Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading

TL;DR

This paper provides an exact analysis of zero-forcing detection in rank-1 LoS Rician MIMO channels, using computer algebra and differential equations to improve evaluation accuracy and efficiency over traditional series methods.

Contribution

It introduces a novel automated approach employing computer algebra to derive differential equations for performance measures, enhancing evaluation reliability and speed in Rician fading MIMO systems.

Findings

HGM outperforms infinite series in accuracy and speed

Differential equations enable reliable performance evaluation

Method applicable to large MIMO systems with high Rician K-factors

Abstract

We study zero-forcing detection (ZF) for multiple-input/multiple-output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix transformations and multivariate statistics, our exact analysis yields the signal-to-noise ratio moment generating function (m.g.f.) as an infinite series of gamma distribution m.g.f.'s and analogous series for ZF performance measures, e.g., outage probability and ergodic capacity. However, their numerical convergence is inherently problematic with increasing Rician K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we derive differential equations satisfied by the performance measures with a novel automated approach employing a computer-algebra tool which implements Groebner basis computation and creative telescoping. These differential equations are then solved with the holonomic gradient method (HGM) from initial conditions computed with the infinite series. We demonstrate that HGM yields more reliable performance evaluation than by infinite series alone and more expeditious than by simulation, for realistic values of K , and even for N_R and N_T relevant to large MIMO systems. We envision extending the proposed approaches for exact analysis and reliable evaluation to more general Rician fading and other transceiver methods.