Fast eigen-based signal combining algorithms for large antenna arrays

A large array of small antennas can be used to enhance signals with very low signal-to-noise ratio and can also be used to replace large apertures. In this paper, a fast combining algorithm is proposed and analyzed to maximize the combined output signal-to-noise ratio. Our approach does not assume any sequence of trained symbols and is a blind combining technique, which does not require a priori knowledge of spacecraft's or the array's spatial information. Our method for computing the optimal weight is based on the generalized Eigen theory and the algorithms are built upon the Power method. Unique advantages of our proposed algorithm include (i) no formation of covariance matrices and hence less storage is required (ii) the optimal weight is obtained with significant less efforts and thus the optimal weight can be attained more quickly (iii) our proposed algorithm is capable of handling the case when the symbol signal-to-noise-ratios at the receivers are very weak. Mathematical framework for large antenna arrays using the Eigen-based signal combining techniques along with detailed performance analysis, numerical algorithms and computer simulations are presented.