The Gaussian Assumption in Second-Order Estimation Problems in Digital Communications
Javier Villares, G. Vazquez · IEEE Transactions on Signal Processing · 2007
Abstract 2 This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimation methods in the context of digital communications. The low- and high-SNR asymptotic performance of the maximum likelihood estimator –derived assuming Gaussian trasmitted symbols – is compared to the performance of the optimal second-order estimator, that exploits the actual distribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimal second-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitude modulation (QAM) or amplitudephase-shift keying (APSK). On the other hand, the Gaussian assumption can yield important 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. 1Corresponding author.