BPSK-Based Physical-Layer Network Coding Algorithm

Physical-layer network coding (PNC) is an innovative technique that enhances network throughput in wireless communications, while BPSK (Binary Phase Shift Keying) serves as the foundational modulation scheme for PNC due to its simplicity as a basic digital modulation method. This article analyzes the core principles and performance characteristics of BPSK-based PNC implementations.

In traditional relay networks, data transmission requires multiple time slots, whereas PNC enables relay nodes to directly encode superimposed signals. When two terminal nodes simultaneously transmit BPSK signals, the relay node receives analog signals with phase superposition. Since BPSK employs two phases (0° and 180°), the superposition of two signals produces three possible phase states. The relay node decodes these into network-coded symbols using specific mapping rules, which can be implemented through MATLAB's phase detection algorithms and lookup tables.

MATLAB simulations typically evaluate performance across three dimensions: First, Bit Error Rate (BER) curves compare PNC schemes with traditional routing schemes by analyzing BER variations against signal-to-noise ratios, clearly demonstrating PNC's advantages in AWGN channels using functions like berawgn. Second, throughput analysis shows PNC theoretically reduces transmission time slots by 50% through slot efficiency calculations. Finally, constellation diagram simulations visualize phase distribution characteristics after signal superposition using MATLAB's scatterplot function to display the three distinct phase clusters.

Key implementation considerations include: the impact of carrier synchronization errors on phase superposition (simulated using phase offset models), constellation point shifts caused by power imbalance (modeled with amplitude scaling factors), and designing specific decoding algorithms for BPSK-PNC. These factors manifest in MATLAB simulations as elevated BER floors or rotated/diffused constellation patterns, which can be analyzed using error vector magnitude (EVM) measurements and rotation compensation algorithms.