Advanced Wireless Networks - 4G Technologies

Table 3.25 Statistical models and parameters

Global parameters Gtot and Gk

Path loss

PL

20.4 log10(d/d0),

d ≤ 11 m

Shadowing

= −56 + 74 log10(d/d0), d > 11 m

G

tot LN (−PL; 4.3)

Decay constant

ε LN (16.1; 1.27)

Power ratio

r LN (−4; 3)

Local parameters Gk

Energy gains

Gk

(

G

k ; mk )

2

(τk )

mk

TN μm (τk );

σm

m Values

μm (τk ) = 3.5 −

τk

73

σm2 (τk ) = 1.84 −

τk

160

(a)

(b)

Figure 3.24 (a) The measured 49 local PDPs for an example room. (b) Simulated 49 local PDPs for an example room. (Reproduced by permission of IEEE [86].)

UWB CHANNEL MODEL 89

lth cluster, relative to Tl . The parameters and γ determine the intercluster signal level rate of decay and the intracluster rate of decay, respectively. The parameter is generally determined by the architecture of the building, while γ is determined by objects close to the receiving antenna, such as furniture. The results presented in Spencer et al. [95] make the assumption that the channel impulse response as a function of time and azimuth angle is a separable function, or

h (t, θ ) = h (t) h (θ )

(3.74)

from which independent descriptions of the multipath time-of-arrival and angle-of-arrival are developed. This is justified by observing that the angular deviation of the signal arrivals within a cluster from the cluster mean does not increase as a function of time.

The cluster decay rate and the ray decay rate γ can be interpreted for the environment in which the measurements were made. For the results, presented later in this section, at least one wall separates the transmitter and the receiver. Each cluster can be viewed as a path that exists between the transmitter and the receiver along which signals propagate. This cluster path is generally a function of the architecture of the building itself. The component arrivals within a cluster vary because of secondary effects, e.g. reflections from the furniture or other objects. The primary source of degradation in the propagation through the features of the building is captured in the decay exponent . Relative effects between paths in the same cluster do not always involve the penetration of additional obstructions or additional reflections, and therefore tend to contribute less to the decay of the component signals. Results for p(θ ) generated from the data in Cramer et al. [97] are shown in Figure 3.25. Interarrival times are hypothesized [95] to follow exponential rate laws, given by

p (Tl |Tl−1 ) = e− (Tl −Tl−1)

p Tkl Tk−1,l = λe−λ(Tl −Tl−1)

(3.75)

where is the cluster arrival rate and λ is the ray arrival rate. Channel parameters are summarized in Table 3.26.

(a)											(b)
	0.020										100
		Laplacian
		distribution:
	0.015	p(θ ) =	1	−	2θ / σ						80
			2σ e
p(θ)											60
	0.010										(%)
											cdf
											40
	0.005
											20
	0.000										0
	-180	-135	-90		-45	0	45	90	135	180	-180	-135	-90	-45	0	45	90	135	180
						θ (degrees)							Cluster angle-of-arrival relative to reference cluster

Figure 3.25 (a) Ray arrival angles at 1◦ of resolution and a best fit Laplacian density with σ = 38◦. (b) Distribution of the cluster azimuth angle-of-arrival, relative to the reference cluster. (Reproduced by permission of IEEE [97].)

90	CHANNEL MODELING FOR 4G
		Table 3.26	Channel parameters
Parameter UWB [97]		Spencer et al. [95] Spencer et al. [95]		Saleh and Valenzuela [94]
	27.9 ns	33.6 ns	78.0 ns	60 ns
γ	84.1 ns	28.6 ns	82.2 ns	20 ns
1/	45.5 ns	16.8 ns	17.3 ns	300 ns
1/λ	2.3 us	5.1 ns	6.6 ns	5 ns
σ	37◦	25.5◦	21.5◦	—

3.9.6 Path loss modeling

In this section we are interested in a transceiver operating at approximately 2 GHz center frequency with a bandwidth in excess of 1.5 GHz, which translates to sab-nanosecond time resolution in the CIRs.

3.9.6.1 Measurement procedure

The measurement campaign is described in Yano [98] and was conducted in a single-floor, hard-partition office building (fully furnished). The walls were constructed of drywall with vertical metal studs; there was a suspended ceiling 10 feet in height with carpeted concrete floor. Measurements were conducted with a stationary receiver and mobile transmitter; both transmit and receive antennas were 5 feet above the floor. For each measurement, a 300 ns time-domain scan was recorded and the LOS distance from transmitter to receiver was recorded. A total of 906 profiles were included in the dataset with seven different receiver locations recorded over the course of several days. Except for a reference measurement made for each receiver location, all successive measurements were NLOS links chosen randomly throughout the office layout that penetrated anywhere from one to five walls. The remainder of datapoints were taken in similar fashion.

3.9.6.2 Path loss modeling

The average pathless for an arbitrary TR separation is expressed using the power law as a function of distance. The indoor environment measurements show that, at any given d, shadowing leads to signals with a path loss that is log–normally distributed about the mean [99]. That is:

PL (d) = PL0 (d0) + 10N log	d	+ Xσ	(3.76)
	d0

where N is the pathloss exponent, Xσ is a zero mean log–normally distributed random variable with standard deviation σ (dB), PL0 is the free space path loss at reference distance, d0. Some results are shown in Figure 3.27.

Assuming a simple RAKE with four correlators where each component is weighted equally, we can calculate the path loss vs distance using the peak channel impulse response (CIR) power plus RAKE gain, PLPEAK+RAKE, for each CIR, as shown in Figure 3.26(c). The

	3
	0
	-3
	-6
	-9		σN = 4.75 dB
	-12
	-15
(dB)	-18
	-21
PEAK	-24
	-27
PL
	-30
-	-33
	-36
	-39
	-42	Free space
	-45
	-48	N = 2.9
	-51	data
	-54
	100	101	102

Distance (feet)

		(a)
	3
	0
	-3
	-6		σN = 3.55 dB
	-9
	-12
(dB)	-15
	-18
	-21
TOTAL	-24
	-27
-PL	-30
	-33
	-36
	-39
	-42	Free space
	-45
	-48	N = 2.1
	-51	data
	-54
	100	101	102

Distance (feet)

		(b)
	3
	0
	-3
	-6		σN = 4.04 dB
	-9
	-12
(dB)	-15
	-18
PEAK+RAKE	-21
	-24
	-27
	-30
-PL
	-33
	-36
	-39
	-42	Free space
	-45
	-48	N = 2.5
	-51	data
	-54
	100	101	102

Distance (feet)

(c)

Figure 3.26 (a) Peak PL vs distance; (b) total PL vs distance; (c) peak PL + rake gain vs distance. (Reproduced by permission of IEEE [98].)

92 CHANNEL MODELING FOR 4G

τ (ns) RMS

50

45

40 σrms = 5.72 ns

35

30

25

20

15

10

5

0

100

101

102

Distance (feet)

				(a)
	50
	45
	40	σrms = 4.26 ns
	35
(ns)	30
RMS	25
τ
	20
	15
	10
	5
	0
	0	10	20	30	40	50	60

PLPEAK (dB)

(b)

Figure 3.27 (a) The RMS delay spread vs distance; (b) RMS delay spread vs path loss. (Reproduced by permission of IEEE [98].)

exponent N obtained from performing a least-squares fit is 2.5 with a standard deviation of 4.04 dB. The results for delays are shown in Figure 3.27.

3.9.6.3 In-home channel

For the in-home channel Equation (3.76) can be also used to model path loss. Some results are shown in Table 3.27 [100–103]. Table 3.28 presents the results for delay spread in home channel [100].

REFERENCES 93

Table 3.27 Statistical values of the path loss parameters

		LOS			NLOS
	Mean		SD		Mean	SD
P L0 (dB)	47			51
N	1.7		0.3	3.5		0.97
σ (dB)	1.6		0.5	2.7		0.98

Table 3.28 Percentage of power contained in profile, number of paths, mean excess delay and RMS delay spread for 5, 10, 15, 20 and 30 dB threshold levels

			50 % NLOS					90 % NLOS
Threshold	Power %		L	τm(ns)	τRMS(ns)	Power %		L	τm(ns)	τRMS(ns)
5 dB	46.8		7	1.95	1.52	46.9		8	2.2	1.65
10 dB	89.2		27	7.1	5.77	86.5		31	8.1	6.7
15 dB	97.3		39	8.6	7.48	96		48	10.3	9.3
20 dB	99.4		48	9.87	8.14	99.5		69	12.2	11
30 dB	99.97		60	10.83	8.43	99.96		82	12.4	11.5

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