Bit Error Probability of SM-MIMO Over Generalized Fading Channels

Abstract

In this paper, we study the performance of spatial modulation (SM) multiple-input–multiple-output (MIMO) wireless systems over generic fading channels. More precisely, a comprehensive analytical framework to compute the average bit error probability (ABEP) is introduced, which can be used for any MIMO setup, for arbitrary correlated fading channels, and for generic modulation schemes. It is shown that, when compared with state-of-the-art literature, our framework 1) has more general applicability over generalized fading channels, 2) is, in general, more accurate as it exploits an improved union-bound method, and, 3) more importantly, clearly highlights interesting fundamental trends about the performance of SM, which are difficult to capture with available frameworks. For example, by focusing on the canonical reference scenario with independent identically distributed Rayleigh fading, we introduce very simple formulas that yield insightful design information on the optimal modulation scheme to be used for the signal constellation diagram, as well as highlight the different roles played by the bit mapping on the signal and spatial constellation diagrams. Numerical results show that, for many MIMO setups, SM with phase-shift-keying (PSK) modulation outperforms SM with quadrature-amplitude modulation (QAM), which is a result never reported in the literature. In addition, by exploiting asymptotic analysis, closed-form formulas of the performance gain of SM over other single-antenna transmission technologies are provided. Numerical results show that SM can outperform many single-antenna systems and that, for any transmission rate, there is an optimal allocation of the information bits onto spatial and signal constellation diagrams. Furthermore, by focusing on the Nakagami- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> fading scenario with generically correlated fading, we show that fading severity plays a very important role in determining the diversity gain of SM. In particular, the performance gain over single-antenna systems increases for fading channels less severe than Rayleigh fading, whereas it gets smaller for more severe fading channels. In addition, it is shown that the impact of fading correlation at the transmitter is reduced for less severe fading. Finally, analytical frameworks and claims are substantiated through extensive Monte Carlo simulations.