WAVES: weighted average of signal subspaces for robust wideband direction finding

Abstract

Existing algorithms for wideband direction finding are mainly based on local approximations of the Gaussian log-likelihood around the true directions of arrival (DOAs), assuming negligible array calibration errors. Suboptimal and costly algorithms, such as classical or sequential beamforming, are required to initialize a local search that eventually furnishes DOA estimates. This multistage process may be nonrobust in the presence of even small errors in prior guesses about angles and number of sources generated by inherent limitations of the preprocessing and may lead to catastrophic errors in practical applications. In this paper, a new approach to wideband direction finding is introduced and described. The proposed strategy combines a robust near-optimal data-adaptive statistic, called the weighted average of signal subspaces (WAVES), with an enhanced design of focusing matrices to ensure a statistically robust preprocessing of wideband data. The overall sensitivity of WAVES to various error sources, such as imperfect array focusing, is also reduced with respect to traditional CSSM algorithms, as demonstrated by extensive Monte Carlo simulations.

The Analysis of the Influence of Random Array Error to Wideband Signal Doa Estimation Reiterative Algorithm

“…, θ K ] and that the distance of adjacent elements is less than half wavelength of the highest frequency. Passing single wideband signal snapshot through J narrowband filters to obtain narrowband data at frequencies {f j } J j=1 [1,2], the signal Y j ∈ R N ×1 at frequency f j can be represented in vector notation as the N × 1 vector…”

“…Finally, WSERA is compared with coherent subspace method (CSM), WAVES [2] and TOFS [14]. Set ρ = [0, 20], L = 8 and SN R = 10 dB, values for N of 12.…”

“…Coherent subspace method (CSM) [1][2][3] is the traditional method to deal with wideband signal DOA estimate, and it can separate signals whose DOAs are close in ideal condition. But the random array error always exists, which due to antenna element location uncertainty, realistic calibration tolerances, mutual coupling effects between elements, etc., and it will decrease its performance and even can't work, so array calibration [4] is the necessary procedure when there is array error.…”

Improved finite samples resampling for unbiased wide-band direction of arrival estimation

“…Among recent wide-band DOA estimation methods that can avoid preliminary DOA estimates are the Weighted AVErage of Signal-subspaces (WAVES) [21] and the Test of Orthogonality of Projected Subspaces (TOPS) [22]. Although WAVES can avoid preliminary estimates by using a beamforming invariance technique [23], its performance is worse than when it uses focusing matrices with good initial estimates [21].…”

“…Although WAVES can avoid preliminary estimates by using a beamforming invariance technique [23], its performance is worse than when it uses focusing matrices with good initial estimates [21]. The TOPS method is however categorized as incoherent method and hence can not replace coherent ones.…”