 213, or 314 via puncturing. After that, the coded bits are distributed in a round Robin fashion between the MT transmit streams, and the standard frequency interleaving scheme is applied to every stream. In Fig. 1, these two operations are carried out by the space-frequency interleaver. Next, the sequences of interleaved bits are mapped into MT sequences of symbols following the standard quadrature amplitude modulation schemes. Finally, these MT sequences undergo multicamer modulation as per 802.11alg, prior to transmission via MT transmit antennas. At the receiver, the captured signals are filtered and sampled in order to obtain M R symbol-rate discrete-time signals. These signals are fed subsequently to M R FFT blocks. The samples obtained after the FFT are noisy mixtures of the symbols transmitted at the corresponding subcarriers. Denote x(u) = [xi (U), . . . , X M (U)]' ~ a M R x 1 vector sampled at the outputs of the FFT blocks that corresponds to the subcarrier U. One can check that
(2)
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FEC encoder
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c
C
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Fig. 2.MIMO-OFDM receiver: block diagram.
x(uk) = & H ( u ~ ) s ( u ~ )
+ n(uk),
1 Fk I N,
(1)
where s ( u ) = [sI(u), . . . , S M ~ ( U ) ]is~ the vector of data symbols transmitted by the MT antennas at the subcarrier U, n(u) = [nl(u), . . . , n ~ , ( u ) ]is~the corresponding observation noise, H(u) is the MR x MT channel matrix corresponding at the subcamer U , E$ is the signal energy per channel use and { U ] , . . . , U N } is the set of data subcaniers, which is set to N = 48 as per 802.1la/g. We assume complex circular additive white Gaussian noise (AWGN) with variance (No/2) per real dimension. The frequency selective MIMO channel {H(v)} is estimated at the receiver due to a preamble. More details on preamble-based channel estimation and related works may be found in [ 121. In this paper, we will assume perfect channel state information at the receiver. Then, the estimated data symbols ;(U) = [;I (U), . . . , ; M ~ ( U ) ]can ~ be extracted by applying a linear filter at every subcarrier: ;(U)
= F(u)x(u).
(2)
In the following numerical study, we will consider the MMSE and ZF receivers given by
111. RECEIVE ANTENNA SELECTION As already mentioned, antenna subset selection offers a low cost opportunity to increase reliability of a MIMO link in fading environments. As shown in [Ill, adaptive antenna selection is particularly important for spatial multiplexing transceivers with linear (MMSE or ZF) demultiplexing of signals at the receiver. Indeed, linear interference cancellation makes use of the spatial degrees of freedom thereby reducing the effective amount of receive diversity seen at the output of the filter. Adaptive antenna selection compensates for this loss. The selection criterion proposed in [8] maximises the Shannon capacity of a MR x MT flat fading MIMO channel which results from selecting MR out of K R antennas at the receiver. As shown in [lo], the diversity order achieved with this approach equals to the diversity order that can be achieved with a K R x MT MIMO channel. Furthermore, a suboptimal extension of this approach for the frequency selective environments has been developed in [SI. In the present paper, we recall the antenna selection algorithm. Denote I = { Z1, . . . , I M } ~a collection of distinct indexes corresponding to a possible set of MR receive antennas: Zp # Iq andIp E 11,..., K R } , 1 I p # q 5 M R . Let yr(k) = [yr, (k), . . . ,yrM R (k)lT be a M R x 1 sample of signals sampled at the output of the selected antennas in the time domain. A (scaled) covariance matrix of the signals captured with the set I can be estimated: T
RI =
CYr(k)Yr(k)H,
(5)
k= 1
respectively. The extracted data symbols are subsequently fed to a soft-decision demapper with bitwise maximum likelihood metric computation based on the channel state information. The subsequent deinterleaving and soft-input Viterbi decoding provide decisions on the user bits.
where the number of samples T should be at least as big as the expected rank of the true covariance matrix RI = E { yIyF). In practice, T 1 2MR keeps performance losses negligible. It is worthwhile repeating that the entries of yI (k) for all possisets I may be acquired by sounding all K R antennas ble
(2)
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by the available MR receive chains. Finally, the set antennas to be used is identified according to
i of MR
i = argmaxdet( RI ), I
(6)
(2)
wherein the maximisation is over all possible sets I . Note that the complexity of (6) scales exponentially with K R and/or MR. A reduced complexity suboptimal selection rule is described in [SI. To highlight the relationship between the selection rule (6) and the maximum capacity criterion, we recall that Shannon capacity C(H1) of a flat fading channel HI associated with the set I is given by
(
+ (&/No) HI HF )
C(HI) = log2 det I l ~ i ,
whereas the associated covariance matrix R I is given by
R~ =
H~ H;
+ N~ I
~
~
.
More results on the theoretical background of such a selection rule, as well as various implementation aspects and performance analysis may be found in [8], [lo], [ l 11. In this paper, we focus on the system performance study with the proposed selection rule in the context of high throughput WLAN. STUDY I v . NUMERICAL
Link-level simulations are carried out to address the performance of MIMO-OFDM multiplexing systems. We look into the packet error rate for different signal to noise ratios (SNR) and transmission data rates. In all simulations, the packet size is set to about 1000 bytes. The SNR measure that we use does not take into account power losses due to pilot insertion or guard interval insertion, which are intrinsic losses of OFDM. For every transmitTable 1 Data rates and the associated transmission parameters. Rate (Mbps)
108
1 Modulation I Coding rate 16QAM 64QAM 64QAM
213
314
Bytes per packet
-
1002 1008 1008 1008 1026
receive antenna pair an independent ideritically distributed (i.i.d.) channel realization is drawn. Every channel realization is in fact a discrete-time sequence consisting of a number of independently distributed taps. The channel responses follow an exponential powerldelay profile defined by the RMS delay spread. The study has been carried out for three RMS delay spread values: Ons (flat fading), 30ns, and 5011s. None of these delay spread values causes inter-carrier interference
(ICI) due to the cyclic extension of 0 . 8 ~ defined s in the standard. For every packet, a new set of independent channel realizations is used. The examined transmission rates are 12, 24, 48, 96, and 108Mbps. These rates are achieved by making use of the modulation schemes and coding rates of 802.11alg with MT = 2 transmit antennas. Table 1 summarises the coding rates and modulation schemes used for each transmission rate. In Fig. 3, we plot PER versus SNR for a spatial multiplexing transceiver with MT = 2 transmit, MR = 2 receive antennas and h4MSE filtering. In this first case, the RMS delay spread was set to Ons. The performance of the same transceiver with receive antenna subset selection is shown in Fig. 4. Here, a subset of MR = 2 out of K R = 4 receive antennas is adaptively chosen at the receiver as explained in Section 111. Since no preamble is simulated, we substitute the empirical covariance matrices RI by the true values RI. As it follows from Fig. 3 and Fig. 4, receive antenna subset selection yields a gain of about 1 4 S B at PER of lop2 for the 108Mbps transmission mode. For the same PER, antenna selection yields 8dB gain for the l2Mbps mode. The slope of the curves in Fig. 4 is three times steeper than the slope of the curves in Fig. 3. This confirms the equivalence in diversity order between the full system (using all four receive signals) and the system with antenna selection, as anticipated in [131, 1101. In Fig. 5 and Fig. 6 the performance of the two systems is displayed again, but now with 30ns RMS delay spread channels. From Fig. 5 and Fig. 6, it follows that receive antenna selection yields a gain of about 5dB at a PER of for the 108Mbps transmission mode and 3dB gain for the 12Mbps mode. The overall gain obtained through antenna selection has been reduced because the system already presents some sort of diversity, namely frequency diversity. It can be observed that the system without antenna selection substantially benefits as the RMS delay spread changes from Ons to 30ns (more than 5dB gain at PER Conversely, the performance of the system using antenna selection deteriorates when going from Ons to 30ns RMS delay spread because of the effect of frequency selectivity on the FEC performance. In this case, the change in slope due to frequency diversity is not visible in the SNR region of interest (from 20dB to 30dE3). Finally, Fig. 7 and Fig. 8 show results for 50ns RMS delay spread channels. The gain at PER equal to lo-* is 2.5dB for the 108Mbps transmission mode, and to 2dB for the 12Mbps mode. The main observations on the performance gain due to antenna selection are summarised in Table 2. In all the results shown till now, MMSE filters were used to recover the transmitted symbols. The MMSE filter minimises the signal to noise and interference ratio at its output. For poor input signal to noise ratios, the MMSE behaves like a matched filter, and for high signal to noise ratios it behaves like a channel inverse or ZF filter. In principle, the calculation of the MMSE filter coefficients requires more operations than the calculation of the ZF filter coefficients. Therefore, it is
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Table 2 Gain of receive selection: MR = MT = 2, PER =
I Rate (Mbps) I RMS delay spread I Gain ( K R = 4 vs K R = 2) I x 8.0dB
108
Ons 30ns 50ns
e 3.0dB x 2.0dB M 14.SdB z 5.0dB M 2.5dB
interesting to compare the two filtering techniques and see to what extend MMSE is desirable. In Fig. 9 we show the results of a spatial multiplexing system using ZF. The RMS delay spread of the channel is Ons. Comparing Fig. 9 to Fig. 3 for the highest rates, 48, 96, or 108Mbps, we see no significant difference between the two detection strategies. This is to be expected since MMSE is equivalent to ZF in the high SNR region. However, for the 24Mbps transmission mode, a loss of 3.75 dB at a PER of when using ZF is observed. For the 12Mbps transmission mode the loss increases to 8.SdB.
CONCLUSIONS In this paper, we demonstrated the effect of adaptive receive antenna selection for the performance of MIMO-OFDM systems. Specifically, we applied the antenna selection algorithm described in [8] and further analysed in [13], [lo], [ l l ] to study the error rate performance of a typical MIMO-OFDM architecture being considered for high throughput WLANs. For the standard i.i.d. Rayleigh flat and frequency selective fading MIMO channels, we have shown that a simple antenna selection algorithm may achieve more than 14dB gain in a system with two transmidreceive branches when the total number of receive antennas equals four. The maximum gain is achieved in flat fading environments where the spatial dimension is the only source of diversity. The gain is smaller in the case of frequency selective channels (with RMS delay spread of 30ns and higher) where the lack of spatial diversity is partly compensated by the channel diversity in the frequency domain. The presented results suggest a substantial improvement in the performance of MIMO WLAN systems at high data rates in a typical indoor environment where the RMS delay spread is mostly less than 10ns. Additionally, we presented a comparison of the ZF receiver versus the MMSE receiver. This comparison was motivated by the practical consideration of a complexity advantage of the ZF over the MMSE solution, especially for small number of transmitheceive branches. The ZF receiver yields up to 8.5dB loss at low and moderate SNR levels. Hence MMSE is expected to outperform ZF at low rates and medium to high rates if adaptive modulation per transmit antenna is used.
REFERENCES V. Tarokh, N. Seshadri, R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Tu. on info. Theoiy, vol. 44, pp. 744-765, May 1999. A. Paulraj and T. Kailath, “Increasing capacity in wireless broadcast systems using distributed transmissioddirectional reception.” U.S. Patent, 1994. E. Telatar, “Capacity of multiantenna Gaussian channels,” tech. rep., AT&T-Bell Lab. Internal Tech. Memo., June 1995. G. Foschini, “Layered space-time architecture for wireless communication in fading environment when using multielement antennas,” Bell Labs Tech. J., vol. 1 , no. 2, pp. 41-59, 1996. M. Win and J. Winters, “Virtual branch analysis of symbol error probability for hybrid selectiodmaximal-ratiocombining in Rayleigh fading,” IEEE Tr on Comm., vol. 49, pp. 1926 1934, Nov. 2001. D. Gore, R. Nabar and A. Paulraj, “Selectig an optimal set of transmit antennas for a low rank matrix channel,” in Proc. ICASSP, May 2000. A. Molisch and M. Win and J. Winters, “Capacity of MIMO systemswith antenna selection,”in Proc. Int. Con$ Communications, vol. 2, (Helsinki, Finland), pp. 570-574, June 2001. A. Gorokhov, “Antenna selection algorithms for MEA transmission systems,” in Proc. ICASSP, (Orlando, FL), pp. 1926 1934, May 2002. A. Ghrayeb and T. Duman, “Performance analysis of MIMO systems with antenna selection over quasi-static fading channels,” in Proc. Int. Symp. Information Theoly, (Lausanne, Switzerland),U. 333, June 2002. [ 101 A. Gorokhov, D. Gore and A. Paulraj, “Receive antenna selection for MIMO flat fading channels: theory and algorithms,” IEEE Tr on Info. Theory, Oct. 2003. [I I ] A. Gorokhov, D. Gore and A. Paulraj, “Receive antenna selection for MIMO spatial multiplexing: theory and algorithms,” IEEE Tr. on Sig. Proc., Nov. 2003. [ 121 I. Barhumi, G. Leus and M. Moonen, “Optimal training design for MIMO OFDM systems in mobile wireless channels,”iEEE Tu. on Sig. Proc., vol. 51, pp. 1615-1624, June 2003. [I31 A. Gorokhov, D. Gore and A. Paulraj, “Performance bounds for antenna selection in MIMO systems,” in Proc. Int. Con$ Communications, (Anchorage, AL), May 2003.
0
5
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Fig. 3. PER versus SNR for different data rates. RMS delay spread Ons, MR = MT = 2, K R = 2 (no selection).
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Fig. 4. PER versus S N R for different data rates. RMS delay spread Ons, M R = MT = 2, K R = 4 (selection).
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Signal to nwse mho SNR ids)
Fig. 7. PER versus SNR for different data rates. RMS delay spread 50ns, M R = MT = 2, K R = 2 (no selection).
Rate Modes 12 24 48 $6 108 Mbps in 2u MMSE RNS = 30"s
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Fig. 5. PER versus SNR for different data rates. RMS delay spread 30ns, M R = MT = 2, K R = 2 (no selection).
Fig. 8. PER versus SNR for different data rates. RMS delay spread Sons, MR = MT = 2, K R = 4 (selection). Rate Modes 12.24,48.86. 108 Mbps, (n 2x2 ZF Flat lading channel
Rale Modes 12
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. . . . 10
15 20 25 Signal 10 MBLIratlo. SNR (dB)
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Fig. 6. PER versus SNR for different data rates. RMS delay spread 30ns, MR = MT = 2, K R = 4 (selection).
Fig. 9. PER versus SNR for different data rates and ZF receiver. RMS delay spread Ons, MR = MT = 2, K R = 2 (no selection).
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