Finite sample identifiability of multiple constant modulus sources

A. Leshem Nicolas Petrochilos 1 A. van der Veen
1 URCA UFR SEN - URCA - UFR Sciences exactes et naturelles
Abstract : We prove that mixtures of continuous alphabet constant modulus sources can be identified with probability 1 with a finite number of samples (under noise-free conditions). This strengthens earlier results which only considered an infinite number of samples. The proof is based on the linearization technique of the analytical constant modulus algorithm (ACMA), together with a simple inductive argument. We then study the finite-alphabet case. In this case, we provide a subexponentially decaying upper bound on the probability of nonidentifiability for a finite number of samples. We show that under practical assumptions, this upper bound is tighter than the currently known bound. We then provide an improved exponentialy decaying upper bound for the case of-PSK signals (is even).
Keywords : phase-shift keying (PSK). identifiability large deviations Blind source separation Chernoff bound constant modulus signals finite sample analysis
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A. Leshem, Nicolas Petrochilos, A. van der Veen. Finite sample identifiability of multiple constant modulus sources. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2003, 49 (9), pp.2314 - 2319. ⟨10.1109/TIT.2003.815791⟩. ⟨hal-01693662⟩

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