Upper and lower bounds to estimate the random coding exponent for a peak-power-limited channel

In this paper, we consider the estimation of Gallager's (1968) random coding exponent (RCE) for a peak power constraint at the transmitter for the two-dimensional fading channel with additive white Gaussian noise (AWGN) and with perfect channel estimation at the receiver. Despite the fact that many wireless channels are peak-power-limited, the RCE for such channels has not been considered previously in the literature. Such a problem has only been partially solved for the AWGN case due to the difficulty in finding an input signal distribution that yields the RCE. In this paper, we adopt a different approach in which we develop upper and lower bounds to the RCE with the hope of trapping it in a narrow region. Our quest is successful as we can estimate the RCE to an error of only 0.72 bit per modulation symbol. Furthermore, we find that the RCE for the peak-power-limited channel does not represent a severe degradation relative to that attained for the average-power-limited channel. Thus, good modulation and coding schemes at reasonable complexity should exist for a peak-power-constrained fading channel.