Equivalent MIMO Channel Matrix Sparsification for Enhancement of Sensor Capabilities
Abstract
:1. Introduction
- capital letter, e.g., used for matrices;
- : determinant of a matrix;
- : trace of a matrix;
- : Cholesky decomposition of a matrix;
- : transpose of matrix ;
- : inverse of a matrix ;
- : modulo of ;
- : block-component matrix of matrix V;
- : the prior distribution;
- : the equivalent likelihood function.
2. Representation of the MIMO Channel Matrix in the Sparse Format
3. Methods for the Approximation of the Channel Matrix by a Sparse Matrix
3.1. Kullback Distance for the Approximated Channel Model
3.2. Diagonal Matrix Approximation
3.3. Block Diagonal Matrix Approximation
3.4. Strip Matrix Approximation
3.5. Approximation by a Markov Process
- Algorithm with a block-diagonal matrix—“block”;
- Algorithm with a strip matrix and the calculation of the coefficients of the sparse matrix by the method of stochastic optimization—“Opt.”;
- Algorithm with approximation by a Markov process—“Markov’s”.
- These curves are shown for three options of symbols ordering:
- Without ordering—“without order”;
- Simple ordering—“simple order”. In this option, the symbol with the highest total power of all mutual correlation coefficients is put in the first place, and the rest are arranged in descending order of the magnitudes of their mutual correlation coefficients with the first symbols;
- Serial ordering—“serial order”. In this option, the symbol with the highest total power of (m − 1) cross-correlation coefficients is selected, and a set of (m − 1) symbols having the maximum correlation with the first symbol is set. Next, from this set, the second symbol is selected, with the largest total power of (m − 1) cross-correlation coefficients, where (m − 2) symbols are already specified and are taken from the set (except for the first and second selected symbols) and one symbol is selected from the rest, not included in this set. Then, the third symbol is determined according to the same principle, etc.
4. Modeling and Verification
- “Opt.”—optimal soft MIMO demodulator for the exact model (1);
- “MMSE”—MMSE demodulator for the exact model. It also corresponds to the variant of the channel model approximation by a diagonal matrix (Section 3.1);
- “Block”—a demodulator using an approximated block-diagonal MIMO channel model (Section 3.2; Equations (21) and (25)) with a block size of 2 × 2, with an optimal demodulator for each block;
- “Band, Stoh., Opt”—a demodulator using a striped two-diagonal MIMO channel model (Section 3.3; Equation (28)), in which the parameters of the striped channel matrix are calculated by the stochastic optimization method and the optimal demodulator for this model is used;
- “Markov’s, Turbo det”—a Markov approximation of the channel model (Section 3.4) with connectivity parameters and iterative detection using the method of equivalent likelihood functions (Equations (47) and (50)) and the principle of Turbo processing (two iterations);
- “Band, Stoh., MPA det”—iterative MPA detector (three iterations) using a two-diagonal striped MIMO channel model (Section 3.3), in which the channel strip matrix parameters are calculated by the stochastic optimization method.
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Conflicts of Interest
References
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Bakulin, M.; Kreyndelin, V.; Melnik, S.; Sudovtsev, V.; Petrov, D. Equivalent MIMO Channel Matrix Sparsification for Enhancement of Sensor Capabilities. Sensors 2022, 22, 2041. https://doi.org/10.3390/s22052041
Bakulin M, Kreyndelin V, Melnik S, Sudovtsev V, Petrov D. Equivalent MIMO Channel Matrix Sparsification for Enhancement of Sensor Capabilities. Sensors. 2022; 22(5):2041. https://doi.org/10.3390/s22052041
Chicago/Turabian StyleBakulin, Mikhail, Vitaly Kreyndelin, Sergei Melnik, Vladimir Sudovtsev, and Dmitry Petrov. 2022. "Equivalent MIMO Channel Matrix Sparsification for Enhancement of Sensor Capabilities" Sensors 22, no. 5: 2041. https://doi.org/10.3390/s22052041