Optimum Array Processing with Variable Linear Constraint

If the desired signal is uncorrelated with incoming interference signals, a linearly constrained adaptive array successfully estimates the desired signal by reducing the interference signals [1]. If the desired signal is correlated partially or totally (i.e., coherent) with the interference signals, the desired signal is partially or totally cancelled in the array output depending on the extent of correlation between the desired signal and the interference signals. Some methods, such as the spatial smoothing approach [2, 3], master-slave type array processing [4], alternate mainbeam nulling method [5], and general linearly constrained adaptive array [6], have been proposed to prevent the signal cancellation phenomenon in a correlated signal environment. A drawback of the methods proposed in [2-5] is that they employ additional hardware or algorithms to reduce the effect of the coherent interferences. In this study, the general linearly constrained adaptive array is examined in the weight vector space to find the nulling performance in [6] in terms of the gain factor, which turns out to be the reduction of the gain in the look direction in the translated weight vector space. It is shown that the variation of the gain factor results in the variation of the distance between the constraint plane and the origin in the translated weight vector space, which has a geometric effect of shifting the constraint plane with respect to the origin. The simulation results are shown to illustrate the nulling performance with respect to the gain factor. It is shown that the general linearly constrained adaptive array performs better than the linearly constrained adaptive array with respect to the elimination of the coherent interferences.