The optimal focusing subspace for coherent signal subspace processing

say, the center frequency of the spectrum of the signals, and transform the subspace at each frequency bin into the subspace created by the span of the location vectors at the focusing frequency. Then, they use a high-resolmion algorithm such as MUSIC [SI to estimate the DOA's of the sources. They show that focusing reduces the resolution threshold signal-to-noise ratio (SMZ), which is defined as the SNR for a prescribed probability of resolution. They also show that if the integral of the signal covariance matrix taken over the frequency specwm is full rank, the method can be applikd to coherent signal localization. Hupg and Kaveh [5] use a unitary variant of the CSM algorithm to avoid the focusing loss. They use the center frequency for focusing. Swingler and Krolik [9] prove that for h single-source scenario, it is possible to have an unbiased estimate of The DOAk if the centroid of the source spectrum is selected as the focising frequency. In [lo], we showed that for multiple sources, the CSEVI algorithm cannot provide unbiased estimates of the DOA's. In this work, we propose a method to select the focusing subspace. The method is based on minimizing a subspace fitting error. The subspace fitting error for each frequency bin is defined as the distance between the focusing matrix and the rransfomed location matrix. Later, we minimize a tight bound to the error. The simulation results show that using the method proposed here reduces the resolution threshold S N R and the bias of the DOA's estimates.