Complex Gaussian Ratio-Based Bit Error Probability Calculation for PAM-FBMC Systems

The interference induced by doubly-selective channels does not follow a Gaussian distribution, which leads to an inaccurate prediction for the reliability of Pulse Amplitude Modulation-based Filter Bank Multi-Carrier (PAM-FBMC) systems. In this letter, we derive a closed-form expression for the Bit Error Probability (BEP) based on Complex Gaussian Ratio (CGR), which accurately predicts the Bit Error Rate (BER) of the system and provides a basis for system design. Specifically, we first investigate the distribution properties of the ratio between the received symbol and the channel coefficients (i.e., CGR) to derive its joint probability density function. Secondly, based on the joint probability density of the CGR, we derive its Cumulative Distribution Function (CDF). Finally, we calculate the marginal CDF and, in conjunction with the decision boundaries provided by the PAM constellation, derive the BEP. Simulation results show that the CGR-based BEP provides a better agreement with the simulated BER.