Bit Error Probability of Space Modulation over Nakagami-m Fading: Asymptotic Analysis

Recently, the Average Bit Error Probability (ABEP) of Space Shift Keying (SSK) and Spatial Modulation (SM) over Nakagami-m fading has been computed as a single integral involving the Meijer-G function. Even though the frameworks are very accurate, the use of special functions hides some fundamental properties of the aforementioned new modulation schemes, e.g., coding and diversity gains. In this Letter, we exploit a notable limit involving the Meijer-G function near the singular point -1, and provide a simple, closed-form, and asymptotically tight upper-bound of the ABEP. The result is applicable to SM and SSK modulation, to correlated Nakagami-m fading, and to general Multiple-Input Multiple-Output (MIMO) wireless systems. As a case study, numerical examples showing the accuracy for SSK modulation are given, and it is proved that, unlike conventional modulations, the diversity gain is independent of the fading severity m.