Topic
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.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: It is shown for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius √m2+n2 (m,n integers) needs to be used.
Abstract: Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius √m2+n2 (m,n integers) needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.
16 citations
••
TL;DR: An efficient compressed sensing method to solve the measurements of delay and Doppler spreading in underwater acoustic channels (UACs) by inserting a projection matrix that adopts QR decomposition for an efficient computation is proposed.
Abstract: The measurements of delay and Doppler (DD) spreading in underwater acoustic channels (UACs) have multiple applications, including communications as well as the development of a dynamic UAC simulator. However, these measurements suffer from the difficulties of fast time variations and large data sets. This paper addresses an efficient compressed sensing (CS) method to solve these problems. First, the DD spreading in UACs is studied by using a doubly spread model; second, the least-square criterion is implemented and its limit is analyzed. Subsequently, the matching pursuit (MP) method is applied to the problem by exploiting the sparsity of the DD model-based UACs. Although the MP method improves the performance of the LS method, it has unavoidable deficiencies, e.g., the redundant selections of bases that lead to a limited measurement of DD spreading. Thus, this paper proposes an improved version by inserting a projection matrix. The projected MP (PMP) method adopts QR decomposition for an efficient computation. Finally, at-sea data-based comparisons among the abovementioned three methods are conducted to verify the superiority of the PMP method.
16 citations
••
04 Dec 2007TL;DR: A FPGA implementation of a 4 times 4 MIMO MMSE Equalizer based on the QR factorization technique is presented using only 6 unrolled coordinate rotation digital computer (CORDIC) operators, which are efficiently exploited to minimize the latency of computation.
Abstract: In this paper a FPGA implementation of a 4 times 4 MIMO MMSE Equalizer based on the QR factorization technique is presented. Considering fast varying channels a new filter is computed at each new channel realization thanks to an efficient architecture of matrix triangularization. The QR decomposition is performed with only 6 unrolled coordinate rotation digital computer (CORDIC) operators, which are efficiently exploited to minimize the latency of computation. Soft LLR obtained in output of the equalizer are validated on an FPGA hardware bench including a 4 times 4 Rayleigh fading channel and turbo- coding.
16 citations
••
01 Nov 2010TL;DR: The proposed Givens-Rotation-based QR decomposition algorithm features efficient parallel processing with sorting function that resolves the trade-off between the detection performance and hardware utiliztion efficiency.
Abstract: Due to the growing demand of transmission capacity of the wireless communication system, multiple-input multiple-output orthogonal-frequency-division-multiplexing (MIMO-OFDM) communication system requires more and more MIMO antennas and a large number of OFDM subcarriers. Thus, the QR decomposition becomes one of the computational bottlenecks in the QR-based MIMO detection. The proposed Givens-Rotation-based QR decomposition algorithm features efficient parallel processing with sorting function that resolves the trade-off between the detection performance and hardware utiliztion efficiency. According to the algorithm, we designed and implemented a 2×2∼8×8 QR decomposition processor using TSMC 0.18/μm 1P6M CMOS technology. The throughput of the QR decomposition processor achieves 6.8×104 SQRD per second, which outperforms other works in the literature after being normalized by the MIMO dimension.
16 citations
••
TL;DR: In this article, it was shown that any orthogonal transformation is the product of at most two Orthogonal Involutions, which implies that we can write any transformation as a product of two InVIs.
Abstract: The purpose of the present note is to give a partial answer to a question raised by Professor Coxeter, namely, if an orthogonal transformation is expressed as a product of orthogonal involutions, how many involutions do we need? Our answer is partial because we are going to consider only non-degenerate symmetric bilinear forms of index 0 and fields of characteristic ≠2. Under these conditions we prove that any orthogonal transformation is the product of at most two orthogonal involutions, which implies that we can write any orthogonal transformation as the product of two involutions.
16 citations