1. Shadowing

2. A Simplified Large-Scale Path Loss with Shadowing

3. Empirical Methods for Large-Scale Path Loss
In the following Okumura Model is given as an example.

4. Okumura's Model
Okumura's model is one of the most widely used models for signal prediction in urban areas.
This model is applicable for frequencies in the range 150 MHz to 1920 MHz and distances of 1 km to 100 km. It can be used for base station antenna heights ranging from 30 m to 1000 m.
Okumura developed a set of curves giving the median attenuation relative to free space (Amu), in an urban area over a quasi-smooth terrain with a base station effective antenna height (hte) of 200 m and a mobile antenna height (hre) of 3 m.
These curves were developed from extensive measurements using vertical omni-directional antennas at both the base and mobile, and are plotted as a function of frequency in the range 100 MHz to 1920 MHz and as a function of distance from the base station in the range 1 km to 100 km.

5. Okumura's Model (Cont’d)
To determine path loss using Okumura's model, the free space path loss between the points of interest is first determined, and then the value of Amu (f, d) (as read from the curves) is added to it along with correction factors to account for the type of terrain. The model can be expressed as
where L50 is the 50th percentile (i.e., median) value of propagation path loss, LF is the free space propagation loss, Amu is the median attenuation relative to free space, G(hte) is the base station antenna height gain factor, G(hre) is the mobile antenna height gain factor, and GAREA is the gain due to the type of environment.

6. Okumura's Model (Cont’d)
Plots of Amu (f, d) and GAREA for a wide range of frequencies are shown in the following figures. Furthermore, Okumura found the following approximations
Okumura's model is wholly based on measured data and does not provide any analytical explanation.
Okumura's model is considered to be among the simplest and best in terms of accuracy in path loss prediction for mature cellular and land mobile radio systems in cluttered environments.
The major disadvantage with the model is its slow response to rapid changes in terrain, therefore the model is fairly good in urban and suburban areas, but not as good in rural areas.

7. Okumura's Model (Cont’d)
Median attenuation relative to free space (Amu), over a quasi-smooth terrain.
Correction factor GAREA, for different types of terrain.

8. Okumura's Model (Cont’d)
Example:
Find the median path loss using Okumura's model for d = 50 km, hte = 100 m, hre = 10 m in a suburban environment. If the base station transmitter Radiates 1kW at a carrier frequency of 900 MHz.
Solution to Example:

9. Characterization of the wireless channels - Part II
(Small-Scale Fading)

10. Wireless Fading Channels
Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times.
These waves, called multipath waves, combine at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase.
Multipath in the radio channel creates small-scale fading effects. The three most important effects are:
Rapid changes in signal strength over a small travel distance or time interval.
Random frequency modulation due to varying Doppler shifts on different multipath signals.
Time dispersion (echoes) caused by multipath propagation delays.

11. Doppler Shift
Consider a mobile moving at a constant velocity v, along a path segment having length d between points X and Y, while it receives signals from a remote source S.
The difference in path lengths traveled by the wave from source S to the mobile at points X and Y is
where ∆t at is the time required for the mobile to travel from X to Y, and θ is assumed to be the same at points X and Y since the source is assumed to be very far away.

12. Doppler Shift (Cont’d)
The phase change in the received signal due to the difference in path lengths is therefore
And hence the apparent change in frequency, or Doppler shift, is given by fd where
Example:
Consider a transmitter which radiates a sinusoidal carrier frequency of 1850 MHz. For a vehicle moving m/s, compute the received carrier frequency if the mobile is moving (a) directly towards the transmitter (θ=0), (b) directly away from the transmitter (θ=0), (c) in a direction which is perpendicular to the direction of arrival of the transmitted signal.
Solution to Example

13. Solution to Example (Cont’d)
a) The vehicle is moving directly towards the transmitter. The Doppler shift in this case is positive and the received frequency is given by
b) The vehicle is moving directly away from the transmitter. The Doppler shift in this case is negative and hence the received frequency is given by

14. Impulse Response Model of a Multipath Channel
The small-scale variations of a mobile radio signal can be directly related to the impulse response of the mobile radio channel.
In the figure below, the receiver moves along the ground at some constant velocity v. For a fixed position d, the channel between the transmitter and the receiver can be modeled as a linear time invariant system.
However, due to the different multipath waves which have propagation delays which vary over different spatial locations of the receiver, the impulse response of the linear time invariant channel should be a function of the position of the receiver.

15. Impulse Response Model of a Multipath Channel (Cont’d)

16. Time Dispersion Parameters
The mean excess delay, rms delay spread, and excess delay spread (X dB) are multipath channel parameters that can be determined from a power delay profile.
The mean excess delay is the first moment of the power delay profile and is defined to be
The rms delay spread is defined to be

17. Time Dispersion Parameters (Cont’d)
The maximum excess delay (X dB) of the power delay profile is defined to be the time delay during which multipath energy falls to X dB below the maximum.
This figure illustrates the computation of the maximum excess delay for multipath components within 10 dB of the maximum. The maximum excess delay (X dB) defines the temporal extent of the multipath that is above a particular threshold.

18. Coherence Bandwidth
Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered "flat" (i.e., a channel which passes all spectral components with approximately equal gain and linear phase).
Coherence bandwidth (BC)—frequencies separated by less than this width have their fades highly correlated (i.e. Channel bandwidth)
If the coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above 0.5 then the coherence bandwidth is approximately
RMS delay spread increases, coherence bandwidth decreases: Time dilation is equivalent to frequency compression.

19. Flat and Frequency Selective Fading
• Flat Fading Channel:
Coherence (channel) bandwidth > message signal bandwidth.
All the frequency components in the message will arrive at the receiver with little or no distortion.
• Frequency Selective Fading Channel:
Coherence (channel) bandwidth << message signal bandwidth.
Intersymbol interference (ISI) occurs and the received signal is distorted. (Solution: Equalizer (Equalizers are used to render the frequency response—for instance of a telephone line—flat from end-to-end. Equalizing filters must cancel out any group delay and phase delay between different frequency components).
Example
User data rate is 240 kbps. (message signal bandwidth Bs=240 kHz)
For indoor environments: σT = 100 ns, BC = 2 MHz >> Bs (flat fading).
For outdoor urban cellular: σT = 2 ms, BC =100 kHz < Bs (frequency selective fading).

20. Example Solution to Example
Calculate the mean excess delay, rms delay spread, and the maximum excess delay (10 dB) for the multipath profile given in the figure below. Estimate the 50% coherence bandwidth of the channel. Would this channel be suitable for AMPS or GSM service without the use of an equalizer?
Solution to Example
The mean excess delay for the given profile can be calculated by

21. Solution to Example (Cont’d)
The rms delay spread is defined to be
The coherence bandwidth is found from