Exact MIMO Zero-Forcing Detection Analysis for Transmit-Correlated Rician Fading

Abstract

We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF). The distribution of the ZF signal-to-noise ratio (SNR) is characterized when either the intended stream or interfering streams experience Rician fading, and when the fading may be correlated on the transmit side. Previously, exact ZF analysis based on a wellknown SNR expression has been hindered by the noncentrality of the Wishart distribution involved. In addition, approximation with a central-Wishart distribution has not proved consistently accurate. In contrast, the following exact ZF study proceeds from a lesser-known SNR expression that separates the intended and interfering channel-gain vectors. By first conditioning on, and then averaging over the interference, the ZF SNR distribution for Rician-Rayleigh fading is shown to be an infinite linear combination of gamma distributions. On the other hand, for Rayleigh-Rician fading, the ZF SNR is shown to be gammadistributed. Based on the SNR distribution, we derive new series expressions for the ZF average error probability, outage probability, and ergodic capacity. Numerical results confirm the accuracy of our new expressions, and reveal effects of interference and channel statistics on performance.

Schur Complement Based Analysis of MIMO Zero-Forcing for Rician Fading

“…H 2 in the NCWD Gramian matrix W. Note that the SC arises "naturally" in statistical analyses as the (sample) correlation matrix of the conditioned Gaussian distribution [19, p. 186], as also exemplified in [12] and this paper.…”

“…Because [9] found the ZF SNR distribution approximation not consistently reliable and because analytical conditions for its accuracy were unknown, we pursued in [12] an exact ZF-SNR analysis. That analysis was found tractable only for the case when the intended Stream 1 undergoes Rician fading whereas interfering Streams 2, · · · , N T undergo Rayleigh fading, i.e., Rician(1)/Rayleigh(N T − 1) fading, for which, incidentally, r = 1.…”

“…That analysis was found tractable only for the case when the intended Stream 1 undergoes Rician fading whereas interfering Streams 2, · · · , N T undergo Rayleigh fading, i.e., Rician(1)/Rayleigh(N T − 1) fading, for which, incidentally, r = 1. Proceeding in [12] from the vector-matrix partitioning according to fading types H = (h 1 H 2 ), we could write the Stream-1 ZF SNR in terms of the scalar Schur complement (SC) [19] [20] [13, Sec. 3.4] of submatrix…”

“…In [12], we recast the scalar SC as a Hermitian form whereby the vector and matrix correspond, respectively, to the intended and interfering streams [12,Eq. (9)] [8, Eq.…”

“…(7)]. By first conditioning on and then averaging over H 2 , we expressed exactly, in [12,Eq. (31)], the moment generating function (m.g.f.)…”