Wireless relay networking has been proposed as a solution for extending coverage in the past few decades. The relay network facilitates communication between users who are unable to reliably share information due to severe pathloss or blockage. In this paper, we utilize spatial diversity of distributed multiple-input multiple-output systems for the relay network. Hence, the relay network consists of many separate relay nodes. Due to limited computational power, we assume each relay node receives the sum of the transmissions from all users and then performs one-bit quantization. The quantization bits from the relay network are broadcast back to the users through a downlink channel that is modeled as a low-rate binary symmetric channel. Based on the noisy quantization bits from the relay network and its own prior transmission, each user detects the transmitted symbols from other users. We first derive the maximum likelihood detector for the described system. Then we develop a sub-optimal detector called the orthogonal subset maximum likelihood (OSML) detector, which exploits only a subset of relay nodes for detection, to reduce the computational complexity. By using combinatorial geometry, we derive the minimum number of required relay nodes for the OSML detector to operate. The derived results are verified through numerical simulations.

Spatial modulation (SM) is a new modulation technique where the information to be sent is encoded using one or more symbols and the subspace over which the symbols are transmitted. Unfortunately, a general capacity analysis that encompasses different forms of SM systems has not been developed. In this paper, we consider a general form of SM, where the number of transmitted data streams is allowed to vary. We refer to this form of SM as generalized spatial modulation with multiplexing (GSMM). A Gaussian mixture model (GMM) is shown to accurately model the transmitted spatially modulated signal using a precoding framework. Using this transmit model, a closed-form expression for the achievable rate when operating over Rayleigh fading channels is evaluated, and tight upper and lower bounds for the achievable rate are proposed. The expressions of the achievable rate obtained are flexible enough to accommodate any form of SM—where any subspace can be used for the transmission—by adjusting the precoding set. Simulations are presented to show the tightness of the proposed bounds. The effect of the system dimensions and a comparison with other prominent capacity results are also demonstrated in simulations.