David E. Grant Jonathan H. Gross Mimi Z. Lawrence
Appl. Res. Labs., Univ. of Texas, P.O. Box 8029, Austin, TX 78713
Adaptive beamforming algorithms, which use CSM (cross-spectral matrix) data to calculate optimum weights, are sensitive to the number of unsmoothed CSM samples used in the CSM estimate. Assuming that the samples used in the CSM estimate are independent identically Gaussian distributed with zero mean, it is shown that the output power from the estimated CSM is biased low relative to the output power from the real CSM. Using data from a horizontal line array deployed in a shallow water, high noise environment, the adaptive beamformer output power with various numbers of samples used in the CSM estimate has been measured. The number of CSM samples was varied by changing the time--bandwidth product. The measured median beam noise levels are compared with the theory. Since the data do not fit the assumptions stated above, the agreement is not exact. However, the general trends of the data and theory agree quite well. Conclusions are drawn about the number of samples that should be used for a CSM estimate to be reliable, and about the stationarity of the data within the time-bandwidth integration used in the CSM estimates. [This work is supported by the U.S. Navy Space and Naval Warfare Systems Command.]