Advanced Wireless Networks - 4G Technologies

where λ is the wavelength. Path loss over distance d can be described by the path loss exponent model as follows:

where P L(d) is the average path loss value at a transmitter – receiver (TR) separation of d and n is the path loss exponent that characterizes how fast the path loss increases with the increase in TR separation. The path loss values represent the signal power loss from the transmitter antenna to the receiver antenna. These path loss values do not depend on the antenna gains or the transmitted power levels. For any given transmitted power, the received signal power can be calculated as

where Gt and Gr are transmitter and receiver gains, respectively. In this measurement campaign, the transmitted power level was 25 dBm, the transmitter antenna gain was 6.7 dB, and the receiver antenna gain was 29 dB.

3.8.1.2 TOA parameters

TOA parameters characterize the time dispersion of a multipath channel. The calculated TOA parameters include mean excess delay (τ¯ ), rms delay spread (σ τ ), and also timing jitter [δ(x)] and standard deviation [ (x)], in a small local area. Parameters of τ¯ and σ τ are given as [72]:

where Pi and τ i are the power and delay of the ith multipath component of a PDF, respectively, and N is the total number of multipath components. Timing jitter is calculated as the difference between the maximum and minimum measured values in a local area. Timing jitter δ(x) and standard deviation (x) are defined as

where xi is the measured value for parameter x(τ¯ or στ ) in the ith measurement position of the spatial sampling and M is the total number of spatial samples in the local area. For example, for the track measurements, M was chosen to be 80.

UWB CHANNEL MODEL 79

Mean excess delay and rms delay spread are the statistical measures of the time dispersion of the channel. Timing jitter and standard deviation of τ¯ and σ τ show the variation of these parameters over the small local area. These TOA parameters directly affect the performance of high-speed wireless systems. For instance, the mean excess delay can be used to estimate the search range of rake receivers and the rms delay spread can be used to determine the maximum transmission data rate in the channel without equalization. The timing jitter and standard deviation parameters can be used to determine the update rate for a rake receiver or an equalizer.

3.8.1.3 AOA parameters

AOA parameters characterize the directional distribution of multipath power. The recorded AOA parameters include angular spread , angular constriction γ , maximum fading angle θ max and maximum AOA direction. Angular parameters , γ and θ max are defined based on the Fourier transform of the angular distribution of multipath power, p(θ ) [74]:

Fn is the nth Fourier transform of p(θ ). As shown in Durgin and Rappaport [74], angular spread, angular constriction and maximum fading angle are three key parameters to characterize the small-scale fading behavior of the channel. These new parameters can be used for diversity techniques, fading rate estimation, and other space–time techniques. Maximum AOA provides the direction of the multipath component with the maximum power. It can be used in system installation to minimize the path loss. The results of measurements for the parameters defined by Equations (3.51)–(3.57) are given in Table 3.22–3.24 and Figure 3.20. More details on the topic can be found in References [74–85].

3.9 UWB CHANNEL MODEL

UWB channel parameters will be discussed initially based on measurements results in Cassioli et al. [86]. The measurements environment is presented in Figure 3.21 and the signal format used in these experiments in Figure 3.22. The repetition rate of the pulses is 2 × 106 pulses/s, implying that multipath spreads up to 500 ns could have been observed unambiguously. Multipath profiles with a duration of 300 ns were measured. Multipath profiles were measured at various locations in 14 rooms and hallways on one floor of the building presented in Figure 3.21. Each of the rooms is labeled alpha-numerically. Walls around offices are framed with metal studs and covered with plaster board. The wall around the laboratory is made from acoustically silenced heavy cement block. There are steel core support pillars throughout the building, notably along the outside wall and two within the laboratory itself. The shield room’s walls and door are metallic. The transmitter is kept stationary in the central location of the building near a computer server in a laboratory

Table 3.22 Spin measurements: transmitter–receiver separations in meters, time dispersion parameters (τ¯ and σ τ ) in nanoseconds, angular dispersion parameters ( and γ ) are dimensionless, maximum fading angle (θmax) and AOA of maximum multipath (max AOA) in degrees, ratio of maximum multipath power to average power (peak/avg) in decibels and maximum multipath power (Pmax) in dBm [72]

UWB CHANNEL MODEL 81

Separation distance (m)

Figure 3.20 Scatter plot of the measured path loss values.

Measurement grid

Transmitter

Approximate location of measurements

Figure 3.21 The floor plan of a typical modern office building where the propagation measurement experiment was performed. The concentric circles are centered on the transmit antenna and are spaced at 1 m intervals. (Reproduced by permission of IEEE [87].)

82 CHANNEL MODELING FOR 4G

Figure 3.22 The transmitted pulse measured by the receiving antenna located 1 m away from the transmitting antenna with the same height.

denoted by F. The transmit antenna is located 165 cm from the floor and 105 cm from the ceiling.

In each receiver location, impulse response measurements were made at 49 measurement points, arranged in a fixed-height, 7 × 7 square grid with 15 cm spacing, covering 90 × 90 cm. A total of 741 different impulse responses were recorded. One side of the grid is always parallel to north wall of the room. The receiving antenna is located 120 cm from the floor and 150 cm from the ceiling.

3.9.1 The large-scale statistics

Experimental results show that all small-scale averaging SSA-PDPs exhibit an exponential decay as a function of the excess delay. Since we perform a delay axis translation, the direct path always falls in the first bin in all the PDPs. It also turns out that the direct path is always the strongest path in the 14 SSA-PDPs even if the LOS is obstructed. The energy of the subsequent MPCs decays exponentially with delay, starting from the second bin. Let Gk =ˆ ASpa{Gk } be the locally averaged energy gain, where ASpa{·} denotes the spatial average over the 49 locations of the measurement grid. The average energy of the second MPC may be expressed as fraction rof the average energy of the direct path, i.e. r = G2/G1. We refer to r as the power ratio. As we will show later, the SSA-PDP is

completely characterized by G1, the power ratio r, and the decay constant ε (or equivalently,

by the total average received energy Gtot, r and ε).

The power ratio rand the decay constant ε vary from location to location, and should be treated as stochastic variables. As only 14 values for ε and r were available, it was not possible to extract the shape of their distribution from the measurement data. Instead, a model was assumed a priori and the parameters of this distribution were fitted. It was found that the log–normal distribution, denoted by ε LN (μεdB ; σεdB ), with μεdB = 16.1 and σεdB = 1.27, gives the best agreement with the empirical distribution. Applying the same procedure to characterize the power ratios rs, it was found that they are also log–normally distributed, i.e. r LN (μrdB ; σrdB ), with μrdB = −4 and σrdB = 3, respectively.

Table 3.23 Track measurement results: TR separations in meters, time dispersion parameters (τ¯ and στ ) in nanoseconds, variations of time dispersion parameters (δτ¯, τ¯, δστ and στ ) in nanoseconds and average received power (Prx) in dBm [72]

84 CHANNEL MODELING FOR 4G

Table 3.24 Measured penetration losses and results from literature

By integrating the SS A-PDP of each room over all delay bins, the total average energy Gtot within each room is obtained. Then its dependence on the TR separation is analyzed. It was found that a breakpoint model, commonly referred to as dual slope model, can be adopted for path loss PL as a function of the distance, as

where PL is expressed in decibels, d0 = 1 m is the reference distance, and d is the TR separa-

tion distance in meters. Because of the shadowing phenomenon, the Gtot varies statistically around the value given by Equation (3.59). A common model for shadowing is log–normal distribution [87, 88]. By assuming such a model, it was found that Gtot is log–normally distributed about Equation (3.58), with a standard deviation of the associated normal random variable equal to 4.3.

3.9.2 The small-scale statistics

The differences between the PDPs at the different points of the measurement grid are caused by small-scale fading. In ‘narrowband’ models, it is usually assumed that the magnitude of the first (quasi-LOS) multipath component follows Rician or Nakagami statistics and the later components are assumed to have Rayleigh statistics [89]. However, in UWB propagation, each resolved MPC is due to a small number of scatterers, and the amplitude distribution in each delay bin differs markedly from the Rayleigh distribution. In fact, the presented analysis showed that the best-fit distribution of the small-scale magnitude statistics is the Nakagami distribution [90], corresponding to a gamma distribution of the

UWB CHANNEL MODEL 85

Figure 3.23 Scatter plot of the m-Nakagami of the best fit distribution vs excess delay for all the bins except the LOS components. Different markers correspond to measurements in different rooms. (Reproduced by permission of IEEE [86].)

energy gains. This distribution has been used to model the magnitude statistics in mobile radio when the conditions of the central limit theorem are not fulfilled [91]. The parameters of the gamma distribution vary from bin to bin: ( ; m) denotes the gamma distribution that fits the energy gains of the local PDPs in the kth bin within each room. The k are

given as k = Gk , i.e. the magnitude of the SSA-PDP in the kth bin. The mk are related to the variance of the energy gain of the kth bin. Figure 3.23 shows the scatter plot of the mk , as a function of excess delay for all the bins (except the LOS components). It can be seen from Figure 3.23 that the mk , values range between 1 and 6 (rarely 0.5), decreasing with the increasing excess delay. This implies that MPCs arriving with large excess delays are more diffused than the first arriving components, which agrees with intuition.

The mk parameters of the gamma distributions themselves are random variables distributed according to a truncated Gaussian distribution, denoted by m TN (μm ; σm2 ), i.e. their distribution looks like a Gaussian for m ≥ 0.5 and zero elsewhere

where the normalization constant Km is chosen so that the integral over the fm (x) is unity. The mean and variance of such Gaussian distributions that fit the mk as a function of the excess delay, are given by [17]

where the unit of τ k is nanoseconds.

86 CHANNEL MODELING FOR 4G

3.9.3 The statistical model

The received signal is a sum of the replicas (echoes) of the transmitted signal, being related to the reflecting, scattering and/or deflecting objects via which the signal propagates. Each of the echoes is related to a single such object. In a narrowband system, the echoes at the receiver are only attenuated, phase-shifted and delayed, but undistorted, so that the received signal may be modeled as a linear combination of Npath-delayed basic waveforms w(t)

where n(t) is the observation noise. In UWB systems, the frequency selectivity of the reflection, scattering and/or diffraction coefficients of the objects via which the signal propagates can lead to a distortion of the transmitted pulses. Furthermore, the distortion and, thus, the shape of the arriving echoes, varies from echo to echo. The received signal is thus given as

If the pulse distortion was greater than the width of the delay bins (2 ns), one would observe a significant correlation between adjacent bins. The fact that the correlation coefficient remains very low for all analyzed sets of the data implies that the distortion of a pulse due to a single echo is not significant, so that in the following, Equation (3.60) can be used.The SSA-PDP of the channel may be expressed as

where the function g¯ (τ ) can be interpreted as the average energy received at a certain receiver position and a delay τ , normalized to the total energy received at one meter distance, and Nbins is the total number of bins in the observation window. Assuming an exponential decay starting from the second bin, we have

where ε is the decay constant of the SSA-PDP. The total average energy received over the observation interval T is

UWB CHANNEL MODEL 87

The total normalized average energy is log–normally distributed, due to the shadowing, around the mean value given from the path loss model (3.58)

3.9.4 Simulation steps

In the model, the local PDF is fully characterized by the pairs {Gk , τk }, where τ k = (k−1) τ with τ = 2 ns. The Gk are generated by a superposition of large and small-

scale statistics. The process starts by generating the total mean energy Gtot at a certain distance according to Equation (3.67). Next, the decay constant ε and the power ratio rare generated as lognormal distributed random numbers

The width of the observation window is set at T = 5ε. Thus, the SSA-PDP is completely specified according to Equation (3.69). Finally, the local PDPs are generated by computing the normalized energy gains G(ki) of every bin k and every location i as gamma-distributed independent variables. The gamma distributions have the average given by Equation (3.68), and the mk s are generated as independent truncated Gaussian random variables

with μm (τk ) and σm2 (τk ) given by Equation (3.59). These steps are summarized Table 3.25. Some results are shown in Figure 3.24.

3.9.5 Clustering models for the indoor multipath propagation channel

A number of models for the indoor multipath propagation channel [92–96] have reported a clustering of multipath components, in both time and angle. In the model presented in Spencer et al. [95], the received signal amplitude βkl is a Rayleigh-distributed random variable with a mean-square value that obeys a double exponential decay law, according to

where β2 (0, 0) describes the average power of the first arrival of the first cluster, Tl represents the arrival time of the lth cluster, and τkl is the arrival time of the kth arrival within the