Coarray LMS: Adaptive Underdetermined DOA Estimation With Increased Degrees of Freedom

Underdetermined direction of arrival (U-DOA) estimation refers to the ability to estimate the DOA of more sources than the number of sensors in an array. Usually, to perform U-DOA estimation, the difference coarray of the physical array is utilized in techniques like coarray MUSIC. However, existing U-DOA estimation techniques are computationally expensive. To tackle this issue, in this work, we introduce a computationally efficient adaptive filtering technique that is capable of resolving more sources than the number of sensors. The proposed adaptive algorithm utilizes the second-order statistics of the source signals captured by the coarray along with the least mean square (LMS) principle to perform U-DOA estimation. The coarray sensor at the zeroth location is used as a reference coarray sensor and the positive part of the coarray is used as an auxiliary coarray. The auxiliary coarray signal is passed through a linear filter and an error signal of the adaptive process is generated by subtracting the filter output from the reference coarray signal. The error is then minimized iteratively to obtain the final filter weights. The filter is then used to calculate a novel spatial spectrum whose peaks give the estimate of the DOAs. A polynomial rooting version of the proposed algorithm is also introduced. Simulations show the efficacy of the proposed method.