Improved Approximate QR-LS Algorithms for Adaptive Filtering

Abstract

This paper studies a class of ( ) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller.Index Terms-Adaptive filtering, approximate QR-LS algorithm, performance analysis, QR-LMS algorithm, square root free Givens based algorithms, transformed domain LMS algorithm.

High-Throughput FPGA Implementation of QR Decomposition

“…In this figure, two types of lines are described, dotted and continuous; each one represents a Givens rotation made simultaneously. In the first stage, two Givens rotations are performed concurrently, it takes the adjacent rows (1, 2) and (3,4). This means inserting two zeros in rows 2 and 4 as shown on the second stage.…”

“…Many examples of this are found in wireless communication, such as multipleinput-multiple-output (MIMO), beam-forming, multi-user detection and cancellation, etc [1]. One useful operator for these matrix operations is QR factorization, especially for MIMO technologies [2] [3] and adaptive filtering [4]. Some of this applications require high-throughput QR decomposition but are for small matrix sizes.…”

Improved Channel Estimation Algorithms based on a Proposed Signal Model for PUCCH Format 3 in LTE-A

“…In the case of PUCCH transmission, the length of the referencesignal sequence is thus always equal to 12 [1]. UE is based on the parameters configured by reference of network side and broadcast message to determine the parameters of DRMS, including group hopping number u 、 cyclic shift () p  and superimposed orthogonal sequences   p w .The demodulation reference signal sequence for PUCCH format 3 is defined by [8]: The DMRS location for PUCCH in the LTE-A can be seen from Table 2, showing that when UE adopts multiple antennas to transmit uplink control signal of PUCCH format 3, the location of reference signals are the same at the antenna port 0 p and 1 p --for normal CP, DRMS locates the first and fifth OFDM symbol in the each slot; while for the extended CP, DRMS locates the third OFDM symbol in the each slot.…”

Multi core processor for QR decomposition based on FPGA

“…It is used in many fields and the most important of these fields are wireless communication systems, such as beam-forming, multiple input and multiple output (MIMO), cancellation, multi-user detection and so on [1]. The most useful operator in algebraic matrix operations is the QR decomposition, especially for adaptive filtering [2] and MIMO technologies [3]. Some of these systems require high throughput of QR decomposition but they are for small sizes of matrices.…”