Single-RF Spatial Modulation Relying on Finite-Rate Phase-Only Feedback: Design and Analysis

In this paper, we consider a spatial modulation (SM)-based multiple-input-single-output (MISO) system relying on a single radio-frequency chain equipped with a finite-rate feedback channel to provide quantized channel state information (CSI) to the transmitter. First, under the assumption of Rayleigh flat-fading channels and perfect CSI at the transmitter (CSIT), we analyze the symbol error probability (SEP) of an SM scheme, which perfectly compensates the channel phase and employs constellation rotation at the different transmit antennas (TAs). Then, we consider a more practical scenario, where scalar quantization of the channel phase angles is employed, and the quantized CSI is made available to the transmitter via a finite-rate feedback channel. We analyze the SEP reduction, i.e., P-eL, relative to perfect CSIT, imposed by the quantized CSIT (Q-CSIT). We show that at a high feedback rate, P-eL varies as C'2(-2B), where each channel phase angle is quantized to B bits, and C' is a constant. Furthermore, based on the rotational symmetry of the M-ary phase-shift keying (M-PSK) signal constellation, we propose a novel feedback scheme, which requires (n(t) - 1) log(2)(M) fewer bits of feedback with any performance erosion, where n(t) is the number of TAs. We characterize the performance of the SM-MISO system with finite-rate feedback and validate our analysis through Monte Carlo simulations.