A new receiver for additive white Gaussian noise channels

In this paper we study the performance of a wavelet-based receiver for the various digital communications modulation techniques, when the channel corrupts the transmitted signal by the addition of additive white gaussian noise (AWGN). This receiver is similar to the well-known optimum receiver in that it uses a correlator (matched filter) and a maximum likelihood decision stage to decide which signal was transmitted. The key difference lies in the correlation part where the De-Noised wavelet coefficients of the received signal are multiplied with M sets (M-ary system) of wavelet coefficients that correspond to M prototype signals. We derive the probability density function of the decision variable, for the simplest case, Binary Phase Shift Keying (BPSK), and then arrive at an expression for the probability of error. We use simulations to compare the performance of this receiver to that of the classical optimal receiver. We do this for the four modulation techniques; coherent M-ary Phase Shift Keying (MPSK), differential M-ary Phase Shift Keying (differential MPSK), coherent M-ary Frequency Shift Keying (coherent MFSK), and non-coherent M-ary Frequency Shift Keying (non-coherent MFSK). We show an improvement, in terms of probability of error versus signal to noise ratio (SNR), for all four cases. This improvement ranges between 1/4 dB in the case of differential MPSK to as much as 3/4 dB in the other cases at high SNR values.