Diversity Analysis of Analog Network Coding with Multi-User Interferences

Network coding can improve the bandwidth efficiency by letting multiple users share the relay channels. However, the multi-user interferences (MUI) at the intended receiver may degrade the diversity performances. So in this work, we study several diversity strategies for the multiple-access relay channel and analyze the impact of MUI on the diversity performances. Both the variable gain relaying (VGR) and the fixed gain relaying (FGR) are considered, where the relay nodes are subject to instantaneous power constraints and long-term power constraints, respectively. We first develop a Min-Max relay selection strategy and prove that full diversity can be achieved. Next, the distributed space-time block coding (DSTBC) and the diagonal distributed space-time coding (DDSTC) are studied. For DSTBC, we show that full diversity can be achieved by FGR, but the diversity of VGR is upper bounded by \min (L+1, K+1), where L and K are the number of relays and users, respectively. For single-user systems, we then develop a selective DSTBC-VGR scheme to recover the diversity loss by adaptively allocating the relay power. Finally for DDSTC, we show that both FGR and VGR can achieve full diversity, and the optimum code design criterion is to maximize the minimum product distance.