Optimal coefficient selection in Compute and Forward relaying using improved Schnorr–Euchner search algorithm

Abstract

Physical layer Network Coding with Compute and Forward relaying (CF) is a promising transmission strategy that effectively exploits the natural linear computation of the multiuser wireless channel. In CF relaying, the relay nodes receive a linear combination of transmitted signals with additive noise and each relay node computes an integer linear combination of transmitted codewords which are then forwarded to the destination. After receiving enough independent equations from multiple relay nodes, the destination could decode individual source nodes’ messages. The source nodes use nested lattice codes which have the property that an integer linear combination of codewords is a valid codeword in the codeset. The simulation set up includes a K×K×1 network model with K source nodes, K relay nodes and 1 destination node. Relay nodes are assumed to have perfect channel state information, which is used in computing the linear equation. The success of CF relaying lies in choosing the optimal coefficient in computing the independent linear equation at each relay node. Optimal coefficient selection aims to maximize the computation rate which can be achieved when the equation coefficients are matched with complex-valued channel gains. This paper proposes an iterative algorithm for finding the optimal coefficient vector in the Gaussian integer domain using an improved Schnorr–Euchner search strategy. The performance of the proposed coefficient search algorithm in terms of computation complexity and the achievable rate is compared with other existing algorithms through MATLAB simulation. Simulation is performed for networks with 2, 4, 8 and 16 numbers of source and relay nodes. The proposed coefficient selection algorithm is validated for varying Signal to Noise Power under Rayleigh fading channel environment.