Low-complexity quick parallel matrix inversion method

Abstract

The invention discloses a low-complexity quick parallel matrix inversion method. The method comprises the following steps that first, a matrix A is given, a matrix E is made to be a unit matrix with the same order as the matrix A, the matrix A and the matrix E form an expanding matrix B, modified Givens rotation (MSGR, Modified Square Givens Rotations) is carried out on the matrix B, an upper triangular matrix U and , wherein according to the define of the matrix U and , an SGR (Squared Givens Rotations) method is used for deforming the QR division of the matrix A according to the equation, and the relation between the QR division and original QR division meets the equations , , , and ; according to the MSRG method, the square root operation in the process of Givens rotation can be omitted while division operation is reduced, and algorithm complexity is obviously reduced; second, a back substitution method is used for working out the inverse matrix U-1 of the upper triangular matrix U; third, matrix inversion is carried out according to the equation . According to the low-complexity quick parallel matrix inversion method, a large amount of division operation and a large amount of square root operation are omitted, algorithm complexity is reduced, and the method can be used for matrix inversion of the fields of wireless communication, signal processing and numerical calculation.

Description

technical field [0001] The invention relates to a low-complexity fast parallel matrix inversion method for removing square root operations and reducing division operations, and mainly relates to the fields of wireless communication, signal processing, numerical calculation and the like. Background technique [0002] With the continuous development of wireless communication technology, users have higher and higher requirements for the reliability and effectiveness of the communication system. In order to increase the transmission rate of the system and increase the spectrum efficiency of the system, the multiple input multiple output (Multiple Input Multiple Output, MIMO) technology has been extensively researched as a key technology. Wireless communication standards such as IEEE802.11n, IEEE802.11ac, IEEE 802.11ad, and 3GPP-LTE all adopt MIMO technology. [0003] The design of the MIMO communication system at the receiving end is quite complicated. Channel estimation at th...

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Problems solved by technology

[0003] MIMO communication system, the design at the receiving end is quite complicated

Channel estimation at the receiving end will involve a large number of matrix inversion operations, especially as the number of transmitting antennas and receiving antennas increases, the dimension of the matrix also increases, and the computational complexity of matrix inversion will also increase greatly, resulting in matrix inversion. The difficulty of inverse algorithm design and hardware implementation has been greatly increased, which has become a technical problem to be solved urgently in the current MIMO system

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