Space Shift Keying (SSK-) MIMO with Practical Channel Estimates

TL;DR

This paper analyzes the performance of SSK and TOSD-SSK MIMO modulations under imperfect channel knowledge, providing a general analytical framework and demonstrating their robustness through simulations.

Contribution

It introduces a comprehensive analytical model for SSK and TOSD-SSK performance with imperfect channel estimates, applicable to various system configurations.

Findings

SSK modulation is as robust as single-antenna systems under imperfect channel knowledge.

TOSD-SSK offers greater robustness to channel estimation errors than Alamouti scheme.

Few training pilots suffice for reliable channel estimation in SSK systems.

Abstract

In this paper, we study the performance of space modulation for Multiple-Input-Multiple-Output (MIMO) wireless systems with imperfect channel knowledge at the receiver. We focus our attention on two transmission technologies, which are the building blocks of space modulation: i) Space Shift Keying (SSK) modulation; and ii) Time-Orthogonal-Signal-Design (TOSD-) SSK modulation, which is an improved version of SSK modulation providing transmit-diversity. We develop a single-integral closed-form analytical framework to compute the Average Bit Error Probability (ABEP) of a mismatched detector for both SSK and TOSD-SSK modulations. The framework exploits the theory of quadratic-forms in conditional complex Gaussian Random Variables (RVs) along with the Gil-Pelaez inversion theorem. The analytical model is very general and can be used for arbitrary transmit- and receive-antennas, fading distributions, fading spatial correlations, and training pilots. The analytical derivation is substantiated through Monte Carlo simulations, and it is shown, over independent and identically distributed (i.i.d.) Rayleigh fading channels, that SSK modulation is as robust as single-antenna systems to imperfect channel knowledge, and that TOSD-SSK modulation is more robust to channel estimation errors than the Alamouti scheme. Furthermore, it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection, and that transmit- and receive-diversity of SSK and TOSD-SSK modulations are preserved even with imperfect channel knowledge.