Chapter 3: Channel modelling
The time and frequency-varying nature of the channel is maybe one of the most difficult obstacle to apprehend when designing a mobile system. Indeed mobile wireless systems often experience changing channel conditions. The path to go from the transmitter to the receiver can vary from the line-of-sight situation to one which can be blocked by many obstacles, like buildings, hills or in our indoor case pieces of furniture. Hence, this channel is different to the wire channel and is of course much more difficult to predict. It is consequently impossible to describe it with a single model and this has lead to the development of several models in order to describe this wireless channel, as precisely as possible.
Statistical models, which mimic a fading channel response, have been empirically developed on special measurements made for distinct models. Those models have the great advantage to be flexible, which means that the same model could be reused to model the channel with distinct conditions just by changing the parameters. The models usually predict the average received signal strength at a certain distance from the transmitter. We can differentiate two main families of propagating models: large-scale and small-scale propagating models.Large-scale fading is due to the shadowing caused by the environment and the nature of it whereas small-scale fading models the rapid evolutions of the received signal strength over short distances (some wavelengths) or short periods (a few seconds). The Rayleigh, Rician and Nakagami-m are often used to model small-scale fading while empirical models (Hata, Okamura) find the mean signal strength, which represents the large-scale fading consequence, by estimating the pathloss thanks to available measurements [3.1].
We will further focus on the small-scale fading, which is much more important for our project. But we will first describe large-scale fading and then concentrate on the small-scale fading by describing sorts of it and the principle model associated with it.
3.1.Large and medium-scale fading
Large-scale fading typically incorporates the pathloss, which is the average power decay caused by the distance, and the shadowing, which is the variation in the power decay caused by the objects and the environment.
- Pathloss:
It designs the radio wave propagation losses that occur on the signal’s path from the transmitter to the receiver. It usually includes losses due to these phenomena’s: absorption, propagation and diffraction [3.2]. The pathloss is usually characterized as the ratio between the signal’s power at the transmitter output and the signal’s power at the receiver input. The pathloss is usually given in dB.
(3.1)
The absolute mean path loss which is defined in dB in outdoor environments is the sum of the pass loss in dB for the distance d0 and of the logarithm of the last definition. That gives us this equation [3.3]:
(3.2)
This formula isn’t very relevant for indoor environments but the formulas of the pathloss in indoor environments have usually got the same structure. For example in [3.4], researchers have made studies about the propagation in indoor measurements. They have made measurements on the 6th floor of the CTU building in Prague. They used this formula to measure the path loss in their indoor environment:
(3.3)
(3.4)
Where is the pathloss in (dB) at distance d (m)
is the reference loss value for 1m (dB)
is the pathloss exponent
is the wall loss factor for the i-th wall (dB)
A very important factor to estimate the pathloss in indoor environment is to apprehend the pathloss due to the walls. This factor is even more important in NLOS cases. In [3.4] the researchers made measurements with three types of wall to study the Multi-Wall Model. Those three types are: light wall, heavy wall and metal wall. The following figures show the optimised values of empirical parameters for One-Slope Model and Multi-Wall Model.
2.45 / 40.2 / 4.21.9 / 38.0 / 3.5
Figure 3.1: Optimised for One Slope Model
It has been shown that the prediction for the One Slope Model is quite inaccurate because in those experiments it appeared that the mean error of the averaged signal level exceeded 12dB
2.45 / 40.2 / 5.9 / 8.0 / 4.1 / 21.9 / 38.0 / 2.1 / 4.4 / 1.3 / 2
Figure 3.2: Optimised parameters for Multi-Wall Model
In this second model, the prediction was much better because the mean error dropped to 8dB. That’s why the Multi-Wall Model is more suitable for indoor coverage predication in WLAN environments.
Other measurements have been made to evaluate the losses due to different types of wall and also due to floors [3.5]. The following figure show the pathloss measured in function of the number of floors that in which the signal went through. It appears that the losses per floor begin to decrease when increasing the number of floors. The researchers think that this phenomenon can be explained because of diffraction phenomena. This phenomenon is caused by the diffraction of the radio waves that along side of building as the radio waves penetrate the building’s windows.
Figure 3.3: Multiple Floors Indoor Pathloss
The next figure shows the attenuation through obstacles for various obstacles.
2.4 GHz Signal AttenuationWindow Brick Wall / 2dB
Metal Frame Glass Wall into Building / 6dB
Office Wall / 6dB
Metal Door in Office Wall / 6dB
Cinder Block Wall / 4dB
Metal Door in Brick Wall / 12.4dB
Brick Wall next to Metal Door / 3dB
Figure 3.4: Attenuation through obstacles for various obstacles
- Shadowing:
This phenomenon can be summarized as the variation in power decay due to objects in the environment. This effect is a “medium-scale” effect and it occurs only if the antenna has been moved over distances higher than a few ten meters. It has been proved [3.6] that when the path between the transmitter and the receiver is longer than a few hundred meters, the received power varies with a log-normal distribution around the area-mean power. The local mean power is defined as the average power received over about 40 wavelengths in order to avoid multipath fading denoted by a single overline. The area mean power is defined as the average power received over several meters in order to remove multipath fading and shadowing. So we can express the received power in logarithm units as followed [3.6]:
(3.5)
Where is the area mean power and the local mean power.
Then we can define the normal probability density of this received power in logarithm units as [3.6]:
(3.6)
Where is the logarithmic standard deviation in natural units. The standard deviation S is defined in dB as follow:
This definition is one of the most used when speaking about outdoor environments but it is not very relevant for indoor environments. Effectively this definition is valuable for distances higher than a few 10 meters. It is quite scarce to find open offices with distances so big. What is more relevant in indoor environments is the attenuation created by the walls and the effect of body shadowing. We already described the Multi-Wall Model because the attenuation due to the walls is more related to the definition of pathloss. We will now present the effect of body shadowing in indoor environments. [3.7] Body shadowing can considerably affects the channel characteristics in indoor environments principally because the height of the antennas and the emitted power are considerably lower in indoor environments than in outdoor ones. That’s why the propagation loss due to body shadowing can’t be neglected in indoor environments because it can considerably affect the poser strength received by the antennas even if we consider a multipath environment where each ray contributes to the total power received. Most of the models that were created are generally empirical model. In [3.8], researchers have made measurements of body shadowing in a 6 m x 7 m rectangular office situated on the fifth floor of a university building. Those measurements were made with the WLAN technologies at a frequency of 5.2 GHz in a LOS case. They studied 4 cases to make their measurements:
- The empty room
- A single pedestrian walking in the room with a approximate speed of 0.5m/s
- 2 pedestrians walking in the room
- 3 pedestrians walking in the room
Figure 3.5: the room of the experiment with the pedestrian’s trajectory shows with dots [3.8]
They considered that when a pedestrian was obstructing the direct ray between the transmitter and the receiver it created a NLOS event. The sampling was set up at 5 ms. The experiment gave the following results.
Scenario / Mean Received power (dBm) / DynamicRange(dB) / Standard Deviation (dB)
Empty room / -53.4 / 1.0 / 0.2
1 pedestrian / -54.2 / 10.0 / 1.7
2 pedestrians / -53.9 / 10.6 / 2.0
3 pedestrians / -53.7 / 11.6 / 2.1
Figure 3.6: Results of the experiment in the 4 cases [3.8]
Those experiments showed that this NLOS event introduces a fading of approximately 10dB on the received power. We can also notice that the Mean received power is almost the same in the 4 cases although the DynamicRange and the Standard deviation are increasing with the number of pedestrians. Then the researchers have calculated the CDF of their experimental data sets and compared it with the theoretical Rayleigh and Rice distribution. It appears that all the scenarios apart the case of the empty room tended to be Rice distributed. It also appears that, when the number of the pedestrians is increasing, the factor K of the Rice distribution decreases. The reduction of this factor can be explained with the increase of the probability of obstructing both the direct ray and the main multipath components.Those results show that body shadowing effects can have great effects when considering indoor communications.
3.2.Small-scale fading
As we explain in the first section, small-scale fading describes the rapid fluctuations of the received signal strength when the mobile station’s motion is only over a few wavelengths. The signal, which is transmitted from the base station, can travel different ways because of reflections, diffraction and local scatterers. The multiple paths can therefore be associated with different lengths, which involves that the receiver will “see” multiple copies of the same signal arriving at different time and with different amplitudes. The signal can also be shifted in phase, which results in different fades as the different signals superimpose constructively or destructively. Hence, we will observe peaks and valleys of the received signal strength as the signals add or subtract at the receiver.
Fadingis therefore used to describe these rapid fluctuations of phases and amplitudes of the signal over a short distance or duration. In the small-scale fading situation, the received signalpower may vary by as much as three or four orders of magnitude (30 or 40 dB) when the receiver moved only a fraction of a wavelength [3.1].
Figure 3.7: Single bounce multipath with uniformly distributed scatterers
In indoor area fading occurs because of the non-light-of-sight (NLOS) path between the transmitter and the receiver. Even in the case a LOS exists, multipath still happens due to the reflections on the ground and on the surrounding objects. We can therefore observe that the symbols are spread in time: this distortion of the signal is known as the time dispersion. This phenomenon can be better observed when the transmitter sends a very short pulse (ideally a Dirac) on a channel, where multipath occurs. This will indeed result in a train of pulses at the receiver side. When we work with wideband systems, the delay spread due to the multipath channel becomes much greater than the symbol duration and thus we experience inter symbol interference (ISI).
Figure 3.8: Effect of multipath channels with wide band systems
Another unwanted effect with non-stationary channel is the Doppler shift, which showsthe apparent change in the frequency due to the relative motion of the transmitter and receiver. Doppler shift and ISI are caused by the variability of the channel due to the environment and the relative motion of the transmitter and the receiver. The total effect of these phenomena is the poor quality of the signal received in the receiver part, which results in an unacceptable quality of service for the receiver.
3.2.1.Sorts of small-scale fading
When the different received signal superimpose destructively (received signal are out of phase), the signal strength will decrease and fading can occur. The fading will cause a downward fluctuation of the received signal strength. Therefore a momentary degradation in the quality of the received signal will be observed. Small-scale fading is divided into two main parts: the fading caused by multipath time delay and the one caused by the Doppler spread. There are two types of fading based on the multipath time delay: the frequency selective fading and the flat fading. There are also two types of fading based on the Doppler spread: the fast fading and the slow fading.
- Frequency selective fading:
It happens when the bandwidth of the channel is less than the bandwidth of the signal and the symbol period less than the delay spread [3.2]. In other words the channel has a constant gain and a linear phase over a bandwidth, which is less than the bandwidth of the signal. Certain parts of the signal spectrum are hence attenuated whereas other ones are not. The cause of this fading is that the delay spread of the multipath channel is nearly the same or greater than the symbol duration. Because of the frequency selective fading, multiple faded and delayed copies of the transmitted signal are contained into the received signal. ISI is introduced because of the dispersion of the symbol in time and causes a signal distortion. This model is mainly derived from wideband systems. It is more difficult to model, as each multi path has to be modelled separately and the channel has to be modelled as a linear filter. Good performance can however be achieved through adaptive equalization [3.2].
- Flat fading:
It happens when the bandwidth of the channel is greater than the bandwidth of the transmitted signal and the symbol period greater than the delay spread [3.2]. In other words the channel has a constant gain and a linear phase over a bandwidth, which is greater than the bandwidth of the signal. The delay spread of the multi path channel is less than the symbol duration. Therefore adjacent bits do not affect the decision process at the receiver side, which means that there is no ISI. However destructive interferences are still possible in this model.Flat fading channel can be considered as the cause of deep fades and therefore an additional transmitting power of 20dB to 30dB is needed to keep a good quality at the receiver side. This model is mainly derived from narrow band systems. Performance improvement is always possible through diversity [3.9].
- Fast fading:
It happens when the coherence time is less than the symbol duration, and when the channel variations are faster than basedband signal variations. It has a high Doppler spread [3.2]. We have in this case a time selective channel. This fading is only describing the channel’s change due to the motion of the receiver. A signal distortion happens, because of the Doppler spreading and the distortion will increase as the Doppler spread increases.
- Slow fading:
It happens when the coherence time is greater than the symbol duration, and when the channel variations are slower than based band signal variation. It has a low Doppler spread [3.2]. We have a non time selective channel. Therefore we can assume that the channel is constant over a time, which is more than the symbol duration.
3.2.2.Models of small-scale fading
We see that it is very important to know for fading channel the instantaneous signal amplitude in order to design an accurate channel. Main statistical models for the small-scale fading are Rayleigh, Rice and Nakagami-m. To explain those models probabilistic tools are needed. We will use indeed the cumulative density function and the probability density function.
With those tools we can now define in further details the three main statistical models.
- Rayleigh fading:
The Rayleigh distribution is usually used to model the time-varying nature of the received amplitude of a flat fading signal. It involves that the received amplitude changes in time respect to a Rayleigh distribution. Figure 3.10 illustrates the effect of a Rayleigh fade on a signal:
Figure 3.9: Representation of the Rayleigh fade effect on the signal envelop
The impulse response of the channel is random complex numbers, of which real and imaginary parts are independent Gaussians. The envelope of the received signal, which is the absolute value of these numbers, is hence Rayleigh distributed. The Rayleigh distribution of the received signal z(t) is given by:
(3.7)
The fading distribution is used in all the cases where there is a NLOS path between the transmitter and the receiver: