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MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY NGUYEN HONG ANH LOCATION-AWARE MULTIPATH-BASED CHANNEL PREDICTION FOR NEXT GENERATION WIRELESS COMMUNICATION SYSTEMS DOCTORAL DISSERTATION OF TELECOMMUNICATIONS ENGINEERING Hanoi−2022 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY NGUYEN HONG ANH LOCATION-AWARE MULTIPATH-BASED CHANNEL PREDICTION FOR NEXT GENERATION WIRELESS COMMUNICATION SYSTEMS Major: Telecommunication Engineering Code: 9520208 DOCTORAL DISSERTATION OF TELECOMMUNICATIONS ENGINEERING SUPERVISORS: 1.Assoc Prof Nguyen Van Khang 2.Assoc Prof Klaus Witrisal Hanoi−2022 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com DECLARATION OF AUTHORSHIP I declare that I have authored this thesis independently, that I have not used other than the declared sources/resources, and that I have explicitly indicated all material which have been quoted either literally or by content from the sources used Hanoi, / / 2022 PhD Student Nguyen Hong Anh SUPERVISORS Assoc.Prof Nguyen Van Khang i LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ACKNOWLEDGEMENT This dissertation was written during my doctoral course at School of Electronics and Telecommunications (SET), Hanoi University of Science and Technology (HUST) I was also received tremendous supports from the Signal Processing and Speech Communication Laboratory (SPSC), Graz University of Technology (TUGraz), Austria I am so grateful for all people who always support and encourage me for completing this study First, I would like to express my sincere gratitude to my advisors for their effective guidance, their patience, continuous support and encouragement, and their immense knowledge I would like to thank all members of SPSC, TUGraz They have been very kind and supportive during my visits to Graz They helped me a lot with their deep understanding of the group’s topics and researches I also would like to thank all my colleagues in SET, HUST They have always helped me with the research process and given helpful advice for me to overcome my own difficulties During my Ph.D course, I have received many supports from the Management Board of School of Electronics and Telecommunications Thanks to my employer, HUST for all necessary support and encouragement during my Ph.D journey I am also grateful to Vietnam’s Program 911, for their generous financial support Last but not least, I would like to thank OeAD and SPSC for giving funds for my research visits to Graz Special thanks to my family and relatives for their never-ending support and sacrifice Hanoi, 2022 Ph.D Student ii LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com CONTENTS DECLARATION OF AUTHORSHIP i ACKNOWLEDGEMENT ii CONTENTS vi SYMBOLS vi SYMBOLS ix LIST OF TABLES xiii LIST OF FIGURES xiv CHAPTER INTRODUCTION AND MOTIVATION 1.1 Literature review 1.1.1 Location-awareness in mmWave beamforming 1.1.2 Location-awareness in vehicular communications 1.1.3 Location-awareness in adaptive mobile communications, scheduling and routing 1.1.4 Channel quality metric (CQM) 1.2 Challenges and motivations 1.3 Purposes and objectives 1.4 Research hypotheses 1.4.1 Towards a site-specific radio propagation modeling 7 1.4.2 Towards a large-scale predicting of radio channel statistics 1.4.3 Towards a side information-aided single-anchor multipath-based localization 1.5 Contributions and outline CHAPTER SIGNAL AND SYSTEM MODELS 2.1 Introduction 2.2 System model 10 2.2.1 Representation of reflectors using virtual anchors (VAs) 2.2.2 Floor plan/environment information for location-aware applications 10 13 2.3 Hybrid geometric/stochastic signal model 13 2.4 Channel quality indicators 15 2.4.1 SMC amplitude 15 2.4.2 Signal-to-interference-plus-noise ratio (SINR) 16 2.4.3 Channel Capacity 17 iii LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 2.4.4 Position error bound (PEB) 19 2.5 Discussion 20 2.5.1 Energy capture 2.5.2 Contribution of individual SMCs in the overall channel capacity 20 21 2.6 Chapter conclusions 27 CHAPTER GAUSSIAN PROCESS REGRESSION FOR SMC AMPLITUDES 28 3.1 Related Work 28 3.2 SMC propagation model 29 3.3 GP Modeling (GPM) of the SMC Amplitudes 30 3.4 GPR 31 3.4.1 GP Model 31 3.4.2 Prediction 32 3.4.3 Learning 3.4.4 Evaluate the quality of prediction 32 33 3.5 Experiment and result 34 3.5.1 Experiment 3.5.2 Measurement pre-processing 34 34 3.5.3 GPR of SMC Amplitudes 35 3.5.4 GPR of SMC Phases 41 3.6 Chapter conclusions 44 CHAPTER RADIO ENVIRONMENT MAP FOR SITE-SPECIFIC PROPAGATION MODELING 45 4.1 Related work 45 4.2 Radio environment map (REM) using Gaussian Process regression (GPR) 47 4.3 SMC amplitudes 47 4.4 SINR 50 4.5 Position error bound 52 4.6 Chapter conclusions 55 CHAPTER APPLICATION OF GPR - ENABLED REMS TO ROBUST POSITIONING 57 5.1 Related work 57 5.2 Problem formulation 59 5.3 Proposed algorithm 59 5.4 Result 61 iv LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 5.5 Chapter conclusions 64 PUBLICATIONS 67 BIBLIOGRAPHY 68 APPENDICES 81 A Description of channel measurement campaigns 81 A.1 Measurement campaign 81 A.2 Measurement campaign 82 B Variance of νk 88 C Predicted Variance 89 v LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ABBREVIATIONS No Abbreviation Meaning ACF AutoCorrelation Function ADC Analog-to-Digital Converter AOA Angle-Of-Arrival AOD Angle-Of-Departure AWGN Additive White Gaussian Noise BER Bit Error Rate BF Beam Forming BS Base Station CDF Cumulative Distribution Function 10 CIR Channel Impulse Response 11 CRLB Cramer Rao Lower Bound 12 CQM Channel Quality Metric 13 CSI Channel State Information 14 DM Diffuse Multipath 15 DMC Diffuse Multipath Component 16 EC Energy Capture 17 ECC European Communications Committee 18 EFIM Equivalent Fisher Information Matrix 19 EPB East Plaster Board 20 FCC Federal Communications Commission 21 FIM Fisher Information Matrix 22 GNSS Global Navigation Satellite System 23 GP Gaussian Process 24 GPM Gaussian Process Model 25 GPR Gaussian Process Regression 26 GPS Global Positioning System 27 GSCM Geometry-based Stochastic Channel Model 28 IoT Internet-of-Thing 29 LIDAR Light Detection And Ranging 30 LLHF Log LikeliHood Function vi LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 31 M2M Machine-to-Machine 32 MAC Media Access Control 33 MIMO Massive Input Massive Output 34 MINT Multipath-assisted Indoor Navigation and Tracking 35 ML Maximum Likelihood 36 MMSE Minimum Mean Square Error 37 MPC MultiPath Component 38 MRC Maximal Ratio Combining 39 MSLL Mean Square Log Loss 40 NLOS Non-Line-Of-Sight 41 NGW North Glass Window 42 LOS Line-Of-Sight 43 OFDM Orthogonal Frequency Division Multiplexing 44 PA Physical Anchor 45 PAM Pulse Amplitude Modulation 46 PDF Probability Distribution Function 47 PDP Power Delay Profile 48 PHY PHYsical Layer Protocol 49 PEB Position Error Bound 50 QAM Quadrature Amplitude Modulation 51 REM Radio Environment Map 52 RF Radio Frequency 53 RFID Radio Frequency IDentification 54 RRC Root Raised Cosine 55 RSS Received Signal Strength 56 RX Receiver 57 RV Random Variable 58 SALMA Single-Anchor Localization system using Multipath Assistance 59 SEP Symbol Error Probability 60 SIMO Single-Input-Multiple-Output 61 SINR Signal-to-Interference-plus-Noise Ratio 62 SLAM Simultaneous Localization And Mapping 63 SMC Specular Multipath Component 64 SMSE Standard Mean Square Error 65 SNR Signal-to-Noise Ratio vii LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 66 SW South Wall 67 ToF Time-of-Flight 68 TX Transmitter 69 UE User Equipment 70 URLLC Ultra-Reliable Low-Latency Communication 71 UWB Ultra Wide Band 72 VA Virtual Anchor 73 WW West Wall viii LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com [71] Gustafsson F and Gunnarsson F (July 2005) Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements 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Panayiotou C.G., and Stavrou S (2012) 3d ray tracing for device-independent fingerprint-based positioning in wlans In 2012 9th Workshop on Positioning, Navigation and Communication, pp 109–113 doi:10.1109/WPNC.2012.6268748 [103] Hatami A and Pahlavan K (2006) Comparative statistical analysis of indoor positioning using empirical data and indoor radio channel models In CCNC 2006 2006 3rd IEEE Consumer Communications and Networking Conference, 2006., volume 2, pp 1018–1022 doi:10.1109/CCNC.2006.1593192 [104] Chai X and Yang Q (2007) Reducing the calibration effort for probabilistic indoor location estimation IEEE Transactions on Mobile Computing, 6(6):pp 649–662 doi:10.1109/TMC.2007.1025 [105] Youssef M and Agrawala A (2005) The horus wlan location determination system In Proceedings of the 3rd International Conference on Mobile Systems, Applications, and Services, MobiSys ’05, p 205–218 Association for Computing Machinery, New York, NY, USA ISBN 1931971315 [106] Cassarà P., Potortì F., 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Radar Conference Atlanta, GA, USA doi:10.1109/RadarConf2147009 2021.9455311 [120] Wilding T., Leitinger E., and Witrisal K (2021) Multipath-based localization and tracking considering off-body channel effects ArXiv , abs/2110.09932 [121] Meissner P., Leitinger E., Fröhle M., and Witrisal K (2013) Accurate and robust indoor localization systems using ultra-wideband signals In European Navigation Conference European Navigation Conference, ENC ; Conference date: 23-042013 Through 25-04-2013 [122] Santos T., Karedal J., Almers P., Tufvesson F., and Molisch A.F (2010) Modeling the ultra-wideband outdoor channel: Measurements and parameter extraction method IEEE Transactions on Wireless Communications, 9(1):pp 282–290 doi: 10.1109/TWC.2010.01.090391 79 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com [123] Borish J (Mar 1984) Extension of the image model to arbitrary polyhedra JASA, 75(6):pp 1827–1836 [124] Sachs J., Herrmann R., Kmec M., Helbig M., and Schilling K (2007) Recent Advances and Applications of M-Sequence based Ultra-Wideband Sensors, pp 50–55 Singapore doi:10.1109/ICUWB.2007.4380914 [125] Molisch A.F (December 2010) Wireless communications Wiley-IEEE press, edition [126] Cepeda R., Parker S.C.J., and Beach M (2007) The measurement of frequency dependent path loss in residential los environments using time domain uwb channel sounding In 2007 IEEE International Conference on Ultra-Wideband , pp 328–333 doi:10.1109/ICUWB.2007.4380964 [127] Meissner P., Leitinger E., Lafer M., and Witrisal K (2013) MeasureMINT UWB database 80 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com APPENDICES A Description of channel measurement campaigns A.1 Measurement campaign Frequency Domain Measurements - Vector Network Analyzer Frequency-domain measurements have been obtained with a Rhode & Schwarz ZVA24 VNA The frequency range has been chosen as the full FCC bandwidth from 3.1 to 10.6 GHz (corresponding to a wavelength range of 9.67 cm to 2.83 cm), resulting in a delay resolution of 0.1333 ns and a spatial resolution of cm At the l-th trajectory position, a sampled version Hl [k] of the CTF Hl (f ) with a frequency spacing of ∆f is measured The VNA has been calibrated up to (but not including) the antennas with a through-open-short-match (TOSM) calibration The FCC bandwidth has been measured for different discrete frequencies with a frequency resolution of 1.5 MHz The transmit power has been set to 15 dBm Measurement Post Processing For the VNA measurements, the major system influences on the measured CTF H(f ) have already been removed by the previously mentioned TOSM calibration This includes cables and connectors, but not the antennas, which are considered as part of the transmission channel The necessary post-processing tasks reduce to a filtering of the signal to select a desired frequency band out of the FCC range and to downconvert the signal transformed to time domain to obtain a baseband signal The filtering is done with a baseband pulse s(t) that covers the desired bandwidth The CTF is measured at Nf discrete frequencies fk = k∆f + fmin , k = 0, , Nf − 1, where fmin is the lowest measured frequency This sampled CTF H[k] corresponds to a Fourier series representation of the time-domain CIR h(τ ) [121], which is periodic with a period of τmax With f0 and fc denoting the lower band edge and the center frequency of the extracted band, respectively, and using an IFFT with size NFFT = ⌈(∆f ∆τ )−1 ⌉, where ∆τ is the desired delay resolution, the time domain equivalent baseband signal is obtained as r(t) = IFFTNFFT {H[k]S[k]}e−j2π(fc −f0 )t (A.1) Here, S[k] is the discrete frequency domain representation of the pulse s(t) in the desired frequency range This procedure is similar to [122] 81 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Measurement scenario We consider the simple scenario shown in Fig A.1, where one physical anchor is T present at position a1 = [4.2, 4] and the mobile agent is placed at position p = T [3.4, 1.4] UWB grid measurements are available for 484 (22x22) grid points pℓ with a spacing of × cm, surrounding p The measurements were performed using a Rhode & Schwarz ZVA-24 vector network analyzer with frequency range from 3.1 − 10.6 GHz, thereby covering the full FCC-regulated band for UWB Agent and anchor were equipped with dipole-like antennas made of Euro Cent coins mounted at a height of 1.5 m These antennas have an approximately uniform radiation pattern in the azimuth plane and zeros in the directions of floor and ceiling Within the total measured band, we selected the actual signal band using filtering with a raised cosine pulse s(t) with a roll-off-factor of 0.6 Varying values have been selected for the twosided bandwidth, namely 100 MHz, 500 MHz, and GHz, each at a carrier frequency of fc = GHz A.2 Measurement campaign Measurement scenario We consider indoor environments where fixed anchors communicate with a mobile agent by means of radio signals Figure A.3 illustrates the considered scenario, where (1) (2) two physical anchor positions at positions a1 and a1 are shown as blue crosses, the agent positions p along a segmented trajectory, and some exemplary virtual anchors (VAs) are shown The VA positions are mirror images of the physical anchor positions that are induced by reflections at flat surfaces—typically walls—and thus depend on the surrounding environment (floor plan) [123] The position of the k-th VA of the jth (j) (j) physical anchor at position a1 is denoted as ak Note that in this work we consider horizontal propagation only For brevity, we neglect the anchor index j from now on Also, we denote L as the set of measurement points Figure A.3 shows the laboratory room at Graz University of Technology that was used for the experimental validation The room consists of two plaster board walls and two reinforced concrete walls (shown as black outer lines), three glass windows at the north wall (shown as thick gray lines), one white board and one metal door at the south wall (indicated by A∗ and C∗ , respectively) We introduce the following labels to refer to the involved reflection surfaces: EPB East plaster board SW South wall WW West wall NGW North glass wall 82 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com uwin A2 p rwin ym lwall −2 lwin −4 −6 A278 −8 −5 10 15 20 xm (a) Overview of floorplan A2 cpill p ym pl −1 −2 xm 10 12 (b) Close-up of floorplan Figure A.1: Scenario floor-plan: a physical anchor is located at position a1 and an examplary VA is at position a2 The gray grid with positions pℓ indicates the measurement grid with × cm spacing; the red dot indicates its center position p, the actual mobile agent position used in the illustration Blue lines depict specular reflections at wall segments 83 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Figure A.2: Photo of corridor scenario To conduct the channel measurements, an Ilmsens Ultra-Wide band M-sequence device [124] was used, c.f Figure A.4a The measurement principle is correlative channel sounding [125], i.e a binary code sequence with suitable autocorrelation properties is transmitted over the channel At the receiver, the channel impulse response is recovered using a correlation with the known code sequence The channel sounder has one transmitter port and two receiver ports A 12-bit M-sequence has been employed, corresponding to a sequence length of 4095 samples This allows for an unambiguous delay window of 589.2 ns at a clock rate of 6.95 GHz The M-sequence is modulated onto a 6.95 GHz carrier, yielding a probing signal that covers a frequency band between approx 3.5 and 10.5 GHz Each of the ports was connected to a dipole coin antenna as shown in Figure A.4b According to [81], the coin antenna has a very wide bandwidth ranging from to GHz It also has with a nearly isotropic radiation pattern in the horizontal plane We used the two receiver ports as anchors and placed their antennas at fixed po(1) (2) sitions a1 and a1 The transmitter port is connected to another antenna that was moved along a trajectory with 595 points p, as shown in the Figure A.3, to obtain the same number of channel measurements All antennas were mounted on tripods at the same height, therefore only the co-polarized, azimuth radiation pattern of the antenna has an impact on the data The raw measurements at the receiver ports were filtered with an RRC pulse with center frequency 6.95 GHz, roll-off factor 0.5 and bandwidth 84 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 11 10 y-direction in meter segment segment segment segment segment segment segment phys anchor VA (1) a5 F E D C B A D† (1) a4 (1) (1) a2 a1 p C† B† φk A† (2) a4 (2) C ∗ B∗ a2 A∗ −1 −2 −13 (2) a1 (2) a3 −12 −11 −10 −9 −8 −7 −6 −5 −4 x-direction in meter −3 −2 −1 Figure A.3: Floor plan of the evaluation scenario Bold black lines denote walls, thick gray lines represent glass windows, other lines illustrate other materials Two blue crosses represent the physical anchors; orange circles denote virtual anchors (VAs) which were considered in the experimental validation An agent moves along a trajectory segmented into seven parts indicated with distinct colors Capital letters (with or without mark ∗ or †) refer to sub-segments of different materials along each wall 85 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com (a) Ilmsens UWB M-sequence sounder and Ilmsens power supply (b) Europe coin antenna Figure A.4: A photo of the Ilmsens channel sounder, and a photo of the coin antenna used for transmit and receive 1/Tp = GHz to obtain the received signals corresponding to the model in (2.3) The power spectral density of AWGN N0 is known and considered in the training and evaluation process Time domain measurement - M-Sequence Radar Time-domain measurements have been obtained with an Ilmsens Ultra-Wide Band M-Sequence device [124] The measurement principle is correlative channel sounding [125] A binary code sequence with suitable autocorrelation properties (a large peakto-off-peak-ratio) is transmitted over the channel At the receiver, the channel impulse response is recovered using a correlation with the known code sequence This Msequence radar has one transmitter and two receiver ports Hence, the mobile unit that has been moved along the measurement trajectories was the transmitter, and the two receiver ports have been used as anchors The transmit power of the M-sequence device in FCC mode is 18dBm The employed 12-bit M-sequence has a length of 4095 samples At the clock rate of 6.95GHz, this allows for a maximum delay of τmax = 589.2 ns Measurement post-processing Figure A.5 shows a block diagramm of the measurement setup using the M-Sequence radar As in the VNA measurements, the measurement system should be calibrated 86 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Figure A.5: Calibration setup for time domain measurements up to (but not including) the antennas Hence, the influence of the device internal transfer functions and the measurement cables and connectors, combined in the transfer function Hsys,i (f ) for the i-th RX channel, as well as the crosstalk between TX channel and i-th RX channel, Hcross,i (f ), have to be compensated For the further description, we will drop the channel index To achieve this, two types of measurements are necessary First, to determine the crosstalk, the TX antenna is unmounted and the TX port is terminated with a 50Ω match and the crosstalk signals are measured Second, also the RX antennas are unmounted and TX and RX cables are connected In this way, Hmeas (f ) = Hsys (f ) + Hcross (f ) are measured Using the measurement configuration with all the antennas as depicted in Figure A.5 yields Hmeas (f ) = H(f )Hsys (f )+Hcross (f ) Hence, a calibrated version of the radio channel transfer function is obtained as H(f ) = Hmeas (f ) − Hcross (f ) Hsys (f ) − Hcross (f ) (A.2) To avoid excessive noise gain, we use a thresholding on the time-domain representation of the denominator in (A.2) and set samples below the threshold to zero The time domain signal is obtained by an inverse Fourier transformation Finally, the timedomain signal within the desired frequency range around the center frequency fc can be computed using a suitable baseband pulse shape s(t) as r(t) = h(t) ∗ s(t)ej2πfc t e−j2πfc t ∗ δ(t − τshif t ) (A.3) Here, τshif t is a time shift that accounts for the delays of connectors in the calibration 87 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com measurements and the antennas, which have not been removed by (A.2) For connectors, this value can be measured using a VNA, for the antennas, it can be computed using the length of the antennas and the propagation velocity in the materials, which is often given in data sheets This calibration procedure is similar to [126] The publicly available measurements [127] contain extraction functions for Matlab, that directly deliver signals in the form of (A.3) B Variance of νk Here, the variance of DMC νk (p) within one estimated SMC amplitude is derived For the sake of readability, we omit the agent position p The DMC of an estimated SMC amplitude is given as νk = s(τ − λ)ν(λ)s∗ (τ − τk )dτ dλ (B.4) ∞ where the energy of the signal s(t) is assumed to be one, i.e., −∞ |s(t)|2 dt = Using (B.4), the variance of the DMC of an estimated SMC amplitude E |νk |2 = E s(τ − λ)ν(λ)s∗ (τ − τk )s∗ (τ ′ − λ′ )ν ∗ (λ′ )s(τ ′ − τk )dτ dλdτ ′ dλ′ s(τ − λ)s∗ (τ ′ − λ)s∗ (τ − τk )s(τ ′ − τk )Sν (λ)dτ dτ ′ dλ = s˜(τk − λ)˜ s∗ (τk − λ)Sν (λ)dλ = where s˜(t) = (B.5) s(τ )s∗ (t − τ )dτ In the case, a large bandwidth (UWB) is assumed, (B.5) can be approximated by E |νk |2 ∼ = Sν (τk ) |˜ s(t)|2 dt (B.6) ∞ = Sν (τk ) −∞ |S(f )|4 df where S(f ) is the Fourier transform of s(t) and Tp = pulse duration ∞ |S(f )|4 df −∞ (B.7) is the effective Assuming a signal s(t) with block-spectrum, the effective pulse duration is given as Tp = ∞ |S(f )|4 df −∞ = Ts , where Ts is the Nyquist sampling time Assuming a signal s(t) with non-block spectrum signal, the effective pulse duration Tp is different from Nyquist sampling time Ts For example, a raised cosine pulse results in Tp = ∞ |S(f )|4 df −∞ = 1−β β Ts , where β is the roll-factor 88 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com C Predicted Variance The predicted variance V[y(ϕk (p∗ ))|Dk , θk ] at position p∗ approximates the variance of the SMC amplitude values, which relates to the DMC term in (2.7) for position p∗ Assuming the Gaussian approximation to hold for |ˆ αk (p∗ )|, we have V[ψ(ϕk (p∗ ))|Dk , θk ] ≈ Sν (τk ; p∗ )Tp + N0 While the PDP Sν (τk ; p∗ ) decreases with delay τk = 2 dk (p∗ ) c dk (p), (C.8) the squared distance dk (p∗ ) will be increasing, implying a counteracting effect The left-hand side is independent of the distance We can thus re-write the equation to illustrate the shape of the PDP as a function of τk at some angle ϕ∗k , Sν (τk ; ϕ∗k )Tp ≈ τk2 c2 V[ψ(ϕ∗k )|Dk , θk ] − N0 (C.9) This result indicates a reciprocal squared decay in contrast to the usually assumed exponential decay On the other hand, from Appendix B, by neglecting measurement noise, we have: E |νk (p) + wk (p)|2 ≈ E |νk (p)|2 = Tp Sν (τk ; p) (C.10) So, the predicted variance obtained from GPR can be validated by comparing with the DMC power, c.f equations (C.8-C.9) 89 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ... reach their intended destination In its most basic form, given a destination d, a node i with neighbors Ni will choose to forward data to a neighbor closest to the destination 1.1.4 Channel quality... their limited coverage Last but not least, a well-known technique in network routing is geographic routing (georouting), which takes advantage of geographic information of nodes (actual geographic... orientations of the agent and physical anchor antennas are fixed throughout the measurement, the incident angle (at the reflecting surface) and the angles at the agent and anchor (used to compute antenna

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