Adaptive optimization of least-squares tracking algorithms: with applications to adaptive antenna arrays for randomly time-varying mobile communications systems

Adaptive antenna arrays are used for reducing the effects of interference and increasing capacity in mobile communications systems. Typical algorithms recursively compute the antenna weights that minimize the weighted error function (at discrete times kh, k=1,2,..., for a sampling interval h) σ_l=1^kα^k-l[e_l(W)]², where e_l(W) is a measure of the reception error at time lh with antenna weight vector W, and α<1. The forgetting factor α<1 allows tracking as conditions change and the minimization is used only to get the weights. The average detection error rate depends heavily on the chosen value of α, whose optimal value can change rapidly in time, perhaps significantly in seconds. We add another adaptive loop that tracks the optimal value of α and greatly improves the operation when the environment is randomly time-varying. The additional adaptive loop is based on an approximation to a natural "gradient descent" method. The algorithm is practical and can improve the performance considerably. In terms of average detection error rates and for all of the scenarios tested, the new system tracks the optimal value of α well, and always performs better (sometimes much better) than the original algorithm that uses any fixed value of α. Although the initial motivation arises in adaptive antennas, the method can be used to improve algorithms for tracking parameters of time-varying nonlinear systems, where similar issues are involved.