Efficient BER Expressions for MIMO-BICM in Spatially-Correlated Rayleigh Channels Matthew R. McKay Telecommunications Laboratory, School of Electrical and Information Engineering, University of Sydney, Australia and also ICT Centre, CSIRO, Australia mckay@ee.usyd.edu.au Iain B. Collings Wireless Technologies Laboratory, ICT Centre, CSIRO, Australia Iain.Collings@csiro.au Abstract—We derive tight expressions for the coded bit error rate of MIMO bit-interleaved coded modulation (BICM) with zero-forcing receivers in spatially-correlated Rayleigh channels. The analysis is simpler and more direct than the standard BICM error event expurgation technique, and yields efficient, accurate expressions for the error probability. Based on the analytical results, we obtain the diversity order and show that it is unaffected by the presence of spatial correlation. We then show that spatial correlation induces an SNR loss with respect to i.i.d. channels, which is quantified, and found to depend explicitly on the eigenvalues of the spatial correlation matrices and the antenna configuration, but not on the coding and modulation parameters. I. I NTRODUCTION Bit-interleaved coded modulation (BICM) is a pragmatic technique which can achieve large diversity orders in fading wireless channels [1]. Recently, BICM was employed in a multiple-input multiple-output (MIMO) antenna system with maximum likelihood (ML) detection [2], and was shown to perform well in fast fading conditions. Unfortunately, the computational complexity of the ML receiver increases expo- nentially with the product of the number of transmit antennas and the number of bits per modulation symbol, thereby making it prohibitive in practice. A reduced complexity scheme was proposed in [3], and analyzed in [4], which employed a linear zero-forcing (ZF) receiver. It was shown in [4] that this receiver has desirable signal-space properties in i.i.d. Rayleigh fading MIMO-BICM systems, which allow near- ML performance to be achieved in many scenarios. The challenge is to investigate the performance of this practical low-complexity receiver in the more common case of spatially- correlated channels. In this paper, we derive tight analytical expressions for the coded bit error rate (BER) of MIMO-BICM with ZF receivers (hereafter denoted ZF-BICM) in spatially-correlated channels. The results are based on the typical BICM assumption of ideal interleaving. Our analysis is simpler and more direct than the standard BICM expurgation technique (eg. as used in [1], [4]), and yields accurate, efficient BER expressions for channels with both transmit and receive spatial correlation. Based on the analytical results, we obtain the diversity order and show that it is independent of the spatial correlation. Moreover, we show that the presence of spatial correlation induces an SNR loss with respect to i.i.d. channels. We quantify this loss, data a Demux Enc Enc Map Int Map r ˆ data Dec Mux Int -1 Dem Dec Dem ZF 1: Structure of a MIMO-BICM ZF system with 2 × 2 antennas. and show that it is a function of the antenna configuration and the eigenvalues of the spatial correlation matrices, and is independent of the coding and modulation parameters. II. SIGNAL MODEL Consider a MIMO-BICM system with N t transmit and N r receive antennas (denoted N t × N r ). Fig. 1 shows the trans- mitter structure with separate modulators/encoders applied on each of the transmit layers. The data sequence is cyclically demultiplexed across the layers and each resulting stream is binary convolutionally encoded. Bit interleaving is applied within and across the layers, prior to mapping to Gray-labelled 2 M -ary QAM or PSK for transmission. The received signal vector is given by r = √ γ Ha + n (1) where a ∈ C Nt×1 is the transmitted vector with i th el- ement a i chosen from the complex scalar constellation A with unit average power, n ∈C Nr ×1 is the noise vector ∼ CN (0 Nr ×1 , I Nr ), and γ is the average SNR per transmit antenna. Also, H ∈C Nr ×Nt is the spatially-correlated channel matrix, assumed to be known perfectly at the receiver, having the (common) correlation structure H = R 1 2 H w S 1 2 (2) where R ∈C Nr ×Nr and S ∈C Nt×Nt are the normalized receive and transmit correlation matrices respectively, and H w ∈C Nr ×Nt contains independent entries H i,j ∼ CN (0, 1). As such, the average SNR per receive antenna is N t γ . At the receiver, the ZF filtering step is z = Wr = √ γ a + n (3) where W = ( H † H ) −1 H † and n = Wn. The BICM log-likelihood metrics for each of the bits i (= 1,...,M ) 1-4244-0214-X/06/$20.00 c 2006 IEEE 1 7th Australian Communications Theory Workshop