Showing papers by "Mats Viberg published in 2004"

LMMSE channel prediction based on sinusoidal modeling

Abstract: An LMMSE channel prediction algorithm based on sinusoidal modeling is proposed for SIMO systems, assuming random amplitudes and equal mean powers. The potentially ill-conditioned LS estimates of the complex amplitudes is mitigated by regularization. This is interpreted as an LMMSE prediction, where the complex amplitudes are modeled as random (Rayleigh fading). Evaluated by simulations in SISO scenarios without loss of generality the LMMSE predictor presents a similar performance to the non-regularized LS prediction. The CRB of the frequency estimate of the sinusoidal modeling is derived. The performance of the LMMSE prediction with frequencies estimated by Unitary-ESPRIT is very close to those using the "best possible" frequency estimates according to the CRB. It also outperforms by far the AR modeling based linear prediction in the investigated scenarios.

Asymptotic properties of nonlinear weighted least squares in radar array processing

Abstract: This paper treats nonlinear weighted least squares parameter estimation of sinusoidal signals impinging on a sensor array. We give a consistency proof for a more general model than what has been previously considered in the analysis of two-dimensional (2-D) sinusoidal fields. Specifically, the array can have an arbitrary shape, and spatially colored noise is allowed. Further, we do not impose the restriction of unique frequencies within each dimension, and the number of samples is assumed large in only the temporal dimension. In addition to consistency, we establish that the parameter estimates are multivariate Gaussian distributed under a large class of noise distributions. The finite sample performance is investigated via computer simulations, which illustrate that a recommended two-step procedure yields asymptotically efficient estimates when the noise is Gaussian. The first step is necessary for estimating the weighting matrix, which has a dramatic influence on the performance in the studied scenarios. The number of samples required to attain the Crame/spl acute/r-Rao lower bound is found to coincide with the point where the signal sources are separated by more than one discrete Fourier transform bin. This remains true even when the signals emanate from the same direction of arrival (DOA).

A new expression of the asymptotic performances of Maximum Likelihood DOA estimation method with modeling errors

Abstract: This paper provides a new analytic expression of the RMS (Root Mean Square) error and bias of the Maximum Likelihood (ML) Direction Of Arrival (DOA) estimator in the presence of steering vectors modeling errors. The reference [4] proposes a first order approximation of these performances which is adapted to small modeling errors. In order to take into account larger modeling errors and provide tools for designing experimental set-up, a more accurate and easily usable derivation of these performances is necessary For such an investigation, the DOA estimation errors are written as an hermitean form with a stochastic vector composed by the modeling errors. Finally, a closed form expression between the performances (bias and RMS error) and statistical moments of the model error are deduced from the statistics of the hermitean form. Simulations confirm the theoretical results.