The CRB on wideband direction of arrival estimation under the background of colored noises

The CRB on wideband direction of arrival (DOA) estimation of multi-source under the background of colored noises is deduced. According to the expression, the characteristics of wideband CRB and the factors related to the performance of DOA estimation are presented: the wideband CRB of single source can be divided into two items, and one depends on signal characteristics, which include the second frequency moment of the power spectrum ratio of signals to noises, time width of each frequency snapshot, and snapshots number etc. The other one lies on the array geometry composed of array manifold, DOA, the position of reference point and so on. Under the background of white Gaussian noises (WGN), the factors related to the former part can be simplified as the second frequency moment of signal, SNR and snapshots number. According to the CRB expression, not only the best performance of wideband DOA estimation algorithms is given, but also some useful guidance is provided from the point to improve the performance of DOA estimation.