Statistical Analysis of Multi-Antenna Relay Systems and Power Allocation Algorithms in a Relay with Partial Channel State Information

TL;DR

This paper analyzes the performance of dual-hop MIMO relay networks with partial channel information, deriving SNR distributions and proposing a simple, effective power allocation algorithm that performs close to optimal.

Contribution

It introduces a new proportional power allocation algorithm for multi-antenna relay systems with partial CSI, applicable to arbitrary antenna numbers.

Findings

Closed-form asymptotic SNR cdfs for correlated and uncorrelated cases

Proposed power allocation algorithm matches exhaustive search performance

Algorithm is simple, practical, and effective for various antenna configurations

Abstract

The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied and closed-form expressions are derived for the asymptotic cases of the fully-correlated and non-correlated scenarios; moreover, the statistical characteristics of the SNR are further studied and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm which we call "proportional power allocation". The algorithm is explained in detail for the case of two antennas and three antennas at the relay and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.