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.

Square Root Modified Bryson–Frazier Smoother

Abstract: We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being positive semi-definite. Earlier algorithms implemented the computation of intermediate quantities in square root form but still computed the smoothed covariance as the difference of two matrices. We show how to compute the square root of the smoothed covariance by solving an equation in the form CCT=AAT-BBT using QR decomposition with hyperbolic Householder transformations.

Least squares computation at arbitrarily high speeds

Abstract: A technique is described which allows least squares computation to be made at arbitrarily high sampling rates, overcoming the inherent speed limitation due to the recursive algorithms. Previous efforts at high sampling rate systolic implementations of least squares problems have used Givens transformations and QR decomposition, achieving a sampling rate limited by the time required by several multiplication operations. Taking advantage of the linearity of the least squares recursion, the algorithms can be recast into a new realization for which the bound on throughput of least squares computation is arbitrarily high. The technique, which has previously been applied to adaptive lattice filters, is shown to be applicable to the matrix triangularization related problems such as solving general linear systems and computing eigenvalues by the QR algorithm.

A Comprehensive Self-Interference Model for Single-Antenna Full-Duplex Communication Systems

Abstract: Single-antenna full-duplex communication technology has the potential to substantially increase spectral efficiency. However, limited propagation domain cancellation of single-antenna system results in a higher impact of receiver chain nonlinearities on the residual self-interference (SI) signal. In this paper, we offer a comprehensive SI model for single-antenna full-duplex systems based on direct-conversion transceiver structure considering nonlinearities of all the transceiver radio frequency (RF) components, in-phase/quadrature (IQ) imbalances, phase noise effect, and receiver noise figure. To validate our model, we also propose a more appropriate digital SI cancellation approach considering receiver chain RF and baseband nonlinearities. The proposed technique employs orthogonalization of the design matrix using QR decomposition to alleviate the estimation and cancellation error. Finally, through circuit-level waveform simulation, the performance of the digital cancellation strategy is investigated, which achieves 20 dB more cancellation compared to existing methods.

Implementation of QR decomposition for MIMO-OFDM detection systems

Abstract: An improved implementation of QR decomposition for MIMO-OFDM detection based on the Givens rotation method is presented in this paper. The hardware of QR decomposition is constructed by coordinate rotation digital computer (CORDIC) operating with fewer gate counts and lower power consumption than triangular systolic array structures. In wireless communication systems, the accuracy for transmitting signals is essential. Thus, a better data detection algorithm and precise channel estimation method plays an important role here. The channel estimation implemented with QR decomposition is to reduce hardware complexity of MIMO-OFDM detection. The results of implementation reveal that the proposed QR decomposition architecture has shorter clock latency than folding structure and smaller hardware area than Gram-Schmidt.