Sphere Decoding for Spatial Modulation Systems with Arbitrary Nt

Recently, three Sphere Decoding (SD) algorithms were proposed for Spatial Modulation (SM) scheme which focus on reducing the transmit-, receive-, and both transmit and receive-search spaces at the receiver and were termed as Receiver-centric SD (Rx-SD), Transmitter-centric SD (Tx-SD), and Combined SD (C-SD) detectors, respectively. The Tx-SD detector was proposed for systems with Nt ≤ Nr , where Nt and Nr are the number of transmit and receive antennas of the system. In this paper, we show that the existing Tx-SD detector is not limited to systems with Nt ≤ Nr but can be used with systems Nr < Nt ≤ 2Nr − 1 as well. We refer to this detector as the Extended Tx-SD (E-Tx-SD) detector. Further, we propose an ETx-SD based detection scheme for SM systems with arbitrary Nt by exploiting the Inter-Channel Interference (ICI) free property of the SM systems. We show with our simulation results that the proposed detectors are ML-optimal and offer significantly reduced complexity.