Adaptively Optimizing the Algorithms for Adaptive Antenna Arrays for Randomly Time- Varying Mobile Communications Systems

Adaptive antenna arrays are widely used and have great promise to reduce the effects of interference and to increase capacity in mobile communications systems. Consider a single cell system with an (receiving) antenna array at the base station. The usual algorithms for obtaining the antenna weights for the adaptive array depend on parameters that are held fixed no matter what the operating situation, and the performance can strongly depend on the values of these parameters. For example, at time k, we might seek the antenna weights that minimize the performance function E ∑k l=1 α el , where el is the error in reception at sample time l. Typically, α < 1 to allow tracking as conditions change. The performance of the algorithm for adapting the weights in the antenna array depends heavily on the chosen value of the forgetting or discount factor α. Generally, the optimal value will change rapidly in time as the operating conditions change. In some cases (for example, where the Doppler frequency of the mobile being tracked oscillates), the optimal value of α will also oscillate. We are concerned with the adaptive optimization of such parameters by the addition of another adaptive loop. The antenna weights and the value of α must be adapted simultaneously. We give an algorithm for adapting α, which is based on an approximation to a natural “gradient descent” method. The algorithm is practical and can improve the operation considerably. This is justified via simulations under a variety of operating conditions. The algorithm tracks the optimal value of α very well, and always performs better than the algorithm that uses any fixed α, sometimes much better. The adaptation can be based on a pilot signal or it can be partially blind. The adaptive algorithm for the parameter can be analyzed via stochastic approximation (SA) theory, where the SA algorithm is that for adapting α. Methods