The convergence rate performance of generalized sidelobe canceller

The least mean squares (LMS) algorithm is widely used in adaptive array systems since it can provide both low complexity and robust performance. However, the convergence rate of this gradient-descent based algorithm is governed by the eigenvalue spread of the autocorrelation matrix. The eigenvalue spread ratio (ESR) in a generalized sidelobe canceller (GSC) is derived. It can provide insight of how various parameters, related to an adaptive array system, affect the performance of the convergence rate. Finally, numerical and simulation results are used to verify that the derivation of ESR is correct.