Tutorial II: Communication Channels – Types, Characteristics, and Mathematical Models

In tutorial II we discussed about basic elements of any digital communication system. In this tutorial, we will discuss about communication channels, their types, characteristics, mathematical models and matlab code / algorithms.

First of what is channel or more precisely what is communication channel? In simple words, communication channel is a physical medium which is used to send the signal from the transmitter to the receiver or we can also say any physical medium which transmits information or used for transmitting information is known aschannel like: optical fiber, storage media etc.

When a signal transmits through the channel, channel inherently added some noise to the signal. This noise is known as thermal noise. Noise means any undesirable effect on the signal of interest which results in attenuation, degradation or corruption of the signal. The noise generated by the components is categorized as thermal noise. Also known as additive noise. The effect of the noise on the signal can be reduced by increasing the power in the transmitted signal but which results in lesser battery life i.e. more power consumption. There is one more limitation that is available channel bandwidth. Because of these two limitations of the channel, we have to design our communication system such that we can transmit as much data as possible with out getting corrupted i.e. these constraints make us to derive new algorithms or techniques for reliable transmission of information over channel with high data rates. And as an engineer we also go for optimum solutions.

Types and Characteristics of channels:

There are many types of channels. Here we will just discuss their operating frequencies. (Details can be easily found on net)

1. Wire line channels: operates at frequency few kHz to several hundreds of kHz
2. Fiber Optical Channels: provides bandwidth in the magnitude several times higher than that of wire line channel
3. Wireless Electromagnetic Channels: operates in the range of 10kHz to =~ 100 GHz, this is further categorized as long wave radio, short wave radio, microwave radio as they operates in radio frequency they are also known as 'radio' or 'radio channel'.
4. Under Water Acoustic Channels: operated at extremely low frequencies.
5. Storage Channels: like magnetic tapes, magnetic disks etc.

Mathematical Models:

When we design a communication system for transmitting information through the physical channels, we construct a mathematical model that reflects the most important characteristics of the transmission medium. This mathematical model of the transmission medium is used to design the channel encoder, and modulator at the transmitting end and to design the demodulator and channel decoder at the receiving end.

1. The additive noise channel:
   

   It is the simplest mathematical model. Shown below.

    

   

   figure1 additive noise channel

    

   Here s(t) is the input signal to the channel or the transmitted signal from the transmitter.n(t) is the additive random noise process, or we can say it is the noise added by the channel which corrupts the signal. In wireless channels this noise can be generated due to interference. But if this noise is generated primarily by components then it is thermal noise. This type of noise is characterized statistically as Gaussian Noise Process. The resulting mathematical model is usually called as additive Gaussian Noise Channel.

    

   Mathematical Equation

    

   

   equation1 additive noise channel

    

   The matlab code(named as Additive Noise Channel) can be downloaded from Matlab File Exchange
   Resource Center( to download go to matlab or Channel Coding)
   

    

2. The linear Filter Channel:
   

    

   In some physical channels such as wire line channels, filters are used to ensure that the transmitted signal do not exceed specified bandwidth (remembered we were talking about bandwidth considerations in the beginning) and this do not interfere with the one another. Such channels are generally characterized mathematically as linear filter channels with additive noise, see figure 2.

    

   

   figure2 linear filter channel with additive noise

    

   Mathematical equation

    

   

   equation2 linear filter channel

    

    

3. The linear time-variant filter channel:
   

   Physical channels such as underwater acoustics channels and radio channels results in time-variant multipath propagation of the transmitted signal may be categorized mathematically as time-variant linear filters. The model is shown in figure 3.

    

   

   figure3 linear time variant filter channel

    

   Linear filters are characterized by a time variant channel impulse response c(τ;t), where c(τ;t) is the response of the channel at time t due to an impulse applied at time t – τ.

   Mathematical Equation

    

   

   equation3

    

   When we talk about mobile cellular radio channels, concept of multipath signal propagation came into picture, in such cases time variant impulse response is a special case and given by equation (4)

    

   

   equation4

    

   In this case the received signal or the channel output is given by equation (5)

    

   

   equation5

    

   The received signal consists of L multipath components, where each component is attenuated by {ak(t)} and delayed by {τk}

   These three mathematical models are the most basic channel models and will be used throughout our discussions in the coming posts.