The impact of signal bandwidth on indoor wireless systems in dense multipath environments

Abstract Recently there has been a significant amount of interest in the area of wideband and ultra-wideband (UWB) signaling for use in indoor wireless systems. This interest is in part motivated by the notion that the use of large bandwidth signals makes systems less sensitive to the degrading effects of multipath propagation. By reducing the sensitivity to multipath, more robust and higher capacity systems can be realized. However, as signal bandwidth is increased, the complexity of a Rake receiver (or other receiver structure) required to capture the available power also increases. In addition, accurate channel estimation is required to realize this performance, which becomes increasingly difficult as energy is dispersed among more multipath components. In this thesis we quantify the channel response for six signal bandwidths ranging from continuous wave (CW) to 1 GHz transmission bandwidths. We present large scale and small scale fading statistics for both LOS and NLOS indoor channels based on an indoor measurement campaign conducted in Durham Hall at Virginia Tech. Using newly developed antenna positioning equipment we also quantify the spatial correlation of these signals. It is shown that the incremental performance gains due to reduced fading of large bandwidths level off as signals approach UWB bandwidths. Furthermore, we analyze the performance of Rake receivers for the different signal bandwidths and compare their performance for binary phase modulation (BPSK). It is shown that the receiver structure and performance is critical in realizing the reduced fading benefit of large signal bandwidths. We show practical channel estimation degrades performance more for larger bandwidths. We also demonstrate for a fixed finger Rake receiver there is an optimal signal bandwidth beyond which increased signal bandwidth produces degrading results. Acknowledgments At this time I would like to thank Michael Buehrer, William Davis, Jeffery Reed, and Raqib Mostafa for serving on my advisory committee and providing technical expertise as well as encouragement along the way. I would also like to acknowledge the Via family for the generous endowment provided by the Harry Lynde Bradley Fellowship which allowed me to pursue this research almost completely un-tethered from the reins. I would also like to express my appreciation to my fellow graduate students in MPRG, especailly Joseph Gaeddert, Chris Anderson, Brian Donlan, Vivek Bharadwaj, Aaron Orndorf and John Keaveny for their thought provoking discussions and technical assistance with this research. Also my appreciation goes to Samir Ginde, Carlos Aguayo, Nathan Harter and my other lab mates for keeping things in perspective while working at MPRG. Of the MPRG staff, which was extremely helpful, I would like to thank Mike Hill, Shelby Smith, Hilda Reynolds, and Shereef Sayed. I am greatly indebted to Mike Coyle and the staff of the Industrial Design Metal Shop for their help in designing and manufacturing the antenna positioning system. Without Mike’s support the positioning system would not have proceeded beyond the conceptual stage. For donating replacement couplers for the positioning system I would like to thank the staff at Ruland. I also owe thanks to Josiah Hernandez for helping with the measurement campaign. I must also thank Dennis Sweeney from CWT and Carl Dietrich from VTAG for their insight and use of their equipment during the measurement campaign. I owe a very special thanks to Alexander Taylor, who has been my partner in Electrical Engineering crime for the past five years at Virginia Tech and has been an honest friend through it all. Also the friendships forged with Aaron Orndorf and Jeremy Barry have made this experience an interesting one to say the least. Without a doubt none of this work would have been possible without the tireless support and understanding of my fiancé and soon to be wife Ashley K. Rentz. Her encouragement, wisdom, and unwavering love were instrumental in completing this work; thank you for understanding. Finally, I would like to thank my parents Bob and Louise Hibbard, as well as my brother Mark Hibbard for their generous support, love, and understanding throughout this work as well as my entire life. Table of Contents CHAPTER 1 INTRODUCTION AND THESIS OVERVIEW .1 1.1 Motivation 1 1.2 Background and Perspective . 2 1.3 Thesis Overview . 3 CHAPTER 2 RADIO WAVE PROPAGATION AND THE INDOOR PROPAGATION CHANNEL 5 2.1 Introduction . 5 2.2 Propagation Overview . 6 2.2.1 Antennas and Radiation . 6 2.2.2 Propagation Mechanisms . 9 2.2.3 The Friis Transmission Formula and Basic Communication Link 14 2.3 The Indoor Propagation Channel . 17 2.3.1 Large Scale Effects 17 2.3.2 Small Scale Effects 19 2.4 Multipath Mitigation Techniques . 30 2.4.1 Basic Diversity Methods . 30 2.4.2 The Rake Receiver – An Overview . 31 2.5 Impact of Signal Bandwidth on Indoor Wireless Systems – Literature Review . 32 2.6 Summary 38 CHAPTER 3 SLIDING CORRELATOR CHANNEL MEASUREMENT: THEORY AND APPLICATION 40 3.1 Introduction . 40 3.2 Overview of Channel Measurement Techniques . 40 3.3 Sliding Correlator Theory and Operation . 42 3.3.1 Cross Correlation Theory 42 v i 3.3.2 Pseudorandom Noise Sequences and Generators 44 3.3.3 Swept Time Delay Cross Correlation (Sliding Correlator) Theory . 46 3.3.4 Practical Considerations in the Sliding Correlator Measurement System . 51 3.4 Implementation of a Sliding Correlator Measurement System . 53 3.4.1 Transmitter and Receiver Implementation 53 3.4.2 System Calibration 56 3.4.3 System Repeatability . 58 3.5 Mapping Power Delay Profiles to Received Power . 59 3.6 Summary 61 CHAPTER 4 DESIGN AND IMPLEMENTATION OF AN ANTENNA POSITIONING AND ACQUISITION SYSTEM .62 4.1 Introduction . 62 4.2 Positioning System Design Issues 62 4.2.1 Approaches to Antenna Positioning 63 4.2.2 Overall System Constraints . 64 4.2.3 Electrical Impact of Positioning System . 66 4.3 Positioning System Design and Implementation . 67 4.3.1 Design . 67 4.3.2 Implementation . 73 4.4 Antenna Positioning and Acquisition (APAC) Software 74 4.4.1 Defining the 2-D Measurement Grid . 75 4.4.2 Software Implementation Using Labview . 77 4.4.3 Additional Functionality 81 4.5 Positioning System Verification and Calibration 83 4.6 Conclusion 85 CHAPTER 5 INDOOR PROPAGATION MEASUREMENTS AND RESULTS AT 2.5 GHZ 86 5.1 Measurement Overview . 86 5.2 Measurement Campaign 86 5.2.1 Omnidirectional Biconical Antennas . 86 5.2.2 Narrowband (CW) Channel Sounder Configuration . 87 5.2.3 Wideband (Sliding Correlator) Channel Sounder Configuration 88 5.2.4 Measurement Procedure 90 5.2.5 Measurement Locations and Site Information . 91 vi i 5.3 Measurement Results and Processing 95 5.3.1 Large Scale Results . 95 5.3.2 Small Scale Results . 99 5.3.3 A Note on Site Specific Phenomena 118 5.4 Conclusion 121 CHAPTER 6 IMPACT OF SIGNAL BANDWIDTH ON INDOOR COMMUNICATION SYSTEMS .122 6.1 Introduction . 122 6.2 Overview of BPSK Modulation and BER in AWGN 122 6.3 BER performance for BPSK in Measured Channels 124 6.4 Required Fading Margin for Quality of Service . 128 6.5 Spatial Correlation and Two Antenna Selection Diversity . 130 6.6 Rake Receiver Implementation and Channel Estimation . 132 6.6.1 Rake Receiver Performance – Perfect Channel Estimation . 133 6.6.2 Rake Receiver Performance – Imperfect Channel Estimation 134 6.6.3 Selective Rake Receiver Performance . 138 6.6.4 Selective Rake Receiver Performance with Channel Estimation 142 6.7 Conclusions 144 CHAPTER 7 CONCLUSIONS .145 7.1 Summary of Findings . 145 7.1.1 Impact of Spreading Bandwidth on Channel Characteristics 145 7.1.2 Impact of Spreading Bandwidth on DS-SS BPSK Indoor Systems 146 7.1.3 Original Contributions and Accomplishments 146 7.2 Further Areas of Research 147 7.2.1 On the Impact of Spreading Bandwidth 147 7.2.2 On the Use and Processing of Sliding Correlator Measurements 147 7.3 Closing 148 APPENDIX A

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A NA NA 400 26.6 22.6 0.9 8.8 22.2 20.2 Tx106 500 26.0 20.9 1.0 9.6 33.2 28.2 25 14.6 25.9 0.8 7.7 1.9 13.4 100 31.1 31.1 0.6 6.4 9.0 17.5 225 33.3 28.3 0.7 7.1 22.6 25.5 400 31.0 28.7 0.7 7.0 27.4 21.7 Tx107 500 31.1 31.0 0.6 6.5 31.7 21.3 25 11.9 22.3 0.9 9.0 2.2 17.4 100 34.6 31.2 0.6 6.4 11.0 20.4 225 35.8 32.9 0.6 6.1 17.4 14.6 400 32.2 26.6 0.8 7.5 34.8 27.8 Tx108 500 34.1 27.8 0.7 7.2 40.0 26.0 25 8.8 17.8 1.1 11.2 2.1 20.5 100 22.1 26.8 0.7 7.5 9.0 18.9 225 25.2 26.2 0.8 7.6 14.0 16.9 400 25.6 25.3 0.8 7.9 22.2 15.3 Tx109 500 23.4 23.4 0.9 8.5 24.0 17.0 160 Time Dispersion Parameters – Durham Hall 4th Floor – NLOS Measurements (continued) LOCATION SC TX m (nsec) RMS (nsec) BC,90 (MHz) BC,50 (MHz) avg. number of paths Max Avg SNR (dB) 25 7.8 16.2 1.2 12.3 1.9 18.7 100 20.5 22.9 0.9 8.7 8.8 21.7 225 19.5 23.1 0.9 8.7 20.0 26.4 400 20.5 24.4 0.8 8.2 31.1 28.8 Tx110 500 20.4 23.8 0.8 8.4 33.8 26.7 25 7.1 17.4 1.1 11.5 2.1 21.8 100 25.8 29.3 0.7 6.8 9.7 18.9 225 29.3 32.0 0.6 6.3 19.4 18.8 400 28.9 29.7 0.7 6.7 28.2 21.5 Tx111 500 27.0 28.0 0.7 7.1 32.5 23.7 25 8.7 17.1 1.2 11.7 2.4 23.3 100 29.4 29.5 0.7 6.8 11.9 23.2 225 29.4 28.1 0.7 7.1 19.7 22.0 400 32.4 29.8 0.7 6.7 37.2 22.2 Tx112 500 33.0 29.1 0.7 6.9 31.0 16.7 25 7.7 15.7 1.3 12.7 2.25 22.8 100 25.4 26.9 0.7 7.4 11.0 22.6 225 16.6 17.5 1.1 11.4 9.6 15.2 400 30.0 25.5 0.8 7.8 36.1 23.1 Tx113 500 29.0 23.6 0.8 8.5 29.5 19.6 25 7.6 16.9 1.2 11.8 2.3 24.1 100 26.9 28.6 0.7 7.0 11.5 23.0 225 30.6 29.3 0.7 6.8 24.2 26.0 400 32.1 36.1 0.6 5.5 35.1 24.4 Tx114 500 31.6 31.5 0.6 6.3 36.8 23.5 25 9.9 18.7 1.1 10.7 2.4 22.7 100 29.2 30.3 0.7 6.6 10.9 20.7 225 29.2 31.1 0.6 6.4 26.5 27.0 400 29.3 30.1 0.7 6.6 33.4 25.5 Tx118 500 31.0 31.5 0.6 6.3 39.5 24.9 161 A.4 Probability of Error vs. Eb/No for BPSK Modulation A.4.1 LOS Locations 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx000 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx001 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx002 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx003 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 162 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx004 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx005 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx006 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx007 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) LOS Rx008 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN Result 163 A.4.2 NLOS Locations 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx100 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx101 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx103 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx104 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx107 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob a bi lit y of er ro r Eb/No (dB) NLOS Rx108 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 164 b o 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx114 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx113 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx112 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx111 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx109 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y of er ro r Eb/No (dB) NLOS Rx110 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 165 0 5 10 15 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 Pr ob ab ilit y o f e rr or Eb/No (dB) NLOS Rx118 Rayleigh Result B = CW tone B = 25 MHz B = 100 MHz B = 225 MHz B = 400 MHz B = 500 MHz AWGN 166 Appendix B Derivation of Instantaneous Wideband Received Power in a 2 Path Fading Channel This appendix shows in detail the derivation for instantaneous wideband received power. We begin with the general result of the channel response to an arbitrary signal s(t) given by (1) where the complex envelope notation is used without loss of generality. We consider the case where s(t) is a repetitive pulse train p(t) with very narrow pulse width Tbb and repetition period TREP which is much greater than the maximum measured excess delay of the channel MAX. p(t) is defined as (2) From (1) we may write the response of the channel to the probing pulse as (3) To determine the instantaneous received power received at some time t0, the power 2 0 |)(~| tw is found by summing up the multipath powers resolved in the instantaneous multipath power delay profile of the channel 20 |);(| τth . This is equal to the energy received over the time duration of the multipath waveform, divided by the duration of the waveform MAX [1]. Therefore the instantaneous received power at to is given by )( 2 1)(~ 1 0 k j k k tpeatw k τ θ −=  = kj k N k k eatshtshtstw θττδττ ][ 2 1)(~)( 2 1)(~)(~)(~)(~ 1 0 −⊗=⊗=⊗=  − = bb MAX T tp τ2)( = for 0 t Tbb 0)( =tp otherwise 167 (4) (5) (6) Expanding the summations in (6) and applying Euler’s formula yields equation (7) as (7) Recombining the like terms of the first two terms in the integrand yields (9) Noting that integration is a linear operator, the integration is broken into two parts as (9.1) (9.2) Recognizing the form of the autocorrelation of the sounding pulse in (9.2) we may rewrite the result as 1 2 1 2 1 2 1 1 2 0 0 01 2 0 00 1 1| ( ) | ( ) ( ) ( ) ( ) 4 MAX k kj j k k k k k kMAX w t a t e p t a t e p t dt τ θ θ τ τ τ − = =   = − −           ∗ = MAX dttwtwtw MAX τ τ 0 2 0 )(~)(~ 1|)(~|         −−= − = = MAX kk dtetptptatatw jk k kk k k MAX τ θθ ττ τ 0 )(1 0 10 1 0 01 2 0 21 2 1 2 2 )()()()( 4 11|)(~|  −+−= MAX tptatptatw MAX τ ττ τ 0 1 2 0 2 10 2 0 2 0 2 0 )()()()([4 1|)(~| dttptptata )]()()cos()()(2 10100100 ττθθ −−−+   −= = MAX k kk MAX tptatw τ τ τ 0 1 0 2 0 22 )()( 4 1|)(~| )dttptptata )()()cos()()(2 10100100 ττθθ −−−+   = −= MAX k kk MAX dttptatw τ τ τ 0 1 0 0 2 0 22 )()( 4 1|)(~| dttptptata MAX MAX  −−−+ τ ττθθ τ 0 10100100 )()()cos()()(24 1 168 (10.1) (10.2) where Rp() is the autocorrelation of the sounding pulse given by (11) Note that while we defined p(t) in (2) the formulation of (10) is valid for any time limited probing pulse. We will now consider the result of (10) for the pulse shape given by (2). Substituting the definition of p(t) given by (2) into (10.1) and performing the integration yields (12) Noting that the pulse is only defined over the range of times 0 t Tbb the result of the integration is Tbb. Combining like terms in (12) yields (13) We next consider the second integral given by (10.2) of equation (10). Using the definition of p(t) as a square pulse of width Tbb the autocorrelation function of (13) is found by simple convolution , resulting in a triangular function [27] given by (14)  −= = MAX dttptatw k k k MAX τ τ τ 0 2 1 0 0 22 1 )()(4 1|)(~|  = = MAX dt T ta bb MAX k k MAX τ τ τ 0 1 0 0 2 4)( 4 1  = = 1 0 0 22 1 )(|)(~| k k tatw   = −= MAX k kk MAX dttptatw τ τ τ 0 1 0 0 2 0 22 )()( 4 1|)(~| )()cos()()(2 4 1 01100100 ττθθτ −−+ p MAX Rtata ζζττ dptpRp )()()( 0 −=  ∞ =)(τpR -Tbb  0 || > Tbb 0 <  Tbb bb MAX T τ4            + 1 bbT τ  + − 1 bbT τ 0 169 Combining equations (12), (13), and (14) yields the instantaneous received power t0 for the two path channel as (15) where ak is the multipath amplitude, k is the multipath arrival time, k is the multipath phase, and Rp() is the autocorrelation function given by equation (14). )()cos()()(2)(|)(~| 01100100 1 0 0 22 0 ττθθ −−+=  = p k k Rtatatatw 170 Appendix C Antenna Positioning System User Guide and Reference C.1 Introduction This Appendix provides information concerning the use, maintenance, and modification of the 4-bar parallel linkage antenna positioning system described in Chapter 4. Care should be taken in operating the system as mechanical interference is inherent in the design and no other mechanism other than operator awareness will prevent serious or permanent damage to the equipment. It is very important that the user fully understand the operating limitations of the positioning system as well as the stepper motors before performing any positioning tasks. This appendix also contains trouble shooting tips for repairing and maintaining the existing system, since at the time of writing no document as such exists. The scope of this system is limited to an indoor positioning system intended to make measurements within the centimeter to millimeter wavelength band of the radio spectrum in the interest of research. Therefore, no special consideration is given to operation in adverse environments or durability over normal operating conditions in a research environment. C.2 Operating Conditions and Specifications In addition to the originally proposed design, two modifications were made to the system. First, a support for the driven arm was implemented from 5/8” square aluminum stock. This 15” support rests under the driven arm to reduce the deflection of the steel arm. Second, an idler arm offset was added to the idler arm linkage base to provide more range and reduce the catastrophic effects of the possible mechanical interference. (i.e. the system will slip rather than seize the motor or break the coupler). This support simply moves the linkage attachment point to the first quadrant counter-clockwise of the idler arm linkage base mount. These additional components are shown in Figure C.1. 171 Figure C.1 – Driven arm support and idler arm offset components made as modifications to the original design. The assembled system has an antenna mount and antenna weight limitation of 10 pounds. This specification must be adhered to in order to achieve the specified life and performance of the equipment. While overloading may not result in failure, it could significantly reduce the life of the equipment [16]. To operate the positioning system with the Labview software, the positioning system must be in the top-dead-center at home condition at the start of initialization. This position is characterized with the linear track carriage in its “home position” and the linkage arm 27500 motor steps CW from its “home position”. It is suggested that in the native configuration presented here, certain parameters should not be exceeded; these parameters and their values are summarized in Table C.1. Parameter PDX Command Max Value Set Command Linear Track Velocity V1 10 1V10 Linkage Arm Velocity V2 10 2V10 Linear Track Acceleration A1 3 1A3 Linkage Arm Acceleration A2 0.25 2A0.25 Linear Track Homing Max 1GH+ 7 1GH+7 Linkage Arm Homing Max 2GH+ 2 2GH+2 Linkage Arm Movement CW from home position 2D (H+) 2000 steps 2D2000 Linkage Arm Movement CCW from home position 2D (H-) 75000 steps 2D75000 Linkage Arm top-dead-center (TDC) from home position 2D 27500 steps 2D27500 Table C.1 – Suggested maximum values for positioning system in native configuration. See [15] for a complete definition of commands. Values above those specified in Table C.1 can result in abrupt stops inducing excessive force on the mechanism and possibly cause the receive antenna to wobble. Other damage may also occur due to mechanical interference or mechanical limits being reached. While it is not recommended under any circumstances, if these values are exceeded, all precautions should be taken to minimize any component flexing or abrupt stops. The supporting hardware is all American Standard ¼”, 20 threads per inch stainless steel screws with corresponding nuts and stop nuts, except where noted. The 172 interfacing hardware is metric (the linear and rotary tables are specified metric) 6 mm cap screws. All hardware is commercially available from local suppliers and spare parts are located in the MPRG lab. The sealed ball-bearings in the linkage arms are 5/8” O.D. with ¼” I.D. accepting ¼” hardware. These specialized bearings are available from McMaster-Carr (part number 60355 K73 – www.mcmaster.com). Figures C.2 through C.5 illustrate the complete component specifications for the linkage base (parts 1 and 2), linkage arms, and antenna mount linkage. Given dimensions are in inches and are design dimensions; manufacturing tolerance may cause variations on the order of 100 m. 173 Fig u re C .2 – D riv en a rm link ag e b a se m o u nt sp ecificatio n s 174 Fig u re C .3 – Idler a rm link ag e b a se m o u nt sp ecificatio n s 175 Fig u re C .4 – Link ag e a rm sp ecificatio n s 176 Fig u re C .5 – A nten n a m o u nt link ag e sp ecificatio n s 177 Fig u re C .6 – T op , fro nt , a nd right sid e A utoC A D rend ering of 4 -b a r p a rallel link ag e a nten n a p o sitio ning sy stem 178 C.3 Assembly and Removal To assemble the system, first move the linear table and the rotary table to their home positions as shown in Figure C.7. Disconnect the power to both motors before proceeding. Figure C.7 – Linear and rotary table in home position prior to system installation Next, remove the two cap screws holding the rotary table to the carriage which are closest to the linear table drive. Using the blue M6 cap screws, attach the idler arm base linkage mount to the rotary table base, as shown in Figure C.8. Figure C.8 – Rotary table with idler arm base linkage mounted to rotary table base 179 Next, attach the driven arm base linkage mount to the rotary table using the two provided M6 19mm cap screws as shown in Figure C.9. Ensure that the bottom of the mount is flush with the rotary table base. Figure C.9 - Rotary table with driven arm base linkage mounted If using the modified configuration (required for operation with developed software) attach the idler arm offset to the idler arm base linkage mount using a 1-1/2” ¼-20 screw and stop nut, otherwise, skip to the next step. Position the idler arm offset so that it is approximately parallel to the driven arm base linkage mount as shown in Figure C.10. Figure C.10 – Idler arm offset mounted to idler arm linkage base The final step is to attach the linkage arm/antenna mount mechanism to the linkage bases as shown in Figure C.10. To do this, first place driven arm support on top of the driven 180 arm mount and affix the driven arm linkage using two 1-1/2” ¼-20 screws while resting the idler arm on the idler arm offset. Loosely tighten the two screws so there is no mechanical deflection. Second, using a ¼ inch slim-line open end wrench affix and tighten the stop nut to attach the idler arm to the idler arm offset as shown in Figure C.11. At this point, the system will support itself. Figure C.11 – Attaching the linkage arms to the rotary table via the base linkage mounts. Next, adjust the position of the idler arm offset so that the two linkage arms are exactly parallel as shown in Figure C.12. A rigid guide should be used to ensure the bars are parallel along their entire length. When the bars are parallel, the driven arm base and the idler arm offset will NOT be parallel. If the linkage arms are not parallel, the relative position of the antenna cannot be maintained. After making the bars parallel, tighten down the screw holding the idler arm offset to the idler arm linkage base mount. Figure C.12 shows the final configuration of the assembled 4-bar parallel linkage. After the assembly each screw and stop nut should be treated with a machine serviceable adhesive, such as Loctite© to fix their position. The system is now ready to accept a number of antenna mounts for positioning operations. 181 Figure C.12 – Assembled 4-bar parallel linkage antenna positioning system. To attach the PVC antenna mount used in this research, attach the PVC pipe and antenna to the antenna mounting linkage using 4, #6 machine screws with nuts. Attach the PVC so that the coax cable extending from the antenna leaves from the hole in the base of the PVC mount and points away from the mechanism to reduce any interference. Figure c.13 illustrates proper mounting of the PVC mast. Figure C.13 – PVC antenna mount attached to antenna mount linkage 182 To remove the system from the Parker Automation equipment, follow these steps in reverse. Take care when removing the linkage arm/antenna mount mechanism so that no additional force is place on the idler arm offset or rotary table. Excessive loading could cause permanent damage to the positioning equipment. In general, one should not move the positioning equipment with an antenna affixed to the boom. The arm is not designed to withstand all forces possible through accelerating or decelerating the entire system with a load attached. When moving the system with an antenna attached, ensure that movement is fluid and no abrupt stops are made, to protect both the positioning equipment as well as the antenna. C.4 Maintenance To ensure continued proper operation, it is necessary to maintain the positioning system. First, periodically check all mechanical connections to ensure they are tight and have not become lose. Due to vibrations and equipment movement, connections not treated with machine serviceable adhesive or stop nuts are prone to come lose. Inherent in the design is the possibility for mechanical interference between the idler arm linkage offset and driven arm linkage. If an interference condition is encountered follow these steps to safely correct it. First, immediately remove power to the stepper motor. Second, manually rotate the shaft in the direction to move the arm away from the interference. Inspect the region where the interference occurred to see if the idler arm linkage offset or linkage arm show signs of collision. If there is evidence of collision, inspect the coupling between the steeper motor and rotary table drive. If it is damaged or broken, remove and replace with a new coupling. It is necessary to periodically check the RS-232 interfaces on the fan-out box as well as the index command and position sensor lines (located on the PDX indexer units). If the wires on the command lines become lose it may cause the track or parallel linkage to oscillate in a random fashion, as if jammed. If this behavior is observed, ensure that all of the command wires are securely fashioned in the connector and that the jumpered wires are still connected. For details on the proper wiring configuration, refer to [15] as well as the troubleshooting guide. The ball-screw in both the track and the rotary table periodically need lubrication. See [16] and [17] for the proper type of lubrication and schedule for this maintenance. C.5 Troubleshooting Guide This section presents several common problems encountered during operation of the positioning system. A list of the problems followed by possible causes and solutions are presented. 1. Neither the track nor the parallel linkage responds to commands sent. First, verify that the communication link between the indexer and motor is operating properly. This can be checked by toggling the first DIN switch on the indexer labeled “self test”. If the motor moves, the link between the indexer and motor is OK (see [15] for more information on self test conditions). Second, verify that 183 the RS-232 connection is connected to the laptop as well as the fan out box. Verify that the “track” position sensor and command line are connected to the “track” inputs of the fan-out box and PDX indexer, respectively. Also, verify that the “spin” position sensor and command line are connected to the “spin” inputs of the fan-out box and PDX indexer, respectively. On the fan-out box, verify that the switches are set to “track enable” and “spin enable”, respectively. Finally, verify that there are no broken or lose connections between the indexers and positioning equipment. Make sure that the track is not set against one of its limits if trying to execute a move command. 2. The track or parallel linkage shakes/oscillates violently when a command is sent. This problem is most likely due to a loose or disconnected wire on the PDX indexer connector (black connector that plugs into indexers). Carefully remove the black connector and verify that all wires are securely in the plug and that jumpered wires are connected. For details on the proper wiring configuration refer to [15]. 3. The track or parallel linkage will not report status or movement stops after a homing routine. This behavior is most likely due to a buffer problem with the RS-232 link. First, physically disconnect the serial connection on the laptop and reestablish the link. Verify the two way link is operational by sending an R command. If both indexers are operational the return value should be *R. This is a good way to check on the status of the indexers. For more information on using this command, see the programming reference [15]. 4. Execution of the Labview application halts after initializing the track and the track stops moving. This behavior is caused by the motor_done_moving VI (see Section C.7 for software related issues) becoming stuck waiting for the indexer to respond with *R, indicating the end of a move. This can be caused by executing the initialization routine after an abrupt termination of the link or a buffer overrun. To correct this problem, refer to item number 3. When using a polling technique to wait on moves, it is imperative that a two way link be established and verified. 5. After apparent normal operation for several measurements the track stops operating. The serial buffer has a set limit (see [15]) of the number of characters that can be stored without clearing. This behavior will only occur for a long set of consecutive instructions or numerous back to back measurements. If this occurs, terminate the current session; disconnect the serial connection, and then begin a new session after reconnecting the serial cable. Refer to item numbers 3 and 4 for similar problems of this type. C.6 Positioning System Suggested Upgrades At the time of writing, there are several improvements that can be made to the existing positioning system to further improve its effectiveness. Hopefully, as time goes on and further contributions to this system are made, the list will become obsolete. 1. Upgrade the 1/4” plate steel linkage arms to 5/8” square aluminum stock. This upgrade will reduce the overall weight and reduce the deflection due to the 184 antenna mount. Furthermore, it will help eliminate the wobble encountered when moving the antenna at a high rate of speed. 2. Design and Implement a biasing scheme to eliminate transition regions. This upgrade will increase the useable repeatable range from approximately 170 degrees to 330 degrees. This will also make the maximum possible coverage area realizable. 3. Design and Implement a counter-weight to increase the end load capability. By implementing a counter weight system, the effective moment seen at the base can be reduced and a corresponding increase in length of the linkage arms or increase in end load. This system must be implemented while maintaining the 150 lbs maximum weight specification. For details on counter-weighing and moment arm calculations, see [19]. 4. Design and Implement smoother casters for easy mobility. The current configuration uses removable wood mounted casters which do not turn and bind easily. A system that allows smooth motion would aid in moving the track. 5. Fabricate linkage arms of various lengths for covering various areas. Larger or smaller areas (with improved resolution) can be obtained if families of linkage arms are manufactured. It is imperative however, that the maximum loading of the system is not violated. C.7 APAC System Requirements and Additional Support This section provides additional information on the Antenna Positioning and Acquisition Control (APAC) application designed in conjunction with the antenna positioning system. Covered in this section are the required software packages and drivers as well as details of the algorithm implementations. The APAC VI is available from MPRG which contains additional information in the form of comments concerning very specific implementation issues. Furthermore, the APAC CD (on file with MPRG) contains a directory template and installation files for all supporting programs (not Labview) for use with the sliding correlator measurement system. C.7.1 System Requirements In order for the APAC VI to operate, several additional Labview modules must be installed, which are all available for download from the internet. The following list details the requirements, including additional external hardware. 1. PC running Windows 98 or later with one available serial port 2. National Instruments Labview 6.0 or higher (Labview 7.0 recommended) with Measurement and Automation option installed 3. NI-VISA 2.5 or higher run-time environment for Windows 98/2000/ME/XP 4. TDS 5000 Series Digital Phosphor Oscilloscope Instrument Driver (available from www.ni.com) or equivalent corresponding to Oscilloscope used 5. NI-GPIB card (or equivalent) and installed drivers In addition to the requirements listed above, APAC expects a fixed directory structure consistent with legacy MPRG propagation measurement storage conventions. 185 A sample directory structure is contained with the source files for APAC and repeated here for completeness. The VI library APAC.llb should be place in a directory in which the installed instrument drivers are located (usually the default Labview directory). If the library file is placed elsewhere, it may be necessary to manually link the drivers to the library the first time it is opened. The following is a suggested directory structure for use with APAC. The subfolder structure of Measurements is required for proper operation. Table C.2 – Directory structure for proper operation of APAC In this structure, the APAC.llb file is placed in the Labview 7.0 folder. In configuring APAC the measurement directory field contained in CONFIGURE ALL should be set to the folder Measurements shown here. The folder DeleteAfterMeasCampaign must be created manually and the contents of it deleted regularly. As an artifact of the software, if there are multiple tracks per location, temporary folders are written to DeleteAfterMeasCampaign to avoid system errors. The temporary folders will have random names, denoted here by XXX, all of these should be deleted at the end of a measurement campaign. The folder loc999 must also be created manually, and by convention is the calibration directory. Within this folder, subfolders corresponding to the 3 digit transmitter chip rate in MHz must be created (denoted here by ZZZ). These subfolders are used to store the calibration waveforms and log files. When a log file is created using CREATE LOG TRACK LOCATION the location field specifies AAA and the track number specifies BBB. There can be multiple tracks per location, except they must be written sequentially (an error will occur if track002 is created and track001 does not exist). The contents of trackBBB will be N2 text files and one log file, pertaining to a grid measurement. There can be an arbitrary number of locations as long as each has a unique name. Additional information on the legacy storage structure of propagation measurements at MPRG can be found in the appendix of [5]. C.7.2 Converting User Parameters to 2-D Grid Definition As mentioned in Chapter 4, the convention which uses measurements per wavelength to define the grid adds an additional point to the grid when the number of measurements per wavelength is less than 1. Figure C.14 illustrates the spacing 186 convention and shows why the additional point is added. The example of Figure C.14 is one row of a measurement grid which is specified as a two wavelength grid with 4 measurements per wavelength. The top row of numbers corresponds to grid point while the bottom row corresponds to measurement number of the current wavelength. Since the convention was arbitrarily defined as shown, to measure a grid which is actually two wavelengths long, the additional point (denoted by X) must be added. Figure C.14 – Grid spacing convention used to derive measurement spacing from measurements per wavelength. C.7.3 System Specific Parameters As described in Chapter 4, there are several system specific parameters that will only change if the native configuration of the system changes. The lower level system parameters, such as linkage arm length, home reference and motor resolution can all be accessed by opening the sub VI sub_configure_track. After opening the VI and scrolling down, the data fields shown in Figure C.15 are accessible. The boom arm length (linkage length) and home reference are equal and are given by the center to center distance between the pivot point of the linkage base and the antenna mount. If the lengths of the linkage arms are changed, these parameters must be changed. The maximum grid length is determined empirically from the number of motor steps from the positioning system home to the point of mechanical interference. Similarly, the minimum XY resolution is calculated using equation (4.4). This should be entered as the worst case linear and angular resolution. This portion of the VI also allows the user to see the number of motor steps corresponding to the moves stored in the three positioning vectors [i], d[i], and sa[i]; i = 0:1:N-1. (0) (1) 1 2 3 4 1 2 3 4 X (2) (3) (4) (5) (6) (7) (8)   187 Figure C.15 – Configuration options that can only be accessed through opening the sub_configure_track VI separately and scrolling down. In the native configuration, these parameters will never change. C.7.4 A Note on Modifying APAC for Fast Acquisition There may be instances where rapid measurements are desired for continuous motion of the positioning system, for instance in the case of Doppler shift. In its native configuration APAC does not support this type of measurement. To modify the application an additional module would be required which significantly reduced the overhead associated with acquiring waveforms. The two areas this overhead can be reduced are in the scope acquisition time and APAC file storage time. The scope can be configured for fast frame acquisition using the existing scope drivers in APAC (refer to online help for more information). Reducing the file storage time should be addressed by storing the waveform in the form of two parameters (time start and offset) and values (voltage) for later reconstruction offline. Incorporating these ideas into a virtual instrument will be essential in successfully performing fast acquisition. C.7.5 APAC Suggested Upgrades At the time of writing there are several suggested upgrades o the APAC system. In light of these upgrades, it follows what the current limitations of the system are. The interested researcher is encouraged to address these issues in a second-generation version of this application. 1. Integrated DSO card operating in the Labview Environment. This improvement would significantly ease the burden (time and computational) of acquiring measurements. It would also make it easier for expansion of the acquisition functionality (such as in fast frame acquires) 2. Control signal generators and PN generators using APAC. This would allow easier set-up and variation of measurement parameters. 3. Automated calibration process. Making use of initial attenuation, attenuation step and, number of steps, a VI which semi-automated the process could be 188 implemented. A further improvement would be to make use of digitally controlled attenuators on the measurement system front end to completely automate the process. 4. Arbitrary two dimensional measurement grid. The extension to a rectangular grid would immediately provide more coverage area since the track is 1.2 m long. Further development could extend to arbitrary grid shapes, such as circular shapes. 5. Arbitrary positioning anywhere within the measurement grid. The current configuration allows for only complete sweeps of the grid. Adding a so called “jog” mode which allowed the user to position the system anywhere within the grid would be a valuable addition. This feature would allow missed points to be easily accessed. 6. Implement a “PAUSE” and “EMERGENCY STOP” feature. A pause feature would allow the measurement to cease if channel conditions suddenly changed (e.g. a bystander walks in front of the receiver). An emergency stop would reduce the risk of equipment damage if a possible interference condition is seen. 7. File writing overhaul. In the current configuration the directory structure for correct operation is very specific. A possible upgrade would be a routine which created the directory structure if it did not exist. Furthermore, the need for the temporary directory DeleteAfterMeasCampaign should be eliminated in any upgrades. C.8 Additional Support In addition to this user’s guide there is information available in the MPRG lab. This information includes the data sheets for the existing equipment as well as hardcopies of the design documents and the APAC code. For other support the following references are helpful: 1. Parker Automation: Daedal Division – www.daedalpositioning.com – linear table, rotary table, and indexer support. 2. McMaster-Carr – www.mcmaster.com – specialty hardware and materials for modification needs. 3. National Instruments – www.ni.com – Labview developer and support site 4. Labview Developers Zone - =labviewzone – code sharing and forum support 5. Labview Instrument Driver Network - - Specific hardware drivers for oscilloscopes and other equipment. 189 References [1] Rappaport, T. S., Wireless Communications: Principles and Practice 2nd Edition. New Jersey: Prentice-Hall 2002. [2] Proakis, J. G., Digital Communications Fourth Edition. Boston: McGraw-Hill 2001. [3] Parsons, J. D., The Mobile Radio Propagation Channel 2nd Edition. New York: John Wiley & Sons 2000. [4] Hashemi, H., “The Indoor Radio Propagation Channel,” IEEE Proceedings Vol. 81, Issue 7, pp. 943-968, July 1993. 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A., “On the Robustness of Ultra-Wide Bandwidth Signals in Dense Multipath Environments,” IEEE Communications Letters, Vol. 2, No. 2, pp. 51-53, February 1998. [22] Zaghoul, H., Morrison, G., and Fattoucher, M., “Comparison of Indoor Propagation Channel Characteristics at Different Frequencies,” Electronics Letters, Vol. 27, No. 22, pp. 2077-2079, October 1991 [23] Devasirvatham D.M.J., "Time Delay Spread and Signal Level Measurements of 850 MHz Radio Waves in Building Environments," IEEE Trans. on Ant. and Prop., Vol. AP-34, No. 11, Nov. 1986. [24] Devasirvatham D.M.J., Murray R.R., Wolter D.R., "Time Delay Spread Measurements in a Wireless Local Loop Testbed," Proc. IEEE VTC '95, Vol. 1, July 1995. 191 [25] J. D. Parsons, D. A. Demery, A. M. D. Turkamani, “Sounding Techniques for Wideband Mobile Radio Channels: A Review,” IEE Proceedings, vol. 138, no. 5, pp. 437-446, October 1992. [26] Tranter, W. H. Shanmugan, K. S., Rappaport, T., S., and Kosbar, K. L., Computer-Aided Design and Analysis of Communication Systems. New Jersey: Prentice Hall 2003. [27] Couch, L. W., Digital and Analog Communication Systems sixth edition. New Jersey: Prentice Hall 2001. [28] Schaffner, J., “A Constraint on the Length of the PN-code in the Sliding Correlator Spread Spectrum Channel Sounder,” Hughes Research Laboratories Technical Report. 2000. [29] Hao, X., “Terrestrial radio wave propagation at millimeter-wave frequencies,” Doctoral Dissertation, Virginia Polytechnic Institute and State University, April 2000. [30] Hansen, J., “An Analytical Calculation of Power Delay Profile and Delay Spread with Experimental Verification,” IEEE Communications Letters, Vol. 7, No. 6, pp. 257 - 259, June 2003. [31] Martin, G., “Wideband Channel Sounding Dynamic Range Using a Sliding Correlator”, Proc. IEEE VTC 2000, Vol. 3, pp. 2517 – 2521, May 2000. [32] Kivinen, ., Korhonen, P., Aikio, P., Gruber, R., Vainikainen, P. and Häggman, S., “Wideband Radio Measurement System at 2 GHz”, IEEE Transaction of Instrumentation and Measurement, Vol. 48, No. 1 February 1999. [33] Buehrer, R. M., Safaai-Jazi, A., Davis, W., Sweeney, D. et all, “Ultra-wideband Propagation Measurements and Modeling Final Report,” DARPA NETEX Program Final Report 2003. [34] Papoulis, A., Pillai, S., Probability, Random Variables and Stocahstic Processes 4th Edition, New York: McGraw-Hill, Inc. 2002. [35] Suzuki, H’, “A statistical model for urban raido propagation,” IEEE Trans on Communications, Vol. COM-25, pp. 673-680, July 1997. [36] McKinstry, D., “Ultra-Wideband Small Scale Channel Modeling and its Application to Receiver Design,” Masters Thesis, Virginia Polytechnic Institute and State University, May 2002. 192 [37] Win, M. Z., Scholtz, R. A., “Characterization of Ultra-Wide Bandwidth Wireless Indoor Channels: A Communication-Theoretic View”, IEEE Journal on Selected Areas in Communications, Vol. 20, No. 9 December 2002. [38] Qui, R. C., “A study of the Ultra-Wideband Wireless Propagation Channel and Optimum UWB Receiver Design”, IEEE Journal on Selected Areas in Communications, Vol. 20, No. 9 December 2002. [39] Huang, Y., Fan, X., Wang, J., Bi, G., “Analysis of the Energy Dynamic of UWB Signal in Multi-path Environments”, Proc. IEEE VTC ’03, Vol. 1, pp. 15 – 18 April 2003. [40] Cassioli, D., Win, M. Z., Molisch, A. F., “Effects of Spreading Bandwidth on the Performance of UWB Rake Receivers” IEEE International Conference on Communications, Vol 5, pp. 3545 – 3549, May 2003 [41] Zheng, C., Medard, M., “How Far Should We Spread Using DS-CDMA in Time and Frequency Selective Fading Channels?” IEEE Global Telecommunications Conference ’03, Vol. 3, pp. 1563 – 1567, Dec 2003. [42] Amoroso, F., “Use of DS/SS Signaling to Mitigate Rayleigh Fading in a Dense Scatterer Environment”, IEEE Personal Communications, Vol 3, Issue 2, April 1996. [43] Amoroso, F., Jones, W. W., “Modeling Direct Sequence Psuedonoise (DSPN) Signaling With Direction Antennas in the Dense Scatterer Mobile Environment”, Proc. IEEE VTC 1988, Vol. 3, pp. 2517 – 2521, May 2000. [44] Holtzman, J. H., Jalloul, M. A., “Rayleigh Fading Effect Reduction With Wideband DS/CDMA Signals”, IEEE Transactions on Communications, Vol. 42, No. 4 April 1994. [46] Amoroso, F., “Investigation of Signal Variance, Bit Error Rates, and Pulse Dispersion for DSPN Signaling in a Mobile Dense Scatterer Ray Tracing Model”, International Journal on Satellite Communications, Vol. 12, No. 5, pp. 579-588, December 1994. [47] Medard, M., Gallager, R. G., “Bandwidth Scaling for Fading Multipath Channels”, IEEE Transactions on Information Theory, Vol. 48, No. 4, pp. 840 – 852, April 2002. [48] Talbi, L., Delisle, G. Y., “Comparison of indoor propagation channel characteristics at 893 MHz and 37.2 GHz”, Proc. IEEE VTC 2000, Vol. 2, pp. 689 - 694, Sept. 2000. 193 [49] Davis, W. A., “Antenna Parameters and Modeling for Transient Applications (UWB)”, Virginia Tech EM Seminar, February 12, 2004. PowerPoint Presentation. [50] Ramirez-Mireles, F., Scholtz, R. A., “Performance of Equicorrelated ultra- wideband pulse-position-modulated signals in the indoor wireless impulse radio channel”, IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing, Vol. 2, pp. 640 – 680, Aug. 1997. [51] Cheng, J., Beaulieu, N. C., “Maximum-Likelihood Based Estimation of the Nakagami m Parameter”, IEEE Communications Letters, Vol. 5, No. 3, pp. 101- 103, March 2001. [52] Yan, j., Kozono, S., ”Study of Nakagami m parameter in mobile wide band channel –Case of no line of sight-“, Proc. IEEE VTC 2000, Vol.3, pp. 2162 - 2166, May 2000. [53] Weisstein, E., “mathworld: the web’s most extensive mathematics resource” Wolfram Research, Online. April 2004. www.mathworld.wolfram.com. [54] Arnold, J. T., Johnson, L. W., Riess, D. R., A Brief Introduction to Matrices and Vectors. Addison Wesley Longman 1998. [55] Duda, R. O., Hart, P. E., Stork, D. G., Pattern Classification 2nd Edition. New York: John-Wiley & Sons, INC. [56] W. C. Lau, M.-S. Alouini, M. K. Simon, “Optimum spreading bandwidth for selective Rake reception over Rayleigh fading channels”, IEEE Journal Selected Areas in Communications Vol. 19, pp. 1080-1089, June 2001. [57] Win, M. Z., Kostic, Z. A., “Virtual Path Analysis of Selective Rake Receiver in Dense Multipath Channels”, IEEE Communication Letters, Vol. 3, pp. 308-310, Nov 1999. [58] Babich, F., Lombardi, G., “Statistical analysis and characterization of the indoor propagation channel”, IEEE Transactions on Communications, Vol. 48, Issue 3, pp. 455 – 464, March 2000. [59] Schramm, P., “Analysis and Optimization of Pilot-Channel-Assisted BPSK for DS-CDMA Systems”, IEEE Transactions on Communications, Vol. 46, No. 9, pp. 1122 – 1123, Sept. 1998. [60] Nobel Lectures. Amsterdam: Elsevier Publishing Company. Online: 194 Vita Daniel James Hibbard was born in Williamsburg, Virginia and was raised in Toano, Virginia; graduating from Lafayette High School in 1998. Hibbard enrolled in Virginia Polytechnic Institute and State University in the fall of 1998 to pursue a Bachelor of Science degree in Electrical Engineer. In 2000, he was awarded the Rappaport wireless communication award for interest in the area of wireless communications. While at Virginia Tech, Hibbard participated in the Co-Op work experience as an electrical designer for Mathew J. Thompson III Consulting Engineers in Newport News, Virginia. As an undergraduate, he was a member of the Tau Beta Pi National Engineering Honor Society and IEEE, also earning the Engineer in Training (EIT) designation in 2002. Hibbard graduated Suma Cum Laude in the spring of 2002. In the fall of 2002, Hibbard began work towards a Master of Science degree in Electrical Engineering with Virginia Tech’s Mobile and Portable Radio Research Group. Also in 2002, Hibbard was awarded the Harry Lynde Bradley Fellowship for Graduate Study, which provided full research funding for the duration of his Masters research. In 2003 Hibbard worked as a summer intern at Raytheon in Falls Church, Virginia. He completed his Masters degree in the spring of 2004 and accepted a full time position with Raytheon in Falls Church. Hibbard’s research interests include radio wave propagation, propagation prediction, and propagation measurement systems as well as spread spectrum communication systems. Hibbard actively writes and records musical arrangements. He also actively participates in surfing, snowboarding, and mountain biking in his free time.

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