Analysis of cooperative communication spatial modulation with imperfect channel estimation

In this paper, spatial modulation (SM) is considered in a cooperative communication system and the effect of imperfect channel estimation on the overall system performance is analyzed. SM is a multiple-input multiple-output (MIMO) technique that considers the multiple transmit antennas as an added constellation points and utilizes them to boost the spectral efficiency. In our analysis, a wireless communication system, where a source communicating with a destination through a direct link and multiple decode and forward (DF) relays, is considered. Imperfect channel knowledge is assumed at each relay and at the destination node. In cooperative mode, only the relays that correctly decode the source signal forward the decoded message to the destination. A closed form expression of the pair wise error probability (PEP) is obtained for a system consisting of two transmit antennas, multiple DF relays and single receive antenna and a tight upper bound is given for the average error probability. As well, asymptotic expression for the PEP at high signal to noise ratio (SNR) is derived.