QR decomposition

About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.

QR decomposition and Gram Schmidt Orthogonalization based low-complexity multi-user MIMO precoding

Abstract: Block diagonalization (BD) is a well-known linear precoding scheme for multi-user multiple-input multipleoutput (MU-MIMO) downlink transmission. BD precoding achieves good performance but results in high computational complexity overheads due to two singular value decomposition (SVD) operations for each user. By replacing the first SVD operation with a less complex solution, the QR decomposition based block diagonalization (QRBD) precoding scheme reduces the computational complexity. In this paper, we present a QR decomposition and Gram Schmidt Orthogonalization (QR-GSO) based MUMIMO precoding scheme as a new approach for MUMIMO downlink transmission. The proposed scheme introduces an improved QR decomposition and Gram Schmidt Orthogonalization method to significantly reduce the computational complexity. Our results show that the proposed QR-GSO precoding scheme achieves the same performance as BD and QR-BD precoding schemes, while requiring much lower computational complexity.

Symbol detector and sphere decoding method

Abstract: A QR decomposer performs a QR decomposition process on a channel response matrix to generate a Q matrix and an R matrix. A matrix transformer generates the inner product matrix of the Q matrix and the received signal. A scheduler reorganizes a search tree, and decomposes the search into a plurality of independent branches. A plurality of Euclidean distance calculators is controlled by the scheduler to operate in parallel, each having a plurality of calculation units cascaded in a pipeline structure to search for the maximum likelihood solution based on the R matrix and the inner product matrix.

Power Reduction through Upper Triangular Matrix Tracking in QR Detection MIMO Receivers

Abstract: QR decomposition is a computationally intensive process often required for MIMO detection. A technique that allows a reduction in the computational complexity of MIMO QR detection receivers is proposed for non-stationary channel . The technique involves tracking of the upper triangular matrix and reduction of the frequency of QR decomposition. This reduction comes at the cost of increased equalization error from the outdated Q matrix that must be used between successive QR decompositions. When compared to the similar setup but with the channel matrix tracking, the proposed method yields 33% computational complexity reduction without any loss of performance.

MMSE SQRD based SISO detection for coded MIMO-OFDM systems

Abstract: In this paper, we propose a minimum mean square error (MMSE) sorted QR decomposition (SQRD) based soft-input soft-output (SISO) detection algorithm for coded multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The proposed detection is derived from the SISO MMSE detection, which is a popular detection strategy for iterative receivers. For each transmitted symbol in the proposed detection, a soft successive interference cancellation (SIC) is performed based on a posteriori probabilities of past detected symbols. Simulation results show that the proposed detection, while needing less computational efforts, achieves significant performance gain compared with the SISO MMSE detection.

Two resultant based methods computing the greatest common divisor of two polynomials

Abstract: In this paper we develop two resultant based methods for the computation of the Greatest Common Divisor (GCD) of two polynomials. Let S be the resultant Sylvester matrix of the two polynomials. We modified matrix S to S*, such that the rows with non-zero elements under the main diagonal, at every column, to be gathered together. We constructed modified versions of the LU and QR procedures which require only the of floating point operations than the operations performed in the general LU and QR algorithms. Finally, we give a bound for the error matrix which arises if we perform Gaussian elimination with partial pivoting to S*. Both methods are tested for several sets of polynomials and tables summarizing all the achieved results are given.