Performance Analysis of Spatial Modulation Under Rapidly Time-Varying Rayleigh Fading Channels

Due to the problem of inter-channel interference, the average bit error probability (ABEP) performance of the traditional multiple transmit and multiple receive antenna systems obviously deteriorates. A promising scheme to address this issue is the spatial modulation (SM) which activates only one transmit antenna at each signaling period. In addition, the demand to provide data services for high mobility users is ever increasing, where fading channels are more likely to be rapidly time-varying. Therefore, in this paper, we investigate the ABEP performance of SM under the assumption that system's fading channels are Rayleigh and varying from one signaling period to another within the same transmitted data block. Further, to simplify the decoding complexity at the receiver, the channel is assumed to be estimated at the first location of each data block and then used to detect the received symbols at the remaining locations of the block. For such a system, and unlike other literature works, we derive novel, exact and closed-form reduced enough expressions for the average pairwise error probabilities (average-PEPs), which are then used to compute the system's overall per-block ABEP efficiently. The derived expressions are generic and valid for both time-varying and slow fading environments. Furthermore, the obtained analytical results are exploited to quantitatively show that the time-varying fading environment degrades the SM system's performance through irreducible error floors. Numerical and simulation results of various examples are provided to validate the theoretical analyses and also to get some insights into the effect of the different system parameters (such as the speed of the mobile, the carrier frequency, and the block size of the channel variations) on the overall SM error performance.