Under-Determined DOA Estimation: A Method Based on Higher-Order Statistics and Non-Uniform Arrays

Direction of arrival (DOA) estimation is widely used in many applications. Traditional DOA estimation generally adopts the second-order statistics and the uniform linear array (ULA) structure. However, the second-order statistics and the uniform array structure restrict the number of DOAs that can be accurately estimated. In addition, the performance of the second-order statistics-based methods is sensitive to noise. As the wireless environment is becoming increasingly complex with the advent of the 5G era, the propagation channel can be composed of numerous paths. When the number of paths exceeds the size of the antenna array, DOA estimation becomes an under-determined problem, which the second-order statistics-based traditional methods fail to deal with. In order to address the under-determined DOA estimation problem, this paper proposes a method based on higher-order statistics and non-uniform array structure. Higher-order statistics-based methods can not only expand the array aperture, but also suppress the additive Gaussian noise. However, if combined with a uniform array structure, the degrees of freedom of the expanded array is limited. Therefore, we further adopt a non-uniform array structure and optimize its structure. Consequently, the proposed method is capable of achieving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M^{2}$ </tex-math></inline-formula>-level DOA estimation with an M-element array, while simultaneously providing good robustness to noise. For instance, using the proposed method, the DOAs of 20 incoming wave directions can be accurately estimated with a 6-antenna non-uniform array when the signal-to-noise ratio is as low as 0 dB.