Performance analysis for DOA estimation algorithms: unification,simplification, and observations

Subspace based direction-of-arrival (DOA) estimation has motivated many performance studies, but limitations such as the assumption of an infinite amount of data and analysis of individual algorithms generally exist in these performance studies. The authors have previously proposed a unified performance analysis based on a finite amount of data and achieved a tractable expression for the mean-squared DOA estimation error for the multiple signal classification (MUSIC). Min-Norm, estimation of signal parameters using rotational invariance techniques (ESPRIT), and state-space realization algorithms. However, this expression uses the singular values and vectors of a data matrix, which are obtained by the highly nonlinear transformation of the singular value decomposition (SVD). Thus the effects of the original data parameters such as numbers of sensors and snapshots, source coherence and separations were not explicitly analyzed. The authors unify and simplify this previous result and derive a unified expression based on the original data parameters. They analytically observe the effects of these parameters on the estimation error     

Evaluation and reduction of multipath-induced bias on GPS time-of-arrival

New expressions are presented for the multipath-induced pseudorange error (i.e. bias) and variance introduced by multipath onto the time-of-arrival estimate obtained using a noncoherent early-late gate discriminator. The results include the effect of front-end bandwidth and early-late gate spacing. We also investigate a blind method for cancelling the multipath, in order to improve the time-of-arrival estimate. Our approach uses early-late gate processing on an objective function derived from an adaptive finite impulse response (FIR) filter that attempts to match the crosscorrelation of the received signal with a multipath-free replica of the desired crosscorrelation. This method performs reasonably well, and decreases the multipath-induced pseudorange error by approximately a factor of 2, even in very stressing multipath environments.     

Wideband cancellation of interference in a GPS receive array

We have demonstrated that by using an adaptive space-time array the interference from multiple, strong interferers plus multipath can be canceled down close to the noise floor without producing serious loss or distortion of a GPS signal. Design criteria are presented and limitations are examined. We also compare space-time processing with suboptimum space-frequency processing, and demonstrate by simulation that for equal computational complexity space-time processing slightly outperforms suboptimum space-frequency processing     

Analysis of Min-Norm and MUSIC with arbitrary array geometry

A nonasymptotic performance comparison is presented between the Min-Norm and MUSIC algorithms for estimating the directions of arrival of narrowband plane waves impinging on an array of sensors. The analysis is based on a finite amount of sensor data. The analysis makes the assumption of high signal-to-noise ratio (SNR), and it applies to arrays of arbitrary geometry. It is shown that Min-Norm can be expressed as a certain data-dependent weighted MUSIC algorithm, and that this relationship allows a unified performance comparison. It is also shown that the variances of the estimated directions-of-arrival from the MUSIC algorithm are always smaller than those of the Min-Norm algorithm at high SNR when both algorithms employ a numerical search procedure to obtain the estimates     

Sensitivity analysis of DOA estimation algorithms to sensor errors

A unified statistical performance analysis using subspace perturbation expansions is applied to subspace-based algorithms for direction-of-arrival (DOA) estimation in the presence of sensor errors. In particular, the multiple signal classification (MUSIC), min-norm, state-space realization (TAM and DDA) and estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms are analyzed. This analysis assumes that only a finite amount of data is available. An analytical expression for the mean-squared error of the DOA estimates is developed for theoretical comparison in a simple and self-contained fashion. The tractable formulas provide insight into the algorithms. Simulation results verify the analysis