In massive MIMO systems, the high complexity of signal detection comes mainly from computing a Gram matrix and its inversion. In this correspondence, we propose a low-complexity MIMO detection method based on the Neum...
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In massive MIMO systems, the high complexity of signal detection comes mainly from computing a Gram matrix and its inversion. In this correspondence, we propose a low-complexity MIMO detection method based on the Neumann series (NS), which does not require explicitly computing the Gram matrix and its inversion. The proposed method leverages the statistical information of the Gram matrix to compute an initialization matrix, which guarantees the convergence of NS expansion. The signal detection is conducted implicitly by transforming matrixinversion and product operations into matrix-vector multiplication operations. By doing so, it reduces the computational complexity of MIMO signal detection from O(BU2 + U-3) to O(BUN), where B, U, and N are the numbers of antennas at the base station, at the user equipment, and NS terms, respectively. Simulation results show that, compared with existing approaches, the proposed method can significantly reduce the signal detection complexity while achieving similar performance.
Many of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrixinversion, which could be a trouble in the case of real-time implementation. This paper...
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Many of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrixinversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrixinversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrixinversion by multiple sums and the second methodology is based on an estimation of the matrixinversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
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