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MMSE-Based Algorithm for Joint Signal Detection, Channel and Noise Variance Estimation for OFDM Systems

MMSE-Based Algorithm for Joint Signal Detection, Channel and Noise Variance Estimation for OFDM Systems

Vincent Savaux, Yves Louët

ISBN: 978-1-119-00508-7

Sep 2014, Wiley-ISTE

132 pages

Description

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
INTRODUCTION  ix

CHAPTER 1. BACKGROUND AND SYSTEM MODEL 1

1.1. Channel model 1

1.1.1. The multipath channel 1

1.1.2. Statistics of the channe l2

1.2. Transmission of an OFDM signal 7

1.2.1. Continuous representation 7

1.2.2. Discrete representation 9

1.2.3. Discrete representation under synchronization mismatch 12

1.3. Pilot symbol aided channel and noise estimation 12

1.3.1. The pilot arrangements 12

1.3.2. Channel estimation 15

1.3.3. Noise variance estimation 19

1.4. Work motivations 22

CHAPTER 2. JOINT CHANNEL AND NOISE VARIANCE ESTIMATION IN THE PRESENCE OF THE OFDM SIGNAL  25

2.1. Presentation of the algorithm in an ideal approach 25

2.1.1. Channel covariance matrix 25

2.1.2. MMSE noise variance estimation 27

2.1.3. Proposed algorithm: ideal approach 27

2.1.4. Simulation results: ideal approach 41

2.2. Algorithm in a practical approach 48

2.2.1. Proposed algorithm: realistic approach 48

2.2.2. Convergence of the algorithm 51

2.2.3. Simulations results: realistic approach 60

2.3. Summary  65

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

3.1. Spectrum sensing 67

3.1.1. Non-cooperative methods 69

3.1.2. Cooperative methods 71

3.2. Proposed detector 73

3.2.1. Detection hypothesis 73

3.2.2. Convergence of the MMSE-based algorithm under the hypothesis H0 74

3.2.3. Decision rule for the proposed detector 79

3.3. Analytical expressions of the detection and false alarm probabilities 82

3.3.1. Probability density function ofMunder H1 82

3.3.2. Probability density function ofMunder H0 85

3.3.3. Analytical expressions of Pd and Pfa 86

3.4. Simulations results 88

3.4.1. Choice of the threshold ς 88

3.4.2. Effect of the choice of eσ on the detector performance 89

3.4.3. Detector performance under non-WSS channel model and synchronization mismatch 92

3.4.4. Receiver operating characteristic of the detector  94

3.5. Summary  98

CONCLUSION  99

APPENDICES  101

BIBLIOGRAPHY  109

INDEX 119