Steady state analysis of the generalized sidelobe canceller by adaptive noise cancelling techniques

Narrow-band adaptive noise cancelling techniques are used to study the generalized sidelobe canceller (GSC), a general form of linearly constrained adaptive beamforming structure. In an environment which consists of a look-direction signal, one jammer, and additive receiver noise, exact expressions are derived for the Wiener solution, the steady state output signal-to-interference-plus-noise ratio (SINR0), and performance improvement due to adaptation (PIA), defined as the ratio of SINR0after adaptation to SINR0 before adaptation. These expressions are in terms of the signal directions and power levels, an arbitrary array geometry, and a general signal blocking matrix. Next, easily evaluated scalar equations for PIA are given for two classes of constraints. The first is constant gain in the look direction, and the second is constant gain plus a main beam zero first derivative in the look direction. Under the further assumption of an equally spaced line array, even simpler equations for PIA result, and are used to show that for jammers arriving outside the heamwidth between first nulls (BWFN) region of the unadapted beampattern, the introduction of the additional main beam zero first derivative constraint leads to negligible degradation in PIA.