A unifying analysis of error exponents for MIMO channels with application to multiple-scattering

Abstract

Expressions for Gallager's Random Coding Error Exponent (RCEE) and the corresponding Expurgated Error Exponent (EEE) are derived in a unifying framework, as functions only of the squared singular values of the channel matrix. The results encompass spatially Kronecker-correlated Rayleigh channels (whose error exponents expressions are already present in the literature), line of sight MIMO systems, multiple-scattering channels, multi-hop amplify and forward MIMO channels with non-noisy relays and noisy destination. As an instance of application of our framework, we consider a multiple-scattering Rayleigh MIMO channels, with an arbitrary but finite number of scattering stages and channel state information (CSI) available at the receiver only. In this scenario, we evaluate closed-form expressions for both RCEE and EEE in terms of Meijer's G functions.