New Analysis of the Adaptive Array Performance in the Presence of Multiple Interfering Sources

Adaptive array weight adjustment algorithms are described by time varying stochastic differential equations. A new method employing a two-variable perturbation analysis is used to investigate the effects of the weight fluctuations on the Applebaum algorithm performance in the presence of multiple jammers. An explicit solution of the directivity pattern in the direction of the jammers for the two-jammer problem is derived. An improved formula for the output signal-to-interference plus noise ratio (SINR) is obtained. It is shown as expected that the greater the number of signals at the array input the greater the degradation in the directivity pattern in the direction of the interfering signals and the greater the degradation in the output SINR. In addition, we show that the performance degrades uncontrollably when the number of independent jammers approaches the number of array elements. A comparison is made of the new results and those obtained using standard approximations. Substantial differences are caused by first-order terms in the perturbation.