Unifying analysis of ergodic MIMO capacity in correlated Rayleigh fading environments

Abstract

SUMMARYWe present a novel mathematical approach that for the first time allows for calculating the moment generating function (MGF) of mutual information of Rayleigh fading MIMO channels with arbitrary fading correlation at transmitter and receiver. Specifically, we make use of certain hypergeometric functions of matrix argument, which are frequently used in multivariate statistics. This allows for a concise general expression for the MGF and we specialise the general result to scenarios with one-side correlated and uncorrelated channels. Using the MGF, we derive exact formulas of the ergodic capacity, thus unifying the capacity analysis of correlated Rayleigh fading MIMO channels. It turns out that the ergodic capacity in all cases can be expressed in terms of a sum of determinants with elements that are a combination of polynomials, exponentials and the exponential integral E 1 solely. The analysis is verified by Monte-Carlo simulations and shows a perfect match.

On the capacity of doubly correlated MIMO channels

“…It should be noted that alternative derivation of the moment generating function (MGF) of the capacity for doubly correlated MIMO channels can also be found in [19]. In this study, the MGF was obtained indirectly from the case of a square channel matrix (n T = n R ) using the limiting approach of [20] and then, the first moment (ergodic capacity) was deduced from it in terms of a sum of min {n T , n R } determinants.…”

Analysis of MIMO Systems in the Presence of Co-channel Interference and Spatial Correlation

“…The mentioned-above correlated MIMO channel model is one of several classical correlated MIMO channel models [Kermoal et al (2002)]. It is very convenient for mathematical tractability, and has been used by many papers [Kiessling (2005)], [Paulraj et al (2003)]. With it, the MIMO channel correlation is separable [Kermoal et al (2002)], [Paulraj et al (2003)], i.e.,…”

“…In downlink transmission, this particularly true for small and lightweight hand-held/portable receive terminals for which the size of practical adaptive array will typically be restricted to one or two antenna elements. A general hypergeometric function of one Hermitian matrix argument can be expressed in terms of scalar hypergeometric functions [Kiessling (2005)], which is of the practical relevance of Theorem 1.…”

“…Both of the capacity analysis and performance analysis strongly rely on random matrix theory and matrix variate distributions. So far the capacity issues of MIMO systems have been extensively studied in the literature, yet with main focus on the scenario without interference [Teletar (1999)]- [Kiessling (2005)]. In cellular systems, however, multiple users share the same radio spectrum, which typically causes co-channel interference.…”

Dimensioning cellular networks with fixed relay stations

“…Exact expressions for the general correlated MIMO ergodic capacity are given in [7]. With the transmission strategy proposed, the achievable rate for user i is…”