Detection of number of uncorrelated and coherent narrowband signals with L-shaped sensor array

This paper deals with the problem of estimating the number of mixed narrowband signals of uncorrelated and coherent signals impinging on the L-shaped sensor array, which is structured by two uniform linear arrays (ULAs). Since the total number of incident signals can be estimated as the rank of a combined matrix formed from the cross-correlations between the received data of two ULAs, and the number of uncorrelated signals can be obtained from rank of the cross-covariance matrix of two ULAs, a new QR-based detection method without eigendecomposition is proposed to estimate the number of incident signals and that of uncorrelated signals from the values of the running indexes of two ratio criteria for which the criteria are maximized, where the criteria are formed from the elements of QR upper-triangular factors of the autoproducts of two aforementioned matrices. The statistical analysis clarifies that the proposed detection is asymptotically consistent. Furthermore the effectiveness of proposed method is confirmed through numerical examples.