Numerical calculation of symmetric capacity of Rayleigh fading channel with BPSK/QPSK

In this letter, we develop a simple series representation for the symmetric capacity of a Rayleigh fading channel with BPSK/QPSK when perfect channel state information is available at the receiver. This series expansion provides a simple and numerically efficient way to calculate the capacity. We also note that the bounds on the capacity developed in the paper by Baccarelli and Fasano (2000) are loose under the cases considered in this letter.