The Gaussian assumption in second-order estimation problems in digital communications
2007
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-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator—derived assuming Gaussian
transmitted symbols—is compared with the performance of the optimal second-order estimator, which 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 amplitude-phase-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.
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