Comparative analysis of ML and MAP detectors for PAM constellations in AWGN channel

Abstract

In this paper we perform a comparative performances analysis of ?maximum a posteriori? (MAP) and ?maximum likelihood? (ML) detectors for one-dimensional constellation in the adaptive white Gaussian noise (AWGN) channel. More precisely, error probabilities per symbol for the aforementioned detectors are compared for the case when the pulse amplitude modulation (PAM) constellation with the equidistant and non-equiprobable constellation points is used as one-dimensional constellation. We perform analysis for different distributions of the constellation point probabilities and different values of the signal-to-noise ratio (SNR). The analysis indicates which detector can be adequate choice for the certain distribution of constellation point probabilities and the SNR. Besides this, for the straightforward performance assessment of the MAP detector we derive a formula for the symbol error probability. Our analysis also points out that the nonuniform distribution of the constellation points probabilities does not necessarily improve the symbol error probability. With the aim to decrease the symbol error probability we propose a method for defining constellation point probabilities. The presented results show that PAM constellation designed by utilizing the method we propose significantly outperforms the conventional PAM constellation in terms to the symbol error probability.