Chapter 3 Measurement System and Environment
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.
(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
at no.2 of NLOS situatio.
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
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
When bandwidth is decreased to half, f=F/2,
( ) ( )
the power of second bin can be expressed as
F F then the power ratio with bandwidth f can be expressed as
F F
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, canbe expressed as Comparing Equations (4.2) and (4.5), it is found that the decay constant is not dependent on the bandwidth since εf and εF 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,
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.
0 50 100 150
The bandwidth is 2GHz
measured
power ratio=0.0164, decay constant=14.73
(a)
The bandwidth is 1.5GHz
measured
power ratio=0.0194, decay constant=16.09
(b)
0 50 100 150
The bandwidth is 1GHz
measured
power ratio=0.0290, decay constant=15.49
(c)
The bandwidth is 500MHz
measured
power ratio=0.0401, decay constant=17.33
(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 MHz with r=0.041,ε=17.33(ns).
0 50 100 150
The bandwidth is 2GHz
measured
power ratio=0.0166, decay constant=14.75
(a)
The bandwidth is 1.5GHz
measured
power ratio=0.0198, decay constant=17.62
(b)
0 50 100 150
The bandwidth is 1GHz
measured
power ratio=0.0210, decay constant=15.97
(c)
The bandwidth is 500MHz
measured
power ratio=0.0312, decay constant=19.74
(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
=19.74(ns).
0 50 100 150
The bandwidth is 2GHz
measured
power ratio=0.1704, decay constant=23.94
(a)
The bandwidth is 1.5GHz
measured
power ratio=0.1734, decay constant=25.70
(b)
0 50 100 150
The bandwidth is 1GHz
measured
power ratio=0.1718, decay constant=25.33
(c)
The bandwidth is 500MHz
measured
power ratio=0.2632, decay constant=21.58
(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
=21.58(ns).
0 50 100 150
The bandwidth is 2GHz
measured
power ratio=0.1006, decay constant=28.82
(a)
The bandwidth is 1.5GHz
measured
power ratio=0.1006, decay constant=28.61
(b)
0 50 100 150
The bandwidth is 1GHz
measured
power ratio=0.1010, decay constant=26.76
(c)
The bandwidth is 500MHz
measured
power ratio=0.1850, decay constant=22.82
(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
=22.82(ns).
-20 -19 -18 -17 -16 -15 -14 -13
-18 -16 -14 -12 -10 -8 -6
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=
Decay constant (10Log10(e/1ns))
Probability density
fitting curve measured
(a)
10.50 11 11.5 12 12.5 0.5
1 1.5
Decay constant (10Log10(e/1ns))
Probability density
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))
Probability density
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)
The bandwidth is 500 MHz withμε= 11.87 dB and σε= 0.52 dB.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
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
Figure 4-8. Decay constantεversus signal bandwidth at different measurement subpoints for the LOS 0-4m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
Figure 4-9. Power ratio r versus signal bandwidth at different measurement subpoints for the LOS 4-10m situation.
500MHz14 750MHz 1GHz 1.5GHz 2GHz
16
Figure 4-10. Decay constantεversus signal bandwidth at different measurement subpoints for the LOS 4-10m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
Figure 4-11. Power ratio r versus signal bandwidth at different measurement subpoints for the NLOS 0-4m situation.
500MHz14 750MHz 1GHz 1.5GHz 2GHz
16
Figure 4-12. Decay constantεversus signal bandwidth at different measurement subpoints for the NLOS 0-4m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
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
Figure 4-14. Decay constantεversus signal bandwidth at different measurement subpoints for the NLOS 4-20m situation.
(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
distribution around the receiver within a radius of 45cm in the laboratory.
(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
the receiver; (c) There is nearer scatterer distribution around the receiver.
-23 -22 -21 -20 -19 -18 -17 -16 -15
-22 -21 -20 -19 -18 -17 -16 -15 -14 -13
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)
Decay constant (10Log10(e/1ns))
Probability density
fitting curve measured
(a)
10.6 10.8 11 11.2 11.4 11.6 11.8
Decay constant (10Log10(e/1ns))
Probability density
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.
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 curve is shown in figure 4-23. In the figure 4-24, it is also found that the histogram of
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.
0 10 20 30 40 50 60 70 80
The bandwidth is 2GHz
measured
power ratio=0.165, decay constant=26.38
(a)
The bandwidth is 500MHz
measured
power ratio=0.292, decay constant=25.70
(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
bandwidth is 500 MHz with r=0.292,ε=25.7(ns).
0 10 20 30 40 50 60 70 80 90 100
The bandwidth is 2GHz
measured
power ratio=0.012, decay constant=19.40
(a)
The bandwidth is 500MHz
measured
power ratio=0.068, decay constant=17.00
(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
bandwidth is 500 MHz with r=0.068,ε=17(ns).
Figure 4-21 The power ratio versus the distance between Tx and Rx.
(b)
Figure 4-22 The decay constant versus the distance between Tx and Rx.
-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4
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.
Decay constant (10Log10(e/1ns))
Probability density
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.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
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
Figure 4-26. Decay constantεversus signal bandwidth at different measurement points for the LOS 0-4m situation.
4.3 Effect of Signal Bandwidth on Amplitude fading
For multipath propagation of narrowband signal, there is a large number of MPCs in each delay bin and the complex received amplitude has a complex Gaussian distribution, which results in a Rayleigh or Rician distribution of the amplitudes.
Therefore, it is usually assumed that the envelope of the first received bin, which may have direct path, follows a Rician or Nakagami distribution and the envelope of the later bins are assumed to have Rayleigh statistics [6]. However, in UWB propagation each resolved MPC is due to smaller number of scatter wave, and the amplitude distribution in later delay bin may differ markedly from the Rayleigh distribution.
This phenomenon has been observed in figure 4-27(a) and (b) where the Nakagami distribution can fit better for the amplitude pdf of the 38th bin’s and the 65th bin’s, respectively. Here, the amplitude statistics of the first arrived bin for each measured point has been fitted by using a Ricain distribution. Some examples are shown in Figures 4-28(a), (b), (c) and (d) for measured point nos.2, 16, 21, and 41, respectively.
It is found that the Rician distribution yields good fitting result.
In figure 4-29, the Ricain factor versus signal bandwidth is shown. It is observed that the Rician factor is decreased as the signal bandwidth increases. It is true for the LOS condition such as the measured point nos. 4, 5, 16, 34, 35, 36, 37, 38 and 42.
Similar result is observed for situations of LOS 4-10 m.
However, for the NLOS condition, the Rician factor is increased as the signal bandwidth increases such as the measured point nos. 21, 28, 29, 30, 31 and 32, which is shown in figure 4-30. It is because that in the NLOS 0-4m condition, the numbers of scattered multipath received at the first bin is decreased as the signal bandwidth increases, i.e., the timewidth of the bin decreased. Similar results are observed in the NLOS 4-20 m situation.
In figure 4-33, the Ricain factor of each measured point is pilotted as a function of Tx-Rx distance both LOS and NLOS conditions. With the existence of direct path, the Rician factor in LOS condition is larger than that of the NLOS condition. It seems that the Rician factor in the both conditions is independent of the Tx-Rx distance.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Figure 4-27(a) PDF of measured and fitted signal amplitudes of the 38th bin in Room 303 for NLOS environment. The bandwidth is 2GHz.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Figure 4-27(b) PDF of measured and fitted signal amplitudes of the 65th bin in Room 303 for NLOS environment. The bandwidth is 2GHz.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
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.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
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.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
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.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
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.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
Figure 4-29 Rician factor K versus signal bandwidth at different measurement points of the LOS 0-4m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
5
Figure 4-30 Rician factor K versus signal bandwidth at different measurement points of the NLOS 0-4m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
Figure 4-31 Rician factor K versus signal bandwidth at different measurement points of the LOS 4-10m situation.
500MHz0 750MHz 1GHz 1.5GHz 2GHz
5
Figure 4-32 Rician factor K versus signal bandwidth at different measurement points of the NLOS 4-20m situation.
Figure 4-33 The Rician factor versus the distance between Tx and Rx.
Chapter 5 Conclusion
In this article, the effect of signal bandwidth on multipath channel has been studied. The measurement was performed by using Agilent 8719 ET vector network analyzer in the 4th Engineering Building of NCTU. For UWB application, the swept frequency band is from 3GHz to 5GHz (2GHz of frequency span). A method based on STDL model is proposed and validated by measurement results. From the analysis of the measurement results, it is found that the decay constantεand power ratio r of the PDP and amplitude distribution of small-scale fading are dependent on propagation environment and signal bandwidth.
The power ratio is increased and the decay constant is decreased as the local scatterers move closer to receiver. This is due to the number of scattered multipath is increased of the second bin when the scatterer is closed to receiver.
The power ratio r is increased as the bandwidth decreases. This is due to the proportion of power of the second received bin is increased when bandwidth is decreased. The power of each bin is dependent only on delay time. The decay constant is independent on the bandwidth. It is found that the decay constant and the power delay profile can be well described by a lognormal distribution.
The Rician factor is increased when bandwidth is increased of NLOS condition.
Because the numbers of scattered multipath arrived at the first received bin is decreased as the bandwidth increases.
As results, those parameters, including the power ratio r, decay constantε and Rician factor K are not only dependent on the propagation environment but dependent on the signal bandwidth.
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