Some Notes on the Fourier Transform Methods for Error-Rate Analysis of Equal-Gain Combining

Transform techniques based on moment generating functions (MGFs) and characteristic functions (CHFs) have recently provided efficient analytical tools for the performance evaluation of digital communication systems over fading channels. More recently, the convolution theorem of the Fourier transform has been employed to obtain unified expressions for the average error probabilities of equal gain combining (EGC) diversity reception in terms of the CHFs of the branches' amplitude gains. In this paper, we prove that these expressions include redundant terms. Furthermore, simpler analytical expressions for the average error rates of EGC diversity reception can be obtained when the convolutional theorem of the sine and cosine transforms are used instead of the conventional Fourier transform.