Cramer-Rao Bound Approach and Error Performance for Spatial Modulation over Beckmann Fading Channels

Spatial modulation (SM) is a promising low-complexity alternative to the state-of-art multiple-input multiple-output (MIMO) schemes due to its unique transmission approach. In this work, the impact of channel imperfections on the performance of SM-MIMO systems are investigated over generalized Beckmann fading channels, which introduce a versatile multipath fading model that includes several distributions such as Ricean, Nakagami-m and Beaulieu-Xie, as special cases. Specifically, an optimum maximum likelihood detection (MLD) method is proposed and the average pairwise error probability (APEP) is calculated by analytical derivations. Cramer-Rao bound approach is utilized for further improvement on decreasing the deteriorating effects that rise from estimation errors. The obtained results, confirmed by computer simulations, provide a comprehensive perspective to the performance of the SM-MIMO wireless communication systems.

I. Introduction

The radio signal in wireless environments is built from the superposition of many individual waves, each with a certain amplitude and phase due to the presence of multiple scatterers. Assuming a large number of paths, the received signal, Z, can be modelled as a complex Gaussian random variable (RV) in compliance with the Central Limit Theorem [1]. This model was discussed in a general form, which is called Beckmann fading channel model, by assuming arbitrary mean and variance values for the independent real and imaginary parts of Z in [2]. Unlike other envelope fading models, Beckmann fading considers the effect of imbalances in line-of-sight (LOS) and non-LOS (NLOS) components simultaneously. It hence effectively captures the correlation between the amplitudes and phases of each ray component [3].