Performance analysis of Spatial Modulation MIMO in a poisson field of interferers

In this paper, we introduce a mathematical framework for computing the Average Symbol Error Probability (ASEP) of Spatial Modulation (SM) Multiple-Input-Multiple-Output (MIMO) wireless systems in the presence of multiple-access interference, Rayleigh fading, and additive noise. The interferers are assumed to be randomly distributed in the bi-dimensional plane according to a homogenous Poisson Point Process (PPP). By leveraging recent application of stochastic geometry to the analysis of random wireless networks, we provide a closed-form mathematical expression of the ASEP averaged over both the channel fading and the spatial locations of the interferers, which accounts for an arbitrary number of antennas at the transmitter (N_t) and at the receiver (N_r), as well as for an arbitrary modulation order (M) and amplitude path-loss exponent (b > 1). The proposed mathematical framework unveils the following performance trends: i) by relying on the Nearest Neighbor (NN) approximation, we show that the ASEP is (almost) independent of N_t if M > 4; ii) the diversity order is independent of N_r, but the coding gain increases with N_r; and iii) if the transmit-power of the interferers is independent of the transmit-power of the useful user, the diversity order is equal to 1/b. On the other hand, if the transmit-power of the interferers scales linearly with the transmit-power of the useful user, an error-floor emerges. The mathematical framework is substantiated through extensive Monte Carlo simulations and design guidelines from the performance trends are discussed.