An accurate frame error rate approximation of coded diversity systems with non-identical diversity branches

This paper presents an accurate approximation of the frame error rate (FER) of coded wireless communication systems with receiver diversity, such as single-input multiple-output (SIMO) systems with maximum ratio combining (MRC) or hybrid automatic repeat request (HARQ) systems with Chase combining. The signals at different diversity branches experience independent but non-identically distributed Rayleigh fading. The FER approximation is obtained with a threshold-based method. Specifically, the threshold value, which is critical to the FER approximation accuracy, is modeled as a linear function of the frame length in the log-domain, with the slope and intercept of the linear function determined by the underlying modulation and channel coding schemes. The analytical FER approximation is expressed as an explicit function of parameters related to modulation, coding, frame length, number of diversity branches, and the power distribution across the diversity branches. Such an FER approximation summarizes the complex physical layer operations into a few parameters, and it provides the parametric flexibility that is not available in most existing FER approximations. Simulation results show that the proposed FER approximation can accurately predict the FER performance of a wide range of receiver diversity systems.