In this paper, we present an analysis of a spatial smoothing scheme extended for the estimation of two-dimensional (2-D) directions of arrival (DOA's) of coherent signals using a uniform rectangular array. The uniform rectangular array is divided into overlapping rectangular subarrays by the extended scheme, which is referred to as the 2-D spatial smoothing scheme. The analysis shows that when the extended preprocessing scheme is used in conjunction with the eigenstructure technique, the size of the subarrays should be at least (K + 1) x (K + 1), and the number of the subarrays must be no less than K x K in order to guarantee the "decorrelation" of K coherent signals for all possible scenarios. The minimum size of the total uniform rectangular array is thus shown to be 2K x 2K. Instead of using a uniform rectangular array, a minimal subarray structure incorporated with a minimal subarray grouping is also devised for resolving the 2-D DOA's of K coherent signals. The number of sensor elements of the minimal total array is then (K2 + 4K - 2) instead of 4K2.