Signal Correlation and DOA Estimation

In the model of Direction-Of-Arrival (DOA) estimation of narrowband signals, the concept of coherent signals seem more confused. In some published references, the signals of different frequency were simply considered as incoherent, whereas those of same frequency as coherent signals. So, those publications adopted the signals of different frequency to build the DOA estimation model of incoherent signals but the same center frequency in its directional matrix. This is considered unadvisable in this paper. If the center frequencies of the signals are different, the directional matrix should be built with correspond frequency of each signal source. The DOA should be estimated by the method for wideband signals, i.e., the different frequency should be gathered. The directional matrix built with the same center frequency is fitly the same as that of the gathered model. In result, its estimation result is correct, but the signal model does not match the fact. According to the strict definition of coherent signal, this paper proves that only the signals of the same frequency and original phase are coherent. Our conclusion is validated by computer simulation.