Description Of Binary Symmetric Channel Computer Science Essay

Published: Last Edited:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

Radio communications often need a more elaborated model to reduce fading effects, which affect the power of the signal. This attenuation of the signal is mainly due to an environment of propagation rich in echoes and thus characterized by many multi-paths, but also to the relative movement of the transmitter and involving receiver causing channel temporal variations.

Transmission channels types

Binary Symmetric Channels BSC

The binary symmetric channel (BSC) is a discrete channel of which alphabets of entry and of exit are finished and equal to {0; 1}.

We consider in this case that the channel includes all the elements of the chain ranging between the coder of channel and the corresponding decoder (figure 1)








Figure 1 : Description of Binary Symmetric Channel

We note ak and yk respectively the elements at the entry and the exit of the CBS. If the noise and other disturbances cause statistically independent errors in the binary sequence transmitted with a probability p, then:

Pr(yk = 0|ak = 1) = Pr(yk = 1|ak = 0) = p

Pr(yk = 1|ak = 1) = Pr(yk = 0|ak = 0) = 1-p

The functioning of the BSC is summarized in the form of diagram on figure 2. Each binary character at the exit of the channel depending only on the binary character entering corresponding, the channel is called memoryless.

Figure 2: Binary Symmetric Channel diagram

Additive White Gaussian Noise AWGN

Additive white Gaussian noise (AWGN) is the commonly used to transmit signal while signals travel from the channel and simulate background noise of channel. The mathematical expression in received signal is

r(t) = s(t) + n(t); that passed through the AWGN channel where s(t) is transmitted signal and n(t) is background noise.

Figure 3 : Block diagram of AWGN channel model

An AWGN channel adds white Gaussian noise to the signal that passes through it. It is the basic communication channel model and used as a standard channel model.

1.3 Fading channels

In wireless communications, fading is deviation of the attenuation affecting a signal. The fading may vary with many factors such as geographical position, radio frequency or delay and is modeled as stochastic processes. We can simply say that a fading channel is a communication channel includes fading.

Causes of fading

In wireless systems, fading may be caused by different physical phenomenon:

Doppler Shift:

When a mobile is moving at a constant velocity Vs along a path, f' is the observed frequency and f is the emitted frequency. All these terms will be related by the following equation:

f'= (V/V+Vs)f [1]

We can say after the above equation that the detected frequency increases when the mobile is moving towards the observer and decreases as the source moves away, this is called the Doppler Effect


Reflection occurs when the electromagnetic wave encounters an object while propagating and generating a subsequent long wavelength compared to wavelength of the propagating wave.

As a result, signal can taking a large number of different path.


Diffraction takes place because of the obstacles of the path radio and irregular edges of a surface between the transmitter and the receiver, even when a Line of Sight does not exist between transmitter and receiver the secondary waves will be spread over the space.


Scattering will be produced when the wave is propagated through a medium consisting of objects of dimension smaller than the wavelength and having larger volumes of obstacles per unit volume.

The scattered waves are produced due to irregularities in the channel and rough surfaces of small objects.

For the different causes of fading, there are panoply types of fading.

Types of fading

We can make out several types of fading according to effect of multipath, effect of Doppler Spread and delay Spread.

According to Doppler Spread

Slow fading

The slow fading can be caused by the large difference between the coherence time of the channel and the delay constraint of the channel.

A large building that obscures the signal path between the transmitter and the receiver can also cause a slow fading.

The amplitude and phase imposed by the channel remain constant over the period of use.

Fast fading

When the coherence time of the channel is smaller than the delay constraint of the channel causes the fast fading. The amplitude and phase change imposed by the channel varies considerably over the period of use.

According to delay spread

There are two types of fading according to the effect of Delay Spread. These are

Flat Fading and Frequency Selective Fading

Flat Fading

We called flat fading the fading that occurs when the band length of the mobile channel is greater than the length of the transmission channel band.

Among the characteristics of such fading is that frequency components of a received radio signal vary in the same proportion simultaneously

Frequency Selective Fading

Partial cancellation of a radio signal by itself causes frequency selective fading.

Indeed, the signal comes through two different paths and at least one of them undergoes a lengthening or shortening.

View that the effect of constellation is deeper at a particular frequency that is constantly changing, the fading frequency selective then appears as a slow cyclic perturbation.

According to multipath

According to the effect of multipath, there are two types of fading:

Large Scale Fading

This type of fading is caused by the gradual variation of the power of the received signal caused by the attenuation of the signal determined by the geometry of the path profile.

Small Scale Fading

Small changes (even smaller than half the wavelength) in the position in the space between the transmitter and the receiver can cause dramatic changes in the amplitude and phase of the signal.

This is called Small-Scale Fading.

There are many models that describe the phenomenon of small scale fading. Out of these models, Rayleigh fading, Ricean fading and Nakagami fading models are most widely used.

Types of Small Scale Fading

4.1 Rayleigh fading model

The Rayleigh fading is mainly caused by multipath reception. Rayleigh fading is most applicable when there is no line of sight between the transmitter and receiver.

Ricean fading model

This model seems a lot of Rayleigh model except the strong presence of dominant component is a stationary signal known as LOS (Line Of Sight).

Nakagami fading model

Apparaition of instances of multipath scattering with relatively large delay-time spread, with different clusters of reflected waves encourages the use of Nakagami fading channel.

Always, we find Nakagami m-fading, the parameter m is called the 'shape factor' of the Nakagami.

In the special case m = 1, Rayleigh fading is recovered, with an exponentially distributed instantaneous power

For m > 1, the fluctuations of the signal strength reduce compared to Rayleigh fading.


Diversity techniques can be used to improve system performance in fading channels i.e instead of transmitting and receiving the desired signal through a single channel, there is obtained L copies of the desired signal by M different channels and if some copies may undergo deep fades, others do not.

We might then be able to get enough energy to make the right decision on the transmitted symbol. There are several types of diversity are used in wireless communication systems.

5.1 Frequency Diversity

Frequency diversity is the use of multiple frequencies for transmitting the signal. It is a technique used to overcome the effects of multipath fading, At the receiver, the L independently faded copies are combined to give a statistic for decision.

Time Diversity

Another approach to overcome the effect of fading and achieve diversity is to send the same signal in different time periods i.e. each symbol is transmitted repeatedly. The intervals between transmissions of the same symbol should be at least the coherence time so that different copies of the same symbol undergo independent fading.

Spatial diversity

Diversity can also be expected from the use of M antennas are used to receive the M copies of the transmitted signal, this is called MIMO system. The antennae should be spaced far enough apart so that different received copies of the signal undergo independent fading.

This technique does not need additional work at the reception or bandwidth or transmission time additional

Presently, two different forms of MIMO system:

Multi-antenna types

Multi-antenna MIMO technology has been developed and implemented in some standards, e.g. 802.11n products.


A communication model SISO (single input single output) makes it clear that spatial diversity cannot be applied.

However, this case is included to assess its performance in fading channels and to show clearly the advantage of spatial diversity.


SIMO-communication systems (Single Input Multiple Output) use one antenna to the transmitter and multiple antennas at the receiver. Thus, any signal transmitted from the single antenna transmission arrives at all the antennas of the receiver by the various sub-channels. It is assumed that the sub-channels are completely uncorrelated we obtain therefore several independent copies of the same signal arrive at the receiver.


MISO (Multiple Input Single Output) is a special mode of operation of MIMO devices. It is used in NLOS conditions or in a noisy RF. the source antennas are combined to minimize errors and optimize data speed.

MISO technology is used in widespread applications such as digital television (DTV), wireless local area networks (WLANs), metropolitan area networks (MAN) and mobile communications


Technology Multiple-input multiple-output (MIMO) has recently emerged as one of the most important techniques of modern digital communications thanks to its promise of very high data rates, free additional spectrum and transmission power. Wireless communication can be benefited from MIMO in two different ways:

Spatial multiplexing and diversity. In the first case, the data is transmitted from separate antennas in order to maximize throughput. In the second case, the same signal is transmitted along multiple paths fade independently with the aim to improve the robustness of the link BER at each user.

Multi-user types

Multi-user MIMO (MU-MIMO)

Multi-user MIMO (MU-MIMO) is a set of technologies that exploit MIMO several radio terminals to improve the communication capabilities of each terminal. In contrast, single-user MIMO considers that access to multiple antennas that are physically connected to each individual terminal. MU-MIMO can be seen as a broader concept that allows a terminal to transmit (or receive) signal to (or from) multiple users in the same band simultaneously.

MIMO Routing

The routing is done cluster by cluster in each hop; where each cluster contains at least one node.

This type of system uses different routing protocols to those used in the SISO view that it is routing node by node each hop.

Cooperative MIMO (CO-MIMO)

CO-MIMO, also known as network MIMO (Net-MIMO), or Ad-hoc MIMO uses distributed antennas that belong to other users.

A cooperative communication system therefore consists of wireless nodes distributed interact to transmit information.

Indeed, several radio terminals relaying the signal to each other to form a virtual network of antennas, and collaboration allows exploiting the spatial diversity fading channels.

In many wireless applications, users may not be able to support multiple antennas due to size, complexity, power, or other constraints that is why there is a resort to antennas neighbors to relay the message.

Cooperative communication for wireless networks

For its ability to mitigate fading in wireless networks through achieving spatial diversity and solving the difficulties of installing multiple antennas on small terminals communications, cooperative communications in wireless networks have gained much interest.

Cooperative communications are based on the combination of multiple nodes (each with a single antenna) in a cluster to form a large issue and / or receive cluster. Collaborative groups are formed in an "ad hoc" fashion through negotiations between neighboring nodes without centralized control. The cooperative diversity arises naturally in ad hoc networks, since it allows good energy saving, with a large number of nodes, while supporting decentralized routing

In traditional cooperative diversity setups, a user is unilaterally designated to act as a relay for the benefit of another one, at least for a given period of time. In [2], Laneman and Wornell proposed different cooperation protocols including fixed and adaptive relaying protocols. In the fixed relaying protocol, such as the amplify-and-forward and decode-and-forward protocols, the relays always help in forwarding the source information. [3]

The cooperative transmission protocols used in the relay station are either Amplify and Forward (AF) or Decode and Forward (DF). These protocols describe how the received data is processed at the relay station before the data is sent to the destination.

6.1 Amplify and Forward (AF)

This method is often used when the relay has only limited computing time/power available or the time delay has to be minimized. The signal received by the relay is attenuated and needs to be amplified before it can be sent again, and the noise in the signal is also amplified as well, which is the major drawback of this protocol.

Indeed, the signal amplification is done in block.

Figure 4: Amplify and forward technique [4]

Decode and forward (DF)

Nowadays, the relay has enough computing power, which then promotes the use of Decode and Forward protocol to handle data in the relay.

The idea is that the relay decodes the received packet and transmits a codeword, using the same code as the one used at the source or another.

There is therefore no amplified noise in the signal, as is the case when using the AF protocol.

The relay can decode the original message completely or just decoded and recoded symbol by symbol.

The first method requires more execution time and it has the advantage of using the checksum to detect bit error in the received message.

Performance metrics

Signal to noise ratio (SNR) and bit error rate (BER) and/or symbole error rate (SER) are common performance metrics for assessing the quality of communication.

Signal to Noise Ratio SNR

Signal to noise ratio is a relative measure of the signal power compared to the noise power. Assuming gaussian noise model for wireless channels and complex signals,

Bit to Noise Ratio BER

Bit error rate (BER) performance metric is a commonly used which describes the probability of error as a function of the number of error bits per bit transmitted. BER is a direct effect of channel noise models for Gaussian noise channel. For fading channels, BER is worse and can be directly linked to the performance of the Gaussian noise channel

Chapter 2


The relay channel was treated for the first time by van der Meulen [5][6].

Relay channel model helps a pair of terminal to communicate. This might occur, for example, in a multi-hop wireless network or a sensor network where nodes have limited power to transmit data.

Illustrative example: Wireless Mesh Network and Relaying



Architectures of WMN

The architecture of WMNs can be classified into three main groups based on the functionality of the nodes:

Infrastructure/Backbone WMNs

Client WMNs

Hybrid WMNs

One Way Relay

A one-way relay, in which there is a source, a relay and a destination, and the relay helps the source by forwarding the message to the destination.

Two way Relay

Relay channel models

One relay

In this model we have three terminals: Source, destination and the relay node which handles the routing of information to the destination.

Multiple relays

It is known that multiple antennas can greatly increase the capacity and reliability of a wireless communication link in a fading environment.

Thus, recently, it appeared several architectures with relay selection strategies.

Indeed, the source sends the signal to multiple relays and a single relay is selected to forward the message to its destination.

The selection process is usually based on a calculation of BER (or SER).

For example, we will select the relay that minimizes the BER or the one that minimizes the maximum REC (max min procedure).

Chapter 3: Contribution


In this contribution we investigate the signal to noise ratios in two-way relaying amplify and forward relays then we derive explicit SNR expressions to study their behavior.

System model

We will study the behavior of the SNR in Rayleigh fading channel. Binary phase shift keying (BPSK) is used for modulation.

Several studies have been interested in studying two way relay network with its various aspects and parameters.

Some work is to find a fixed power allocation coefficient for the three nodes S1, S2 and the relay depending on the distance and positioning of the relay.

Other work seeks to reduce the BER playing on the parameters of TWRN system.

Our work is around this.

Figure 5: Description of 2-TS two way AF relayingOur contribution is to make the use of relay incremental, i.e. if the calculated SNR at the relay is above a threshold SNR, the relay will forwarder the signal else the direct link between S1 and S2 will be used.

In our work, we will analyze 2-TS two way AF relaying network as shown in the figure below

In the first TS (time slot) S1 transmit his signal to S2 and relay node.

In the second TS, S2 transmit his signal to S1 and relay node.

At this stage we calculate the SNR at the relay and compared it to a threshold SNR, if the calculated value is greater than the defined then relay is used for relaying traffic else the direct link between S1 and S2 will be used.


[1] Fumiyaki Adachi, "error Rate Analysis of Differentially Encoded and detected 16-APSK under Rician fading", IEEE Transactions on Vehicular Technology, Vol. 45, No. 1, February 1996.

[2] J. N. Laneman and G. W. Womell, "Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,"

IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2415-2425, Oct. 2003

[3] Wireless Transmission With Cooperation On Demand for Slow and Fast Fading Environments

Kamel Tourki, Mohamed-Slim Alouini, Mazen Omar Hasna. IEEE Trans 2008

[4] Performance Analysis of Cooperative Communication System with a SISO system in Flat Fading Rayleigh channel Sara Viqar , Shoab Ahmed , Zaka ul Mustafa and Waleed Ejaz National University of Sciences and Technology, Islamabad, Pakistan Sejong University, Seoul, Republic of Korea

[5] E. C. van der Meulen, "Transmission of information in a T -terminal discrete memoryless channel," Ph.D. dissertation, Univ. California,

Berkeley, CA, Jun. 1968.

[6] "Three-terminal communication channels," Adv. Appl. Probab.,

vol. 3, pp. 120-154, 1971.