Models of channel fading

Communications over wireless medium are very appealing, because they enable mobility, however are special challenging due to the variation of the channel over the time and over frequency band. Channel is the physical medium that is used to send the signal from the transmitter to the receiver.

The radio link between the transmitter and receiver may vary from the ones where transmitter and receiver are in simply line of sight to the ones where the communication nodes are severely obstructed by the building, mountain etc. , and hence suffer from severe attenuation. Wireless channel are very different from the stationary and predictable wired channels because of their randomness and signal attenuation known as fading.

In the wireless medium, a signal can travel from a transmitter to a receiver over multiple reflective paths. This phenomenon is referred to as multipath propagation. There are several kinds of communication impairments that are typical of a wireless medium. Impairments may result mainly from multipath propagation, attenuation of signal power from large objects, relative motion between transmitter and receiver, interference, spreading of electromagnetic power and thermal noise. The nature of these impediments changes over time in unpredictable ways due to user movements causing fluctuation of the received signal.

Figure 1 represents a taxonomy of the various kinds of channel fading. Fading effects can be classified into two large groups of fading: large scale fading and small scale fading. A first criterion that allows us to distinguish between large scale and small scale fading is the variation of source position between the source and destination. If the relative movement of the source is very large, the receiver will experience large scale fading but if the variation is small, the receiver just experiences small scale fading and when a receiver moves a lot  it experiences  both large scale and small scale fading.

Fig.1 Fading Taxonomy

Large scale fading, refers to path loss caused by the effects of the signal traveling over large areas, and shadowing that is the effect fluctuating the received signal power  due to objects obstructing the propagation path between transmitter and receiver . These fluctuations are experienced on local-mean powers, that is, short-term averages to remove fluctuations due to multipath propagation.  Path loss may occur due to many effects, such as free-space loss, refraction, diffraction, reflection. Path loss is also influenced by terrain contours, environment (urban or rural, vegetation and foliage), propagation medium (dry or moist air), the distance between the transmitter and the receiver.

Small scale fading  consists of two  main concepts of coherence time and frequency coherence . The coherence time of the channel is related to a quantity known as the Doppler spread of the channel. When a user (or reflectors in its environment) is moving, the velocity of user causes a shift in the frequency of the signal transmitted along each signal path. This phenomenon is known as the Doppler shift. In general, coherence time is inversely related to Doppler spread. The delay spread of the channel dictates its frequency coherence. Wireless channels change both in time and in frequency. The time coherence shows us how quickly the channel changes in time, and similarly, the frequency coherence shows how quickly it changes in frequency. Coherence time is actually a statistical of the time duration over which the channel impulse response is essentially invariant, and quantifies the similarity of the channel response at different times and the coherence bandwidth is a statistical measurement of the range of frequencies over which the channel can be considered “flat”over this bandwidth.

The distinction between slow and fast fading is important for the mathematical modeling of   fading channels and for the performance evaluation of communication systems operating over these channels. The fading is called fast if the coherence time  is much shorter than the delay requirement of the application, and slow if coherence time is longer. The operational significance of this definition is that, in a fast fading channel, one can transmit the coded symbols over multiple fades of the channel, while in a slow fading channel, one cannot. Thus, whether a channel is fast or slow fading depends not only on the environment but also on the application.

Frequency selectivity is also an important characteristic of fading channels. If all frequency components of a signal will experience the same magnitude of fading then it is called frequency flat fading. Frequency flat fading occurs when the coherence bandwidth of the channel is larger than the bandwidth of the signal and if the frequency components of a transmitted signal are affected by different amplitude gains and phase shifts then the fading is said to be frequency selective. Frequency selective fading occurs when transmitted signal bandwidth is bigger than the coherence bandwidth channel. There are different models describing frequency flat fading, e.g. Rayleigh Model, Nakagami-q (Hoyt) Model, Nakagami-n (Rice) Model, Log-Normal Shadowing and, Weibull fading model.

[1]E. Biglieri, J. Proakis, S. Shannai (Shitz), “Fading channels: Information-theoretic and communication aspects”, IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2619-2692, 1998.

[2] Fundamentals of wireless Communication, David Tse and Pramod Viswanath.

[3]M.G. Saduque et al., “Modeling and Chaarcterization of Different Types of Fading Channel”, International Journal of Science Engineering and Technology Research, vol. 4, no. 5, May 2015.