Blind channel identification and blind signal estimation

Blind identification and blind estimation are emerging fields of fundamental research with a wide range of practical applications. Motivated by practical signal processing problems, the blind identification and blind estimation address the needs of estimating the source signals without knowing the transmission channel.; A mathematical framework is first developed and various theoretical aspects of the blind identification and estimation investigated. In order to obtain the optimal (in the sense of preserving the waveforms of the source signals) blind signal estimation, a waveform-preserving equivalence relation is introduced so that the issues of indeterminacy and identifiability can be properly addressed. Under the proposed mathematical framework, the following theoretical results are obtained: (i) a dual relation between the blind channel identification and the blind signal waveform preserving estimation; (ii) a necessary and sufficient condition for the identifiability of memoryless channels with respect to the independent source models; (iii) a necessary condition and some sufficient conditions for the identifiability of memoryless channels with respect to the source correlation models; (iv) the identifiability of FIR MIMO channels.; Several blind identification and blind estimation algorithms are proposed for different channel and source models. The EFOBI algorithm is developed for the blind identification of memoryless channel with independent sources whose kurtosises are distinct, while the proposed cumulant-based algorithms obviate such constraints on the source kurtosises. The AMUSE algorithm is proposed for the blind identification and estimation of memoryless channel with the source correlation models. A finite-step global convergence algorithm is proposed for the identification of FIR MIMO channels and solving a class of nonlinear matrix equations.