Statistical performance analysis of the algebraic constant modulus algorithm

Veen, Alle-Jan van der

doi:10.1109/tsp.2002.805502

Cited by 16 publications

(5 citation statements)

References 25 publications

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“…We will need the following results on the variances of products of independent complex circularly symmetric CM signals, which are not hard to derive [10]: var sis 3 j = 0; i= j 1; i6 = j var s i s 3 j s k s 3 l = 0; (i = j^k = l) or (i = l^j = k) 1; otherwise.…”

mentioning

confidence: 99%

Finite sample identifiability of multiple constant modulus sources

Leshem

Petrochilos

Veen

2003

IEEE Trans. Inform. Theory

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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).

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confidence: 99%

Finite sample identifiability of multiple constant modulus sources

Leshem

Petrochilos

Veen

2003

IEEE Trans. Inform. Theory

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“…where Σ k is in size of q × (q − 1) and spans a (q − 1)dimensional subspace orthogonal to g k . Substituting (31) into (32), we obtain…”

Section: Performance Of the CM Estimatormentioning

confidence: 99%

Multiuser Channel Estimation for Ultra-Wideband Systems Using up to the Second-Order Statistics

Tang

Liu

2005

EURASIP J. Adv. Signal Process.

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In a pulse-position modulation-based ultra-wideband (UWB) communication system, multiple access is enabled by assigning unique time-hopping sequences to different users. Each user's data information is carried by positions of short pulses which are directly transmitted through an unknown and possibly dense multipath channel. Single-user channel estimation methods have been proposed by maximum likelihood optimization that treats multiple access interference as Gaussian noise. In this paper, multiuser channel estimation methods are proposed based on a pulse-rate discrete-time system model and up to the second-order statistics of the channel outputs. The model can be regarded in a trilinear structure and also resembles a code-division multiple-access (CDMA) system with newly defined hopping-code dependent matrices and inputs for each user. Considering that either the mean or covariance of received signals contains sufficient information for all unknown channels, least squares and covariance matching ideas are successfully applied to estimate all channels blindly. Accordingly, closed-form solutions are derived. Those channel estimates can be used to design typical linear receivers. Performance of each proposed estimator is analyzed and also verified by computer simulations. Corresponding receivers' performance is also studied numerically.

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“…We will need the following results on the variances of products of independent complex circularly symmetric CM signals, which are not hard to derive [10]: …”

Section: B the Finite-alphabet Case-large Deviations Boundmentioning

confidence: 99%

“…Proof: Let v v v(n) be defined as in (10). We would like to bound separately to the real and imaginary parts ofR R R ij we obtain…”

Section: Lemmamentioning

confidence: 99%

Finite sample identifiability of multiple constant modulus sources

Leshem

Petrochilos

Veen

Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002

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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).Index Terms-Blind source separation, Chernoff bound, constant modulus signals, finite sample analysis, identifiability, large deviations, phaseshift keying (PSK).

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Statistical performance analysis of the algebraic constant modulus algorithm

Cited by 16 publications

References 25 publications

Finite sample identifiability of multiple constant modulus sources

Finite sample identifiability of multiple constant modulus sources

Multiuser Channel Estimation for Ultra-Wideband Systems Using up to the Second-Order Statistics

Finite sample identifiability of multiple constant modulus sources

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