Computationally Efficient Algorithms For Super-resolution DOA Estiamtion Based On Spectral Compression Thoery

The years since the publication of the Multiple Signal Classification (MUSIC)algorithm have witnessed a growing research interest in super-resolution techniquesfor estimating the direction of arrival (DOAs) of multiple signals. With more thanthirty years of great developments, brilliant achievements have been published forsuper-resolution DOA estimate. Unfortunately, growing examinations demonstratethat most of the state-of-the-art approaches in fact suffer from poor robustness,prohibitive computational complexity and fatal dependence on array configurationsin engineering, although they indeed perform almost perfectly in laboratories.Aiming to make super-resolution estimators more implemental in practice, thispaper, which is supported by the national project, considers the problem of DOAestimation with the concerns of low computational cost as well as no dependence onarray geometries, showing numerical novel algorithms for super-resolution DOAestimate as well as offering a theoretical basis for real-world applications. The pri-mary contributions of this paper can be summarized as follows:A new concept of symmetrical compressed (SC) spectral is proposed based onthe idea of mirror virtual sources, giving a SC-MUSIC estimator for finding1-DDOAs of multiple narrow-band signals. Like the conventional MUSIC, SC-MUSICis suitable for arbitrary linear array structures, but it involves a factor2on the red-uction of complexity. Numerical simulations illustrate that SC-MUSIC also showsimproved resolution probability for closely-spaced sources as compared to MUSIC.SC-MUSIC is extended to estimate2D DOAs with arbitrary plane array geometriesbased on another newly developed concept of transformed domain DOA (TD-DOA),leading to a corresponding2D-SC-MUSIC algorithm accordingly.The non-asymptotic performance of SC-MUSIC is theoretically analyzed byusing the theory of subspace perturbation and Taylor’s expansion series, for whichtwo approaches convenient for computing the noise subspace of SC-Musicale alsopresented. These two methods are referred to as sum-decomposition algorithm andproduct-decomposition algorithm, respectively. With the above results, the unbiase-dness and consistency of SC-MUSIC are theoretically proved. Furthermore, a clos-ed-form expression is derived to predict the Mean Square Error (MSE) of DOA es- timate by SC-MUSIC, which agrees closely with simulations.A novel concept of High-order compressed (HC) spectral is proposed based onseveral key techniques including spatial dividing, subspace mapping and TD-DOA,leading to two promising estimators named HC-MUSIC and2D-HC-MUSIC, res-pectively. Although HC-MUSIC can be taken as a further developed version of SC-MUSIC, the former shows a much better efficiency to the latter, and the foundationsof the two algorithms are significantly different. During the derivations of HC-MU-SIC, two new methods for calculating the noise subspace of HC-MUSIC are pres-ented, which are named as continuous sum-decomposition algorithm and continuousproduct-decomposition algorithm, respectively. Compared with existent techniques,the proposed approaches involve much lower computational load, and can be alsoused with more scenarios.The unbiasedness, consistency as well as the MSE for DOA estimation by HC-MUSIC is asymptotically analyzed with a finite number of snapshots, based on con-tinuous sum-decomposition algorithm. Furthermore, the relationship between MSEfor DOA estimate by conventional MUSIC and that by the newly proposed HC-MU-SIC estimator is theoretically discussed.A new concept of DOA estimate with semi-real-valued operations is proposedby combining real-valued computations with arbitrary array structures, leading totwo novel efficient estimators named SU-MUSIC algorithm and Capon-Like tech-nique, respectively. Both the two methods exploit results behind only either the realpart-or the imaginary part-of the array output covariance matrix (AOCM), givingequivalent reductions on complexity as well as much more applicability on arrayconfigurations as compared to their real-valued versions. Besides, numerical resultsproduced during the derivations of SU-MUSIC and Capon-Like estimators firstlyreveals the mathematical relationships among the subspace decomposition-and theinverse-on the entire AOCM as well as those on only the real part-or the imaginarypart-of AOCM.