The Gaussian Assumption in Second-Order Estimation Problems in Digital Communications

Abstract

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimation\n\t\t\t\t methods in the context of digital communications. The low- and\n\t\t\t\t high-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator—derived assuming Gaussian\n\t\t\t\t transmitted symbols—is compared with the performance of the optimal second-order estimator, which exploits the actual\n\t\t\t\t distribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimal\n\t\t\t\t second-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitude\n\t\t\t\t modulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield important\n\t\t\t\t losses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK)or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.