On the stability of adaptive antenna arrays with weights at an intermediate frequency

This paper focuses on the stability problem that exists in adaptive antenna arrays when the weighting functions operate at a nonzero frequency. It begins with the application of the LMS algorithm when the weights are written in terms of an in-phase and a quadrature component. The behavior of the signal processing algorithm is then described by a set of coupled differential equations which are derived under zero-delay conditions. When time delays that may be present in the feedback loops due to filtering are taken into account, the stability and therefore the performance of the array are greatly affected. This paper shows how stability can be achieved by a simple time-compensation procedure. Simulation results show that interference rejection comparable to the zero-delay case is experienced. The importance of this study is twofold: (1) it is an analytical supplement to an experimental array built with the same type of weights, and (2) it provides the condition of stability that will allow a digital implementation of the weight processor.