Advanced Wireless Networks - 4G Technologies

68 CHANNEL MODELING FOR 4G

3.6.2 Capacity computation

In a fading channel, the capacity is a random variable, depending on the local (or instantaneous) channel realization. In order to determine the cdf of the capacity, and thus the outage capacity, we would have to perform a large number of measurements either with slightly displaced arrays, or with temporally varying scatterer arrangement. Since each single measurement requires a huge effort, such a procedure is highly undesirable.

To improve this situation, an evaluation technique that requires only a single measurement of the channel is used. This technique relies on the fact that we can generate different realizations of the transfer function by changing the phases of the multipath components. It is a well-established fact in mobile radio that the phases are uniformly distributed random variables, whose different realizations occur as transmitter, receiver or scatterers move [27]. We can thus generate different realizations of the transfer function from the mth transmit to the kth receive antenna as

hk,m ( f ) = i	ai exp − j	2π	d k sin φR,i + m sin φT,i
		λ		(3.39)
× exp (− j2π f τi ) exp ( jαi )

where αi is a uniformly distributed random phase, which can take on different values for the different MPCs numbered i. Note, however, that αi stays unchanged as we consider different antenna elements k and m. To simplify discussion, we for now consider only the flat-fading case, i.e. τi = 0. We can thus generate different realizations of the channel matrix H

		h11	h12	· · ·	h1NT
H	=	h21	h22	· · ·	h2NT	(3.40)
		· · ·	· · ·	· · ·	· · ·
		hNR1	hNR2	· · ·	hNR NT

by the following two steps:

(1)From a single measurement, i.e. a single snapshot of the channel matrix, determine the DOAs, and DODs of the MPCs as described earlier in the section.

(2)Compute synthetically the impulse responses at the positions of the antenna elements, and at different frequencies. Create different realizations of one ensemble by adding random phase factors (uniformly distributed between 0 and 2π ) to each MPC. For each channel realization, we can compute the capacity from [ 97]

C = log2 det I +	ρ	HHH	(3.41)
	NT

where ρ denotes the SNR. I is the identity matrix and superscript H means Hermitian transposition. For the frequency-selective case, we have to evaluate the capacity by integrating over all frequencies

		ρ
C =	log2 det I +	NT HH ( f ) H ( f ) d f.	(3.42)

Here, H( f ) is the frequency-dependent transfer matrix. The integration range is the bandwidth of interest.

WIRELESS MIMO LAN ENVIRONMENTS (5.2 GHz)

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3.6.3 Measurement environments

As an example the following scenarios are evaluated with the procedure described above [52]:

Scenario I – a courtyard with dimensions 26 × 27m, open on one side. The RX-array broadside points into the center of the yard; the transmitter is located on the positioning device 8 m away in LOS.

Scenario II – closed backyard of size 34 × 40 m with inclined rectangular extension. The RX-array is situated in one rectangular corner with the array broadside of the linear array pointing under 45◦ inclination directly to the middle of the yard. The LOS connection between TX and RX measures 28 m. Many metallic objects are distributed irregularly along the building walls (power transformers, air-condition fans, etc.). This environment looks very much like the backyard of a factory (Figure 3.13).

Scenario III – same closed backyard as in Scenario II but with artificially obstructed LOS path. It is expected that the metallic objects generate serious multipath and higher-order scattering that can only be observed within the dynamic range of the device if the LOS path is obstructed.

Scenario IV – same as scenario III but with different TX position and LOS obstructed. The TX is situated nearer to the walls. More details about the senarios can be found in Steinbauer et al. [57].

Some of the measurements results for these scenarios are presented in Figure 3.14

	0	RX
	-5
	-10
	-15
(m)	-20				TX
Y-Coordinate	-25
	-30
	-35
	-40
	-45
	-50
		0	10	20	30	40	50	60

X-Coordinate (m)

Figure 3.13 Geometry of the environment of scenarios II–IV (backyard) in top view. Superimposed are the extracted DOAs and DODs for scenario III. (Reproduced by permission of IEEE [52].)

70 CHANNEL MODELING FOR 4G

cdf (Capacity)

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0.5

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0

0

Scenario I

Scenario II

Scenario III

Scenario IV

Ideal

II	I	ideal

III IV

10

20

25

Capacity (bits/s/Hz)

Figure 3.14 The CDFs of the MIMO channel capacity encountered in scenarios I–IV, and the cdf for an ideal channel. The SNR is 20 dB, and 4 × 4 antenna elements were used.

3.7 INDOOR WLAN CHANNEL (17 GHz)

In this section we discuss the indoor radio propagation channel at 17 GHz. The presentation is based on results reported in Rubio et al. [58]. Wideband parameters, such as coherence bandwidth or rms delay spread, and coverage are analyzed for the design of an OFDM-based broadband WLAN. The method used to obtain the channel parameters is based on a simulator described in Rubio et al. [58]. This simulator is a site-specific propagation model based on three-dimensional (3-D) ray-tracing techniques, which has been specifically developed for simulating radio coverage and channel performance in enclosed spaces such as buildings, and for urban microcell and picocell calculations. The simulator requires the input of the geometric structure and the electromagnetic properties of the propagation environment, and is based on a full 3-D implementation of geometric optics and the uniform theory of diffraction (GO/UTD). Examples of the measurement environments are given in Figure 3.15. The results for coherence bandwidth Bc = 1/ατrms are given in Table 3.13 and Figure 3.16.

A further requirement related to the correct and efficient channel estimation process by the receiver is the selection of a number of subcarriers in OFDM satisfying the condition of being separated between approximately Bc/5 and Bc/10. Results for delay spread are shown in Figure 3.17 and Tables 3.14 – 3.17.

The results for the path loss exponent and k factor are given in Figure 3.18 and Table 3.18 and Table 3.19. For channel modeling purposes, the mean power of the received signal will be represented as

		∞
PRX|dB = PTX|dB + GTX|dB + GRX|dB − Lfs|dB + 10 · log	0	PDP (t) dt	(3.43)

where TTX is the mean power at the transmitting antenna input, GTX is the transmitting antenna gain while GRX is the receiving antenna gain. Lfs is free space propagation losses,

Figure 3.15 (a) ETSIIT hall (49 × 26 m); (b) DICOM, floors 2 and 3 (34 × 20 m); (c) office building (72 × 38 m); 3-D representations 63. (Reproduced by permission of IEEE [58].)

	Table 3.13		Bc at 17 GHz
		Coherence bandwidth (MHz)
Place		Mean	Standard deviation
Hall	24.85		12.35
Floors	14.44		9.85
Building	22.86		10.24
Total	20.72		11.56

72CHANNEL MODELING FOR 4G

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Figure 3.16 Bc CDF at 17 GHz. (Reproduced by permission of IEEE [58].)

CDF

CDF

(a)

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Figure 3.17 (a) The RMS delay spread CDF (Bc = 1/ατrms ). (b) Maximum delay CDF, 30 dB criterion. (c) Maximum delay CDF, 20 dB criterion. (d) Alpha CDF.

	INDOOR WLAN CHANNEL (17 GHz)		73
Table 3.14 The RMS delay spread CDF. (Reproduced by permis-
	sion of IEEE [58])
CDF value	RDS value
0.2	12.1 ns
0.4	14.3 ns
0.6	17.5 ns
0.8	34.3 ns
1	58.3 ns
RDS, root delay spread.
Table 3.15 Maximum delay CDF, 30 dB criterion. (Reproduced
	by permission of IEEE [58])
CDF value	Tmax value
0.2	62 ns
0.4	76 ns
0.6	101 ns
0.8	122 ns
1	197 ns

Table 3.16 Maximum delay CDF, 20 dB criterion. (Reproduced by permission of IEEE [58])

CDF value			Tmax value
0.2			51 ns
0.4			56 ns
0.6			69 ns
0.8			94 ns
1			156 ns
	Table 3.17	Alpha CDF, Bc = 1/ατrms
	CDF value	Alpha value
0.2		2.17
0.4		2.67
0.6		3.75
0.8		4.44
1		5.78

74 CHANNEL MODELING FOR 4G

CDF

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n

Figure 3.18 CDF of path loss exponent n.

Table 3.18 Mean values of n

Type of path	LOS	OLOS		NLOS
n Mean value	1.68	2.14	2.61
	Table 3.19 Fading statistic over distance, LOS case
	Radius (m)		K factor
	4		17
	5		10
	6		9
	7		8
	8		6
	9		5
	10		1

given by

Lfs|dB = 32.45 dB + 20 · log10 (dkm + fMHz)

and PDP(t) the modeled power delay profile. Once the PDF is modeled, to obtain the discrete channel impulse response, hi , we only have to add a random phase to the square root of each delay bin amplitude, as follows:

hi = √		e jφi φi r.υ. unif [0, 2π ]	(3.44)
	pi

where hi is the ith bin of the modeled channel impulse response and pi , the module of the ith bin of the modeled power delay profile.

INDOOR WLAN CHANNEL (17 GHz)

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It can be assumed that phases of different components of the same channel impulse response are uncorrelated at the frequency of interest (17 GHz), because their relative range is higher than a wavelength, even for high-resolution models [59]. As the total bandwidth assigned to the communication is 50 MHz, a selection of 10 ns for the bin size must be made. Using 99 % of the total power criterion for the maximum duration of the PDF, the former bin size selection leads to a total of nine taps for the LOS case and 17 for the NLOS case.

The statistical variability of the bin amplitudes has been modeled following different probability density functions. Taking into account the fact that the area of service of future applications (SOHO – small office, home office) has small ranges, the variability has been analyzed considering a medium-scale, that is, the environment is divided in to the LOS area and the NLOS one. In the LOS case, a Frechet PDF [60] is chosen for the first bin and exponential PDFs for the rest. A continuous random variable X has a Frechet distribution if its PDF has the form

f (x; σ ; λ) =

λ

σ

λ+1

exp −

σ

λ

; x ≥ 0; σ, λ > 0

(3.45)

σ

x

x

A Frechet variable X has the CDF

F (x; σ ; λ) = exp

−

σ λ

(3.46)

x

This model has a scale structure, with σ a scale parameter and λ a shape parameter.A continuous random variable X has an exponential distribution if its PDF has the form

	=	σ			−	σ			≥
f (x; μ)			1	exp		x − μ		; x		0; μ, σ > 0	(3.47)

This PDF has location-scale structure, with a location parameter, μ, and a scale one, σ . The CDF of the exponential variable X is

	F (x; μ)	=	1	−	exp	−	x − μ	(3.48)
							σ

These PDFs were considered the most suitable after a fitting process. The NLOS case needs a combination of exponential and Weibull PDFs for the first bin and exponential PDFs for the others. A continuous random variable X has a Weibull distribution if its PDF has the form

f (x; σ ; λ) =	λ		x	λ−1		x	λ	; x ≥ 0; σ, λ > 0			(3.49)
				exp −
	σ		σ			σ
While the CDF is
		F (x; σ ; λ) = 1			− exp			−	x	λ	(3.50)
									σ

This model has a scale structure, that is, σ is a scale parameter, while λ is a shape parameter. Tables 3.20 and 3.21 show the probability density functions employed for LOS and NLOS channel models [58].

For both tables, the units of σ parameters are Hz (s−1), while λ has no units. These units have no physical correlation but make the last term of Equation (3.43) nondimensional, as it represents a factor scale between the free space behavior and the real one. The mean

Table 3.20 Wind-flex channel model PDFs, LOS case. (Reproduced by permission of IEEE [58])

Bin 1	Frechet (σ = 2.66 × 108, λ = 7)	Bin 4
Bin 2	exp (σ = 5.44 × 107)	Bin 5
Bin 3	exp (σ = 2.51 × 107)	Bin 6

exp (σ = 1.45 × 107)	Bin 7	exp (σ = 0.41 × 107)
exp (σ = 1.03 × 107)	Bin 8	exp (σ = 0.27 × 107)
exp (σ = 0.79 × 107)	Bin 9	exp (σ = 0.71 × 107)

Table 3.21 Wind-flex channel model PDFs, NLOS case. (Reproduced by permission of IEEE [58])

Bin 1	0.5*[exp (σ = 4.378 × 106)+	Bin 7	exp (σ = 1.88 × 105)	Bin 13	exp (σ = 9.21 × 104)
	Weibull(σ = 4.207 × 107, λ = 5)		exp (σ = 2.51 × 105)		exp (σ = 1.27 × 105)
Bin 2	exp (σ = 3.04 × 106)	Bin 8		Bin 14
Bin 3	exp (σ = 2.47 × 106)	Bin 9	exp (σ = 5.69 × 105)	Bin 15	exp (σ = 2.76 × 104)
Bin 4	exp (σ = 2.14 × 106)	Bin 10	exp (σ = 1.53 × 105)	Bin 16	exp (σ = 6.71 × 104)
Bin 5	exp (σ = 1.1 × 106)	Bin 11	exp (σ = 3.29 × 105)	Bin 17	exp (σ = 6.42 × 104)
Bin 6	exp (σ = 3.71 × 105)	Bin 12	exp (σ = 2.67 × 105)

4G FOR MODELING CHANNEL 76

INDOOR WLAN CHANNEL (60 GHz)

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value of the probability density functions is so high due to the ulterior integral over the time (in seconds) required, and the PDF duration (tens of nanoseconds). As expected, the mean value of the first bin is the highest, since it includes the direct ray (LOS case). Additional details on the topic can be found in References [59–71].

3.8 INDOOR WLAN CHANNEL (60 GHz)

Based on the results reported in Hao et al. [72], in this section we present spatial and temporal characteristics of 60 GHz indoor channels. In the experiment, a mechanically steered directional antenna is used to resolve multipath components. An automated system is used to precisely position the receiver antenna along a linear track and then rotate the antenna in the azimuthal direction, as illustrated in Figure 3.19. The precisions of the track and spin positions are less than 1 mm and 1◦, respectively. When a highly directional antenna is used, the system provides high spatial resolution to resolve multipath components with different angles of arrival (AOAs). The sliding correlator technique was used to further resolve multipath components with the same AOA by their times of arrival (TOAs). The spread spectrum signal has a RF bandwidth of 200 MHz, which provids a time resolution of approximately 10 ns.

For this measurement campaign, an open-ended waveguide with 6.7 dB gain is used as the transmitter antenna and a horn antenna with 29 dB gain is used as the receiver antenna. These antennas are chosen to emulate typical antenna systems that have been proposed for millimeter-wave indoor applications. In these applications a sector antenna is used at the transmitter and a highly directional antenna is used at the receiver. Both antennas are vertically polarized and mounted on adjustable tripods about 1.6 m above the ground. The theoretical half-power beamwidths (HPBW) are 90◦ in azimuth and 125◦ in elevation for the open-ended waveguide and 7◦ in azimuth and 5.6◦ in elevation for the horn antenna.

Track measurements

		λ/4
	TX	20λ
		Rx
	Track step: λ/4	Number of steps: 80
	Spin measurements
	TX	20λ
		Rx
	Track step: 5λ	Number of steps: 4
	Spin step: 5°	Number of steps: 72

Figure 3.19 Track and spin measurement procedure.(Reproduced by permission of IEEE [72].)