Use of shanks transformation for speeding up adaptation process in antenna arrays

Use of the Shanks transformation is considered for speeding up optimization of the weight vector during adaptation in antenna arrays by the method of steepest descent. The transient process for each weight factor is evaluated accordingly as the sum of m exponent terms, m being smaller than or equal to the number of adaptation channels and 2m+1 readings of the mean weight vector sufficing for determination of its optimum value. Since it is not possible to estimate exactly the optimization error as a function of the deviations from the mathematical expectations of weight factors and as a function of the transient response parameters, this is done only approximately: with m+1 readings during the transient period and with a Shanks transformation based on three readings. A theoretical analysis reveals that the error can be large, determined principally by the smallest eigenvalue of the correlational interference matrix. Numerical simulation and a comparative analysis of the results reveal how much faster the algorithm of the Shanks transformation converges than other adaptation algorithms such as those of the instantaneous mean, the sliding mean, and independent averaging.