An Implementation of MMSE Demodulation Algorithm with Reduced Computational Complexity and without Performance Loss

The estimation (demodulation) algorithm, optimal for the criterion of the minimum mean square error (MMSE algorithm), is very often used various areas. In the process of developing communication systems, there is a problem data dimension increase. As a result, the dimension of the matrices and vectors included in the MMSE algorithm increases. This, in turn, leads to an increase in the load on computing devices that implement signal processing algorithms, including the MMSE algorithm. Therefore, it needs to reduce the complexity of the MMSE algorithm while maintaining its noise immunity. The paper proposes a new simplified implementation of the MMSE algorithm, based on the use of various known fast algorithms for multiplying complex numbers and matrices, as well as matrix inversion. In this case, if possible, the properties of matrices are used, for example, the properties of Hermitian and symmetry. In the previous work of the authors, a simplified implementation of the MMSE algorithm has already been proposed. This work proposes its further development. The approach to implementing the MMSE algorithm described in this work allows to reduce a computational complexity in 1.3 … 2.15 times (with dimensions of matrices and vectors from 32 to 1024) compared to its traditional implementation without using fast algorithms. The additional gain in computational complexity is 1.07 … 1.15 times. These gains are due only to the organization of the computational process and are achieved without reducing the noise immunity of the MMSE algorithm.