A note on spatially weighted subarray covariance averaging schemes

In spatial smoothing, the effective correlation among the impinging sources goes to zero only asymptotically with the number of subarrays. K. Takao and N. Kimura (ibid., vol.AP-35, p.1389-96, Dec. 1987) and A. Paulraj et al. (IEEE J. Ocean Eng., vol.OE-12, p.163-72, Jan. 1987) proposed Toeplitzization and adaptively weighted subarray covariance averaging methods, respectively, wherein the impinging sources are perfectly decorrelated whenever the number of subarrays exceeds a minimum value. While both methods achieve the same result, the formulations of the two methods are different. The present work first suggests an alternate formulation of the same problem and then compares the three methods showing that the solutions obtained by them are equivalent