Fractional Pilot Duration Optimization for SIMO in Rayleigh Fading With MPSK and Imperfect CSI

In a communication system employing coherent reception, pilot symbols are used for estimating the channel state information (CSI) at the receiver. The amount of training, which is quantified by the fractional pilot duration for a fixed-length pilot-plus-data frame, should be kept as low as possible for saving bandwidth and increasing data rate. However, reducing training leads to degraded error performance due to poor CSI estimate although it increases data rate, while increasing training improves error performance but reduces data rate. Expressing the tradeoff between symbol error probability (SEP) and data rate by the normalized error-free data rate, we present an analytical framework for its maximization with respect to pilot symbol duration fraction in a pilot-aided single-input multiple-output wireless communication system with reception over independent and identically distributed flat Rayleigh fading diversity branches, employing M -ary phase-shift keying, and using maximal-ratio combining. Closed-form expressions for the approximate optimal pilot symbol duration fraction are derived for the high signal-to-noise ratio (SNR) case. Numerical results are presented to highlight the system behavior with changes in parameters like SNR, pilot symbol quality, and number of receive diversity branches. It is found that the optimization maximizes normalized error-free data rate with close to minimum SEP.