# QR-RLS Based Adaptive Channel TEQ for OFDM Wireless LAN

07 Feb 2008-pp 46-51

TL;DR: Q-RLS based adaptive channel TEQ (Time Domain Equalizer) to make the OFDM systems robust for delay spreads exceeding the CP is presented and simulation results show that this method gives better results as compared to the aforementioned methods.

Abstract: In this paper, QR-RLS based adaptive channel TEQ (Time Domain Equalizer) to make the OFDM systems robust for delay spreads exceeding the CP (cyclic prefix) is presented. The performance of the proposed method is compared with standard LMS and exponentially weighted RLS based TEQ, in terms of computational complexity and BER. QR decomposition using Givens transformation results in better computational complexity compared to standard RLS and QRD based on gram Schmidt orthogonalization process. The simulation results show that this method gives better results as compared to the aforementioned methods.

##### Citations

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24 May 2009

TL;DR: Implementation of an iterative QR decomposition (QRD) (IQRD) architecture based on the modified Gram-Schmidt (MGS) algorithm is proposed in this paper and the hardware is constructed by the diagonal and the triangular process with fewer gate counts and lower power consumption.

Abstract: Implementation of iterative QR decomposition (QRD) architecture based on the modified Gram-Schmidt (MGS) algorithm is proposed in this paper. In order to achieve computational efficiency with robust numerical stability, a triangular systolic array (TSA) for QRD of large size matrices is presented. Therefore, the TSA architecture can be modified into iterative architecture for reducing hardware cost that is called iterative QRD (IQRD). The IQRD hardware is constructed by the diagonal process (DP) and the triangular process (TP) with fewer gate counts and lower power consumption than TSAQRD. For a 4×4 matrix, the hardware area of the proposed IQRD can reduce about 76% of the gate counts in TSAQRD. For a generic square matrix of order n IQRD, the latency required is 2n−1 time units, which is based on the MGS algorithm. Thus, the total clock latency is only n(2n+3) cycles.

51 citations

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01 Jan 2016

TL;DR: Applying this scheme in real MDM systems can produce more cost effective and smaller digital signal processing parts for MDM equipment and can accelerate the work on the standardization of MDM for being commercially used as a multiplexing technique for optical communication networks.

Abstract: Optical networks is considered as the main backbone networks that handled the Internet traffic worldwide. Currently, the Internet traffic has had huge annual growth due to the increment in connected devices. At this rate, it is believed that the current technology in optical network will not able to handle this growth in the near future. Till recently, multiplexing techniques in the optical communication rely on modulation techniques
where polarization, amplitude and frequency of the signal are used as the main data carrier. In these techniques, light modes are considered as an undesired effect causing modal dispersion. In contrast, mode division multiplexing (MDM) was introduced as a multiplexing approach which relies on the utilization of the light modes for the benefit of increasing the capacity-distance product of the optical network. As per any new technology, it is still facing a lot of problems preventing it from being commercially standardized and used. One of the main MDM issues is the mode coupling,
which is an inventible phenomena occurs when the energy of one mode transfers to another mode during their propagation throughout the optical fibre causes inter-symbol interference (ISI), increasing the bit error rate (BER) and reducing the overall system performance. Different equalization schemes have been proposed so far attempting to mitigate the effect of mode coupling on the MDM optical signal. However, they suffer from high computational complexity and rely on training signals in estimating the optical channel which increases the overhead payload. These technique mainly rely on Least Mean Squared (LMS) and Recursive Least Squared (RLS) algorithms. The purpose of this study is to introduce a Zero Forcing LU-based equalization scheme for MDM.
Previous research in the radio domain on multiple-input multiple output (MIMO) and orthogonal frequency division multiplexing (OFDM) demonstrated that zero forcing schemes have low computational complexity compared to current schemes as they
equalize the signal without training signals, thus reducing the overhead payload. All of the previous points motivate the work of this study to adapt this approach in optical communications. The study adopts the four stages of the Design Research Methodology (DRM). The initial data was collected from the optical simulator, processed and used to derive the transfer function (H) of the system. Then it was used to develop the equalization scheme in MATLAB. The experimentation on Zero Forcing LU based equalization scheme shows O(N) complexity which is lower than RLS which has O(N2) and faster than LMS, in fact, LMS needs an average of 0.0126 seconds to process the signal while ZF LU-based needs 0.0029 seconds only. On the other hand, the proposed equalization reduces the time delay
spread of the channel, resulting three times increment in the capacity of the MDM channel
and even lower computational complexity. The main contribution of this study is the reduction of the computational complexity of the previous equalization schemes in MDM. Applying this scheme in real MDM systems can produce more cost effective and smaller digital signal processing (DSP) parts for MDM equipment and can accelerate the work
on the standardization of MDM for being commercially used as a multiplexing technique
for optical communication networks.

3 citations

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27 Jun 2010

TL;DR: In this article, a novel method for OFDM-MIMO channel estimation using QR-RLS(square root-recursive least square) estimator is presented, which uses QR-factorization of the correlation matrix and thus avoids square matrix inverse results in less computations as well as less roundoff error.

Abstract: In this paper, A novel method for OFDM-MIMO channel estimation using QR-RLS(Square Root-Recursive Least Square) estimator is presented. Preamble aided channel estimation is performed in time-domain, estimated channel is then used for data detection during data transmission within that frame. The performance results are compared with wiener RLS channel estimator in terms of channel estimator MSE performance. Wiener based Standard-RLS estimator uses correlation matrix inverse for estimation and recursion, Correlation matrix may become singular under low noise/high correlated channels, results in round-off error. On the other hand, Square-Root estimator use QR-factorization of the correlation matrix and thus avoids square matrix inverse results in less computations as well as less round-off error. The simulation results shows that square root QR-RLS estimator give better results in terms of Estimation error.

3 citations

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TL;DR: In this article, the authors proposed a new scheme to overcome the high computation complexity problem, both in the derivation of TEQ and in the operation of channel shortening, by using a multistage structure, replacing a high order TEQ with a cascade of several low-order TEQs.

Abstract: In an orthogonal frequency division multiplexing (OFDM) system, it is known that when the delay spread of the channel is larger than the cyclic prefix (CP) size, intersymbol interference will occur. The time-domain equalizer (TEQ), designed to shorten the channel impulse response (CIR), is a common device to solve this problem. Conventionally, the TEQ is treated as a finite-impulse-response (FIR) filter, and many TEQ design methods have been proposed. However, a wireless channel typically has multi-path responses, exhibiting FIR characteristics. Thus, the corresponding TEQ will have an infinite impulse response (IIR), and the FIR modeling of the TEQ is inefficient, i.e., the required order for the TEQ will be high. The conventional approach will then suffer from the high computation complexity problem, both in the derivation of TEQ and in the operation of channel shortening. In this paper, we propose a new scheme to overcome these problems. In the derivation of the TEQ, we propose to use a multistage structure, replacing a high-order TEQ with a cascade of several low-order TEQs. In the shortening operation, we propose to use an IIR TEQ approximating a high-order FIR TEQ. Since the ideal TEQ exhibits low-order IIR characteristics, the order of the IIR TEQ can be much lower than the FIR TEQ. Simulations show that while the proposed method can reduce computational complexity significantly, its performance is almost as good as existing methods.

1 citations

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##### References

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01 Jan 1986

TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.

Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.

16,058 citations

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31 Dec 1999

TL;DR: In this paper, the authors present a comprehensive introduction to OFDM for wireless broadband multimedia communications and provide design guidelines to maximize the benefits of this important new technology, including modulation and coding, synchronization, and channel estimation.

Abstract: From the Book:
The manifestations of the mode of goodness can be experienced when all the gates of the body are illuminated by knowledge
The Bhagavad Gita (14.11)
During the joint supervision of a Master's thesis "The Peak-to-Average Power Ratio of OFDM," of Arnout de Wild from Delft University of Technology, The Netherlands, we realized that there was a shortage of technical information on orthogonal frequency division multiplexing (OFDM) in a single reference. Therefore, we decided to write a comprehensive introduction to OFDM. This is the first book to give a broad treatment to OFDM for mobile multimedia communications. Until now, no such book was available in the market. We have attempted to fill this gap in the literature.
Currently, OFDM is of great interest by the researchers in the Universities and research laboratories all over the world. OFDM has already been accepted for the new wireless local area network standards from IEEE 802.11, High Performance Local Area Network type 2 (HIPERLAN/2) and Mobile Multimedia Access Communication (MMAC) Systems. Also, it is expected to be used for the wireless broadband multimedia communications.
OFDM for Wireless Multimedia Communications is the first book to take a comprehensive look at OFDM, providing the design guidelines one needs to maximize benefits from this important new technology. The book gives engineers a solid base for assessing the performance of wireless OFDM systems. It describes the new OFDM-based wireless LAN standards; examines the basics of direct-sequence and frequency-hopping CDMA, helpful in understanding combinations of OFDM and CDMA. It also looks at applications of OFDM, includingdigital audio and video broadcasting, and wireless ATM. Loaded with essential figures and equations, it is a must-have for practicing communications engineers, researchers, academics, and students of communications technology.
Chapter 1 presents a general introduction to wireless broadband multimedia communication systems (WBMCS), multipath propagation, and the history of OFDM. A part of this chapter is based on the contributions of Luis Correia from the Technical University of Lisbon, Portugal, Anand Raghawa Prasad from Lucent Technologies, and Hiroshi Harada from the Communications Research Laboratory, Ministry of Posts and Telecommunications, Yokosuka, Japan.
Chapters 2 to 5 deal with the basic knowledge of OFDM including modulation and coding, synchronization, and channel estimation, that every post-graduate student as well as practicing engineers must learn. Chapter 2 contains contributions of Rob Kopmeiners from Lucent Technologies on the FFT design.
Chapter 6 describes the peak-to-average power problem, as well as several solutions to it. It is partly based on the contribution of Arnout de Wild.
Basic principles of CDMA are discussed in Chapter 7 to understand multi carrier CDMA and frequency-hopping OFDMA, which are described in Chapters 8 and 9. Chapter 8 is based on the research contributions from Shinsuke Hara from the University of Osaka, Japan, a postdoctoral student at Delft University of Technology during 1995-96, Chapter 9 is based on a UMTS proposal, with main contributions of Ralf Bohnke from Sony, Germany, David Bhatoolaul and Magnus Sandell from Lucent Technologies, Matthias Wahlquist from Telia Research, Sweden, and Jan-Jaap van de Beek from Lulea University, Sweden.
Chapter 10 was written from the viewpoint of top technocrats from industries, government departments, and policy-making bodies. It describes several applications of OFDM, with the main focus on wireless ATM in the Magic WAND project, and the new wireless LAN standards for the 5 GHz band from IEEE 802.11, HIPERLAN/2 and MMAC. It is partly based on contributions from Geert Awater from Lucent Technologies, and Masahiro Morikura and Hitoshi Takanashi from NTT in Japan and California, respectively.
We have tried our best to make each chapter quite complete in itself This book will help generate many new research problems and solutions for future mobile multimedia communications. We cannot claim that this book is errorless. Any remarks to improve the text and correct any errors would be highly appreciated.

4,000 citations

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19 Apr 1996

TL;DR: The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering.

Abstract: From the Publisher:
The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering. Scores of worked examples illustrate fine points, compare techniques and algorithms and facilitate comprehension of fundamental concepts. Also features an abundance of interesting and challenging problems at the end of every chapter.

2,495 citations

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Tellabs

^{1}TL;DR: Various methods of determining the coefficients for this time-domain finite impulse response (FIR) filter are explored and an optimal shortening and a least-squares approach are developed for shortening the channel's impulse response.

Abstract: In discrete multitone (DMT) transceivers an intelligent guard time sequence, called a cyclic prefix (CP), is inserted between symbols to ensure that samples from one symbol do not interfere with the samples of another symbol. The length of the CP is determined by the length of the impulse response of the effective physical channel. Using a long CP reduces the throughput of the transceiver, To avoid using a long CP, a short time-domain finite impulse response (FIR) filter is used to shorten the effective channels impulse response. This paper explores various methods of determining the coefficients for this time-domain filter. An optimal shortening and a least-squares (LS) approach are developed for shortening the channel's impulse response. To provide a computationally efficient algorithm a variation of the LS approach is explored. In full-duplex transceivers the length of the effective echo path impacts the computational requirements of the transceiver. A new paradigm of joint shortening is introduced and three methods are developed to jointly shorten the channel and the echo impulse responses in order to reduce the length of the CP and reduce computational requirements for the echo canceller.

548 citations

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TL;DR: It is shown that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity, and a new characterization of the optimum delay is described and shown how to compute it.

Abstract: A unified approach for computing the optimum settings of a length-N/sub f/ input-aided equalizer that minimizes the mean-square error between the equalized channel impulse response and a target impulse response of a given length N/sub b/ is presented. This approach offers more insight into the problem, easily accommodates correlation in the input and noise sequences, leads to significant computational savings, and allows us to analyze a variety of constraints on the target impulse response besides the standard unit-tap constraint. In particular, we show that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity. Furthermore, we show that, under the assumed constraint of finite-length filters, the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance. We describe a new characterization of the optimum delay and show how to compute it. Finally, we derive reduced-parameter pole-zero models of the equalizer that achieve the high performance of a long all-zero equalizer at a much lower implementation cost.

245 citations

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