Direction Finding With Partly Calibrated Uniform Linear Arrays in Nonuniform Noise

We recently proposed an ESPRIT-like method for direction finding with partly calibrated uniform linear arrays. It has been shown that the unknown gains/phases and direction-of-arrivals (DOAs) can be estimated jointly. However, this approach relies on the assumption of uniform white noise, i.e., all sensor noise powers are identical. Besides, at most M - 2 sources can be handled for an M-element array. This motives us to develop enhanced methods for circumventing the limitations above. This paper extends the uniform white noise to nonuniform noise on one hand, and, on the other hand, allows us to estimate up to M - 1 DOAs of uncorrelated signals. More exactly, for uncorrelated signals, the array can be calibrated according to the specific structure of the array covariance matrix, and the nonuniformity of sensor noises can then be simply eliminated by reformulating the calibrated array covariance matrix. For correlated signals, the nonuniformity of sensor noises is mitigated by solving a least squares minimization problem, such that the signal/noise subspace can be properly determined. Thus, our previously developed ESPRIT-like approach can be adopted to determine the DOAs. The effectiveness of the proposed methods is confirmed by numerical examples.