MMSE-based Algorithm forJoint Signal Detection,

Channel and NoiseVariance Estimation for

OFDM Systems

FOCUS

Vincent Savaux and Yves Louët

WAVES SERIES

MMSE-based Algorithm for Joint Signal Detection, Channel and

Noise Variance Estimation for OFDM Systems

FOCUS SERIES

Series Editor Bernard Dubuisson

MMSE-based Algorithm for Joint Signal Detection, Channel and Noise Variance Estimation

for OFDM Systems

Vincent Savaux Yves Louët

First published 2014 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA

www.iste.co.uk www.wiley.com

© ISTE Ltd 2014 The rights of Vincent Savaux and Yves Louët to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2014945529 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISSN 2051-2481 (Print) ISSN 2051-249X (Online) ISBN 978-1-84821-697-6

Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . ix

CHAPTER 1. BACKGROUND AND SYSTEM MODEL . . 1

1.1. Channel model . . . . . . . . . . . . . . . . . . . . . 11.1.1. The multipath channel . . . . . . . . . . . . . . 11.1.2. Statistics of the channel . . . . . . . . . . . . . 2

1.2. Transmission of an OFDM signal . . . . . . . . . 71.2.1. Continuous representation . . . . . . . . . . . 71.2.2. Discrete representation . . . . . . . . . . . . . . 91.2.3. Discrete representation under

synchronization mismatch . . . . . . . . . . . . 121.3. Pilot symbol aided channel and noise estimation 12

1.3.1. The pilot arrangements . . . . . . . . . . . . . . 121.3.2. Channel estimation . . . . . . . . . . . . . . . . 151.3.3. Noise variance estimation . . . . . . . . . . . . 19

1.4. Work motivations . . . . . . . . . . . . . . . . . . . 22

CHAPTER 2. JOINT CHANNEL AND NOISEVARIANCE ESTIMATION IN THE PRESENCE OF THEOFDM SIGNAL . . . . . . . . . . . . . . . . . . . . . . . . 25

2.1. Presentation of the algorithm in an idealapproach . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.1.1. Channel covariance matrix . . . . . . . . . . . 252.1.2. MMSE noise variance estimation . . . . . . . 27

vi MMSE-based Algorithm for Joint Signal Detection

2.1.3. Proposed algorithm: ideal approach . . . . . . 272.1.4. Simulation results: ideal approach . . . . . . . 41

2.2. Algorithm in a practical approach . . . . . . . . . 482.2.1. Proposed algorithm: realistic approach . . . . 482.2.2. Convergence of the algorithm . . . . . . . . . . 512.2.3. Simulations results: realistic approach . . . . 60

2.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . 65

CHAPTER 3. APPLICATION OF THE ALGORITHM ASA DETECTOR FOR COGNITIVE RADIO SYSTEMS . . . 67

3.1. Spectrum sensing . . . . . . . . . . . . . . . . . . . 673.1.1. Non-cooperative methods . . . . . . . . . . . . 693.1.2. Cooperative methods . . . . . . . . . . . . . . . 71

3.2. Proposed detector . . . . . . . . . . . . . . . . . . . 733.2.1. Detection hypothesis . . . . . . . . . . . . . . . 733.2.2. Convergence of the MMSE-based algorithm

under the hypothesis H0 . . . . . . . . . . . . . 743.2.3. Decision rule for the proposed detector . . . . 79

3.3. Analytical expressions of the detection and falsealarm probabilities . . . . . . . . . . . . . . . . . . . 82

3.3.1. Probability density function of M under H1 . 823.3.2. Probability density function of M under H0 . 853.3.3. Analytical expressions of Pd and Pfa . . . . . 86

3.4. Simulations results . . . . . . . . . . . . . . . . . . 883.4.1. Choice of the threshold ς . . . . . . . . . . . . . 883.4.2. Effect of the choice of eσ on the detector

performance . . . . . . . . . . . . . . . . . . . . . 893.4.3. Detector performance under non-WSS

channel model and synchronization mismatch 923.4.4. Receiver operating characteristic of the

detector . . . . . . . . . . . . . . . . . . . . . . . . 943.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . 98

Contents vii

CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . 99

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . 101

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . 109

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Introduction

The wireless communications field is facing a constantincrease in data-rate-consuming transmissions, due to themultitude of services and applications enabled by advanceddevices. Moreover, the users expect a good reliability whiledemanding increasingly mobility. Figure I.1 illustrates thisconstant evolution for mobile communications, from the“archaic” (from the present point of view) first generation(1G) telecommunications standard in the 1980s to the fourthgeneration (4G) today, and the fifth generation (5G)tomorrow. This evolution is made feasible by means of aconstant improvement of the networks, the devices and theembedded algorithms. In this context, this book provides anoriginal solution improving the quality of the received signaldue to a quasi-optimal channel and noise level estimation,and the detection of a multi-carrier signal in a given band.

In wireless communications, the signal is transmitted overa multipath channel. This kind of channel induces frequencyfading, i.e. some holes in the signal spectrum that may bedestructive for the signal. The multi-carrier modulations area good solution for fighting against this fading, since the datais spread into a large number of subcarriers in a givenchannel. Among them, the orthogonal frequency divisionmultiplexing (OFDM) is widely used in a large number of

x MMSE-based Algorithm for Joint Signal Detection

standards for wireless communications (e.g. Digital VideoBroadcasting (DVB) [ETS 04] or Wireless Fidelity (Wi-Fi)IEEE 802.11) and for wired communications (e.g. digitalsubscriber line (xDSL)) as well. This craze for OFDM ismainly due to the fact that a simple one-tap-per-carrierequalization can be performed at the receiver to invert thechannel and limit the errors in the transmitted signal. Thus,the equalization performance is directly linked to theaccuracy of the channel estimation. That is why the channelestimation process plays a key role in the performance of anywireless communication system.

Figure I.1. Evolution of the mobile communicationsfrom the 1G to 4G and beyond

The linear minimum mean square error (LMMSE) method[EDF 98] is the optimal channel estimator in the sense of themean square error. However, its practical implementation islimited since it requires the second-order moments of thechannel and the noise knowledge, which are a prioriunavailable at the receiver side. The algorithm originallyproposed in [SAV 12, SAV 13a] and detailed in this booksolves this problem by iteratively estimating the noise level

Introduction xi

and the channel frequency response, each parameter feedingthe estimation process of the other parameter. In addition tothe estimation, the proposed technique allows the receiver todetect the presence and absence of an OFDM signal in agiven band. In the present wireless communication networks,the opportunistic spectrum access enabled by an accuratefree-band detection seems to be a very promising solution tothe increase in data rate-consuming transmissions. Thus, theproposed algorithm performs two key roles at the receiverside of an OFDM transmission. For a practicalimplementation, it results in a benefit in terms of space inthe device, complexity and, thus, energy consumption.

This book is organized into three chapters. Chapter 1 is abackground in which the system model is presented, andsome basics concerning the channel statistics and thetransmission of an OFDM signal over a mutlipath channelare recalled. In Chapter 2, the proposed iterative algorithmfor the noise variance and the channel estimation is detailed.Two cases are considered: an ideal case in which the channelcovariance matrix is supposed to be known at the receiver asoriginally presented in [SAV 12] and a realistic case in whichthis matrix is estimated as in [SAV 13a]. In Chapter 3, anapplication of the algorithm for the free-band detection isproposed. In both Chapters 2 and 3, the principle of thealgorithm is presented in a simple way, and more elaboratedevelopments (e.g. the proofs of convergence and thetheoretical probability density functions) are also provided.The different assumptions and assertions in thedevelopments and the performance of the proposed methodare validated through simulations, and compared to methodsof the scientific literature.