Abstract
SummaryIn this paper, we focus on physical‐layer network coding (PNC) used in multiple‐input multiple‐output (MIMO) Y channels, where K users simultaneously exchange messages with each other via a shared relay. For MIMO‐PNC, signal space alignment for network coding (SSA‐NC) is a promising precoding method and can achieve K(K‐1) degrees of freedom if certain conditions can be satisfied. An important one is that the number of relay antennas is less than twice of the user antennas, that is, the dimensionality constraint of SSA‐NC. In this paper, we focus on a particular scenario where the dimensionality constraint is not satisfied. In order to resolve this problem, we develop a scheme of jointly selecting relay antennas and precoding vectors. In particular, a novel precoding and detection method is presented to alleviate the interference caused by simultaneous transmissions. Through analyzing the symbol error rate performance of MIMO‐PNC, we establish the relationship between the achievable flow diversity gain and the optimal number of the antennas, and a precoding selection method is designed under a given relay antenna configuration. Finally, we propose a joint scheme to select the optimal relay antenna configuration and precoding vectors. Numerical results demonstrate that the presented scheme can effectively support MIMO‐PNC in various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.
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