室內超寬頻無線電通道頻寬效應之研究

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國

立

交

通

大

學

電信工程學系碩士班

碩士論文

室內超寬頻無線電通道頻寬效應之研究

Effect of Bandwidth on Indoor

UWB Radio Channels

研究生 : 沈鳴君

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室內超寬頻無線電通道頻寬效應之研究

Effect of Bandwidth on Indoor UWB Radio Channels

研究生：沈鳴君 Student : Ming-Jiun Shen

指導教授：唐震寰 Advisor : Dr. Jenn-Hwan Tarng

國立交通大學

電信工程學系碩士班

碩士論文

A Thesis

Submitted to Department of Communication Engineering

College of Electrical and Computer Engineering

National Chiao Tung University

in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

in

Communication Engineering

July 2004

Hsinchu, Taiwan, Republic of China

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室內超寬頻無線電通道頻寬效應之研究

研究生：沈鳴君指導教授：唐震寰博士

國立交通大學

電信工程研究所

摘要

本論文主要是研究室內環境超寬頻無線電傅播之頻寬效應，在此論文中，吾人是以隨機節拍-延遲-線模型，描述室內超寬頻通道的特性，在此模型是以兩種參數：功率比值r 以及衰減常數ε來描述平均功率延遲曲線圖，而這些參數可經由在大樓內進行大量的量測之後計算得到，而所量測頻段為3 GHz 至 5 GHz。由計算結果發現以下之現象：（1）衰減常數僅稍微與訊號頻寬有關；（2）功率比值會隨著頻寬增加而變小；（3）衰減常數會隨著區域散射體愈靠近接收端而變小；（4）功率比值會隨著區域散射體愈靠近接收端而變大；（5）在視線內環境，Rician 因子會隨著頻寬增加而變小；（6）在非視線內環境，Rician 因子會隨著頻寬增加而變大。

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Effect of Bandwidth on Indoor UWB Radio

Channels

Student : Ming-Jiun Shen Advisor : Dr. Jenn-Hwan Tarng

Department of Communication Engineering and Institute of Communication National Chiao Tung University

Abstract

Effects of bandwidth on Ultra-Wideband (UWB) radio propagation in indoor environments are investigated. To characterize the indoor UWB channels, the stochastic tapped-delay-line (STDL) model is employed. With the STDL model, the power delay profile (PDP) can be described by using power ratio r and decay constant εas described. Those parameters can be calculated with a large number of measurement data carried out at an education building. The measured frequencies are ranged from 3 GHz to 5GHz. It is found that (1) The decay constant of the PDP is only slightly dependent on the signal bandwidth; (2) The power ratio of the PDP is decreased when the signal bandwidth is increased; (3) The decay constant is decreased as the local scatterers move closer to receiver; (4) The power ratio is increased as the local scatterers move closer to receiver; (5) The Rician factor is decreased when radio bandwidth is increased of LOS condition; (6) The Rician factor is increased when radio bandwidth is increased of NLOS condition.

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誌謝

首先，我要對我的指導教授唐震寰老師致上最誠摯的感謝，感謝

老師在我碩士兩年的研究生涯中，給于我最細心與凡心的指導與叮

嚀，並帶領我一窺無線通訊領域研究的奧妙。

其次，對於波散射與傳播實驗室的學長與同學們也要致上我深深的謝

意，他們所給予我在知識上和精神上的啟示與鼓勵以及在實驗量測中

的協助，對完成本篇論文有莫大的助益。

最後，要感謝的是我的家人，由於他們給予我的支持與關懷，使我在

人生的過程裡得到最細心的呵護與照顧，讓我在成長與求學的過程中

能夠有所依靠。

僅以此篇論文獻給所有關心我的人。

沈鳴君

國立交通大學，新竹市

中華民國九十三年七月

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K

Model...12

2.3 Received Envelope Distribution...15

2.3.1 Rayleigh Fading...15

2.3.2 Rician Fading ...15

2.3.3 Nakagami Fading ...16

Chapter 3 Measurement System and Environment...17

3.1 Measurement System and Setup...18

3.2 Measurement Environment Description...24

3.3 Measurement Result ...32

Chapter 4 Effects of Signal Bandwidth and Propagation on UWB Channels ...34

4.1 Effect of Bandwidth and Propagation on Instantaneous Power Delay Profile ...34

4.2 Effect of Bandwidth and Propagation on Averaged Power Delay Profile (Not including local scattering effects)...58

4.3 Effect of Signal Bandwidth on Amplitude fading ...65

Chapter 5 Conclusion...73

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Figure Captions

Figure 2-1 Transmitting energy versus radio signals...6

Figure 2-2 Power delay profiles of ultra wideband and narrowband communications. UWB systems have very high resolution. ...6

Figure 2-2 The average power delay profile versus the excess delay...10

Figure 2-3 An illustration of channel impulse response. ...12

Figure 2-4 An illustration of exponential decay of mean cluster power and ray power within clusters. ...12

Figure 2-5. Illustration of theΔ-K process. ...13

Fig. 3-2 A photo of the frequency domain channel sounding system...21

Fig. 3-3 A photo of the wideband antenna. ...21

Figure 3-4 (a) Vertical and (b) Horizontal pattern of the transmitted and received antennas...23

Fig. 3-5 (a) Small-scale variation square grid; (b) The variation of Rician factor for different square grid...25

Figure 3-6 9th floor layout of the 4th Engineering Building. (a) There are 5 measured points in Room 901; (b) There are 6 measured points in Room 911A. ...26

Figure 3-6 2nd floor layout of the 4th Engineering Building. (c) There are 5 measured points in Room 203; (d) There are 4 measured points in Room 215...27

Figure3-6 (e) 3rd floor layout of the 4th Engineering Building. ...28

Figure 3-6 (f) 7th floor layout of the 4th Engineering Building. ...29

Figure 3-7 Power delay profiles measured at 64 locations separated by λ/2 on indoor. (a)The measured PDP at no.1 of LOS situation; (b) The measured PDP at no.2 of NLOS situatio. ...33

Figure 4-1 The normalized instantaneous PDP of subpoint no.110 in Room 901 for different bandwidth. (a) The bandwidth is 2 GHz with power ratio r=0.016,decay constantε=14.73(ns); (b) The bandwidth is 1.5 GHz with r=0.019,ε=16.09(ns); (c) The bandwidth is 1 GHz with r=0.029,ε=15.49(ns); (d) The bandwidth is 500 MHz with r=0.041,ε=17.33(ns)...39 Figure 4-2 The normalized instantaneous PDP of subpoint no.124 in Room

901 for different bandwidth. (a) The bandwidth is 2 GHz with r=0.016,ε=14.75(ns); (b) The bandwidth is 1.5 GHz with r=0.019,ε=17.62(ns); (c) The bandwidth is 1 GHz with r=0.021,ε=15.97(ns); (d) The bandwidth is 500 MHz with

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r=0.031,ε=19.74(ns)...41 Figure 4-3 The normalized instantaneous PDP of subpoint no.2430 in Room

r=0.263,ε=21.58(ns)...43 Figure 4-4 The normalized instantaneous PDP of subpoint no.2450 in Room

r=0.185,ε=22.82(ns)...45 Figure 4-5 The histogram of the power ratio (in dB scale)can be fitted well

by a normal distribution. (a)The bandwidth is 2 GHz withµr= -16.44 dB and σr= 1.55 dB; (b)The bandwidth is 1 GHz withµr= -13.66 dB and σr= 1.78 dB; (c) The bandwidth is 500 MHz withµr= -11.6 dB and σr= 2.13 dB...47 Figure 4-6 The histogram of the logarithmic decay constant can be fitted

well by a normal distribution. (a)The bandwidth is 2 GHz withµε= 11.48 dB and σε= 0.19 dB; (b)The bandwidth is 1 GHz withµε= 11.58 dB and σε= 0.31 dB; (c) The bandwidth is 500 MHz withµε= 11.87 dB and σε= 0.52 dB...48 Figure 4-7. Power ratio r versus signal bandwidth at different measurement

subpoints for the LOS 0-4m situation...49 Figure 4-8. Decay constantεversus signal bandwidth at different

measurement subpoints for the LOS 0-4m situation...49 Figure 4-9. Power ratio r versus signal bandwidth at different measurement

subpoints for the LOS 4-10m situation...50 Figure 4-10. Decay constantεversus signal bandwidth at different

measurement subpoints for the LOS 4-10m situation...50 Figure 4-11. Power ratio r versus signal bandwidth at different measurement subpoints for the NLOS 0-4m situation. ...51 Figure 4-12. Decay constantεversus signal bandwidth at different

measurement subpoints for the NLOS 0-4m situation...51 Figure 4-13. Power ratio r versus signal bandwidth at different measurement subpoints for the NLOS 4-20m situation. ...52 Figure 4-14. Decay constantεversus signal bandwidth at different

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measurement subpoints for the NLOS 4-20m situation...52 Figure 4-15 (a) There are near local scatterers distribution around the

receiver within a radius of 20cm in a laboratory. (b) There is slightly far local scatterers distribution around the receiver within a radius of 45cm in the laboratory. ...53 Figure 4-16 The effect multipath number versus the delay bin for different

local scatterer distribution around the receiver. (a) There is no local scatterer distribution around the receiver; (b) There is farer scatterer distribution around the receiver; (c) There is nearer scatterer

distribution around the receiver. ...54 Figure 4-17 The power ratio historgrams of different local scatterers

distribution around the receiver conditions. (a)µr= -19.84 and σr= 1.57 of no local scatterers situation; (b) µr= -18.92 and σr= 1.414 of farer local scatterers situation; (c) µr= -18.15 and σr= 1.6 of nearer local scatterer situation. ...56 Figure 4-18 The decay constant historgrams of different local scatterers

distribution around the receiver conditions. (a) µε= 11.33 and σε=0.2 of no local scatterer situation; (b)µε= 11.11 and σε=0.18 of farer local scatterers situation; (c) µε=11.09 and σε= 0.19 of nearer local scatterers situation...57 Figure 4-19 The normalized average PDP of point no.24 in Room 302 for

different bandwidth. (a) The bandwidth is 2 GHz with r=0.165,ε=26.38(ns); (b) The bandwidth is 500 MHz with

r=0.292,ε=25.7(ns)...60 Figure 4-20 The normalized average PDP of point no.15 in Room 203 for

different bandwidth. (a) The bandwidth is 2 GHz with r=0.012,ε=19.4(ns); (b) The bandwidth is 500 MHz with

r=0.068,ε=17(ns)...61 Figure 4-21 The power ratio versus the distance between Tx and Rx...62 Figure 4-22 The decay constant versus the distance between Tx and Rx....62 Figure 4-23 The histogram of the power ratio (in dB scale) can be fitted

well by a normal distribution withμr=-13.81 dB and σr=4.25 dB...63

Figure 4-24 The histogram of the logarithmic decay constant can be fitted well by a normal distribution with με=12.07 dB and σε=1.45 dB. .63

Figure 4-25. Power ratio r versus signal bandwidth at different measurement points for the LOS 0-4m situation. ...64 Figure 4-26. Decay constantεversus signal bandwidth at different

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Figure 4-27(a) PDF of measured and fitted signal amplitudes of the 38 bin in Room 303 for NLOS environment. The bandwidth is 2GHz.

th ...67 Figure 4-27(b) PDF of measured and fitted signal amplitudes of the 65 bin

in Room 303 for NLOS environment. The bandwidth is 2GHz. th ...67 Figure 4-28(a) PDF of measured and computed signal amplitudes of the

first bin at point no.2 follows a Rician distribution with K= 8.7...68 Figure 4-28(b) PDF of measured and calculated signal amplitudes of the

first bin at point no.16 follows a Rician distribution with K=26.4...68 Figure 4-28(c) PDF of measured and computed signal amplitudes of the

first bin at point no.21 follows a Rician distribution with K=16.4...69 Figure 4-28(d) PDF of measured and computed signal amplitudes of the

first bin at point no.41 follows a Rician distribution with K= 17.2...69 Figure 4-29 Rician factor K versus signal bandwidth at different

measurement points of the LOS 0-4m situation. ...70 Figure 4-30 Rician factor K versus signal bandwidth at different

measurement points of the NLOS 0-4m situation...70 Figure 4-31 Rician factor K versus signal bandwidth at different

measurement points of the LOS 4-10m situation. ...71 Figure 4-32 Rician factor K versus signal bandwidth at different

measurement points of the NLOS 4-20m situation...71 Figure 4-33 The Rician factor versus the distance between Tx and Rx. ...72

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Table Captions

Table 1-1 Several result on UWB channel model have been explored...3 Table 2-1 UWB compared to existing data communications standards. ....8 Table 3-1 The main parameters in the measurement. ...20 Table 3-2 The different channel scenarios...30

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Chapter 1 Introduction

In recent years, ultra-wideband (UWB) communications has received great interest from both the research community and industry. The potential strength of the UWB radio technique lies in its use of extremely wide transmission bandwidths, which results in desirable capabilities including accurate position location and ranging, lack of significant fading, high multiple access capability, covert communications, and possible easier material penetration. UWB is an old technology with a new lease on life. Long used by the U.S. military, In February 2001, the American Federal Communications Commission (FCC) issued a report and order that allows the transmission of UWB signals if certain power restrictions are fulfilled.

Wireless communication plays an important role in our daily life. With lower price and more applications, wireless communication is getting popularized. Folks can easily afford to build a local-area network (LAN) at home and use the mobile computing devices without any cable limits. In the future, people will be eager to retire the miscellaneous cables and wires, and use wireless technologies to enjoy their home electric appliances.

Accurate performance prediction of such systems in a realistic environment necessitates the knowledge of UWB multipath channel characteristics, especially the statistical distribution of small-scale fluctuations. It is because that channel capacity is a function of the signal to interference ratio [1].

Currently, IEEE 802.15 study group SG3a is developing a high rate physical (PHY) for wireless personal area network (WPAN). UWB may be selected for this PHY due to its unique suitability for this application. For the varied WPAN

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applications, different radio bandwidth is needed to meet the data rate and quality of service requirements [2]. According to the FCC regulations of UWB radio technology and systems [3], the radio bandwidth that affects the resolvable multipath number may vary in a wide range from several hundred MHz to a few GHz. Several contributions on UWB channel model have been showed in Table 1-1.

However, few researches focused on the studies of the effect of radio bandwidth on propagation channel model so far. In this article, the stochastic tapped-delay-line (STDL) model is used, which describes the indoor UWB channels with the parameters such as delay constant and power ratio of the averaged power-delay profile (PDP). The effect of radio bandwidth on these two parameters is analyzed by measurement results. The amplitude distribution of small-scale fading was estimated the effect of radio bandwidth on the multipath phenomenon.

This article is organized as follows. In chapter 2, we will describe radio propagation characteristics and some popular indoor channel models for UWB channel. In the same chapter, several amplitude statistics of small-scale fading will be discussed. In chapter 3, is the UWB channels measurement. We will describe the measurement system and environment. In chapter 4, from our measurement and analysis results, the Rican factor and those parameters of STDL model will be calculated. The effect of radio bandwidth on small scale fading and those parameters will be analyzed. A brief conclusion is provided in Chapter 5.

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Ref.

No. Measurement Environment Measurement Result

[6] _{In an office building} The PDP can be modeled by a single exponential decay.

The energy statistics follows a Gamma distribution

The fading of each bin is uncorrelated

[14] _{In a home environment} _{The S-V model and lognormal amplitude} distribution can fit the PDP of the

measurement data

[15] _{In an office/laboratory building S-V model which demonstrated the} clustering phenomenon

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Chapter 2 UWB Propagation Characteristic and Modeling

Wireless propagation channels have been investigated for more than 50 years, and a large number of channel models are available in the literature. The signal that has propagated through a wireless channel consists of multiple replicas (echoes) of the originally transmitted signal; this phenomenon is known as multipath propagation. The different multipath components (MPCs) are characterized by different delays and attenuations. Thus, at the receiver, all the MPCs can interfere (constructively or destructively). If there is a large number of MPCs, the complex amplitude has a complex Gaussian distribution, which results in a Rayleigh or Rician distribution of the amplitudes.

UWB systems have very large bandwidth. Thus, the different delays of the multipath components influence the system performance, and have to be modeled. The power delay profile of the channel describes how much power arrives within a certain delay interval. For system analysis, the delay axis is typically divided into bins whose size is comparable to the inverse of the system bandwidth. If enough MPCs fall within such a delay bin, there is still interference between the MPCs, and the amplitude statistics within each delay bin is Rayleigh or Rice. However, UWB systems have very high resolution in the time domain and only a small number of multipath components fall into each bin of the delay profile, the small scale distributions of the path gains may not follow the traditional amplitude statistics. In this chapter we will describe UWB characteristics and three indoor channel models. At last, we will describe several amplitude statistics of small-scale fading.

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2.1 UWB Basic Characteristics

The FCC has defined that UWB transmissions fall within the frequencies of 3.1 to 10.6 GHz, with a minimum spectral width of 500 MHz , or 25 percent of the center

frequency (3.5 to 4.5 GHz for a center frequency of 4 GHz). By dividing the power of the signal across a range of frequencies, the affect upon any frequency is below the acceptable noise floor for unintentional emitters that FCC Part 15 rules define. Table 2-1 showed the UWB compared to existing data communications standards.

An UWB signal is generally defined to be a radio signal with fractional bandwidth greater than 0.25 or bandwidth more than 500MHz, where fractional bandwidth (FBW) is defined as

FBW=2*(f

H

-f

L

)/(f

H

+f

L

)

(2.1)

where fH is the upper frequency of the –10 dB emission point and fL is the lower

frequency of the –10 dB emission point. The center frequency of the transmission was defined as the average of the upper and lower –10 dB points, i.e., (fH + fL)/2. The

Commission proposed to base its modified definition of an UWB device on –10 dB bandwidth, rather than the –20 dB bandwidth, because under the Part 15 limits, UWB devices operate so close to the noise floor that in many cases it may not be possible to measure the –20 dB bandwidth.

UWB systems can use very low transmit power without interfering with existing communication systems. However, lower power levels typically limits the signals to shorter ranges. Narrowband communications pack transmitting energy into a small fractional bandwidth. Ultra wideband communications spread transmitting energy across a wide spectrum frequency, such that the energy in any frequency band is below the noise flow. This is illustrated in Figure 2-1 below.

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Transmitting energy

Figure 2-1 Transmitting energy versus radio signals.

Within the power limit allowed under current FCC regulations, UWB can carry huge amounts of data over a short distance at very low power, while also having the ability to carry signals through doors and other obstacles that tend to reflect signals at more limited bandwidths and a higher power. At higher power levels, UWB signals can travel to significantly greater ranges.

The ultra-short signal in UWB systems creates dramatic gains in path resolution when compared to narrowband and wideband communication systems. For UWB signals with GHz bandwidths, the multipath resolution is on the order of a nanosecond or less, i.e., down to path length differentials on the order of 0.3m or less. The higher path resolution of UWB systems leads to a smaller number of paths in each bin than that of narrowband or wideband systems. This is illustrated in Figure 2-2 below.

Figure 2-2 Power delay profiles of ultra wideband and narrowband communications. UWB systems have very high resolution.

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transmission bandwidths, resulting in the following desirable capabilities including: • Accurate position location and ranging, and lack of significant multipath fading

due to fine delay resolution.

• Multiple access due to wide transmission bandwidth.

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Zigbee Bluetooth 802.15.3 UWB 802.11b 802.11a 802.11g IEEE Task

Group 802.15.4 802.15.1 802.15.3 802.15.3a 802.11b 802.11a 802.11g

Frequency band 2.4GHz 900Mhz 2.4 GHz 2.4GHz 3.1-10.6GHz 2.4 GHz 5 GHz 2.4 GHz Data rate 40 to 240 Kbps Up to 1 Mbit/s Up to 55 Mbit/s >100 Mbit/s Up to 22 Mbit/s Up to 54 Mbit/s > 22 Mbit/s Range 20 meters 10-20 meters Up to 10 meters 10-30 meters 100 meters 100 meters 100 meters QoS/MAC In progress No video support. Peer-to peer and ad hoc netwrkg. Guarantee d time slots. Ad hoc netwrkg. Power mgmnt. TBD Guaranteed time slots for video, ad hoc netwrkg.

Will use 802.15.3

MAC.

Non-guaranteed QoS, no video support, no ad hoc netwrkg—New MAC standards such as 802.11d and .11h expect to include video and multimedia support.

PHY DSSS-- BPSK O-QPSK FSK QPSK 16.32.64 QAM Multi-band OFDM CCK OFDM 8-PSK or OFDM and CCK Spatial

Capacity/m2 Unknown 30 kbps Unknown >1000 kbps 1 kbps 55-83 kbps

Table 2-1 UWB compared to existing data communications standards. Legend:

CC = Complementary Code Keying

OFDM= Orthogonal Frequency Division Multiplexing QAM= Quadrature Amplitude Modulation

QPSK= Quadrature PSK FSK= Frequency Shift Keying PSK= Phase Key Shifting

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2.2 UWB Multipath Model Comparison

Although UWB systems can be described by frequency-domain or time-domain models, our work focus on evaluating discrete time models. This model is based upon the following channel impulse response model [19]:

) ( ) ( 1 0 l L l l t t h =

∑

−α δ −τ = (2.2) where α_l is the amplitude fading factor on path l (could be complex), τ_l is the random delay of path l, L is the number of multipath components, and δ(t) is the Derac delta function.

In practice, the rays of the received signal arrive in clusters. The formation of the clusters is related to the building superstructure (e.g., large metalized external or internal walls and doors). The rays within a cluster are formed by multiple reflections from objects in the vicinities of the transmitter and the receiver (e.g., room walls, furnishings, and people). There are three main indoor channel models can demonstrated the realistic multipath phenomenon :the tap-delay line model[20], the Saleh-Valenzuela (S-V) model [4], and theΔ-K model described in [5], as well as several novel modifications to these approaches that better matched the measurement characteristics. The following sections describe different multipath channel models.

2.2.1 Stochastic Tapped Delay Line Model (STDL)

The STDL model characterizes the shape of the PDP of the UWB indoor channel in terms of path power and delays of a subsequent discrete taps with equal time spacing, i.e., by the pairs {Pk, τk} with τk=(k-1)∆, where ∆ is the tap spacing which is inversely proportional to the radio bandwidth of the considered system. Therefore, the power of each tap, Pk, results from the square of the sum of the complex fields of multipath components (MPCs) arriving within ∆τ of the corresponding bin varies rapidly [4]. The power delay profile is shown below in Figure 2-2.

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exponentially (linearly on a decibel scale) with delay starting from the second bin, and may be expressed as

( )

N

(

)

(

)

N

(

k 2

)

(

k k 1 1 2 k 1 k 2 P τ P δ τ τ Pδ τ τ P exp τ τ δ τ τ_k

)

ε = = − ⎛ ⎞ = − = − + _⎜− _⎟ ⎝ ⎠

∑

− (2.3)

(

)

N

(

k 2

)

(

1 1 k 2 P δ τ τ r exp τ τ δ τ τ ε = ⎧ ⎛ − ⎞ ⎫ ⎪ ⎪ = _⎨ − + _⎜− _⎟ − _⎬ ⎪ ⎝ ⎠ ⎪ ⎩

∑

k

)

⎭ (2.4) where N is the total number of bins in the observation window, r = P / P is the ratio ₂ ₁ of the average power of the second tap to the first tap, and ε is the exponentially power decay constant. It is noted that, P_k are normalized to the power of the first tap, and τk are translated to the delay of the first tap.

Figure 2-2 The average power delay profile versus the excess delay.

2.2.2 Saleh-Valenzuela Model (S-V)

The major difference between Saleh-Valenzuela model [4] and STDL model is that Saleh-Valenzuela model doesn’t assume the arrival of paths on each sampling time interval. Instead, two Poisson models are employed in the modeling of the arrival

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time. The first Poisson model is for the first path of each path cluster and the second Poisson model is for the paths (or rays) within each cluster. Following the terminology in [8], we define

Tl = the arrival time of the first path of the l-th cluster;

τk,l = the delay of the k-the path within the l-th cluster relative to the first path

arrival time, Tl;

Λ = cluster arrival rate;

λ = ray arrival rate, i.e., the arrival rate of path within each cluster.

By definition, we have τ_0l = . The distribution of cluster arrival time and the ray T_l arrival time are given by

(

)

(

)

(

)

(

)

1 1 , ( 1), , ( 1), exp , 0 exp , 0 l l l l k l k l k l k l p T T T T l p τ τ λ λ τ τ k − − − − ⎡ ⎤ = Λ _⎣−Λ − _⎦ > ⎡ ⎤ = _⎣− − _⎦ > (2.5)

The magnitude of the k-th path within the l-th cluster is denoted by βkl. It is

Rayleigh distributed with a mean given by

( )

(

)

(

)

2 2 _{0,0 exp} _/ _exp _/ _,

l kl

kl T

β =β − Γ −τ λ (2.6)

where _β2

( )

_0,0 _{is the average power of the first arrival of the first cluster.}

Illustrations of channel impulse responses are shown below in Figure 2-3 and the double exponential decay model in Figure 2-4.

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Path Magnitude Time cluster 0

T 1 13 τ 13 β

Figure 2-3 An illustration of channel impulse response.

Figure 2-4 An illustration of exponential decay of mean cluster power and ray power within clusters.

2.2.3 Turin’s Δ-

K

Model

Turin’s Δ- model [10] proposes a modified Poisson process to take into account the possibility that multipath may arrive in-group. In this model, time axis is partitioned into bins with width Δ which is equal to the time resolution of the transceiver, the arrival rate of multipath is a function of whether or not an arrival occurred in the previous bin, and is a function of empirically based measurements of the probability of path occurrences at different delays. It can be stated as the branching process of Figure 2-5: when a path occurs in bin i, the path arrival rate of

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the next binλ_{i 1}₊ is increased by a factor . For >1, the process exhibits a clustering property and large K leads a large clustering phenomenon. For =1, this process reverts to a standard Poisson process. It is noted that the clustering phenomenon or value is dependent on the propagation environment.

K K

K

As shown in Figure 2-5, there exists the following relation between the empirical path occurrences rate P_i, and the path arrival rate λ_i.

( )

i i i 1 P K 1 P 1 λ − = − + ( i≠1) (2.7) where λ₁=P₁.

Figure 2-5. Illustration of theΔ- K process.

The impulse response of bin i is denoted as α_i, and the path amplitude |α_i| is lognormal distributed with an exponentially decaying multipath intensity profile (MIP). 2 T / 0 E i i e Γ α Ω − ⎡ _{⎤ =} ⎣ ⎦ (2.8)

where is the excess delay of bin i and T_i Ω is the mean power of the first ₀ path of the first cluster.

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This model can also capture the multipath clustering phenomenon, similar to the S-V model.

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2.3 Received Envelope Distribution

The small-scale effects are manifested in the changes of the PDP caused by small changes of the receiver position, while the environment around the receiver does not change significantly. The statistics of small scale signal fading on individual multipath components can provide insight into jitter and equalizer requirements.

Most common distributions found in literature, used to describe rapid fading variations, are the Rayleigh, Rice, Nakagami, and Lognormal distributions [11]. Several amplitude distribution of the multipath components have bee descried in below.

2.3.1 Rayleigh Fading

When the composite received signal consists of a large number of plane waves, the received envelope has a Rayleigh distribution, i.e.

2 2 ( ) exp 2 z 2 x x p x σ σ ⎧ = _⎨− ⎩ ⎭ ⎫ ⎬

(2.9)

For a Rayleigh distributed envelope, the average power is_Ω ₂ 2

p = σ , so that 2 2 ( ) exp Ω Ω z p p x x p x = ⎧⎪_⎨− ⎪ ⎪ ⎩ ⎭ ⎫⎪ ⎬

(2.10)

Rayleigh fading usually applies to any scenario where there is no LOS path between the transmitter and receiver antennas.

2.3.2 Rician Fading

For a multipath-fading channel containing a LOS component, the complex envelope has a Rician distribution, i.e.

2 2 2 2 ( ) exp 2 z 2 x x s xs p x σ σ σ ⎧ + ⎫ ⎛ = _⎨− _{⎬ ⎜} ⎝ ⎠ ⎩ ⎭I0 ⎞ ⎟

(2.11)

The Rice distribution is often characterized by the K-factor that is defined as the ratio of the power of the direct path component _s2 and the random one

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2

2σ ,_K ₌_s2_{/ 2}_σ2

(

_{K 0}_≥

)

_{. When K=0 the channel exhibits Rayleigh fading, and}

when the channel does not exhibit fading. For a Rician distributed envelope, the average power

= ∞ K 2 Ω_p ₌s ₊2_σ2_{, so that} ( 1) ( 1) ( 1) ( ) exp 2 Ω Ω ⎛ ⎞ ⎧ ⎫ ⎪ ⎪ = _⎨− − _{⎬ ⎜}⎜ ⎪ ⎪ ⎩ ⎭ ⎝ ⎠ 2 z p p 2x K + K + x K K + p x K I0 x _Ω ⎟⎟ p

(2.12)

2.3.3 Nakagami Fading

The Nakagami distribution was introduced by Nakagami in the early 1940’s to characterize rapid fading in long distance HF channels [12]. The Nakagami distribution was selected to fit empirical data, and is known to provide a closer match to some experimental data than either the Rayleigh, or Ricean distributions [13]. In essence, the Nakagami distribution describes the received envelope, i.e.

2 1 2 2 ( 1) ( ) exp Γ( )Ω Ω ⎧ ⎫ ⎪ ⎪ = _⎨− _⎬ ⎪ ⎪ ⎩ ⎭ m m-z m p p m x K + mx p x m

1 2 ≥ m

(2.13)

The Nakagami distribution is often used to model multipath fading for the following reasons. First, the Nakagami distribution can model fading conditions that are either more or less severe than Rayleigh fading. When m=1, the Nakagami distribution becomes the Rayleigh distribution, when m=1/2 it becomes a one-sided Gaussian distribution. Second, the Rice distribution (which does have physical significance) can be closely approximated by using the relation ( 1)2

(2 1)

K + m =

K +

,

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Chapter 3 Measurement System and Environment

In a typical indoor environment, due to reflection, refraction and scattering of radio waves by structures inside a building, the transmitted signal most often reaches the receiver by more than one path, resulting in a phenomenon known as multipath fading. In UWB pulse transmission, the effect is to produce a series of delayed and attenuated pulses (echoes) for each transmitted pulse.

The main objective of a channel sounding is to model the UWB channel correctly. Consequently, if the multipath is well characterized, transmitter and receiver can be designed in order to decrease the consequences of these phenomena.

In order to obtain the channel characteristics in different environments, the UWB channel measurement methods are proposed for analyzing each composition of multipath response. We also classified the propagation scenarios into four categories base on measurement report [7]:

1. LOS (Line-of-Sight) scenario, the scope of distance between transmitter and receiver is 0-4m.

2. LOS scenario, the scope of distance between transmitter and receiver is 4-10m.

3. NLOS (Non-Line-of Sight) scenario, the scope of distance between transmitter and receiver is 0-4m.

4. NLOS scenario, the scope of distance between transmitter and receiver is 4-20m.

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3.1 Measurement System and Setup

In order to obtain the channel characteristics, the UWB channel measurement is performed to analyze the MPCs. A typical frequency domain channel sounder is shown in Fig. 3-1. A vector network analyzer contains a synthesized frequency sweeper and an S-parameter test set. At Port 1 the S-parameter test set transmits a known signal level for each frequency step and detects the received complex response of the channel, S21 (f), at port 2.

Figure 3-1 Frequency domain channel response measurement system [9].

In our study is performed in frequency domain through a Vector Network Analyser whose specifications are detailed further. This method consists in exciting the channel with tones over a wide range of frequencies. The attenuation and phase shift of each frequency component caused by the propagation medium is measured. Moreover, the exact time-domain response is also obtained by taking the inverse

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Fourier transform. Each measurement is performed in time and frequency domain thanks to the Vector Network Analyzer. This device will be commanded through the LAN network for exporting the S21 parameters representing the linear attenuation factor in domains, frequency and time. For UWB application, the swept frequency band is from 3GHz to 5GHz (2GHz of frequency span). With 2.5MHz steps, corresponding to 801 points, we would be able to detect multipath with a time delay up to 400ns

An Agilent 8719ET Vector Network Analyzer (VNA) is exploited to measure the channel response between two ends. The transmitted signal is sent from the VNA to the transmitting antenna through a low-loss 10-m coaxial cable. For our measurement campaign, we used a pair of omni-directional wideband antennas by Electro-Metrics (EM-6865), which frequency range is 2-18 GHz and antenna gain is 0dBi. The signal from the receiving antenna through a preamplifier (with a gain of 30 dB) via a low-loss 30-m coaxial cable, then returned to port2 of the VNA. Besides the network analyzer, the time-domain channel response can be obtained by taking the inverse Fourier transform (IFFT) of the frequency-domain channel response. Table 3-1 lists the main parameters in the measurement.

During the measurement, both the Rx and Tx antennas are at a height 1.5m above the ground. The measurement system is shown in Figure 3-2 and Figure 3-3. The radiation pattern is described in Figure 3-4.

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Parameter Value

Frequency band 3GHz to 5GHz

Bandwidth (frequency span) 2GHz Number of points over the band 801

Transmitted power 10dBm

Preamplifier gain 30dB

Antenna gain 0dBi

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Fig. 3-2 A photo of the frequency domain channel sounding system.

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@ f (GHz) 3.94 (magenta) 4.00 (blue) 4.20 (green) 4.40 (red) 4.60 (cyan) 4.80 (black) @ f (GHz) 5.00 (magenta) 5.20 (blue) 5.40 (green) 5.60 (red) 5.80 (cyan) 5.99 (black) (a)

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@ f (GHz) 3.94 (magenta) 4.00 (blue) 4.20 (green) 4.40 (red) 4.60 (cyan) 4.80 (black) @ f (GHz) 5.00 (magenta) 5.20 (blue) 5.40 (green) 5.60 (red) 5.80 (cyan) 5.99 (black) (b)

Figure 3-4 (a) Vertical and (b) Horizontal pattern of the transmitted and received antennas.

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3.2 Measurement Environment Description

The measurement was performed in 2nd floor, 3rd floor, 7th floor, and 9th floor of the 4th Engineering Building at the National Chiao-Tung University, Hsinchu, Taiwan. The floor layouts of these measurement sites are shown in Fig. 3-6. In order to minimize the grid number, channel frequency responses measurements were sampled at 441 measurement subpoints, arranged in a 21×21 square grid. The spacing between two neighboring subpoints is 1.875cm. Rician factor was be statistics and calculated for different square grid (corresponding to the center of 21×21square grid). The Rician factor values become unstable as grid number smaller than 6. In order to obtain large number of measurement samples, we selected 8×8 square grid. The result is described in figure 3-5.

Figure 3-6(a) illustrates the measurement points in Room 901; there are many measurement equipments and iron tables in the laboratory. In figure 3-6(b), there are six measured points in Room 911A. Both Room 901 and 911A are enclosed with gypsum-board walls and wooden door. Figure 3-6(c) illustrates the measurement points in Room 203; there are many wooden chairs in the classrooms. In figure 3-6(d), there are four measured points in Room 215. Both Room 203 and 214 are lightly cluttered with wooden chairs. In Figure 3-6(e), the Room 303, 302, and 301 were under NLOS condition with Tx at hallway. In Figure 3-6(f), there are ten iron tables in the Room 713, and there are five computers on each table. Thus obstructed LOS always exists in this measurement environment. In each receiver location, channel frequency responses measurements were made at 64 measurement points, arranged in a fixed-height, 8×8 square grid with 3.75cm spacing, covering 26.25cm×26.25cm. A total of 2688 different channel frequency responses were recorded. One side of the grid is always parallel to wall of the room. The propagation scenarios into four

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categories are described in Table 3-2.

The frequency response data have been exploited to analyze the UWB channel characteristics. We observe the frequency response between 3GHz to 5GHz with 801 sweep points.

(a)

(b)

Fig. 3-5 (a) Small-scale variation square grid; (b) The variation of Rician factor for different square grid.

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(a)

(b)

Figure 3-6 9th floor layout of the 4th Engineering Building. (a) There are 5 measured points in Room 901; (b) There are 6 measured points in Room 911A.

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(c)

(d)

Figure 3-6 2nd floor layout of the 4th Engineering Building. (c) There are 5 measured points in Room 203; (d) There are 4 measured points in Room 215.

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(40)

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Table 3-2 The different channel scenarios.

Environment Distance (Tx-Rx) Point

4 5 11 16 34 35 36 37 38 0-4m 42 1 6 7 8 12 13 14 15 17 18 19 20 33 39 40 LOS 4-10m 41 21 28 29 30 31 0-4m 32 2 3 NLOS 4-20m 9

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10 22 23 24 25 26 27

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3.3 Measurement Result

A total of 42 measured points in the 4th Engineering Building were chosen for measurement data. At each measurement point, the receiver was located at 64 different subpoints separated by one half wavelengthλ(λ=7.5 cm). At each subpoint the power delay profile was recorded with the help of a portable computer for subsequent processing. Power delay profiles obtained from the measured frequency-domain channel responses to time-domain by taking the inverse Fourier transform (IFFT). A series of typical power delay profile for the 64 receiver locations at a LOS site and at a NLOS site are shown in Figures 3-7(a), (b).

Figure 3-7(a) illustrates that the power delay profile has a large initial pulse, followed by delayed pulses of small amplitude. Even though LOS conditions exist, the main received pulse is composed of two or more ray arrivals, as evidenced by spatial fading as the receiver position is moved. It appears that the fading is due to interference between the direct and reflected rays.

The power delay profiles in Figure 3-7(b) for a NLOS site exhibit many individually identifiable peaks whose amplitudes vary rapidly with the location of the receiver.

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(a)

(b)

Figure 3-7 Power delay profiles measured at 64 locations separated by λ/2 on indoor. (a)The measured PDP at no.1 of LOS situation; (b) The measured PDP

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Chapter 4 Effects of Signal Bandwidth and Propagation on

UWB Channels

In this chapter, effects of signal bandwidth and propagation on indoor UWB channels are investigated through the analysis of UWB measurement. On one hand the parameters of the STDL model will be investigated to see how it changes as the signal bandwidth varies. With the STDL model, the power ratio and decay constant of the sampled power delay profiles will be extracted from the measurement data, which can quantify the channel characteristics. It is found that they are dependent on signal bandwidth and local scatterer distribution around the receiver and the transmitter. On the other hand, amplitude fading statistics has been explored. Due to the extreme wide signal bandwidth, UWB systems achieve very high multipath resolution and only few multipath components exist within each resolvable delay bin, and the amplitude fading statistics for NLOS (Non Light-of -Sight) may no longer follow Rayleigh distribution. We had observed this phenomenon from the measured data and found that the received amplitude can be described well by Nakagami distribution. For LOS situation, the received amplitude of the first bin can be described well by Rician distribution.

4.1 Effect of Bandwidth and Propagation on Instantaneous

Power Delay Profile

At each subpoint instantaneous PDP was sampled and there are 64 samples of each measured point. Every PDP was normalized by its peak power. With the STDL model, the PDP can be described by using power ratio r and decay constantεas

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described in Section 2.2.1.

Figures 4-1 (a), (b), (c) and (d) illustrate the normalized instantaneous PDPs of subpoint no.110 measured in Room 901 with signal bandwidths 2 GHz, 1.5 GHz, 1 GHz and 500 MHz, respectively. Here, the power ratio r is increased as the bandwidth decreases. From Equation (2.4), the power of each bin, , with bandwidth F, can be expressed as F j

P

(

)

F 1 F F F j F

P

1 j 2

P

r

exp

∆

,

j

ε

⎧

=

⎪

⎡

− ×

⎤

⎨

= ×

_⎢

−

_⎥

≥

⎪

⎣

⎦

⎩

2

(4.1)

When bandwidth is decreased to half, f=F/2,

(

)

(

)

f F F F 1 1 2 F F f F F F i 2i 1 2i F F F F F F F F F

P P P 1 r

2i 3

2i 2

P P

P

r

exp

2 (i 2) 2

r

exp

,

i 2

∆

ε

∆

ε

−

⎧

⎪

= + = +

⎪

_⎧

_⎡

_⎤

_⎡

_⎤

_⎫

− ×

⎪

₌

₊

_{= ×}

⎪

₋

₊

₋

⎪

⎨

⎢

⎥

⎢

⎥

⎬

⎪

⎣

⎦

⎣

⎦

⎪

⎩

⎭

⎪

_⎡

_⎛

_⎞

_⎛

_⎞

_⎤

_⎛

_⎞

×

− × ×

⎪ = ×

_⎢

_⎜

−

_⎟

+

_⎜

−

_⎟

_⎥

×

_⎜

−

_⎟

≥

⎪

_⎣

_⎝

_⎠

_⎝

_⎠

_⎦

_⎝

_⎠

⎩

(4.2)

the power of second bin can be expressed as

F F f F F F 2 3 4 F

2 P

P

r

exp

∆

exp

∆

ε

⎧

⎡

⎤

⎡

×

⎤

⎫

=

+

= ×

_⎨

_⎢

−

_⎥

+

_⎢

−

_⎥

_⎬

⎣

⎦

⎣

⎦

⎩

F

⎭

(4.3)

then the power ratio with bandwidth f can be expressed as

F F f F F F F

r

2 r

exp

1 r

2 r

1 r

∆

ε

F F

⎡

⎛

⎞

⎛

×

⎤

=

×

_⎢

_⎜

−

_⎟

+

_⎜

−

⎞

_⎥

+

_⎣

_⎝

_⎠

_⎝

⎟

_⎠

_⎦

×

≈

+

(4.4)

However, the decay constant ε is independent of the signal bandwidth. When bandwidth is decreased to half, the power of each bin,

P

_if, with bandwidth f=F/2, can

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be expressed as

(

)

f 1 f f f f

P

1 i 2

P

_i

r

exp

∆

,

i

ε

⎧ =

⎪

⎡

− ×

⎤

⎨

= ×

_⎢

−

_⎥

≥

⎪

⎣

⎦

⎩

2

(4.5)

Comparing Equations (4.2) and (4.5), it is found that the decay constant is not dependent on the bandwidth since εf_{and ε}F_{are equal (}

_∆

f

_{= ×}

₂

_∆

F

).

Figures 4-2, 4-3 and 4-4 shows the normalized instantaneous PDPs measured at subpoints no.124, 2430 and 2450, respectively. The first subpoint is in LOS situation and the other two subpoints are in Room 303 of NLOS situation. In each figure, PDPs for signal bandwidths of 2 GHz, 1.5 GHz, 1 GHz and 500 MHz are also illustrated. From these figures, the trend of the power ratio or the decay constant versus signal bandwidth is the same as that in figure 4-1. However, due to local scattering effect, PDPs of the subpoints belong to the same point such as subpoints 110 with 124 and subpoints 2430 and 2450 are quite different. For further investigation, 64 sampled PDPs of each point were collected to calculate the corresponding power ratio and decay constant. Figures 4-5 (a), (b), and (c) illustrate power ratio histograms of point No.1 with signal bandwidths 2 GHz, 1 GHz and 500 MHz, respectively. It is found that these histograms can be well-fitted by a lognormal distribution. Figures 4-6 (a), (b), and (c) illustrate decay constant historgrams of point No.1 with signal bandwidths 2 GHz, 1 GHz and 500 MHz, respectively. The decay constant histogram can also be well described by a lognormal distribution.

Figure 4-7 illustrates the power ratio versus signal bandwidth for the LOS 0-4m situation. It is found that the power ratio r is increased when the bandwidth is decreased. Figure 4-8 illustrates the decay constant versus signal bandwidth for the LOS 0-4m situation. It is found that the decay constant is only slightly dependent on the signal bandwidth. Similar results are observed for situations of LOS 4-10 m,

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NLOS 0-4 m and NLOS 4-20m.

In addition, we consider local scatterer effect on instantaneous PDP. Figure 4-15(a) illustrates that there are local scatterers distributed closed to the receiver within a radius of 20cm in a laboratory. Figure 4-15(b) illustrates there are slightly far local scatterers distributed around the receiver within a radius of 45cm in the laboratory.

Figure 4-16(a) describes no local scatterer near the receiver. There are less multipath components within the second bin. It leads to the power ratio decrease. Figures 4-16(b) and (c) describes farer scatterer and nearer scatterer distribution around the receiver, respectively. There are more multipath components within the second bin from those scatterers, the multipath components lead to the larger power ratio and smaller decay constant. Figures 4-17 illustrate power ratio historgrams of different local scatterers distribution around the receiver conditions. The power ratio is increased as the local scatterers move closer to receiver. Figures 4-18 illustrate decay constant historgrams of different local scatterers distribution around the receiver conditions. The decay constant is decreased as the local scatterers move closer to receiver.

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0 50 100 150 -80 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) N o rm a liz ed P o wer (dB ) The bandwidth is 2GHz measured

power ratio=0.0164, decay constant=14.73

(a) 0 50 100 150 -80 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) Norm a liz e d P o wer (d B ) The bandwidth is 1.5GHz measured

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0 50 100 150 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) No rm a liz e d P o we r ( d B ) The bandwidth is 1GHz measured

(c) 0 50 100 150 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) No rm a liz e d P o we r (d B ) The bandwidth is 500MHz measured

(d)

Figure 4-1 The normalized instantaneous PDP of subpoint no.110 in Room 901 for

different bandwidth. (a) The bandwidth is 2 GHz with power ratio r=0.016,decay

constantε=14.73(ns); (b) The bandwidth is 1.5 GHz with r=0.019,ε=16.09(ns); (c) The bandwidth is 1 GHz with r=0.029,ε=15.49(ns); (d) The bandwidth is 500

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0 50 100 150 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) Norm a liz ed P o w e r (d B ) The bandwidth is 2GHz measured

(a) 0 50 100 150 -80 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) No rm a liz e d P o we r (d B ) The bandwidth is 1.5GHz measured

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0 50 100 150 -70 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) N o rm al iz ed P o w e r (dB ) The bandwidth is 1GHz measured

(c) 0 50 100 150 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) No rm a li z e d P o we r (d B ) The bandwidth is 500MHz measured

(d)

Figure 4-2 The normalized instantaneous PDP of subpoint no.124 in Room 901 for

different bandwidth. (a) The bandwidth is 2 GHz with r=0.016,ε=14.75(ns); (b)

The bandwidth is 1.5 GHz with r=0.019,ε=17.62(ns); (c) The bandwidth is 1 GHz with r=0.021,ε=15.97(ns); (d) The bandwidth is 500 MHz with r=0.031,ε

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0 50 100 150 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) N o rm al iz ed P o w e r (dB ) The bandwidth is 2GHz measured

(a) 0 50 100 150 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) N o rm al iz ed P o w e r (dB ) The bandwidth is 1.5GHz measured

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0 50 100 150 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) N o rm a li z e d P o w e r (d B ) The bandwidth is 1GHz measured

(c) 0 50 100 150 -60 -50 -40 -30 -20 -10 0 Excess Delay (ns) Norm a liz ed P o w e r (d B ) The bandwidth is 500MHz measured

(d)

Figure 4-3 The normalized instantaneous PDP of subpoint no.2430 in Room 303

for different bandwidth. (a) The bandwidth is 2 GHz with r=0.17,ε=23.94(ns); (b)

The bandwidth is 1.5 GHz with r=0.173,ε=25.7(ns); (c) The bandwidth is 1 GHz with r=0.172,ε=25.33(ns); (d) The bandwidth is 500 MHz with r=0.263,ε

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0 50 100 150 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) N o rm al iz ed P o w e r (d B ) The bandwidth is 2GHz measured

(a) 0 50 100 150 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) N o rm al iz ed P o w e r (dB ) The bandwidth is 1.5GHz measured

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0 50 100 150 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) Norm a liz ed P o w e r (d B ) The bandwidth is 1GHz measured

(c) 0 50 100 150 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) No rm a liz e d P o we r (d B ) The bandwidth is 500MHz measured

(d)

Figure 4-4 The normalized instantaneous PDP of subpoint no.2450 in Room 303

for different bandwidth. (a) The bandwidth is 2 GHz with r=0.101,ε=28.82(ns);

(b) The bandwidth is 1.5 GHz with r=0.101,ε=28.61(ns); (c) The bandwidth is 1 GHz with r=0.101,ε=26.76(ns); (d) The bandwidth is 500 MHz with r=0.185,ε

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-20 -19 -18 -17 -16 -15 -14 -13 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Power ratio (dB) P robabi lit y dens it y fitting curve measured (a) -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Power ratio (dB) P robabi lit y den s it y fitting curve measured (b)

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-18 -16 -14 -12 -10 -8 -6 0 0.05 0.1 0.15 0.2 0.25 0.3 Power ratio (dB) P ro b a b ilit y d e n s it y fitting curve measured (c)

Figure 4-5 The histogram of the power ratio (in dB scale)can be fitted well by a normal distribution. (a)The bandwidth is 2 GHz withμr= -16.44 dB and σr=

1.55 dB; (b)The bandwidth is 1 GHz withμr= -13.66 dB and σr= 1.78 dB; (c)

The bandwidth is 500 MHz withμr= -11.6 dB and σr= 2.13 dB.

11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 0 0.5 1 1.5 2 2.5 3

Decay constant (10Log₁₀(e/1ns))

P ro b a b ilit y d e n s it y fitting curve measured (a)

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10.50 11 11.5 12 12.5 0.5

1 1.5

P ro b a b ilit y d e n s it y fitting curve measured (b) 10.50 11 11.5 12 12.5 13 13.5 14 0.2 0.4 0.6 0.8 1 1.2

Decay constant (10Log

10(e/1ns)) P robabi lit y dens it y fitting curve measured (c)

Figure 4-6 The histogram of the logarithmic decay constant can be fitted well by a normal distribution. (a)The bandwidth is 2 GHz withμε= 11.48 dB and σε=

0.19 dB; (b)The bandwidth is 1 GHz withμε= 11.58 dB and σε= 0.31 dB; (c)

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500MHz0 750MHz 1GHz 1.5GHz 2GHz 0.02 0.04 0.06 0.08 0.1 0.12 signal bandwidth P o w e r ra ti o r no.513 no.543 no.1122 no.1159 no.1628 no.1641 no.3604 no.3607 no.3810 no.3812

Figure 4-7. Power ratio r versus signal bandwidth at different measurement subpoints for the LOS 0-4m situation.

500MHz10 750MHz 1GHz 1.5GHz 2GHz 12 14 16 18 20 22 24 26 28 30 signal bandwidth D e ca y co n s ta n t ( n s) no.513 no.543 no.1122 no.1159 no.1628 no.1641 no.3604 no.3607 no.3810 no.3812

Figure 4-8. Decay constantεversus signal bandwidth at different measurement subpoints for the LOS 0-4m situation.

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500MHz0 750MHz 1GHz 1.5GHz 2GHz 0.02 0.04 0.06 0.08 0.1 0.12 0.14 signal bandwidth P o w e r ra ti o r no.601 no.664 no.1202 no.1263 no.1704 no.1706 no.3320 no.3322 no.4002 no.4005

Figure 4-9. Power ratio r versus signal bandwidth at different measurement subpoints for the LOS 4-10m situation.

Figure 4-10. Decay constantεversus signal bandwidth at different measurement subpoints for the LOS 4-10m situation.

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500MHz0 750MHz 1GHz 1.5GHz 2GHz 0.01 0.02 0.03 0.04 0.05 0.06 signal bandwidth P o w e r ra ti o r no.2111 no.2112 no.2850 no.2851 no.2928 no.2929 no.3003 no.3007 no.3130 no.3132

Figure 4-11. Power ratio r versus signal bandwidth at different measurement subpoints for the NLOS 0-4m situation.

Figure 4-12. Decay constantεversus signal bandwidth at different measurement subpoints for the NLOS 0-4m situation.

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500MHz0 750MHz 1GHz 1.5GHz 2GHz 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 signal bandwidth P o w e r ra ti o r no.205 no.208 no.914 no.916 no.2226 no.2227 no.2531 no.2560 no.2724 no.2725

Figure 4-13. Power ratio r versus signal bandwidth at different measurement subpoints for the NLOS 4-20m situation.

500MHz 750MHz 1GHz 1.5GHz 2GHz 15 20 25 30 35 40 signal bandwidth D e ca y co n s ta n t ( n s) no.205 no.208 no.914 no.916 no.2226 no.2227 no.2531 no.2560 no.2724 no.2725

Figure 4-14. Decay constantεversus signal bandwidth at different measurement subpoints for the NLOS 4-20m situation.

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(a)

(b)

Figure 4-15 (a) There are near local scatterers distribution around the receiver within a radius of 20cm in a laboratory. (b) There is slightly far local scatterers

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(a)

(b)

(c)

Figure 4-16 The effect multipath number versus the delay bin for different local scatterer distribution around the receiver. (a) There is no local scatterer distribution around the receiver; (b) There is farer scatterer distribution around

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-23 -22 -21 -20 -19 -18 -17 -16 -15 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Power ratio (dB) P ro b a b ilit y d e n s it y fitting curve measured (a) -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Power ratio (dB) P rob ab ili ty d ens it y fitting curve measured (b)

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-22 -21 -20 -19 -18 -17 -16 -15 -14 -13 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Power ratio (dB) P ro babi li ty d ens it y fitting curve measured (c)

Figure 4-17 The power ratio historgrams of different local scatterers distribution around the receiver conditions. (a)μr= -19.84 and σr= 1.57 of no local scatterers

situation; (b) μr= -18.92 and σr= 1.414 of farer local scatterers situation; (c)

μr= -18.15 and σr= 1.6 of nearer local scatterer situation.

10.50 11 11.5 12 0.5 1 1.5 2 2.5

P roba bi lit y den s it y fitting curve measured (a)

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10.6 10.8 11 11.2 11.4 11.6 11.8 0 0.5 1 1.5 2 2.5 3

P ro b a b ilit y d e n s it y fitting curve measured (b) 10.6 10.8 11 11.2 11.4 11.6 11.8 0 0.5 1 1.5 2 2.5 3 3.5

Decay constant (10Log

10(e/1ns)) P ro b a b ilit y d e n s it y fitting curve measured (c)

Figure 4-18 The decay constant historgrams of different local scatterers distribution around the receiver conditions. (a) με= 11.33 and σε=0.2 of no

local scatterer situation; (b)με= 11.11 and σε=0.18 of farer local scatterers

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4.2 Effect of Bandwidth and Propagation on Averaged

Power Delay Profile (Not including local scattering effects)

At each measurement point PDPs of the 64 subpoints were sampled and each PDP was normalized by its peak power. Then, these 64 normalized PDPs were collected and averaged to yield an averaged PDP for the measurement point. With the STDL model, the averaged PDP can also be described with power ratio r and decay constantε.

Figures 4-19, and 4-20 illustrate the normalized averaged PDPs of point no.24 and no.15, respectively. The first point is in Room 302 of NLOS situation and the other point is in Room 203 of LOS situation.

As shown in the figures, the normalized power in LOS environment decreases faster than that in NLOS environment, which is reasonable since profiles measured in the Room 203 contain less multipath components.

In figure 4-21, the power ratio of each measured point is drawn as a function of Tx-Rx distance both LOS and NLOS conditions. When propagation distance is increased, there is more multipath fall within the second bin. Therefore, the power ratio r is increased when propagation is increased. In figure 4-22, the decay constant of each measured point is drawn as a function of Tx-Rx distance both LOS and NLOS conditions. It seems that the decay constant in the both conditions is independent of the Tx-Rx diatance.

The power ratio and decay constant can be calculated for each measured point. With the result of total 42 measured points, the histogram of the power ratio can be fitted well by a lognormal distribution (in linear scale) or a normal distribution (in dB scale) with mean μr=-13.81 dB and standard deviationσr=4.25 dB, and the fitting

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the logarithmic decay constant can be described by a normal distribution with με

=12.07 dB and σε=1.45 dB.

Figure 4-25 illustrates the power ratio versus signal bandwidth for the LOS 0-4m situation. It is found that the power ratio r is increased when the bandwidth is decreased. Figure 4-26 illustrates the decay constant versus signal bandwidth for the LOS 0-4m situation. It is found that the decay constant is only slightly dependent on the signal bandwidth.

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0 10 20 30 40 50 60 70 80 -25 -20 -15 -10 -5 0 Excess Delay (ns) No rm a liz e d P o we r (d B ) The bandwidth is 2GHz measured

(a) 0 20 40 60 80 100 120 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) No rm a liz e d P o w e r (d B ) The bandwidth is 500MHz measured

(b)

Figure 4-19 The normalized average PDP of point no.24 in Room 302 for different

bandwidth. (a) The bandwidth is 2 GHz with r=0.165,ε=26.38(ns); (b) The

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0 10 20 30 40 50 60 70 80 90 100 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) No rm a liz e d P o w e r (d B ) The bandwidth is 2GHz measured

(a) 0 20 40 60 80 100 120 140 160 180 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Excess Delay (ns) Norm al iz e d P o we r (d B ) The bandwidth is 500MHz measured

(b)

Figure 4-20 The normalized average PDP of point no.15 in Room 203 for different

bandwidth. (a) The bandwidth is 2 GHz with r=0.012,ε=19.4(ns); (b) The

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Figure 4-21 The power ratio versus the distance between Tx and Rx.

(b)

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-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 0 0.05 0.1 0.15 0.2 0.25 Power ratio (dB) P rob ab ili ty d ens it y fitting curve measured

Figure 4-23 The histogram of the power ratio (in dB scale) can be fitted well by a normal distribution withμr=-13.81 dB and σr=4.25 dB.

8 9 10 11 12 13 14 15 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

P rob abi li ty d ens it y fitting curve measured

Figure 4-24 The histogram of the logarithmic decay constant can be fitted well by a normal distribution with με=12.07 dB and σε=1.45 dB.

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500MHz0 750MHz 1GHz 1.5GHz 2GHz 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 signal bandwidth P o w e r ra ti o r No.4 No.5 No.11 No.16 No.34 No.35 No.36 No.37 No.38 No.42

Figure 4-25. Power ratio r versus signal bandwidth at different measurement points for the LOS 0-4m situation.

500MHz8 750MHz 1GHz 1.5GHz 2GHz 10 12 14 16 18 20 22 24 26 28 30 signal bandwidth D e ca y co n s ta n t ( n s) No.4 No.5 No.11 No.16 No.34 No.35 No.36 No.37 No.38 No.42

Figure 4-26. Decay constantεversus signal bandwidth at different measurement points for the LOS 0-4m situation.

室內超寬頻無線電通道頻寬效應之研究

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