A new method is proposed to estimate the direction‐of‐arrivals (DOAs) of multiple narrow‐band signals using a co‐prime array (CPA). The CPA is divided into two uniform linear arrays (ULAs) and two polynomials are derived by utilising the unitary transformation technique on the covariance matrices of these two ULAs. Rather than rooting the two polynomials straightforwardly, their first‐order derivatives are exploited to construct a new difference polynomial, and DOAs are uniquely estimated without ambiguity by finding the roots of this difference polynomial that lie closest to the unit circle. The new technique shows improved accuracy with reduced complexity as compared to most state‐of‐the‐art methods, which are verified by numerical simulations.

A second forward/backward (SFB) averaging technique is presented to transform the real symmetrical covariance matrix of the popular unitary root-MUSIC (U-root-MUSIC) into a real bisymmetrical one, based on which a SFB-U-root-MUSIC direction of arrival (DOA) estimation algorithm with reduced computational complexity is developed. The proposed SFB-U-root-MUSIC algorithm reduces the computational complexity in the eigenvalue decomposition (EVD) stage by a factor about four because it performs real-valued EVDs on two sub-matrices of about half sizes. The proposed SFB averaging technique is further extended as a generalized dimension reduction method to other unitary DOA estimators for low-complexity EVD computation, and numerical simulations are conducted to demonstrate such a dimension reduction technique sacrifices statistically nonsignificant root mean square (RMSE) performance that is acceptable.

Most popular techniques for super-resolution direction of arrival (DOA) estimation rely on an eigen-decomposition (EVD) or a singular value decomposition (SVD) computation to determine the signal/noise subspace, which is computationally expensive for real-time applications. A two-step root multiple signal classification (TS-root-MUSIC) algorithm is proposed to avoid the complex EVD/SVD computation using a uniform linear array (ULA) based on a mild assumption that the number of signals is less than half that of sensors. The ULA is divided into two subarrays, and three noise-free cross-correlation matrices are constructed using data collected by the two subarrays. A low-complexity linear operation is derived to obtain a rough noise subspace for a first-step DOA estimate. The performance is further enhanced in the second step by using the first-step result to renew the previous estimated noise subspace with a slightly increased complexity. The new technique can provide close root mean square error (RMSE) performance to root-MUSIC with reduced computational burden, which are verified by numerical simulations.

A low-complexity algorithm is presented to dramatically reduce the complexity of the multiple signal classification (MUSIC) algorithm for direction of arrival (DOA) estimation, in which both tasks of eigenvalue decomposition (EVD) and spectral search are implemented with efficient real-valued computations, leading to about 75% complexity reduction as compared to the standard MUSIC. Furthermore, the proposed technique has no dependence on array configurations and is hence suitable for arbitrary array geometries, which shows a significant implementation advantage over most state-of-the-art unitary estimators including unitary MUSIC (U-MUSIC). Numerical simulations over a wide range of scenarios are conducted to show the performance of the new technique, which demonstrates that with a significantly reduced computational complexity, the new approach is able to provide a close accuracy to the standard MUSIC.