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.

Analysis and Architecture Design of a Downlink $M$ -Modification MC-CDMA System Using the Tomlinson–Harashima Precoding Technique

Abstract: This paper investigates the feasibility of applying Tomlinson-Harashima precoding (THP) to multicarrier code-division multiple-access (MC-CDMA) system downlinks, in which multiple-access interference and possible complexity in the mobile terminal (MT) are major burdens. A THP based on the minimum mean-square error (MMSE) criterion is also presented, making it possible to realize a low-complexity receiver at the MT. The hardware architecture of the MMSE THP with modified QR decomposition at the transmitter is presented, along with the required word length analyzed. Pipeline and parallel schemes are adopted to reduce the execution time. For a generic square matrix of order for RQ decomposition, the required latency is time units, which is based on the modified Gram-Schmidt algorithm.

Modal parameter estimation for stable filters

Abstract: A filter synthesizer and method are disclosed for generating and outputting a stable filter from frequency response data, including coherence values. A processing unit has a processor, memory, and stored programs. The processor, operating the modal analysis program, processes the frequency response data, generates orthogonal polynomial data from a cost function of the frequency response data including coherence values, and generates the modal parameters of a transfer function from the orthogonal polynomial data, which represents Forsythe polynomials. The processor generates the orthogonal polynomial data from least squares processing the cost function of the frequency response data, including coherence values. The processor generates the modal parameters, including a pole of the transfer function, and determines an instability condition from the pole. If a pole is unstable, the processor refits the frequency response data to generate a stable transfer function. A least squares optimization procedure is performed on the frequency response data, including the coherence values. A residue is generated corresponding to a pole, and the residue is revised in response to a condition of the pole being unstable. The modal parameters are generated by determining a companion matrix from the first orthogonal polynomial data and the frequency response data; performing QR decomposition on the companion matrix; and generating a pole as a eigenvalue of the companion matrix from the QR decomposition.

An mmse mimo decoder using qr decomposition

Abstract: Aspects of the disclosure provide unbiased channel equalization applied in a MIMO OFDM system with spatial multiplexing. According to certain embodiments, a MMSE receiver can be implemented with the QR decomposition (QRMMSE detection) instead of direct inversion of channel matrix by exploiting an augmented channel matrix. A simple and efficient bias removal technique is presented herein, whereby unbiased QRMMSE equalization may provide identical detection accuracy as a conventional unbiased MMSE approach. For certain embodiments, multiple access interference may be further reduced if the VBLAST version of the unbiased QRMMSE detection is applied.

A novel algorithm for calculating the QR decomposition of a polynomial matrix

Abstract: A novel algorithm for calculating the QR decomposition (QRD) of polynomial matrix is proposed. The algorithm operates by applying a series of polynomial Givens rotations to transform a polynomial matrix into an upper-triangular polynomial matrix and, therefore, amounts to a generalisation of the conventional Givens method for formulating the QRD of a scalar matrix. A simple example is given to demonstrate the algorithm, but also illustrates two clear advantages of this algorithm when compared to an existing method for formulating the decomposition. Firstly, it does not demonstrate the same unstable behaviour that is sometimes observed with the existing algorithm and secondly, it typically requires less iterations to converge. The potential application of the decomposition is highlighted in terms of broadband multi-input multi-output (MIMO) channel equalisation.

Orthogonal Reduction of Sparse Matrices to Upper Triangular Form Using Householder Transformations

Abstract: In this paper we consider the problem of predicting where fill-in occurs in the orthogonal decomposition of sparse matrices using Householder transformations. We show that a static data structure can be used throughout the numerical computation, and that the Householder transformations can be saved explicitly in a compact format.