MMSE-Based Algorithm for Joint Signal Detection, Channel and Noise Variance Estimation for OFDM Systems E-Book
Vincent Savaux
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book presents an algorithm for the detection of an orthogonal frequency division multiplexing (OFDM) signal in a cognitive radio context by means of a joint and iterative channel and noise estimation technique. Based on the minimum mean square criterion, it performs an accurate detection of a user in a frequency band, by achieving a quasi-optimal channel and noise variance estimation if the signal is present, and by estimating the noise level in the band if the signal is absent.
Organized into three chapters, the first chapter provides the background against which the system model is presented, as well as some basics concerning the channel statistics and the transmission of an OFDM signal over a multipath channel. In Chapter 2, the proposed iterative algorithm for the noise variance and the channel estimation is detailed, and in Chapter 3, an application of the algorithm for the free-band detection is proposed. In both Chapters 2 and 3, the principle of the algorithm is presented in a simple way, and more elaborate developments are also provided. The different assumptions and assertions in the developments and the performance of the proposed method are validated through simulations, and compared to methods of the scientific literature.
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Seitenzahl: 116
Veröffentlichungsjahr: 2014
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Contents
Introduction
1 Background and System Model
1.1. Channel model
1.2. Transmission of an OFDM signal
1.3. Pilot symbol aided channel and noise estimation
1.4. Work motivations
2 Joint Channel and Noise Variance Estimation in the Presence of the OFDM Signal
2.1. Presentation of the algorithm in an ideal approach
2.2. Algorithm in a practical approach
2.3. Summary
3 Application of the Algorithm as a Detector for Cognitive Radio Systems
3.1. Spectrum sensing
3.2. Proposed detector
3.3. Analytical expressions of the detection and false alarm probabilities
3.4. Simulations results
3.5. Summary
Conclusion
Appendices 1 Appendix to Chapter 2
Appendices 2 Appendix to Chapter 3
Bibliography
Index
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
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www.iste.co.uk
John Wiley & Sons, Inc.
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USA
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
Introduction
The wireless communications field is facing a constant increase in data-rate-consuming transmissions, due to the multitude of services and applications enabled by advanced devices. Moreover, the users expect a good reliability while demanding increasingly mobility. Figure I.1 illustrates this constant evolution for mobile communications, from the “archaic” (from the present point of view) first generation (1G) telecommunications standard in the 1980s to the fourth generation (4G) today, and the fifth generation (5G) tomorrow. This evolution is made feasible by means of a constant improvement of the networks, the devices and the embedded algorithms. In this context, this book provides an original solution improving the quality of the received signal due 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 over a multipath channel. This kind of channel induces frequency fading, i.e. some holes in the signal spectrum that may be destructive for the signal. The multi-carrier modulations are a good solution for fighting against this fading, since the data is spread into a large number of subcarriers in a given channel. Among them, the orthogonal frequency division multiplexing (OFDM) is widely used in a large number of standards for wireless communications (e.g. Digital Video Broadcasting (DVB) [ETS 04] or Wireless Fidelity (Wi-Fi) IEEE 802.11) and for wired communications (e.g. digital subscriber line (xDSL)) as well. This craze for OFDM is mainly due to the fact that a simple one-tap-per-carrier equalization can be performed at the receiver to invert the channel and limit the errors in the transmitted signal. Thus, the equalization performance is directly linked to the accuracy of the channel estimation. That is why the channel estimation process plays a key role in the performance of any wireless communication system.
Figure I.1.Evolution of the mobile communications from 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 the mean square error. However, its practical implementation is limited since it requires the second-order moments of the channel and the noise knowledge, which are a priori unavailable at the receiver side. The algorithm originally proposed in [SAV 12, SAV 13a] and detailed in this book solves this problem by iteratively estimating the noise level and the channel frequency response, each parameter feeding the estimation process of the other parameter. In addition to the estimation, the proposed technique allows the receiver to detect the presence and absence of an OFDM signal in a given band. In the present wireless communication networks, the opportunistic spectrum access enabled by an accurate free-band detection seems to be a very promising solution to the increase in data rate-consuming transmissions. Thus, the proposed algorithm performs two key roles at the receiver side of an OFDM transmission. For a practical implementation, it results in a benefit in terms of space in the device, complexity and, thus, energy consumption.
This book is organized into three chapters. Chapter 1 is a background in which the system model is presented, and some basics concerning the channel statistics and the transmission of an OFDM signal over a mutlipath channel are recalled. In Chapter 2, the proposed iterative algorithm for the noise variance and the channel estimation is detailed. Two cases are considered: an ideal case in which the channel covariance matrix is supposed to be known at the receiver as originally presented in [SAV 12] and a realistic case in which this matrix is estimated as in [SAV 13a]. In Chapter 3, an application of the algorithm for the free-band detection is proposed. In both Chapters 2 and 3, the principle of the algorithm is presented in a simple way, and more elaborate developments (e.g. the proofs of convergence and the theoretical probability density functions) are also provided. The different assumptions and assertions in the developments and the performance of the proposed method are validated through simulations, and compared to methods of the scientific literature.
1
Background and System Model
In this first chapter, some basics regarding the propagation channel and the wireless transmission of an orthogonal frequency division multiplexing (OFDM) signal are recalled. Moreover, a brief state of the art of the pilot aided channel estimation methods is provided. Although the latter cannot be exhaustive, it covers some relevant techniques, in particular in an OFDM context.
1.1. Channel model
1.1.1. The multipath channel
The transmission channel (or propagation channel) is the environment situated between the transmitting and the receiving antennas. Whether an indoor or outdoor environment is considered, the signal transmitted over the channel suffers from some perturbations of different kinds: reflection, diffraction or diffusion. These phenomena are due to obstacles in the propagation environment, like buildings or walls. Besides, the transmitter, the receiver or both of them may be in motion, which induces Doppler effect.
In certain contexts, the transmitter and the receiver are in line of sight (LOS), so the channel is not destructive for the signal. On the contrary, in non-line of sight (NLOS) transmissions, the signal goes through several paths before reaching the receiving antenna. In that case, the propagation environment is called a multipath channel, and is mathematically written as a sum of weighted delayed Dirac impulses δ(τ):
[1.1]
where the channel impulse response (CIR) h(t, τ) depends on the number of paths L, the complex gains hl and the delays τl. In this work, we will instead take an interest in NLOS transmissions. The channel frequency response (CFR) is obtained from [1.1] by means of the Fourier transform (FT) operation denoted by FT:
[1.2]
where the subscript in FT(.) denote the variable on which the Fourier transform is processed. Figure 1.1 illustrates this relationship ((a): h(t, τ), and (b): H(t, f)). We can observe that the FT is made on the delay τ, which makes the frequency response H(t, f) a time-varying function. When the channel does not vary, it is called static, and when the variations are very slow, the channel is called quasi-static. In this book, we will assume the latter scenario.
1.1.2. Statistics of the channel
1.1.2.1. Rayleigh channel
As numerous natural phenomena, the transmission channel is subject to random variations. Therefore, the instantaneous CIR [1.1] and CFR [1.2] are not sufficient to completely describe the channel. It becomes relevant to use the statistical characterization of the CIR and the CFR to study this random process.
Figure 1.1.Illustration of a time-varying impulse response h(t, τ) and a frequency response H(t, f) of a multipath channel. For a color version of the figure, see www.iste.co.uk/savaux/mmse.zip
In an NLOS transmission, due to the channel, the signal comes from all possible directions at the receiving antenna that is assumed to be isotropic. Thus, each delayed version of the received signal is considered as an infinite sum of random components. By applying the central limit theorem, h(t) is then a zero-mean Gaussian complex process whose gain |h(t)| follows a Rayleigh distribution [PAT 99] pr, Ray(r) of variance :
[1.3]
where r is a positive real value. The probability density function (PDF) of the phase of a Rayleigh process follows a uniform distribution, noted pϕ, Ray (θ):
[1.4]
The Rayleigh channel model is very frequently used, particularly in theoretical studies, since it is relatively close to reality, and the literature on Rayleigh distribution is very extensive. For these reasons, Rayleigh channels are considered all along this work. However, it does not cover all the possible scenarios: in a LOS context, the direct path adds a constant component to the previous model. In that case, |h(t)| follows a Rice distribution, which is described in [RIC 48]. More recently, the Weibull model [WEI 51] has been proposed in order to describe real channel measurements with more accuracy. Nakagami model [NAK 60], later generalized in [YAC 00] by the κ − μ distribution, is also a global model from which Rayleigh’s and Rice’s are particular cases.
1.1.2.2. WSSUS model
The channel being a time-frequency varying random process, it is relevant to characterize it through its first and second-order statistic moments. According to Bello’s work [BEL 63], let us assume a wide sense stationary uncorrelated scattering (WSSUS) model, defined as follows:
[1.5]
Each path hl(t) of the channel is then wide sense stationary.
[1.6]
This model is used in the following to apply the proposed detection and channel estimation algorithm. However, it does not necessarily match the reality, so we will also study the performance of the proposed method under channel model mismatch, particularly in Chapter 3.
Let us also define two very useful statistical functions that characterize the channel along the delay and the frequency axes:
These two functions are linked by Fourier transform:
[1.7]
Figure 1.2 depicts the decreasing intensity profile and the real and imaginary parts of the frequency correlation function.
Figure 1.2.Link between the channel intensity profile and the frequency correlation function
1.2. Transmission of an OFDM signal
When combined with a channel coding, the transmission of data using a frequency multiplexing is very robust against the frequency selective channels, in comparison with single-carrier modulations [SCO 99, DEB]. The use of orthogonal subcarriers has been proposed since the 1950s, in particular for military applications, but the acronym OFDM appeared in the 1980s, when the evolution of the technology of semiconductors enabled a great development of the implementation of complex algorithms, especially the algorithms based on large size FFT/IFFT. This kind of modulation is now used in a large number of wired and wireless transmission standards.
1.2.1. Continuous representation
In the continuous formalism, the baseband OFDM signal is written as:
[1.8]
where sn(t) is the nth OFDM symbol, Π(t) is the rectangular function of duration Ts as
[1.9]
[1.10]
[1.11]
So as to cancel the intersymbol interferences (ISIs) due to the delayed paths of the channel, the solution consists of adding a guard interval (GI) at the head of each OFDM symbol. If the GI length is greater than the maximum delay of the channel, it contains all the interferences from the previous symbol, and the GI removal cancels the ISI. In the following, let us assume that the GI is a cyclic prefix, i.e. the end of each OFDM symbol is copied at its head. As noted later, in addition to the ISI cancellation, the use of a CP gives a cyclic structure to the OFDM symbols. Let us denote by TCP the duration of the CP.
Figure 1.3 shows the effects of the channel on the OFDM signal in the time and the frequency domains. Figure 1.3(a) illustrates, in the time domain, the ISI cancellation due to the CP removal. The frequency orthogonality is displayed in Figure 1.3(b). The robustness of the OFDM against the multipath channel lies in the fact that, by considering a sufficiently small intercarrier spacing Fs
