On the Capacity and Performance of Generalized Spatial Modulation

Generalized spatial modulation (GSM) uses $N$ antenna elements but fewer radio frequency (RF) chains ($R$) at the transmitter. Spatial modulation and spatial multiplexing are special cases of GSM with $R=1$ and $R=N$, respectively. In GSM, apart from conveying information bits through $R$ modulation symbols, information bits are also conveyed through the indices of the $R$ active transmit antennas. In this paper, we derive lower and upper bounds on the the capacity of a ($N,M,R$)-GSM MIMO system, where $M$ is the number of receive antennas. Further, we propose a computationally efficient GSM encoding (i.e., bits-to-signal mapping) method and a message passing based low-complexity detection algorithm suited for large-scale GSM-MIMO systems.