## 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 nonidentiflability 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 L-PSK signals (L is even).

Original language | American English |
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Pages (from-to) | 2314-2319+2323 |

Journal | IEEE Transactions on Information Theory |

Volume | 49 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2003 |

Externally published | Yes |

### Bibliographical note

Funding Information:Manuscript received August 10, 2001; revised January 26, 2003. The work of A. Leshem was supported in part by the NOEMI project of the STW under Contract DEL77-4476. The material in this correspondence was presented in part at the IEEE Sensor Arrays and Multichannel Signal Processing 2002 Workshop, Washington DC, August 2002.

## Keywords

- Blind source separation
- Chernoff bound
- Constant modulus signals
- Finite sample analysis
- Identifiabllity
- Large deviations
- Phase-shift keying (PSK)