Master of Science Thesis in Electrical Engineering Department of Electrical Engineering, Linköping University, 2018 Reducing Effects of Multipath Propagation With A Blind Equalizer Emma Söderström Master of Science Thesis in Electrical Engineering Reducing Effects of Multipath Propagation With A Blind Equalizer Emma Söderström LiTH-ISY-EX--18/5171--SE Supervisor: Kamil Senel isy, Linköpings universitet Mattias Avesten SAAB Aeronautics Rikard Bergsten SAAB Aeronautics Examiner: Mikael Olofsson isy, Linköpings universitet Division of Communicationsystems Department of Electrical Engineering Linköping University SE-581 83 Linköping, Sweden Copyright © 2018 Emma Söderström Abstract When transmitting data from an aircraft being prepared at the apron (the area in front of the hangar) telemetry data is transmitted to ground personnel. The transmitted data is subject to severe distortion due to multipath propagation cre- ated by the surroundings, resulting in erroneous detection. By equalizing the signal using the Constant Modulus Algorithm a significant increase in detection performance has been observed, both in simulations and tests on collected data. The most sufficient parameters were chosen after testing a set of different param- eter combinations on simulations with single delays. These parameters were then used to equalize simulated multipath as well as collected data. The results show that short delays with low power can be resolved without any equalizer. Longer delays with relatively low power can be resolved using the proposed equalizer but long delays with high power cannot be resolved by the equalizer at all. The thesis shows that it is worth investigating implementation of the equalizer. iii Contents List of Figures vii List of Tables ix Notation xi 1 Introduction 1 1.1 Motivation . 1 1.2 Purpose . 3 1.3 Problem statement . 3 1.4 Limitations . 4 1.5 Thesis outline . 4 2 Theory 5 2.1 Basic Concepts . 5 2.1.1 The Telemetry System . 5 2.1.2 Line Codes . 5 2.1.3 Randomizers . 7 2.1.4 Numerically Controlled Oscillators . 8 2.1.5 Analog Modulation . 9 2.1.6 Mixers . 12 2.2 Complex Matrix Calculus . 12 2.3 Multipath Propagation . 13 2.3.1 Fading Channel Model . 13 2.3.2 Multipath Effects on Frequency Modulated Signals . 14 3 Channel Equalization 17 3.1 Equalizers . 17 3.1.1 Linear Adaptive Equalization Using Training Symbols . 19 3.1.2 Linear Adaptive Blind Equalization . 19 3.1.3 Equalizing PCM/FM . 19 3.1.4 Previous Research . 20 3.1.5 The Constant Modulus Algorithm . 20 v 4 Method 23 4.1 Test Bed . 23 4.1.1 Current Telemetry System . 23 4.1.2 Communication Model . 24 4.1.3 CMA Parameters . 25 4.2 Equalizer Analysis . 26 4.2.1 Simulation Setup . 26 4.2.2 Simulation correctness . 26 4.2.3 Test Cases . 27 4.2.4 Test on Real Data . 28 5 Results 31 5.1 Simulation Correctness . 31 5.2 Single Delays . 32 5.3 Multiple Delays . 34 5.4 Test on Real Data . 35 6 Discussion 39 6.1 Results . 39 6.1.1 Simulation Correctness . 39 6.1.2 Single Delays . 39 6.1.3 Multiple Delays . 40 6.1.4 Simulation Results in Relation to the Apron . 42 6.1.5 Real Data . 42 6.2 Method . 43 6.3 A wider perspective . 44 7 Conclusion 45 7.1 Future work . 45 A Communication Model Listings 49 B Simulation Results for Single delays 53 C Simulation Results for Multiple Delays 69 Bibliography 79 vi LIST OF FIGURES vii List of Figures 1.1 An illustration of the surroundings of the apron and how the re- flection causes multipath propagation. 2 1.2 Example of ber as a function of snr. The increasing snr is re- trieved by adding white Gaussian noise to a fm modulated signal before fm demodulation. 3 1.3 ber as function of snr of a multipath signal. The receiver receives a strong reflection that has traveled 150m longer than the main signal, along with the main signal. 4 2.1 Different line codes and their voltage responses to a binary sequence [8]...................................... 6 2.2 Randomized nrz encoder as defined in IRIG106 [17]. 7 2.3 Randomized nrz decoder as defined in IRIG106 [17]. 8 2.4 Phase wheel representing a period of a signal, the number of points is determined by 2n and M is the jump size. 9 2.5 I/Q plot showing the envelope and phase of a passband signal . 10 2.6 An example of fm modulation . 11 2.7 A Tapped Delay Line [2] . 14 2.8 The result of multipath on fm-modulated signals. 15 3.1 Simple tapped delay line used as an equalizer for known delays. 18 4.1 A general outline of the communication model. 24 4.2 Transmitter part of generated signal for testing the simulation cor- rectness . 27 4.3 RF receiver setup. 27 4.4 Explanation of areas in the area plots . 28 4.5 Test-sender setup with two antennas to mimic the actual aircraft. 29 4.6 Real setup of test-sender . 29 5.1 Figure showing the eye-diagrams of a generated, known, signal without multipath and the simulation of the same signal . 31 5.2 Figure showing the eye-diagrams of a generated, known, signal with 117m multipath and the simulation of the same signal . 32 viii LIST OF FIGURES 5.3 Figure showing the eye-diagrams of a generated, known, signal with 150m multipath and the simulation of the same signal . 32 13 5.4 Sub-plot group of one of the best results for cma with µ = 2− . 33 14 5.5 Sub-plot group of one of the best results for cma with µ = 2− . 33 5.6 Eye-diagram before and after cma when ber = 0 both before and after . 36 5.7 Eye-diagram before and after cma when ber is not zero before but is after equalizer . 36 5.8 Eye-diagram before and after cma when the cma is unable to re- solve the multipath . 37 6.1 The three areas and their abbreviations . 41 10 B.1 Sub-plot group for µ = 2− and update every sample . 54 10 B.2 Sub-plot group for µ = 2− and update interval 12 . 54 10 B.3 Sub-plot group for µ = 2− and update interval 23 . 55 10 B.4 Sub-plot group for µ = 2− and update interval 46 . 55 10 B.5 Sub-plot group for µ = 2− and update interval 92 . 56 11 B.6 Sub-plot group for µ = 2− and update every sample . 56 11 B.7 Sub-plot group for µ = 2− and update interval 12 . 57 11 B.8 Sub-plot group for µ = 2− and update interval 23 . 57 11 B.9 Sub-plot group for µ = 2− and update interval 46 . 58 11 B.10 Sub-plot group for µ = 2− and update interval 92 . 58 12 B.11 Sub-plot group for µ = 2− and update every sample . 59 12 B.12 Sub-plot group for µ = 2− and update interval 12 . 59 12 B.13 Sub-plot group for µ = 2− and update interval 23 . 60 12 B.14 Sub-plot group for µ = 2− and update interval 46 . 60 12 B.15 Sub-plot group for µ = 2− and update interval 92 . 61 13 B.16 Sub-plot group for µ = 2− and update interval 12 . 61 13 B.17 Sub-plot group for µ = 2− and update interval 23 . 62 13 B.18 Sub-plot group for µ = 2− and update interval 46 . 62 13 B.19 Sub-plot group for µ = 2− and update interval 92 . 63 14 B.20 Sub-plot group for µ = 2− and update interval 12 . 63 14 B.21 Sub-plot group for µ = 2− and update interval 23 . 64 14 B.22 Sub-plot group for µ = 2− and update interval 46 . 64 14 B.23 Sub-plot group for µ = 2− and update interval 92 . 65 15 B.24 Sub-plot group for µ = 2− and update interval 12 . 65 15 B.25 Sub-plot group for µ = 2− and update interval 23 . 66 14 B.26 Sub-plot group for µ = 2− and update interval 46 . 66 14 B.27 Sub-plot group for µ = 2− and update interval 92 . 67 C.1 BER vs SNR of short resolvable multipath combinations without equalizer . 70 C.2 BER vs SNR of short resolvable multipath combinations with equal- izer . 70 C.3 BER vs SNR of long resolvable multipath combinations without equalizer . 71 C.4 BER vs SNR of long resolvable multipath combinations with equal- izer . 71 C.5 BER vs SNR of combination of Resolvable with equalizer multipath combinations without equalizer . 72 C.6 BER vs SNR of combination of Resolvable with equalizer multipath combinations with equalizer . 72 C.7 BER vs SNR of non-resolvable with equalizer multipath combina- tions without equalizer . 73 C.8 BER vs SNR of non-resolvable with equalizer multipath combina- tions with equalizer . 73 C.9 BER vs SNR of combination of resolvable with equalizer and resolv- able multipath combinations without equalizer . 74 C.10 BER vs SNR of resolvable with equalizer and resolvable multipath combinations with equalizer . 74 C.11 BER vs SNR of non-resolvable with equalizer and resolvable multi- path combinations without equalizer . 75 C.12 BER vs SNR of non-resolvable with equalizer and resolvable multi- path combinations with equalizer . 75 C.13 BER vs SNR of non-resolvable with equalizer and resolvable with equal- izer multipath combinations without equalizer . 76 C.14 BER vs SNR of non-resolvable with equalizer and resolvable with equal- izer multipath combinations with equalizer .