Detecting Number of Coherent Signals in Array Processing by Ljung-Box Statistic

We investigate the detection of the number of coherent signals in array processing. Because of the rank deficiency of the coherent signal covariance matrix, the conventional approaches, exploiting the structures of the eigenvalues of the signal covariance matrix, are not applicable to the coherent case. We propose to use the whiteness of the residue to detect the number of coherent signals. The steps of the proposed approach include estimation of the signal parameters in the model, subtraction of the estimated signals from the observed sequences, and computation of the whiteness measure by the Ljung-Box statistic. The rationale of the proposed scheme and related issues, including direction of arrival estimation, complexities, and performance, are discussed. The proposed approach is simulated and compared with well-known approaches, including the Akaike information criterion and the minimum description length (MDL) and its recent versions MDLB and MDLC, through numerical examples. The effectiveness of the proposed approach is verified by the numerical examples of 2-, 3-, and 4-source signals.