Characterization of the coding gain for M-PSK with conjoint signals under correlated Nakagami-m fading channels

Abstract

In the paper, a comprehensive analysis is presented on the conjoint coding gain achieved in arbitrarily correlated M-ary phase-shift keying (M-PSK) signals in a spatial diversity system. The system operates over Nakagami-m fading channels and is affected by additive white Gaussian noise (AWGN). The proposed signal synthesizer primarily induces an even phase shift in the output signals. To enhance the coding gain, an orthogonal transformation matrix is introduced, which effectively preserves energy and operates independently of the channel correlation matrix, making it blind to signal information measurements. The main objective is to generate additional copies of conjoint signals from the received signals, simulating the scenario as if there were more antennas deployed. To evaluate the system’s performance in terms of symbol error rate (SER), an analytical framework is developed and its accuracy is validated through Monte-Carlo simulations. Moreover, extensive tests are conducted to explore the impact of different antenna configurations and fading severity levels. The fading severity, denoted as ’m’, is varied in the experiments, considering values of 0.5, 1, 3, and 7. Additionally, the measurements incorporate varying antenna spacing values relative to the signal carrier wavelength, specifically 0.1, 0.2, and 0.5. The results obtained from the experiments demonstrate that the coding gains achieved depend on the value of ’m’, with higher gains observed for lower ’m’ values. However, as ’m’ increases, the coding gains become negligible.