# Wireless Communication And The Diversity Technique Computer Science Essay

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Diversity can be achieved at the receiving side by increasing the number of receiving antenna but there are different complexities in doing so. It is difficult to increase number of antenna in mobile set as the size of mobile set is becoming more compact and handy. Transmit diversity would be the ultimate solution and the possibility of this diversity come into the lime light after the scheme proposed by S. Alamouti in his paper 'A simple transmit diversity scheme for wireless communication' in 1998. His scheme was one of the major break through in wireless communication in tackling multipath fading. Rayleigh was the fading model and the BPSK was the modulation scheme used in his paper.

BPSK uses two point on the constellation diagram. One drawbacks of BPSK is that it can only able to modulate at 1 bit/symbol and so is inappropriate for high data-rate applications when bandwidth is limited. QPSK uses four points on the constellation diagram, equispaced around a circle. Using four phases, QPSK can encode two bits per symbol. Hence the advantage can be either to double the data rate compared to a BPSK system while maintaining theÂ bandwidthÂ of the signal or to maintain the data-rate of BPSK but halve the bandwidth needed. Observing this advantage implementation of QPSK will be a good modulation in this scheme

Rayleigh fading is a reasonable model when there are many scatters objects in the environment. Rayleigh fading can be a useful model in heavily built-up city centers where there isÂ no line of sightÂ between the transmitter and receiver and many buildings and other objectsÂ attenuate,Â reflect,Â refract andÂ diffractÂ the signal thatÂ scatterÂ the radio signal before it arrives at the receiver. When there is aÂ line of sight, then the mean of the random process will no longer be zero, varying instead around the power-level of the dominant path. So if the environment is such that, in addition to the scattering, there is a strongly dominant signal seen at the receiver then Recian model is used. Regarding this facts this thesis work is towards the implementing Recian fading model and studying the effect when there is completely different environment exist than that of the paper.

## Objective

The objectives of the thesis are:

Simulation of receive and transmit diversity in BPSK and Rayleigh fading model as proposed in Alamouti paper as a basic requirement for the thesis work.

To use higher modulation technique QPSK to improve bandwidth efficiency than that of BPSK.

To use Recian Fading model and find the possibility of using Alamouti scheme other than Rayleigh Fading model as used in the paper.

## 1.3 Methodology

Thesis work is completely simulation based and need Monte Carlo simulation technique. Monte Carlo simulations are a class of computational algorithms that rely on repeated random sampling to compute their results. It can handle every complex an realistic system but has to repeat for each decision point. In order to support the code MATLAB is used. MATLAB is a high-level language and interactive environment that enables to perform computationally intensive tasks faster than with traditional programming language. MATLABÂ is aÂ numerical computingÂ environment andÂ fourth generation programming language. MATLAB allowsÂ matrixÂ manipulation, plotting ofÂ functionsÂ and data, implementation ofÂ algorithms, creation ofÂ user interfaces, and interfacing with programs in other languages. C programming is also used for the generation of the matrix for noise and channel and transmitting the symbol and receiving the signal using combining scheme.

## .

## CHAPTER 2

## Literature Review

## Wireless communication and the diversity technique

Wireless Communication is one of the most energetic areas in this ever going field of communication today. Wireless communication is the transfer of information over a distance without the use of electrical conductors or wire. The exact form of wireless transmission can vary. Two fundamental aspects of wireless communication that make the problem challenging and interesting are fading and interference. These aspects are not significant in wire line communication. Fading can be define as the variation of channel strength over time and frequency. The variation can be divided into two parts as large scale fading and small scale fading. Large scale fading is due to the path loss of signal as a function of distance and shadowing by large objects such as buildings and hills. This is typically frequency independent. Small scale fading is due to the constructive and destructive interference of multiple signal paths between the transmitter and receiver [3].

Variations in the received signal from various components of the transmitted signal that are propagated over different paths are known as multipath fading. So the multipath fading must be handle properly in order to minimize its effect. One solution for minimizing this problem is to increase transmit power but increasing transmit power is a difficult solution because of different constraints. Very useful solution comes from the concept of diversity. Diversity is used where two or more inputs at the receiver are used to get uncorrelated signals [5]. In conventional wireless communications, a single antenna is used at the source, and another single antenna is used at the destination. In some cases, this gives rise to problems with multipath effects. When an electromagnetic field is met with obstructions such as hills, canyons, buildings, and utility wires, the wave fronts are scattered, and thus they take many paths to reach the destination. The late arrival of scattered portions of the signal causes problems such as fading, cut-out (cliff effect), and intermittent reception. In digital communications systems such as wireless Internet, it can cause a reduction in data speed and an increase in the number of errors. The use of two or more antennas, along with the transmission of multiple signals (one for each antenna) at the source and the destination, eliminates the trouble caused by multipath wave propagation, and can even take advantage of this effect.

## 2.2 Different type of diversity technique

## 2.2.2 Time Diversity

When different time slots are used for diversity; it is called time diversity. Independent fades can be obtain if two time intervals separated for more than the coherence time and with this fact different copies of transmitted signal are send through separated time slot. These phenomena of time diversity can be describe as using a repetition code. Signals representing the same information are sent over the same channel at different times is time diversity and it is used in such type of system that suffers from burst error.

## . 2.2.3 Spatial Diversity

Spatial diversity uses multiple antennas, usually with the same characteristics, that are physically separated from one another. Depending upon the expected incidence of the incoming signal, sometimes a space on the order of a wavelength is sufficient. Other times much larger distances are needed. Cellularization or sectorization, for example, is a spatial diversity scheme that can have antennas or base stations miles apart. This is especially beneficial for the mobile communications industry since it allows multiple users to share a limited communication spectrum and avoid co-channel interference.

## 2.2.4 Space Diversity

The concept of space diversity is that the antenna should be spaced far enough apart so that different received copies of the signal undergo independent fading, so that at least any one of the copy of signal may not suffer from deep fading. In space diversity no additional work is required on the transmission end, and no additional bandwidth or transmission time is required but the physical constraints which are associated with it may limit its applications. This features of space diversity is completely differ it from frequency and time diversity. The spacing is an important factor in space diversity [3]. Fading is different at different points on the earth, so two antenna a few wavelengths apart will have uncorrelated fading and this is the fact of space diversity.

## 2.2.5 Pattern Diversity

Pattern diversity consists of two or more co-located antennas with different radiation pattern. This type of diversity makes use of directive antennas that are usually physically separated by some (often short) distance. Collectively they are capable of discriminating a large portion of angle space and can provide a higher gain versus a Single Omni directional radiator.

## 2.2.6 Frequency Diversity

Fading are different at different frequencies so frequency diversity is used. Different carrier frequencies are used to transmit the signal copies. To achieve diversity, the carrier frequencies should be separated by more than the coherence bandwidth of the channel. Frequency diversity suffers from bandwidth deficiency because different frequency is use to transmitted the replica of signal. Frequency means bandwidth which is very precious Also the receiver needs to tune to different carrier frequencies [10].

## 2.2.7 Polarization Diversity

Polarization diversity combines pairs of antennas with orthogonal polarizations. Reflected signals can undergo polarization changes depending on the media. By pairing two complementary polarizations, this scheme can immunize a system from polarization mismatches that would otherwise cause signal fade. Additionally, such diversity has proven valuable at radio and mobile communication base stations since it is less susceptible to the near random orientations of transmitting antennas.

## 2.2.8 Angular Diversity

Angular diversity uses directional antennas to achieve diversity so that the different copies of the transmitted signal are collected from different angular directions. This different signal collected from different angles travels different path and all signal will not suffer from deep fading. Unlike multiple antennas, it doesn't need separate physical locations like using multiple antennas so it is also very good for small devices [10]. An angular-diversity radiating system is described for troposphere-scatter radio links.

## 1.3 Space time coding

Space time coding (STC) rely on transmitting multiple, redundant copies of a data stream to the receiver. Multiple, redundant copies is send so that, at least some of them may survive the physical path between transmission and reception in a good enough state to allow reliable decoding. A space-time code (STC) is a method employed to improve the reliability of data transmission in wireless communication systems using multiple transmit antennas.

Space-time coding is a communications technique for wireless systems that employ multiple transmit antennas and single or multiple receives antennas. Information theory has been used to demonstrate that multiple antennas have the potential to dramatically increase achievable data rates. Space-time codes realize these gains by introducing temporal and spatial correlation into the signals transmitted from different antennas. There is, in fact, a diversity gain that results from multiple paths between base station and mobile terminal, and a coding gain that results from how symbols are correlated across transmit antennas. Significant increases in throughput are possible with only two antennas at the base station and one or two antennas at the mobile, and with simple receiver structures. The second antenna at the mobile terminal can be used to further increase system capacity through interference suppression [7].

The main objective of space-time codes is to achieve the maximum possible diversity. Space-time codes provide a diversity gain equal to the product of the number of transmit and receive antennas. The use of multiple antennas results in increasing the capacity of MIMO channels. In fact, when the number of transmit and receive antennas are the same, the capacity grows at least linearly by the number of antennas. There is a tradeoff between the spatial multiplexing gain and the diversity gain of MIMO systems.

## 2.4 Multiple-Input Multiple-Output (MIMO)

Wireless technique supports wide range of application, while supporting these applications using wireless techniques poses a significant technical challenge. Physical properties impose a vital challenge in wireless communication channel. These physical properties can be described in terms of several distinct phenomena, including ambient noise, propagation losses, multipath and interference. Increasing demand for higher data rates, better quality of service, and higher network capacity are always additional challenging in this field. To meet these needs there is a requirement for new techniques that improve the spectral efficiency and increase the reliability of system.

One of the technology that promises a cost-effective way to provide these capabilities is Multiple-Input Multiple-Output (MIMO). A MIMO system comprises a wireless communication link with multiple antenna elements in both transmitter and receiver. With this configuration, MIMO takes advantage of the multipath scenario by sending a single transmission from the transmitter antenna array to bounce along multiple paths to a receiver. Transmitting data on multiple signal paths increases the amount of information transferred in a system. Therefore, the system is able to handle more information and at a faster rate than a single-input single-output (SISO) scenario with a single path.

MIMO was conceived in the early 1970s by the researchers at Bell Laboratories while they were trying to address the bandwidth limitations that signal interference caused in large, high-capacity cables. However it was not thought to be practical in that era because of the high expense incurred in generating the processing power necessary to handle MIMO signals. Later, with the advancement of technology and cost reductions in signal-processing schemes and with the need to meet the increasing demands, the researchers were compelled to reconsider MIMO for wireless systems.

A MIMO system comprises a wireless communication link with multiple antenna elements in both transmitter and receiver.. A vector of signals is transmitted from the transmitter antenna array simultaneously and then travels through the wireless channel. These signals are then received at the receiver antenna array which combines the signals in such a way that the quality of the communication in terms of BER and data rate is significantly improved for each MIMO user. MIMO systems are based on a space-time signal processing architecture where time is complemented with space or distance which is obtained from the spatial distribution of antennas in the transmitter as well as the receiver. Space-time processing in MIMO systems basically increases data rate (spatial multiplexing) and link reliability (space-time coding). An interesting feature of MIMO is that it exploits the multipath scenario, a drawback of wireless transmission communication, to its advantage. MIMO benefits from it by transmitting data on multiple signal paths which increases the amount of information transferred in a system which in turn increases the number of users it can serve.

Use of MIMO system is increasing day by day in communication systems due to the potential gains in capacity they realize when using multiple antennas. MIMO doesn't required additional bandwidth but only increase numbers of antenna. The most significant advantage of the MIMO systems is the improved BER performance. From Shannon's information theory we can know about channel capacity, bandwidth and signal to noise ratio (SNR). From Shannon's information theory, the capacity represents the highest possible data rate that channel can support is known and also, his classic formula for channel capacity is a function of bandwidth and signal-to-noise ratio (SNR). Increasing signal power and increasing bandwidth are two spontaneous ways to improve capacity. But it is difficult to use this option because both of this power is generally limited in mobile devices and the channel bandwidth is usually limited by certain regulations and also it is very expensive in the rapidly growing world of wireless communication Thus, many approaches like advanced modulation and coding schemes have been proposed to achieve higher spectral efficiency. The concept of utilizing the degrees of freedom in the spatial domain through antenna arrays is emerging nowadays [8]. In particular, researchers have shown that schemes with multiple antennas on both sides can tremendously enhance the system throughput, reliability and coverage, without the necessity of extra power and bandwidth [9]. Multiple-input multiple-output (MIMO) architecture has emerged as a popular solution to the nonstop search for increased capacity in modern wireless communication systems. It promises enormous capacity with a marginal increase in cost and complexity. This technology is now poised to penetrate large-scale commercial wireless products and networks such as broadband wireless access systems, wireless local area networks LAN, third-generation (3G) networks and

beyond.

## 2.5 Diversity Combining Scheme

## 2.5.1 Selection Combing

Selection Combining technique is the simplest diversity technique. The receiver having the highest instantaneous SNR is connected to the demodulator. It selects the best signals among all of them .A practical selection diversity cannot function on a truly instantaneous basis, it must be designed so that the internal time constant of the circuit is shorter than the reciprocal of the signal fading [1].

Variable Gain

2

G1

1

Gm

3

G2

Switching Logic

or

Demodulators

Output

Antenna

## Figure.2.1 Block diagram of Selection Combining

## 2.5.2 Feedback or Scanning Combining

In feedback combining all signal are scanned in a fixed sequence until one is found to be above of predetermined threshold [1]. The signal is then received until it falls below threshold and the scanning process again starts after the signal lies below threshold level.

## 2.5.3 Maximal Ratio Combining

In Maximum Ratio combining each signal branch is multiplied by a weight factor that is proportional to the signal amplitude. That is, branches with strong signal are further amplified, while weak signals are attenuated. Individual signal are co-phased before being summed. This combining scheme produces an SNR output equal to the sum of individual SNR.

## .

## .

## .

Antenna

Adaptive Control

m

2

1

G1

G2

Gm

Cophase

and

Sum

Detector

Output

r1

r2

rm

## Figure 2.

## 2.5.4 Equal Gain Combining

In certain cases where variable weighting is not convenient, each branch weight are set to unity which is known as Equal Gain Combining

## CHAPTER 3

## Research Methodology

## 3.1 Classical Receive Diversity Scheme

At a given time, a signal is sent from the transmitter. The channel including the effects of the transmit chain, the airlink, and the receive chain may be modeled by a complex multiplicative distortion composed of a magnitude response and a phase response. The channel between the transmit antenna and the receive antenna zero is denoted by ho and between the transmit antenna and the receive antenna one is denoted by h1. [6]

Figure 3.1: Two branch classical Maximal-Ratio Receive Combining (MRRC) Scheme

The channel transfer functions h0 and h1 are expressed as

h0 =

h1 =

Noise and interference are added at the two receivers. The resulting received baseband signals are

r0=h0s0+n0

r1=h1s1+n1

The received vector is expressed as

## =.s+

where n0 and n1 represent complex noise and interference and assume as Gaussian distribution

The receiver combining equations for the two branches MRRC is as follows

S0=h0*r0+h1* r1

= h0* (h0S0+ n0) + h1* (h1S0 + n1)

= (Î±02 + Î±12)S0 + h0* n0+ h1* n1........................................................................1

The Euclidean distance is used for the detection purpose where xi is chosen whenever the following condition is satisfied.

d2 (xi , y) <= d2 (xk ,y) for all i â‰ k

Where, d2 (x, y) = (x - y) (x*-y*)

In case of the two branch MRRC

SO= (Î±02 + Î±12)s0 + h0* n0+ h1* n1

si is chosen if,

d2 (s0, (Î±02 + Î±12)si )<= d2 (s0, (Î±02 + Î±12)sk )

If signals are equal constellations (i.e. for PSK signals)

d2(s0, si ) <= d2(s0, sk) for all i â‰ k

## 3.2 The New Transmit Diversity Scheme

The scheme uses two transmit antennas and one receive antenna and may be defined by the following three functions:

â€¢ The encoding and transmission sequence of information symbols at the transmitter

â€¢ The combining scheme at the receiver

â€¢ The decision rule for maximum likelihood detection.

## ~

s1

## ~

s0

h0

h1

h1

h0

Interference and noise

n0

n1

rx antenna

h0=Î±0ejÑ²0

h1=Î±1ejÑ²1

s0

-s1*

tx antenna 1

Combiner

Channel Estimator

Maximum Likelihood Detector

tx antenna 0

s1

s0*

Figure 3.2: The new transmit diversity scheme with one receiver.two-branch

## Encoding and Transmission sequence

Two signals are simultaneously transmitted from the two antennas at a given symbol period. The signal transmitted from antenna zero and antenna one is denoted by S0 and S1 respectively . During the next symbol period signal -S1* i.e. negative conjugate of S1 is transmitted from antenna zero, and S0* conjugate of signal S0 is transmitted from antenna one. Transmission of the sequence is shown in Table I

..t+3T

T+2t

t+T

T

Antenna 0

-S3*

S2

-S1*

S0

Antenna 1

S2*

S3

S0*

S1

TABLE 3.1 Symbol transmitted in Alamouti scheme

In this table the encoding is done in space-time coding. The encoding can also be done in space and frequency. Instead of two adjacent symbol periods, two adjacent carriers may be used which is known as space-frequency coding

The fading is assumed to be constant across two consecutive signals. The received signal is then expressed as

r0=r(t)=h0S0+h1S1+n0..............................2

r1=r(t+T)=-h0S1*+h1S0*+n1.....................3

## The combining Scheme:

The combining scheme is used as shown in equations 4 and 5

S0=h0*r0+h1r1*..........................................4

S1=h1* r0-h0r1*..........................................5

## The Maximum Likelihood Decision Rule

The resulting combined signals in equation 4 and 5 are equivalent to that obtained from two-branch MRRC in equation 1. The only difference is phase rotations on the noise components which do not degrade the effective SNR. Hence the New diversity scheme i.e. new two-branch transmit diversity scheme with one receiver is equal to that of two-branch MRRC.

These combined signals are then sent to the maximum likelihood detector which, for each of the signals and uses the decision rule expressed in as

d2 (s0 , si) <= d2 (s0 ,sk) for all i â‰ k

Implementing the above decision rule, Si is chosen whenever

d2(SO , (Î±02+ Î±12) Si ) <= d2(SO , (Î±02 + Î±12) Sk)

which is equivalent to two-branch MRRC.

## 3.3 Two branches transmit diversity with M antennas:

There may be applications where a higher order of diversity is needed and multiple receive antennas at the remote units are feasible. In such cases, it is possible to provide a diversity order of 2 with two transmit and receive antennas.[6]

Combiner

h3

## ~

s1

## ~

s0

h1

h0

h2

Maximum Likelihood Detector

h1

h0

Channel Estimator

h3

h2

## ^

s0

## ^

s1

Channel Estimator

rx antenna0

n0

n1

n2

n3

h1

h0

rx antenna1

tx antenna 1

tx antenna 0

s0

-s1*

s1

s0*

h2

Interference & noise

Interference & noise

h3

Figure 3.3: The new two-branch transmit diversity scheme with two receivers.

## Rx antenna 0

## Rx antenna 1

## Tx antenna 0

## h0

## h2

## Tx antenna 1

## h1

## h3

## Table 3.2: Definition of channels between the transmit and receive antennas

## Rx antenna 0

## Rx antenna 1

## Time t

## r0

## r2

## Time t+T

## r1

## r3

## Table 3.3: Receive signal at two receiver

## Encoding and Transmission sequence

The encoding and transmission sequence is identical to 2 transmit one receive diversity which is shown in table I

## The combining Scheme

The combining process is done as below

## = +

The result of combining signals are given as

## = .

Which is equivalent to

## =.+ .

## The Maximum Likelihood Decision Rule

The value of Si is chosen whenever the following condition is satisfied.

d2(sO , (Î±02 + Î±12+ Î±32) si ) <= d2(sO , (Î±02 + Î±12+ Î±32) sk )

If signals are equal constellations:

d2(s0, si ) <= d2(s0, sk)

## Chapter

## Comparison of different modulation technique

## Modulation

Modulation is the process of encoding information from a message source in a manner suitable for transmission. Modulation can be done by varying the amplitude, phase or frequency of a high frequency carrier in accordance with the amplitude of the message[1] This chapter describes the various modulation technique use in the thesis work.

## BPSK

BPSKÂ uses two phases which are separated by 180Â°. It lies totally in one axis i.e. x-axis. It has no y-axis projection. The vector flip-flops on x-axis depending on the value of bit [11]. It does not particularly matter exactly where the constellation points are positioned.Â This modulation is the most strong of all the PSK since it takes the highest level of noise or distortion to make theÂ demodulator reach an incorrect decision. It's drawbacks is that it can only able to modulate at 1 bit/symbol and so is inappropriate for high data-rate applications when bandwidth is limited.

In BPSK, the phase of a constant amplitude carrier signal is switched between two values according to two possible signals m1 and m2 corresponding to binary 1 and 0, respectively. If sinusoidal carrier has an amplitude Ac and energy per bit Eb=1/2Ac2tb, then transmitted BPSK signal is either [1]

Sbpsk(t)= cos(2fc t+c) (binary 1)

Sbpsk(t)= cos(2fc t++c)

= -cos(2fc t+c) (binary 0)

It is often convenient to generalize m1 and m2 as binary data signal m(t), which takes on one of the two possible pulse shapes. Then the transmitted signal may be expressed as

Sbpsk(t)= m(t)cos(2fc t+c)

From this expression the constellation diagram is drawn as shown in the figure.

## â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦

From the constellation diagram, it can be seen that the distance between adjacent points in the constellation is 2. Using this in the average probability of bit error in additive white Gaussian noise (AWGN), the average probability of bit error is obtain as

Pe, BPSK = Q

Where N0 is noise spectral density.

## QPSK

Quadrature phase shift keying (QPSK) uses four points on the constellation diagram, equispaced around a circle. Using four phases, QPSK can encode two bits per symbol. Also withÂ the use of Gray coding, itÂ minimize the BER, twice the rate of BPSK. Hence the advantage can be either to double the data rate compared to a BPSK system while maintaining theÂ bandwidthÂ of the signal or to maintain the data-rate of BPSK but halve the bandwidth needed. In QPSK, information is conveyed through phase variations, so that in each time period, the phase can change only once. Since there are four possible phases, there are 2 bits of information conveyed within each time slot. The rate of change (baud) in this signal determines the signal bandwidth, but the throughput or bit rate for QPSK is twice the baud rate.Â

In QPSK, phase of the carrier takes on one of the four equally spaced values, such as 0, /2, 3/2, where each of the value corresponds to a unique pair of message bits. The Qpsk signal for this set of symbol states may be define as [1]

Sqpsk(t)= cos(2fc t+(i-1) ) i=1,2,3,4

Where Ts is the symbol duration and equal to twice the bit period.

Using Trigonometric identities

Sqpsk(t)= cos[(i-1) )] cos(2fc t)-sin[ (i-1) )]sin(2fct)

If basic function (t)= cos(2fc t) and (t)= sin(2fct) are define over interval for the QPSK signal set, then four signals in the signals in set can be expressed in terms of the basis signal as

Sqpsk(t)= { cos[(i-1) )](t)- sin[ (i-1) ](t) } i=1,2,3,4

Based on this representation, a QPSK signal can be represented using a 2-D constellation-diagram with four points as show in figureâ€¦â€¦â€¦â€¦â€¦.

Distance between adjacent points in QPSK constellation diagram is . Since each symbol corresponds to two bit, then Es=2Eb, thus the distance between two neighboring points in the QPSK constellation is equal to 2. Using this in the average probability of bit error in additive white Gaussian noise (AWGN), the average probability of bit error is obtain as

Pe, QPSK = Q

Similarly the Probability of symbol error rate for QPSK

Pe, QPSK =2Q

Since QPSK is transmitting two bit simultaneously so in order to achieve same error probability as BPSK, QPSK must use twice the power of that of BPSK.

There are various other modulation technique which can be use in this scheme like QAM. QAM (Quadrature amplitude modulation) is a method of combining two amplitude-modulated (AM) signals into a single channel which results in doubling the effective bandwidth. QAM is used with pulse amplitude modulation (PAM) in digital systems, especially in wireless applications. In a QAM signal, there are two carriers, each having the same frequency but differing in phase by 90 degrees. One signal is called the I signal, and the other is called the Q signal. Mathematically, one of the signals can be represented by a sine wave, and the other by a cosine wave. At source two modulated carriers are combined and again at the destination, the carriers are separated, the data is extracted from each, and then the data is combined into the original modulating information.

## Chapter 5

## Comparison of different fading model

## 5.1 Fading

Fading is used to describe the rapid fluctuations of the amplitudes, phases or multipath delays of a radio signal. Fading is caused by interference between two or more version of the transmitted signal which arrive at receiver at different times.Rayleigh and Rician fading channels are useful models, which occurs in real-world in wireless communication. These model are due to phenomena such as time dispersion, multipath scattering effects, and Doppler shifts that arise from relative motion between the transmitter and receiver.

## 5.1.1 Rayleigh fadingÂ

Rayleigh fadingÂ is aÂ statisticalÂ modelÂ for the effect of aÂ propagationÂ environment on aÂ radioÂ signal, such as that used byÂ wirelessÂ devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such aÂ transmission mediumÂ will vary randomly, orÂ fade, according to aÂ Rayleigh distribution.

Rayleigh fading is a reasonable model when there are many objects in the environment thatÂ scatterÂ the radio signal before it arrives at the receiver. TheÂ central limit theoremÂ holds that, if there is sufficiently much scatter, the channelÂ impulse responseÂ will be well-modeled as a Gaussian processÂ irrespective of the distribution of the individual components. If there is no dominant component to the scatter, then such a process will have zeroÂ meanÂ and phaseÂ evenly distributedÂ between 0 and 2Ï€Â radians. The requirement that there be many scatterers present means that Rayleigh fading can be a useful model in heavily built-up city centers where there isÂ no line of sightÂ between the transmitter and receiver and many buildings and other objectsÂ attenuate,Â reflect,Â refract andÂ diffractÂ the signal.

The envelope of the sum of two quadrature gaussian noise signals obey a Rayleigh distribution. The Rayleigh distribution has a probability density function (pdf) given by:

P(r) =

0

Where is the rms value of the received voltage signal before envelope detection and 2 is the time average power of the received signal before envelope detection. [1]

Combination of two Gaussian random variable gives Rayliegh channel model

Rayleigh channel model=Gaussian random variable +j Gaussian random Variable

5.1.2 Ricean Fading

If the environment is such that, in addition to the scattering, there is a strongly dominant signal seen at the receiver, usually caused by aÂ line of sight, then the mean of the random process will no longer be zero, varying instead around the power-level of the dominant path. Such a situation may be better modeled asÂ Rician fading. Rician channel is a transmission channel that may have a line-of-sight component and several scattered of multipath components.

The probability density of the amplitude of Ricean fading channel is given by

P(r)=

0

Where, A is the peak amplitude of the dominant non fading component and I0 is the modified Bessel function of the first kind and zero order. The Ricean factor K specifies the ratio of the deterministic signal power and the variance of the multipath

K=

K(dB)=10 log10 dB

As Aâ†’0 (K â†’ âˆ’âˆž), the power of the dominant path diminishes, and the Ricean PDF converges to the Rayleigh PDF. Airplane to ground communication links and microwave radio channels are the example of Ricean Fading [2].

We can simply change the mean of either real or imaginary or both of the complex Gaussain random variables to get the Ricean fading model .Recian Fading model can be expressed as

Recian channel model= (k*cos(t) + Gaussian random variable)/sqrt(2)+j*(k*sin(t) + Gaussian random variable)/sqrt(2)

where t is any real number ,normally t=n/4 and K is the Ricean factor

## CHAPTER 6

## TECHNIQUES AND IMPLEMENTATION

## 6.1 Algorithm:

Step1- Specify the number of the transmitter and receiver antenna

Step2- Specify SNR value

Step3- Sigma value (variance) for corresponding SNR

Step4- Find the length of Step 3

Step5- Generate the channel matrix

Step6- Generate BPSK or QPSK signal

Step7- Generate the noise

Step8- Generate the received signal

Step9- Use the MRRC method for combining the received signal

Step10- Estimate the received signal

Step11- Compare the estimated signal with the generated signal

Step12- Monte Carlo simulation is done to find the bit error rate

Step13 - Graph plotted for SNR Vs BER

## 6.2 Implementation Issue

Actually in classical diversity scheme, there is presence of one antenna and in transmit diversity there are more than one antenna in the transmitter side. Transmit power from classical diversity scheme with single antenna and total transmit power from the two antennas for the new scheme is assumed to be same.

Similarly for QPSK, two bit are transmitted at a time but here QPSK and BPSK uses the same transmit power. If the transmit power for QPSK is double than that of BPSK, Probability of BER almost identical to BPSK can be obtained

Perfect knowledge of the channel are known to the receiver

Equal error probabilities are assumed for transmitted signal for both BPSK and QPSK

## CHAPTER 7

## CONCLUSION

Thesis work was started with Classical receive diversity scheme using BPSK as a Modulation Technique and Rayleigh Fading Model. In this classical receive diversity, there are three cases:

1. No diversity with one transmit one receive antenna.

2. One transmit two receive antenna and

3 One transmit four receive antenna.

Graph between BER and SNR for all three cases are plotted using Maximal Ratio Combining Scheme. One transmit one receive (no diversity) scheme has the highest BER. Comparing the BER of One transmit two receive antenna with no diversity shows that one transmit two receive antenna has less BER than that of no diversity scheme. Finally when receiver antenna is increased to four, least BER among all of them for a particular SNR is obtained. Hence, we can conclude that one transmit four receive scheme gives the best performance in receive diversity scheme.

After the completion of classical diversity scheme work was continue towards the new transmit diversity. This part explore the possibility of transmit diversity and gives the possibility to increase the antenna at transmitter side which reduce the technical complexity to increase number of receiver antenna at receiver side. In practice it is difficult to increase antenna at receiver side. New combining scheme was used to plot the graph between BER and SNR for the performance evaluation of transmit diversity.

New transmit diversity scheme includes

1. Two branch diversity with one receiver and

2. Two-branch Transmit diversity with M receivers.

Comparison of graph of BER Vs SNR between receive diversity and new transmit diversity shows that transmit diversity result was better than that of no diversity. In case of two transmit two receive diversity, BER was nearly identical to the best scheme so far i.e. one transmit four receive antenna.

After the successful evaluation of classical receive diversity and new transmit diversity scheme using BPSK and Rayleigh fading model, next work was towards bandwidth efficient modulation technique and other Fading Model. From the simulation of both Receive and Transmit diversity in QPSK and Ricean Fading Model different graph between BER and SNR was plotted and following conclusion were drawn. Result from the graph shows use of QPSK gives little bit higher bit error rate than that of BPSK but since QPSK can transmit two bit simultaneously at a time, bandwidth efficient technique is obtain even though the BER was slightly high. Similarly when there is presence of strong line of sight, channel was model with Ricean Fading Model. Use of this model shows that there was tremendous improvement in the BER, due to the presence of strong line of sight between transmitter and receiver.