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769-779. , “Adaptive Nulling with Multiple-Beam Antennas,” IEEE Trans. , Vol. 26, No. 2, 1978, pp. 267-273. , and H. , New York: McGraw-Hill, 1984, Ch. 22, pp. 22-1-22-20. , “Maximizing Jammer Effectiveness for Evaluating the Performance of Adaptive Nulling Array Antennas,” IEEE Trans. , Vol. 33, No. 10, 1985, pp. 1131-1142. , “Interference Sources and Degrees of Freedom in Adaptive Nulling Antennas,” Technical Report 604, Lincoln Laboratory, Massachusetts Institute of Technology, May 12, 1982.
49) where P is the power received at each array element due to an interference source. These sources produce covariance matrix eigenvalues that are large compared to receiver noise, that is, λ >> 1. 50) That is, the eigenvalues are proportional to the incident interference power. 52) PN + 1 λ denote the normalized optimum signal matrix. 40) demonstrates that S n must be a unitary matrix with orthonormal columns, thus the signal matrix S is an orthogonal matrix, meaning that the sources are orthogonal.
One result is that only when the two sources are orthogonal with equal power does the array fail to provide any adaptive cancellation. For an arbitrary adaptive antenna with a given interference signal matrix, a figure of merit was derived to determine how to minimize the difference between the signal matrix and a desired unitary matrix. The figure of merit is used in a gradient search to automatically rearrange a given source distribution to a distribution that minimizes this difference and thus, it is assumed, maximizes consumption of degrees of freedom.