Decode-and-forward with quadrature spatial modulation in the presence of imperfect channel estimation

The performance of quadrature spatial modulation (QSM) multiple-input multiple-output (MIMO) system with cooperative decode and forward (DF) relays is analyzed in this paper. QSM is a new MIMO transmission technique that enhances the overall performance of conventional spatial modulation through exploiting quadrature spatial dimension. A practical scenario is considered where the channel is estimated at the relays and the destination and the impact of channel estimation error is investigated. Two cooperative systems are considered in the study. In the first system, multiple single-antenna DF relays are assumed, whereas, in the second system, single multiple-antennas DF relay is considered. For both systems, an analytical expression for the pair wise error probability (PEP) is obtained. As well, an asymptotic expression for the PEP at high and pragmatic signal to noise ratio is derived. Derived expressions are used to provide an upper bound on the average bit error ratio. The derived analysis is corroborated through Monte Carlo simulations and results demonstrate a close-match for a wide range of SNR values.