Yann Meurisse

Bounds for sparse planar and volume arrays

This paper improves and extends bounds on the numbers of sensors, redundancies, and holes for sparse linear arrays to sparse planar and volume arrays. As an application, the efficiency of regular planar and volume arrays with redundancies but no holes is deduced. Also, examples of new redundancy and hole square arrays, found by exhaustive computer search, are given.

Robustness of narrowband DOA algorithms with respect to signal bandwidth

The purpose of this paper is to determine the domain of validity of spatial covariance-based narrowband DOA algorithms when processing non-narrowband data. By focusing on the case of one source and two equipowered uncorrelated sources of the same bandwidth, we examine order detection and asymptotic bias and covariance w.r.t. the bandwidth and the number of snapshots given by any narrowband algorithm. An order detector scheme, based on numerical analysis arguments introduced in channel order detection, is proposed. Closed-form expressions are given for the asymptotic bias and covariance of the DOAs estimated by the MUSIC algorithm, for which we show the key role that bandwidth plays w.r.t. the demodulation frequency. Furthermore, a common closed-form expression of the Cramer-Rao bound is given for the DOA parameter of a narrowband or wideband source, whose spectrum is symmetric w.r.t. the demodulation frequency, in the case of an arbitrary array. This allows us to prove that the MUSIC atgorithrn retains its efficiency over a large bandwidth range under these conditions.

Performance Limits of Alphabet Diversities for FIR SISO Channel Identification

Finite impulse responses (FIR) of single-input single-output (SISO) channels can be blindly identified from second-order statistics of transformed data, for instance when the channel is excited by binary phase shift keying (BPSK), minimum shift keying (MSK), or quadrature phase shift keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Theoretical performance issues are addressed to evaluate the robustness of standard subspace-based estimators with respect to these identifiability conditions. Then benchmarks such as asymptotically minimum variance (AMV) bounds based on various statistics are presented. Some illustrative examples are eventually given where Monte Carlo experiments are compared to theoretical performances. These comparisons allow to quantify limits to the use of the alphabet diversities for the identification of FIR SISO channels, and to demonstrate the robustness of algorithms based on high-order statistics.

Extension of the matrix Bartlett's formula to the third and fourth order and to noisy linear models with application to parameter estimation

This paper focuses on the extension of the asymptotic covariance of the sample covariance (denoted Bartletts formula) of linear processes to thirdand fourth-order sample cumulant and to noisy linear processes. Closed-form expressions of the asymptotic covariance and cross-covariance of the sample second-, third-, and fourth-order cumulants are derived in a relatively straightforward manner, thanks to a matrix polyspectral representation and a symbolic calculus akin to a high-level language. As an application of these extended formulae, we underscore the sensitivity of the asymptotic performance of estimated ARMA parameters by an arbitrary third- or fourth-order-based algorithm with respect to the signal-to-noise ratio, the spectra of the linear process, and the colored additive noise.

Performance Analysis of Optimal Blind Fusion of Bits

This paper is devoted to a statistical performance analysis of blind estimation of bit error rates (BERs) of a bank of detectors, using empirical estimation algorithms that have appeared in the literature (by Dixit ). In particular, we prove that these blind estimators asymptotically (in the number of observed bits) achieve the accuracy obtained with perfect knowledge of the transmitted bits. We propose a maximum-likelihood solution which follows from the standard expectation-maximization (EM) algorithm, considered to be a reference algorithm. Finally, the optimal fusion rule is revisited and our theoretical results are compared to Monte Carlo simulations

Identifiability of BPSK, MSK and QPSK FIR SISO Channels from Modified Second-Order Statistics

This paper considers the problem of blind estimation of finite impulse responses (FIR) of single-input single-output (SISO) channels from second order statistics of transformed data, when the channel is excited by binary phase shift keying (BPSK), minimum shift keying (MSK) or quadrature phase shift keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Performance issues are also addressed by using standard subspace-based estimators, with benchmarks such as asymptotically minimum variance (AMV) bounds based on different statistics

Asymptotically minimum variance second-order estimation for complex circular processes

This paper addresses asymptotically minimum variance (AMV) of parameter estimators within the class of algorithms based on second-order statistics for estimating parameter of strict-sense stationary complex circular processes. As an application, the estimation of the frequencies of cisoids for mixed spectra time series containing a sum of cisoids and an MA process is considered.