MMSE Demodulator Simplification with Fast Numerical Algorithms

The demodulation algorithm, optimal for the criterion of the Minimum Mean Square Error (MMSE algorithm), is increasingly being used in various communication systems. This is due to its relative ease of implementation compared to other demodulation algorithms at an acceptable level of noise immunity. On the other hand, the MMSE demodulation algorithm is still too complicated for practical implementation with a high dimension of data symbol vector, which is typical for modern communication systems. Based on this, when developing promising communication systems, it is necessary to solve the problem of reducing the complexity of implementing the MMSE algorithm without reducing its noise immunity. The goal of this paper is the development of new implementation of MMSE demodulation algorithm. Various solutions of this problem have been proposed in the prior art. Basically, various approximate iterative implementations of the MMSE demodulation algorithm are also considered. These implementations allow a significant reduction in the complexity of the algorithm, but at the expense of a certain reduction in noise immunity. There are some well-known works that make it possible to reduce the computational complexity of the MMSE demodulation algorithm without loss in its noise immunity. This is due to the use of various fast algorithms for multiplying and complex matrices inversion. Using mentioned methodology, this work proposes a new, original, even more simplified, implementation of the MMSE demodulation algorithm, which uses a combination of fast Winograd and Strassen-Winograd matrix multiplication methods, as well as a modification of the Strassen method for inverting a complex matrix inversion. In the previous works of the authors, various options for simplifying the MMSE demodulation algorithm have been proposed. This paper shows that it is possible to get more than 2.5 times gain in the computational complexity of the MMSE demodulation algorithm.