Analog network coded modulation with maximum Euclidean distance denoising-and-mapping.

Physical-layer network coding (PNC) holds the great potential of improving the power efficiency and the spectral efficiency for its two-stage transmission scheme. In this paper, we investigate the joint network-coded modulation design of the two stages. A universal modulation framework is built, referred to as Analog Network-Coded Modulation Strategy, which is more general than the former modulation design mechanism. More explicitly, we propose a joint design criterion for the modulation and the network coding to guarantee the forwarding reliability at the relay node. That is, the neighboring superposed constellation points, among which the Euclidean distance (ED) is less than a given threshold, are constrained to be mapped to an identical constellation point for broadcasting. This yields a non-convex polynomial optimization problem, for which we propose a joint modulation design algorithm, termed as Enhanced Semidefinite Relaxation (Enhanced-SDR) Algorithm, based on the SDR technique. Simulation results will demonstrate the effectiveness of the proposed algorithm by comparing symbol error rate (SER) performance with the exhaustive search and the existing modulation design methods.