Validation of TR Scheme
2.2 Simulation Approach for TR Validation
2.2.1 Description of Used Channel Model
Before entering the details for the validation of the TR scheme with simulation ap-proach, the channel model used for the validation is described in the following. Since Saleh and Valenzuela [38] proposed their model for UWB channel in 1987, a lot of work has been done after that which is almost always based on the SV model. The research on UWB channel geared up especially after 2002 when FCC allowed a license free communication with UWB signals. IEEE 802.15.3a model was proposed followed by IEEE 802.15.4a standard model for UWB signals which provided the modeling of attenuation and delay dispersion [39]. Both of these models are based on the initial SV model. The difference from the original SV channel model is that the number of clusters in the IEEE 802.15.4a standard model is considered to be a stochastic vari-able rather than a constant. We have used IEEE 802.15.4a standard model for the validation of the TR scheme.
2.2.1.1 Channel Model
The impulse response (in complex baseband) for both SV and IEEE models is given as:
h(t) = XL
l=1
XK k=1
ak,lexp(jφk,l)δ(t−Tl−τk,l) (2.1) whereLis the total number of clusters,K is the number of multi-path components (MPCs) within a cluster, ak,l is the coefficient of the kth tap in the lth cluster, Tl is the cluster arrival time for the lth cluster, τk,l is the delay of the kth MPC relative to the Tl. The number of clusters is an important parameter and is assumed to be Poisson-distributed:
pdfL(L) =
LLexp(−L)
L! (2.2)
here L completely characterizes the distribution. The cluster arrival times are by definition given by a Poisson process:
p(Tl|Tl−1) = Λlexp [−Λl(Tl−Tl−1], l >0 (2.3)
802.15.4a standard for the UWB channels has proposed to model the ray arrival times with a mixture of two Poisson processes to overcome the discrepancy of the classical SV model to fit for the indoor residential, indoor office and outdoor environments.
The IEEE model can be written as:
p(τk,l|τ(k−1),l) = βλ1exp
−λ1 τk,l−τ(k−1),l
+(β−1)λ2exp
−λ2 τk,l−τ(k−1),l
(2.4)
To determine power and shape of the clusters, the power delay profile (PDP) is constructed with an exponential curve within each cluster:
E{|ak,l|2}= Ωl 1
γl[(1−β)λ1+βλ2+ 1]exp(−τk,l/γl) (2.5) where Ωl is the integrated energy of thelth cluster andγl is the intra cluster decay time constant which depends linearly on the arrival time of the cluster:
γl ∝kγTl+γ0 (2.6)
wherekγ is the increase of the decay constant with delay. The mean energy of the cluster experiences an exponential decay:
10 log(Ωl) = 10 log [exp(−Tl/Γ)] +Mcluster (2.7) whereMcluster is a normally distributed variable with a standard deviation ofσcluster. In the case of some NLOS environments (e.g. office and industrial), the shape of the power delay profile can be of a log-linear shape:
E{|ak,1|2}= (1−χ.exp(−τk,l/γrise)).exp(−τk,l/γ1).γ1+γrise
γ1
Ωl
γ1+γrise(1−χ) (2.8) where χ describes the attenuation of the first component, γrise describes the rate of PDP increase to its local maximum andγ1 tells the decay at the late times.
2.2.1.2 Channel Model Parameters
Different channel model parameters are described in the following. These parameters are obtained from [39]. A complete list of all parameters is as under:
• P L0 pathloss at 1m distance
• n pathloss exponent
• σS shadowing standard deviation
• Aant antenna loss
• κ frequency dependence of the pathloss
• L mean number of clusters
• Λ inter-cluster arrival rate
• λ1, λ2, β ray arrival rates (mixed Poisson model parameters)
• Γ inter-cluster decay constant
• kγ, γ0 intra-cluster decay time constant parameters
• σcluseter cluster shadowing variance
• m0, km Nakagami m factor mean
• mˆ0, kˆm Nakagami m factor variance
• m˜0 Nakagami m factor for strong components
• γrise, γ1, χparameters for alternative PDP shape
The parameters for different indoor environments for both LOS and NLOS con-figurations are tabulated inTable 2.1
2.2.1.3 Properties of Channel Impulse Response
The PDP gives the intensity of a signal received through a multi-path channel as a function of time delay. It is easily measured empirically and can be used to extract certain channel’s parameters such as the delay spread. The APDcP of a signal is a measure of how quickly the average power of the signal decays to an arbitrarily low level. It also gives an indication of the delay spread of the signal. APDcP of a CIR is more than just an indication of the delay spread of the CIR. It helps to understand the propagation channel and the measurement configuration. The pattern in which the power decays is an interesting observation. For LOS configurations, generally the power decays sharply at the start and then the decay rate slows down whereas in NLOS configurations, the decay rate is generally constant. Based on the channel models described in the Section 2.2.1, a sample PDP of an arbitrary channel and the average power decay profile (APDcP) of 100 channels in different configurations are compared in Fig. 2.1, Fig. 2.2 and Fig. 2.3. The PDP and APDcP are plotted in three different indoor environments (residential, office and industrial) with both LOS and NLOS configurations.
In NLOS configuration, a lot more multipath components (MPCc) are received.
In LOS configurations, a significant difference can be observed in the APDcP. The APDcP decays rapidly at the start showing the difference in the received power for the direct path and the other paths. After few nano-seconds, the APDcP decays
Parameters
LOS NLOS LOS NLOS LOS NLOS
Path loss
P L0 43.9 48.7 35.4 57.9 56.7 56.7
n 1.79 4.58 1.63 3.07 1.2 2.15
σS 2.22 4.51 1.9 3.9 6 6
Aant (dB) 3 3 3 3 3 3
κ 1.12 ±0.12 1.53 ±0.32 0.03 0.71 -1.103 -1.427 Power delay profile
L 3 3.5 5.4 1 4.75 1
Λ (1/ns) 0.047 0.12 0.016 NA 0.0709 NA
λ1 (1/ns) 1.54 1.77 0.19 NA NA NA
λ2 (1/ns) 0.15 0.15 2.97 NA NA NA
β 0.095 0.045 0.0184 NA NA NA
Γ (ns) 22.61 26.27 14.6 NA 13.47 NA
kγ 0 0 0 NA 0.926 NA
γ0 12.53 17.50 6.4 94 0.651 NA
σcluseter (dB) 2.75 2.93 NA NA 4.32 NA
Small scale fading
m0 (dB) 0.67 0.39 0.42 0.50 0.36 0.30
km 0 0 0 0 0 0
ˆ
m0 (dB) 0.28 0.32 0.31 0.25 1.13 1.15
kˆm 0 0 0 0 0 0
˜
m0 NA NA NA NA 12.99 NA
χ NA NA NA 0.86 NA 1
γrise NA NA NA 15.21 NA 17.35
γ1 NA NA NA 11.84 NA 85.36
Table 2.1: Channel model parameters for residential, office and industrial indoor environments
slowly and gradually to reach a level of −40 dB. In the residential environment, the APDcP takes significantly longer time to decay to −40 dB level in NLOS than the LOS configuration (see Fig. 2.1 ). In the office environment, even in the LOS configuration, a large number of MPCs is observed. The APDcP takes a little longer time in NLOS to decay to−40 dB level than LOS configuration (seeFig. 2.2). The industrial environment gives some very interesting results. In the LOS configuration, the MPCs other than the direct paths are significantly attenuated than the direct path. The APDcP is attenuated to −20 dB with in 10 ns. However, after that the profile decays slowly and takes almost 80 ns to reach −40 dB level. In the NLOS
0 50 100 150
Figure 2.1: Power Delay Profiles and Power Decay Profiles for CIRs in LOS and NLOS configuration for an indoor residential environment
0 20 40 60 80
Figure 2.2: Power Delay Profiles and Power Decay Profiles for CIRs in LOS and NLOS configuration for an indoor office environment
industrial environment, large number of MPCs is observed and the PDP has a very large delay spread. More than 800 ns are required to decay to −40 dB level. One more interesting observation in the APDcP of the industrial environment is that the maximum average power is not observed at the origin but after a few nano-seconds
0 5 10 15 20
Figure 2.3: Power Delay Profiles and Power Decay Profiles for CIRs in LOS and NLOS configurations for the industrial environment
(see Fig. 2.3), suggesting that the first received MPC is not usually the strongest MPC.
(a) PDP TR: residential LOS
150 200 250 300 350 400
−40
(b) APDcP TR: residential LOS
2600 270 280 290 300 310
(c) PDP TR: residential NLOS
150 200 250 300 350 400
−40
(d) APDcP TR: residential NLOS
Figure 2.4: Power Delay Profiles and Power Decay Profiles for TRRs in LOS and NLOS configuration for an indoor residential environment
876 880 884 888
(a) PDP TR: office LOS
800 850 900 950
(b) APDcP TR: office LOS
180 182 184 186 188 190
0
(c) PDP TR: office NLOS
100 150 200 250
(d) APDcP TR: office NLOS
Figure 2.5: Power Delay Profiles and Power Decay Profiles for TRRs in LOS and NLOS configuration for an indoor office environment
185 186 187 188
(a) PDP TR: industrial LOS
100 150 200 250
(b) APDcP TR: industrial LOS
8400 841 842 843
(c) PDP TR: industrial NLOS
600 700 800 900 1000 1100
−40
(d) APDcP TR: industrial NLOS
Figure 2.6: Power Delay Profiles and Power Decay Profiles for TRRs in LOS and NLOS configurations for the industrial environment