On the estimation of random unobserved signals by maximization of target likelihoods and its application to blind timing and phase recovery

Many important problems in signal processing can be reduced to the adequate selection of the parameters of a (possibly nonlinear) filter in order to obtain an output signal that complies with some desired properties. In this work, we analyze a novel criterion for selecting filter parameters that relies on the ability to characterize the desired filter output in terms of a target probability density function (pdf). This target pdf can be handled as a likelihood function to be maximized, thus we refer to the new criterion as maximum target-likelihood (MTL). We present a very general signal model where the MTL criterion can be applied and derive necessary and sufficient conditions for asymptotic convergence of the method. The relationship and differences between MTL and standard maximum likelihood (ML), minimum Kullback-Leibler divergence (MKLD), and minimum entropy (ME) methods are explored. Finally, as an example, we apply the novel criterion to the problem of blind timing and phase recovery in a digital transmission system and show that the resulting algorithm is competitive with existing non-data-aided ML-based algorithms.