New upper bound for high-rate spatial modulation systems using QAM modulation

In this paper, we present a new upper bound for the bit error probability (BEP) of the so-called High-Rate Spatial Modulation (HR-SM) system using QAM modulation introduced by Thu Phuong Nguyen et al. in [1], over a quasi-static Rayleigh fading channel. Our approach based on the Verdu's theorem [2], the concept of the spatial constellation (SC) codewords and maximum likelihood (ML) decoder in [1] results in the new upper bound which is tighter than the union bound due to eliminating a number of redundant pairwise error probabilities (PEPs). Therefore, by using the new upper bound rather than the union bound, we can evaluate the bit-error performance of HR-SM systems more exactly, especially when the signal-to-noise power ratio (SNR) is sufficiently high.