Space Shift Keying (SSK) Transmission Over Rayleigh Fading Channels and Symmetric Alpha-Stable Noise

This paper presents a comprehensive analytical study of the average bit error probability (ABEP) performance of multiple-input multiple output (MIMO) communication systems employing Space Shift Keying (SSK) modulation operating over a mixture of Rayleigh fading and impulsive noise channels modelled by the symmetric alpha-stable distribution. By considering three key receiver structures, namely the genie-aided (GA), minimum distance (MD) and maximum likelihood (ML) type of receivers various analytical ABEP performance evaluation results are presented. Firstly, a novel analytical approach for evaluating the ABEP of SSK-MIMO systems, for the ideal benchmark GA receiver which has a-priori knowledge of both channel and noise coefficients, is introduced. The proposed methodology yields exact expressions for the ABEP performance of multiple-input single output (MISO) systems with two transmit antennas. For the general case of MIMO systems which employ an arbitrary number of transmit and/or receive antennas, accurate approximations and tight upper performance bounds are derived and their ABEP performance is analyzed. An asymptotic ABEP analysis is also carried out from which the diversity and the coding gains are derived. Secondly, a general class of minimum distance (MD) receivers, namely the
$L_{p}$
-norm receivers, is considered. An approximate analytical expression for the ABEP of the special case of
$L_{p}$
-norm (matched filter) receivers, whose performance is optimal for the additive white Gaussian noise channel (AWGN), is derived. For the general case of
$L_{p}$
-norm receivers, their ABEP performance is evaluated by means of Monte Carlo simulations, revealing that they significantly outperform the
$L_{2}$
-norm receivers. Thirdly, by considering the maximum-likelihood (ML) receiver, since its implementation complexity turns out to be prohibitively high, simple, suboptimal receiver configurations structures of the ML receiver are instead proposed. Analytical evaluation results verified by complementary computer simulations have shown that their ABEP performance is asymptotically, i.e., at high signal-to-noise ratios (SNR), optimal. For the GA, suboptimal ML and
$L_{p}$
-norm receiver structures, the impact of spatial correlation on their ABEP performance has also been analyzed and evaluated. The accuracy of the analytical approaches used in deriving the proposed receivers has been validated by equivalent numerical ABEP performance evaluation results accompanied by complementary Monte Carlo simulations.