BER analysis of 2PSK, 4PSK, and 16QAM with decision feedback channel estimation in frequency-selective slow Rayleigh fading

The average bit error rate (BER) performances of coherently detected 2PSK, 4PSK, and 16QAM in frequency-selective slow Rayleigh fading are analyzed. Decision feedback channel estimation (DFCE) is considered, in which the past L-received signal samples are remodulated to remove the modulation phase by feeding back the detected symbol sequence and then averaged. Analytical expressions for the conditional BER for the given transmitted symbol sequence are derived, and the average BER performances are evaluated by Monte Carlo simulation. It is shown that as L increases, the BER performance improves and approaches that of ideal coherent detection (with perfect channel estimation), and the loss in E_b/N₀ required for BER = 0.1% relative to ideal coherent detection becomes as small as 0.4 dB when L = 10. It is found that while the best performance is achieved by 2PSK and 4PSK when additive white Gaussian noise (AWGN) is the predominant cause of error (i.e., low E_b/N₀ regions), 16QAM modulation can achieve almost the same performance as 4PSK when the delay spread is the predominant cause of error (i.e., large E_b/N₀ regions), and the worst performance in this case is by 2PSK. The effects of power delay profile shape (double-spike, exponential, and Gaussian profiles assumed), rolloff factors of the Nyquist transmit/receive filters, and the transmitted symbol sequence pattern on the average BER performance are discussed.