Distributed adaptive algorithms for large dimensional MIMO systems

An algorithm for multi-input multi-output (MIMO) adaptive filtering is introduced that distributes the adaptive computation over a set of linearly connected computational modules. Each module has an input and an output and transmits data to and receives data from its nearest neighbor. A gradient-based algorithm for adapting the parameters in each module to minimize the global mean-squared error is derived using principles of back propagation. The performance surface is explored to understand the characteristics of the adaptive algorithm. The minimum mean-squared error is a many to one function of the parameters; therefore, upper bounds on each parameter are used to prevent excessive parameter drift and insure stability with fixed step sizes. Guidelines for choosing the LMS algorithm step sizes and initial conditions are developed. Several examples illustrate the performance of the algorithm.