DESIGNING AND IMPLEMENTATION OF ALGORITHMS …shodhganga.inflibnet.ac.in/bitstream/10603/19825/3/12_chapter3.pdf · DESIGNING AND IMPLEMENTATION OF ALGORITHMS FOR ANTENNA DIVERSITY

DESIGNING AND IMPLEMENTATION OF ALGORITHMS FOR ANTENNA DIVERSITY TECHNIQUES

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CHAPTER : 3

DESIGNING AND IMPLEMENTATION OF ALGORITHMS FOR

ANTENNA DIVERSITY TECHNIQUES

3.1 Introduction

As per the objective of this research, the main aspect is to study the WiMAX system

along with the implementation of various antenna diversity techniques coupled with

Alamouti scheme in it to improve the capacity of the system with no change in required

bandwidth. This chapter contains the detailed analysis of various antenna diversity

techniques with Alamouti coding scheme followed by MATLAB based simulation of

quality based algorithms for the implementation of the same.

Today, hardly any hardware of some complexity is built without first performing

extensive computer simulations. Communication and radar systems involving antennas is

no exception. However, in almost all cases a communication (or radar) system is

simulated with very crude models of the hardware and underlying physics. In contrast,

the hardware (e.g. antennas) design is based on detailed electromagnetic simulation, but

not taking the system aspects into account. The purpose of this chapter is to describe

some steps in bridging the gaps between system and hardware level simulation, based on

MATLAB. The goal is to be able to directly see the effect of component design, or

architecture, on system level performance measures. The focus in this session is on a

wireless communication system with the implementation of antenna diversity techniques,

and the performance measures are usually given in the form of bit-error rate (BER) or

some other Quality-of-Service (QoS) measure.

This chapter is mainly divided into three units. In first part, the introduction to diversity

phenomenon and its various types has been discussed. The second part is specific to one

of the most promising diversity techniques i.e. antenna or space Diversity technique. At

the end, the practical realization i.e. software implementation of frequency diversity

technique and various antenna diversity techniques i.e. SIMO, MISO and MIMO along


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with its critical comparative analysis by taking several parameters into account has been

carried out so that final conclusion in terms of BER and system capacity can be derived.

3.2 Diversity Techniques

In wireless communication radio waves traveling along different paths arrive at the

receiver at different times with random phases and combine constructively or

destructively as shown in Figure-3.1.

Figure-3.1 Wave propagations mechanism

Figure-3.2 Multi-path components


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1 2

1 2

1 1 2 2

1 2

31 2 3

&j j

j j j

S a e S a e

R S S

a e a e a e

Some of the signal components travel directly from transmitter to receiver in LOS path

while the others will get obstructed by certain objects and then reach to the destination.

According to their direction of arrival they form the various angles at the receiver and

due to that the amount of received power is going to be altered. The phenomenon is

depicted in Figure-3.2 with vectorical combination.

When two or more multipath components are with the same access delay bin arrive at the

same time, the received signal is the vectorial addition of two multipath signals.

Let’s assume that two signals S1 and S2 are arrived at the same time at the receiver and R

is the combined signal at receiver.

The net result is a rapid fluctuation in the amplitude of the received signal in a short

period of time or distance travelled known as fading. However, the large scale average

path loss remains constant. Multipath propagation had previously been considered a

problem, but now it is exploited to achieve higher capacity which is the central idea

behind the development of diversity phenomenon.

Conventionally the design of wireless systems has been focused on increasing the

reliability of the air interface; in this context, fading and interference are viewed as

nuisances that are to be countered. Recent focus has shifted more towards increasing the

spectral efficiency; associated with this shift is a new point of view that fading can be

viewed as an opportunity to be exploited. The one of the objective of this work is to

provide a unified treatment of wireless communication from both these points of view.

While dealing with multipath environment, the individual signal path arriving at the

receiver faces independent or highly uncorrelated fading. This means that when a

particular signal path is in a fade there may be another signal path not in any fade. This

phenomenon of independent fading in various paths can be exploited as an advantage to


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achieve improved performance in wireless communication provided that out of multiple

paths, at least one path can be obtained with minimum distortion and maximum signal

strength. This phenomenon leads towards the concept of diversity which can dramatically

improve the performance over fading channels.

In practice, diversity techniques can be applied in the space, frequency or time domains.

Diversity over time can be obtained via coding and interleaving: information is coded and

the coded symbols are dispersed over time in different coherence periods so that different

parts of the code-words experience independent fades. Analogously, one can also exploit

diversity over frequency if the channel is frequency-selective. In a channel with multiple

transmit or receive antennas spaced sufficiently far enough, diversity can be obtained

over space as well. In a cellular network, macro-diversity can be exploited by the fact that

the signal from a mobile can be received at two base-stations. Since diversity is such an

important resource, a wireless system typically uses several types of diversity. The

following section 3.2.1 illustrates the various types of diversity techniques.

3.2.1 Time Diversity

Time diversity means transmitting identical messages in different time slots as shown in

Figure-3.3. This yields two uncorrelated signals at the receiving end. The same

information symbol is repeatedly transmitted at different time slots with the hope that

they will suffer independent fading and the receiver will combine them properly.

The most suitable example of time diversity is the basic GSM structure where time

division multiple access scheme is based on the same principle of time diversity. GSM is

a frequency division duplex system and uses two 25 MHz bands, one for the uplink

(mobiles to base station) and the other for the downlink (base station to mobiles). The

GSM bands are at 890-915 MHz (uplink) and at 935-960 MHz (downlink). The bands are

further divided into 200 kHz sub-channels and each sub-channel is shared by 8 users in a

time division fashion (time-division multiple access (TDMA)). The data of each user are

sent over time slots of length 577 microseconds (μs) and the time slots of the 8 users

together form a frame of length 4.615 ms. [9].


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Now for the voice processing through GSM, it is coded by a speech encoder into speech

frames each of length 20 ms. The bits in each speech frame are encoded by a 1/2 rate

convolutional coder. The number of coded bits for each speech frame is 456. To achieve

time diversity, these coded bits are interleaved across 8 consecutive time slots assigned to

that specific user: the 0th, 8th, . . ., 448th bits are put into the first time slot, the 1st, 9th, .

. ., 449th bits are put into the second time slot, etc. The process is explained graphically

in Figure-3.3.

Figure-3.3 Transmission of code word: An example of time diversity

While highly effective in fast fading environments, time diversity is not as effective in

slow fading channels unless a large decoding delay can be tolerated. A coding structure

known as interleaving is often used to realize time diversity where the receiver knows the

code before any transmission takes place.

For simplicity, let us consider a flat fading channel. We transmit a codeword

x = [x1. . . xL] t of length L symbols and the received signal is given by

yl = hlxl+ wl where l = 1,2,……,L (3.1)

Assuming ideal interleaving so that consecutive symbols x` are transmitted sufficiently

far apart in time, we can assume that the hl’s are independent. The parameter L is


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commonly called the number of diversity branches. The additive noises w0, . . . ,wL are

random variables.

In practical cases this interleaving process is used to reorder the sequence of coded bits so

that burst errors can be avoided to happen. Such kind of interleaving or more specifically

block interleaving is used as a system block in many modern wireless systems such as

WiMAX. In previous chapter of this thesis, this kind of interleaving has been integrated

with the WiMAX physical layer so as to avail the advantage of time diversity.

3.2.2 Frequency Diversity

To discuss about the concept of frequency diversity, consider first the one-shot

communication situation when one symbol x[0] is sent at time 0, and no symbols are

transmitted after that.

The receiver observes

Y[l] = hl[l]x[0] + w[l] l= 0,1,2,…. (3.2)

Let’s assume that the channel response has a finite number of taps L, then the delayed

replicas of the signal are providing L branches of diversity in detecting x[0], since the tap

gains hl[l] are assumed to be independent. This diversity is achieved by the ability of

resolving the multi-paths at the receiver due to the wideband nature of the channel, and is

thus known as frequency diversity.

A simple communication scheme can be built on the above idea by sending an

information symbol every L symbol times. The maximal diversity gain of L can be

achieved, but the problem with this scheme is that it is very wasteful of degrees of

freedom: only one symbol can be transmitted every delay spread. This scheme can

actually be thought of as analogous to the repetition codes used for both time and spatial

diversity, where one information symbol is repeated L times. In this setting, once one

tries to transmit symbols more frequently, Inter Symbol Interference occurs: the delayed

replicas of previous symbols interfere with the current symbol.

The problem is then how to deal with the ISI while at the same time exploiting the

inherent frequency diversity in the channel. Broadly speaking, there are three common

approaches:


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Single-carrier systems with equalization

By using linear and non-linear processing at the receiver, ISI can be mitigated to some

extent. Optimal ML detection of the transmitted symbols can be implemented using the

Viterbi algorithm. However, the complexity of the Viterbi algorithm grows exponentially

with the number of taps, and it is typically used only when the number of significant taps

is small. Alternatively, linear equalizers attempt to detect the current symbol while

linearly suppressing the interference from the other symbols, and they have lower

complexity.

Direct sequence spread spectrum

In this method, information symbols are modulated by a pseudo noise sequence and

transmitted over a bandwidth W much larger than the data rate. Because the symbol rate

is very low, ISI is small, simplifying the receiver structure significantly. Although this

leads to an inefficient utilization of the total degrees of freedom in the system from the

perspective of one user, this scheme allows multiple users to share the total degrees of

freedom, with users appearing as pseudo noise to each other.

Multi-carrier systems

Here, transmit pre-coding is performed to convert the ISI channel into a set of non-

interfering, orthogonal sub-carriers, each experiencing narrowband flat fading. Diversity

can be obtained by coding across the symbols in different sub-carriers. This method is

also called Discrete Multi-Tone (DMT) or Orthogonal Frequency Division Multiplexing

(OFDM) that has been explained in detail at the end of this chapter. Frequency-hop

spread spectrum can be viewed as a special case where one carrier is used at a time.

For example, GSM is a single-carrier system, IS-95 CDMA and IEEE 802.11b (a

wireless LAN standard) are based on direct sequence spread spectrum, and IEEE 802.11a

is a multi-carrier system. An important conceptual point is that, while frequency diversity

is something intrinsic in a wideband channel, the presence of ISI is not, as it depends on

the modulation technique used. For example, under OFDM, there is no ISI, but sub-

carriers that are separated apart by more than the coherence bandwidth fade more or less

independently and hence frequency diversity is still present.


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3.2.3 Antenna Diversity Techniques

To exploit time diversity, interleaving and coding over several coherence time periods is

necessary. When there is a strict delay constraint and/or the coherence time is large, this

may not be possible. In this case other forms of diversity i.e. Antenna diversity or Space

diversity have to be obtained. Figure-3.4(a), (b) and (c) show various types of antenna

diversity techniques.

Two kinds of space diversity can be obtained to improve the capacity of the system. Tx-

Diversity in which multiple transmit antennae are used for the signal transmission which

in term results in Multiple Input Single Output diversity (MISO) (n x 1 system). While

Rx-Diversity in which multiple receive antennae are used for the signal reception which

in term results in Single Input Multiple Output (SIMO) (1 x n system). Channels with

Multiple Transmit and Multiple Receive antennas so called Multi Input Multi Output

(MIMO) (n x n) channels provide even more potential.

Figure-3.4 (a) SISO (b) MISO (c) MIMO diversity techniques

Antenna diversity, or spatial diversity, can be obtained by placing multiple antennas at

the transmitter and/or the receiver. If the antennas are placed sufficiently far apart, the

channel gains between different antenna pairs fade more or less independently, and

independent signal paths are created. The required antenna separation depends on the

local scattering environment as well as on the carrier frequency. For a mobile which is

near the ground with many scatterers around, the channel de-correlates over shorter

spatial distances, and typical antenna separation of half to one carrier wavelength is

sufficient. For base stations on high towers, larger antenna separation of several to 10’s of

wavelengths may be required.


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The forthcoming section elaborates the various antenna diversity techniques from the

detail analysis point of view so that it would be much easier to implement the same for

real time scenario.

3.3 Performance Analysis of Antenna Diversity Techniques

The idea behind antenna diversity is that if the antennas are spaced sufficiently far apart,

they fade independently. By always selecting the antenna with the best channel, or

(better) combining the two with appropriate weights, the probability of a poor reception

(signal outage) is dramatically reduced. Diversity increases the average signal level,

which in turn improves capacity. Though the capacity increase is significantly less with

diversity than if spatial multiplexing was used, it is in general more robust and can be

used at lower signal-to noise ratios. A particularly clever approach for achieving spatial

diversity at the transmitter, without requiring knowledge of the channel at the transmitter,

is called space time coding i.e. Alamouti coding. Before approaching towards the

different antenna diversity techniques, it’s quite important to understand the traditional

antenna system (SISO system) along with its limitations.

3.3.1 Single Input Single Output System

Figure-3.5 shows the traditional antenna system with single transmitter and single

receiver antenna known as SISO system. The main fundamental behind advance antenna

system implementation is the diversity. In the initial stages, the various modulation

schemes like coherent BPSK, coherent QPSK, coherent 4-PAM, coherent 16-QAM were

there in which error probability decay very slowly proportional to 1/SNR. Basically the

above mention modulation techniques did not use diversity principle that is the single

antenna system were used at transmitter and receiver in both the side anticipating lower

poor spectral efficiency and lesser capacity. However in such a scenario, diversity can be

obtained by implementing the OFDM technique i.e. frequency diversity during the

transmission of symbols. It can be seen that root cause of the poor performance of these

techniques is that reliable communication depends on the strength of the single signal

path only.


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Figure-3.5 Single Input Single Output antenna system

Practically it is observed that bit error rate performance of such a system depends only on

channel SNRs. In this case, there is a significance probability that these path will be in a

deep fade under certain circumstances. However the performance of such a system can be

improved by introducing number of antennas in transmitting side and/or number of

antennas in receiving side.

According to Shannon capacity of wireless channels, given a single channel corrupted by

an additive white Gaussian noise at a level of SNR, the capacity is:

CSHANNON = B.log2 [1 + SNR] (BPS/HZ) (3.3)

Where: C is the Shannon limits on channel capacity, SNR is signal-to-noise ratio, B is

bandwidth of channel. From the above expression it is clear that theoretically capacity

increases as the bandwidth or SNR is increased which is not a feasible case beyond

certain limits. The solution for this is the implementation of diversity mechanism on

transmitter and receiver side. The following sections illustrate the same mechanism [9].

3.3.2 Single Input Multiple Output System

The first step towards the implementation of diversity is to use a single input multiple

output configurations, e.g., one transmit and two receive antennas. This configuration is

called single input multiple output (SIMO) that is shown in Figure-3.6. For example, a

base station with one transmit and two receive antennas would be SIMO (1 X N system).

Figure-3.6 Single Input Multiple Output Antenna System


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In a flat fading channel with 1 transmit antenna and 2 (N) receive antennas; the channel

model is as follows:

yl[m] = hl[m]x[m] + wl[m] Where l = 1, . . . , N (3.4)

where the noise wl[m] is independent across the antennas. We would like to detect x[1]

based on y1[1], . . . , yN[1]. If the antennas are spaced sufficiently far apart, then we can

assume that the gains hl[1] are independent Rayleigh, and we get a diversity gain of N.

For SIMO system, with N=2 receiving antennas for our case, the channel capacity can be

given by,

CSIMO = B.log2 [1 + N.SNR] (BPS/HZ) (3.5)

Where, the value of SNR will be increased by factor L i.e.

SNR= N x SNR

Here if the capacity of SIMO system is compared with that of the SISO system, it can be

clearly understood that now the capacity is not just dependent on channel SNR but also

upon no. of receiving antennas which is what the main advantage of having diversity into

the system.

3.3.3 Multiple Input Single Output Antenna System

One more step for utilizing diversity principle is to use a multiple input single output

configurations, e.g., two transmit antennas and one receive antenna. This configuration is

called multiple inputs single output (MISO) which is shown in Figure-3.7. For example, a

base station with two transmit and one receive antennas would be MISO (M X 1 system).

Figure-3.7 Multiple Input Single Output Antenna System

Now consider the cases when there is M transmit antennas and 1 receive antenna. This is

common in the downlink of a cellular system since it is often cheaper to have multiple

antennas at the base station than to having multiple antennas at every handset. It is easy


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to get a diversity gain of M: simply transmit the same symbol over the M different

antennas during M symbol times. Generally, any time block length M can be used on this

transmit diversity system which simply use one antenna at a time and transmit the coded

symbols of the time diversity code successively over the different antennas. This provides

a coding gain over the repetition code.

The channel capacity of the MISO system is given by:

CMISO = B.log2 [1 + M.SNR] (BPS/HZ) (3.6)

Where, again SNR increases by the factor M which is now no. of transmitting antennas of

the system. Compare to SISO system, the capacity of SIMO and MISO system shows

improvement. The increase in capacity is due to the spatial diversity which reduces

fading and SNR improvement. However, the SNR improvement is limited, since the SNR

is increasing inside the log function.

Moreover to increase the capacity further i.e. to increase no. of antennas within the same

physical dimension, the transmit diversity scheme can be imposed for channel coding.

Space Time Code is one of the most elegant solutions proposed by Alamouti so known as

Alamouti scheme. This is the transmit diversity scheme proposed in several third

generation cellular standards. Alamouti scheme is designed for 2 transmit antennas and

generalization to more than two antennas is possible, to some extent. The following

section explains the detail of the Alamouti coding scheme with MISO diversity.

3.3.4 Mathematical Modeling of MISO System using Alamouti Coding Scheme

Space-time coding (STC) is an efficient approach to exploit the enormous diversity

offered by the Multiple Input Single Output and Multiple Input Multiple Output. It is

used to obtain gains due to spatial diversity via multiple transmit and receive antennas.

Moreover, a diversity gain proportional to the number of antennas at both transmit and

receive sides can be achieved. One popular representation of these codes is the Alamouti

scheme for two transmits antennas. STC techniques are used to improve the performance

of MISO systems. Their central issue is the exploitation of multipath effects in order to

achieve very high spectral efficiencies. With this purpose, the principal aim of the space-

time coding lies in the design of two-dimensional signal matrices to be transmitted during

a specified time period on a number of antennas. Thus, it introduces redundancy in space


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through the addition of multiple antennas, and redundancy in time through channel

coding, enabling us to exploit diversity in the spatial dimension, as well as a obtaining a

coding gain. Therefore, the transmit diversity plays an integral role in the STC design.

Alamouti introduced a very simple scheme of space-time block coding (STBC) allowing

transmissions from two antennas with the same data rate as on a single antenna [19].

Figure-3.8 Mathematical model of MISO

As shown in Figure-3.8, the Alamouti algorithm uses the space and the time domain to

encode data, increasing the performance of the system by coding the signals over the

different transmitter branches. Thus, the Alamouti code achieves diversity two with full

data rate as it transmits two symbols in two time intervals.

In the first time slot, transmit antennas Tx1 and Tx2 are sending symbols s0 and s1,

respectively. In the next time slot, symbols −s1* and s0* are sent, where (·)* denotes

complex conjugation. Each symbol is multiplied by a factor of a squared root of two in

order to achieve a transmitted average power of one in each time step. Furthermore, it is

supposed that the channel, which has transmission coefficients h1 and h2, remains

constant and frequency flat over the two consecutive time steps.

The received vector, r, is formed by stacking two consecutive received data samples in

time, resulting in

(3.7)

where r = [r0, r1]T represents the received vector, h = [h1, h2]T is the complex channel

vector, n = [n0, n1]T is the noise at the receiver, and S defines the STC:

(3.8)


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(3.9)

The vector equation in equation 3.7 can be read explicitly as

(3.10)

(3.11)

At the receiver, the vector y of the received signal is formed according to y = [r0, r_1]T,

which is equivalent to

(3.12)

(3.13)

These both equations can be rewritten in a matrix system as specified in equation (3.14)

(3.14)

The hermitian of the virtual channel matrix is

=

Finally, the estimated transmit signal is given by

y and therefore

=


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=

=

=

= (3.15)

= h2 I2s+ (3.16)

Once the corresponding operations for estimating the transmitted signal have been

performed, the result is represented in Equation 3.16, where:

- h2 = | h1 |2 + | h2 |2 is the power gain of the channel,

- I2 is the 2 x 2 identity matrix,

- s = [s0, s1]T represents the transmitted symbols, and

is some modified noise.

3.3.5 Multiple Input Multiple Output Antenna System

MIMO involves the transmission of two streams using two or more than two spatially

separated antennas. The streams are received at the receiver by using spatially separated

antennas. The streams are then separated by using the space time processing, which

forms the core of the MIMO technology. A base station using two transmit antennas and

two receive antennas is referred to as MIMO (n X n). Figure-3.9 shows the schematic of

MIMO system.

Figure-3.9 Multiple Input Multiple Output Antenna System


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In addition to provide diversity, MIMO channels also provide additional degree of

freedom for communication. The main advantages of MIMO channels over SISO

channels are the array gain, the diversity gain, and the multiplexing gain. Array gain and

diversity gain are not exclusive of MIMO channels and also exist in SIMO and MISO

channels [20]. Multiplexing gain, however, is a unique characteristic of MIMO channels.

Array gain is the improvement in SNR obtained by coherently combining the signals on

multiple transmits or multiple receive dimensions and is easily characterized as a shift of

the BER curve due to the gain in SNR. Diversity gain is the improvement in link

reliability obtained by receiving replicas of the information signal through independently

fading links, branches, or dimensions. It is characterized by a steeper slope of the BER

curve in the low BER region. As discussed in MISO, the improvement of BER can be

achieved using 2 X 1 Alamouti coding scheme, Multiple Input Multiple Output system

also exploits the averaging at receiver (Like 1 X 2 SIMO) and hence the dramatically

improvement of BER performance can be achieved. Basically two kinds of MIMO

Diversity schemes have been identified that are discussed below.

MIMO Matrix A

One technique to use 2 X 2 MIMO is to send identical data streams on both the transmit

antennas and use space time coding techniques (STC) to take advantage of the space and

time diversity achieved. Using STC with 2 X 2 MIMO improves the effective SNR seen

by the receiver and thus permits the use of the highest modulation coding with relatively

low FEC.

Figure-3.10 Matrix A MIMO


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This effectively increases the data transmission rate close to the theoretical maximum

rates of the system. This mode of operation where the two transmit antennas carry two

identical data streams using space time coding is called MIMO Matrix A which has been

depicted by Figure-3.10.

MIMO Matrix B

In a high SINR environment, i.e., when the transmission conditions are good or when the

transmission involves LOS links, the two transmit antennas can carry independent data

streams by using a technique called spatial multiplexing (SM). This provides multi-path

diversity for each of the two streams and the peak data rate handled over the physical

layer can go up to nearly double of a single stream in ideal transmission conditions. The

transmission rate is significantly higher than a single transmitting antenna even in

characteristic field conditions (typically 50 percent higher). This technique of using

MIMO (i.e., by using spatial multiplexing) is called MIMO Matrix B that can be viewed

from Figure-3.11.

Figure-3.11 Matrix B MIMO

In this research work, MIMO Matrix A model is being implemented for the critical

performance analysis of transmitter and receiver diversity technique and for the

implementation of antenna diversity technique in WiMAX system.


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3.3.6 Mathematical Model of MIMO System using Alamouti Coding Scheme

According to the theoretical aspect of MIMO discussed in the above section, the

mathematical model of MIMO system has been developed and can be visualized from the

inspection of Figure-3.12.

Figure-3.12 Mathematical model of MIMO

The received signal from a 2 x 2 Alamouti scheme, as depicted from Figure-3.12, is

y = (3.17)

The estimated transmitted signal can be calculated from Y , where

y = [ r0(1) r0(2) (1) (2)]T (3.18)

The virtual channel matrix, Hv, is expressed as

Hv =

Therefore, the hermitian of the virtual channel matrix is

= (3.19)


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The estimation of the transmitted symbols is performed as follows:

= (|h11|2 + |h21|

2 + |h12|2 + |h22|

2 )

(|| h1 || +||h2|| )I2 + = h2 I2s + (3.20)

Equation 3.20 expresses the obtained result for the process of estimating the transmitted

symbols.

- I2 is the 2 x 2 identity matrix,

- s is the transmitted signal,

- h2 = || h1 || +||h2|| = |h21|2+|h22|

2is the power gain of the channel, and

- =

represents some modified noise.

In order to take the channel correlation into account, which has a strong impact on the

achievable performance of the system; different spatial channel models are considered.

With reference to equation (3.5) and (3.6) for SIMO and MISO respectively, the channel

capacity of MIMO system is given by:

CMIMO = B.log2 [1 + M.N.SNR] (BPS/HZ) (3.21)

where signal to noise ratio is given by,

SNR = M x N x SNR


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As per the above equations and considering M no. of transmitting antennas and N no. of

receiving antennas, it can be said that the channel capacity of MIMO system is the

highest among all diversity techniques.

The following sections describe the various types of MIMO channel models according to

the different conditions and characteristics of the channel.

Narrowband Vs. Wideband

A radio channel is called a narrowband channel if the channel coherent bandwidth is

larger than the base band signal. It is also called a flat channel, because each transmitted

frequency component undergoes the same fading. The frequency structure does not

change. When the channel coherent bandwidth is less than the base band signals, the

radio channel is called wideband channel. It is sometimes called frequency selective

fading channel, because each transmitted frequency component undergoes different

fading. The channel medium is very dispersive in a frequency selective fading channel.

The received signal contains a delayed, distorted, and attenuated version of the

transmitted signal, and this produces inter symbol interference (ISI), which usually

degrades communication performance. Similarly, the MIMO channel models can be

divided into wideband models and narrowband models by considering the bandwidth of

the system. The wideband models treat the propagation channel as frequency selective,

which means that different frequency sub bands have different channel response. In

contrast, the narrowband models assume that the channel is flat-fading and therefore the

channel has the same response over the entire system bandwidth.

Physical Vs. Non-Physical Models

The MIMO channel models can also be divided into physical and non-physical models.

The physical models generally choose some crucial physical parameters to describe the

MIMO propagation channels. The typical parameters include angle of arrival, angle of

departure, and time of arrival. However, under many propagation conditions, the MIMO

channels are not well described by a small set of physical parameters, and this limitation

makes difficult to identify and validate the models. another category is non-physical

models, which are based on the channel statistical charecteristics. In general, the non-


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physical models are easy to simulate under which they were identified. These models,

however, give limited insight into the propagation charactrestics of the MIMO channels,

such as, the bandwidth, configuration, and aperture of the arrays, and the heights of the

transmit and receive antennas in the mesurments.

Measurement Based Vs. Scattering Models

To model a MIMO channel, one approach is to measure the real MIMO Channel

responses through field measurements. Some important characteristics of the MIMO

channel can be extracted from recorded data, and the MIMO channel can be modeled to

have similar statistical characteristics. An alternative approach is to postulate a model

(usually involving distributed scatters) that attempts to capture the channel

characteristics. Such a model can often illustrate the essential characteristics of the

MIMO channel as long as the constructed scattering environment is acceptable.

3.3.7 Advantages and Disadvantages of MIMO

Advantage of MIMO

In wireless communications, the objectives are to increase throughput and transmission

quality. MIMO systems can take advantage of the shortcoming of a wireless channel the

multi-path and turn it into an advantage. In MIMO systems, random fading and multi-

path delay spread can be used to increase throughput. MIMO systems offer an

improvement in error rate without the need to increase bandwidth and/or power.

Apart from improving throughput, MIMO systems can also improve transsmission

quality. Diversity is a technology used in MIMO for this purpose. multiple antennas can

be used to minimize the effect of fading caused by multi-path propagation. When the

antennas at the receive side are adequately spaced, then several copies of the transmitted

signal are received through different channels and with differnet fading [21]. The

probability, that all received copies of the transmitted signal fading,is in deep fading ,can

be regarded as small, thus deduce that diversity should improve of the wireless link.


107

Disadvantage and limitations of MIMO

One obvious disadvantage of MIMO is that they contain more antennas:MIMO increases

complexity, volume, and hardware costs of the system compared to SISO. MIMO

systems are not always beneficial knowing that channel conditions depend on the radio

environment. When there is Line of Sight (LOS), a higher LOS strenth at receive will

result in better performance and capacity in SISO system, while in MIMO systems

capacity is reduced with higher LOS strength. This is beacuse strong contributions from

LOS lead to higher correlation among antennas, which reduce the advantage of using a

MIMO system.

By considering the all above facts, the following section of the chapter describes the real

time implementation of Antenna Diversity algorithms in form of MATLAB R2009a

simulations so as to realize the system performance in the presence of diversities by

analyzing relationships between BERs and SNRs.

3.4 Software Implementation of Antenna Diversity Techniques and

Alamouti Coding Scheme

This section deals with the practical realization of different antenna diversity techniques

and traditional antenna system by implementing the logic in MATLAB. Throughout the

section, total four algorithms have been presented and evaluated in terms of graphs of

BER v/s SNR by passing stream of user defined data. Figure-3.13 illustrates the

generalized design flow of developing the communication system along with the effect of

different diversity techniques inside the wireless channel. The details of the signal

processing depend on the communication protocol, but it contains in general

synchronization, channel estimation, detection (estimation of the bits), channel decoding

and source decoding. Also these operations are omitted herein, and the focus is on

simulation of the RF parts of the antenna system.


108

Define number ofTx and Rx antennaand parameters

Generate randomenvironment or

user defined realtime scenario

Define the channel matrix ofefficient wireless channel

Specify Input data stream

Get the output datastream and conclude interms of BER v/s SNR

Figure-3.13 Generalized flowchart of diversity mechanism

By considering the above facts, the practical realization of such system with traditional

single transmitter – receiver antennas as well as with diversity techniques have been done

on the platform of MATLAB where the simulations were performed to generate various

curves of BER v/s SNR. The consequent sub sections elaborate the algorithms and

respective simulation results of all the diversity techniques.

3.4.1 Software Implementation of Single Input Single Output Antenna System

Figure-3.14 presents the designing algorithm for traditional antenna system i.e. SISO

system. To develop this, several parameters of the antenna as well as of the data stream

have to be set such as no. of transmitting and receiving antenna elements, modulation

order, signal to noise ratio, etc.


109

Figure-3.14 Designing of algorithm for SISO antenna system

Set the values of Transmitting = 1 and Receiving Antennas = 1

Set the values of required SNR Range

Create randomly generated bit pattern of transmitted data according tono. of Transmitting Antenna

Generate single noise matrix from the value of SNR

Generate single Rayleigh channel matrix

Define order of PSK modulation scheme

Get the received symbols

Add noise in the channel matrix

Find the angles of received symbols

Convert angle into normalized degree

Obtain Rx data by putting appropriate threshold detection

Calculate BER from the received data


110

For the realization purpose of antenna diversity techniques, the M-ary PSK modulation

techniques have been considered in all algorithms. After that with the application of

MATLAB commands, signal matrix, noise matrix and the channel matrix have been

created. Initially the Rayleigh channel has been selected as the communication channel

for this code and in next section, the comparison of Bit Error Rate performance can be

made with Additive White Gaussian Noise channel. Finally the BER for the data has

been calculated for multiple values of SNRs, which is used to plot the graph of BER v/s

SNR. For the sake of simplification and understanding, initially the simulation has been

performed by taking small no. of user define data and then whole analogy has been

implemented for the longer stream of data with which real time analysis can be obtained.

3.4.2 Simulation Results and Discussion (TX antenna = 1 and Rx antenna = 1)

To initiate the MATLAB simulation according to the algorithm discussed above, as an

input, 10 user defined data symbols have been considered so as to check the effect of

errors generated at the output due to wireless channel can be very well understood on bit

by bit basis. As a sample data 10 symbols or 20 bits (2 bits per symbol) are transmitted

through the traditional single input single output antenna system with the single channel

and single noise matrix whose numerical value is indicated in the Table 3.1. With no

diversity conditions, the same no. of symbols/bits are going to be received but with

errors. Here to create comparison platform, the channel SNR is selected to be equal to

0.75dB fix.

During transmission, the channel generates noise in the input symbols/bits which has

been shown by red colored font. Under no diversity scenario, out of 10 symbols, 6

symbols get altered i.e. 6 symbols are getting corrupted due to the multipath property of

wireless channel. For example, here first five symbols and 8th symbol are getting

corrupted and it leads to Symbol Error Rate (SER) of 0.6.

Again in terms of bits, if the same analysis is to be undertaken then from the sample table

of simulation, it can be verified that out of 20 transmitted bits, total 11 bits are getting

hampered that are denoted by red color font in the table. The corresponding Bit Error

Rate (BER) can be calculated as 0.55dB.


111

Table 3.1 Simulation results of SISO system with user define sample data

Here it can be observed that the achieved BER is lesser than SER because if single

symbol is represented by two bits then in BER calculation, it might be the case where out

of 2, just one bit gets lost. So this can be represented as single bit loss in BER calculation

but with respect to symbol, it has to be considered as the whole symbol is getting lost. So

SER would always be greater than BER.

Now the analogy of the simulation of SISO system with 10 symbol sample data has been

thoroughly applied to the real time environment for evaluating the performance of SISO

Tx Data

Symbols

2 1 1 1 0 0 2 1 3 2 Total

Symbols

10

Rx Data

Symbols

1 2 3 2 3 0 2 2 3 2 Error

Symbols

6

Channel

Matrix

(H)

-0.151110462752079 + 0.0598519466936464i

Addition

of Signal

Matrix

and

Noise

Matrix

Tx Data

Bits

1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 Total

Bits 20

Rx Data

Bits

0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 Error

Bits

11

SNR 0.75dB Fix

SER 0.600000000000000 (6/10)

BER 0.550000000000000 (11/20)


112

BER Performance of Single Input Single OutputAntenna System

0

0.02

0.04

0.06

0.08

0.1

0.12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

SNR in dB

BER

with the transmission of 10,000 bits. By simulating the above discussed algorithm for

10,000 bits over MATLAB, the graph of BER v/s SNR shown in Figure-3.15 has been

obtained through which the performance of SISO system can be justified.

Figure-3.15 BER vs. SNR for SISO antenna system

As can be seen from Figure-3.15, in case of no diversity, i.e. using single transmitting and

single receiving antenna, initially the BER can be obtained around 0.1 at lower SNR=1dB

and at higher value of SNR, i.e. at SNR=21dB, the achievable BER decreases around

0.02. The values of BER are high as there is no implementation of multiple numbers of

antennas in either transmitter or receiver side and the effect of fading is severe because of

no diversity. In fact throughput of the system totally depends on the channel SNR.

The forthcoming section describes the overall algorithm for the development of SIMO

system under various operating conditions such as multiple modulation techniques, range

of SNR, type of wireless channels, etc. The preliminary assumption for the realization of

SIMO system is single transmitting antenna and two receiving antennas. As a conclusion

the simulation results in terms of graph of BER v/s SNR shows the improvement in

system performance as system capacity.


113

3.4.3 Software Implementation of Single Input Multiple Output Antenna Diversity

Technique

Figure-3.16 Designing of algorithm for SIMO antenna system


Set the values of required SNR range

Create randomly generated bit pattern of transmitted data according tothe one Transmitting antenna

Generate double noise matrix from the value of SNR

Generate single Rayleigh channel matrix









114

Figure-3.16 depicts the basic algorithm of SIMO system based on the developed

MATLAB code.

As the system comprising of single transmitting antenna and multiple i.e. two in our case

receiving antennas, the algorithm initiates with the determination of no. transmitting and

receiving antennas. In the next phase through the MATLAB command the stream of

random data bits would be generated on which the process is to be carried out.

Then to carry out the logic, modulation order and range of signal to noise ratio would be

set to get the respective values of bit error rate. After that with the application of

MATLAB commands, two noise matrices and single Rayleigh channel matrix have been

created as two receiving antennas and single transmitting antenna is there. At the receiver

side, as per the modulation order at the transmitter, symbols of the information can be

received which would be converted to bits through the proper threshold detection

phenomenon. This is how the pure logical transmitter, receiver and channel can be

realized and the analogy of single transmission and multiple receptions can be

implemented.

Finally the BER for the data has been calculated for multiple values of SNRs, which is

used to plot the graph of BER v/s SNR. The graph of BER v/s SNR shows the system

throughput at various transmission conditions which would be the part of the next

forthcoming section.

3.4.4 Simulation Results of SIMO system (TX antenna = 1 and Rx antenna = 2)

Here in case of SIMO, input side single transmitting antenna and output side two

receiving antennas are to be utilized. As per the algorithm shown in previous section, the

MATLAB code has been prepared and for sake of simplicity, initially for 10 sample

symbols the process has been carried out same as the previous case. That data is shown in

the Table 3.2.

Now by transmitting 10 users defined symbols under receive diversity environment, 6

symbols are turning erroneous leading to SER of 0.6dB. Here to realize the SIMO

condition, two noise matrices corresponding to two receiving antennas and one channel

matrix corresponding to one transmitting antenna have been chosen with their transfer

function as indicated in the table. If bit by bit analysis is applied then it can be observed


115

that after transmitting 20 bits, 9 bits (designated by red color font) are getting corrupted

leads to the BER of 0.45 at channel SNR of 0.75dB.

Table 3.2 Simulation results of SIMO system with user define sample data

Now by integrating this process from 20 bits to 10,000 bits for real time realization, the

range of BER would be obtained for the range of SNR. The output of such kind of

simulation has been given in terms of graphs of BER v/s SNR in Figure-3.17.

Tx Data

Symbols

2 1 1 1 0 0 2 1 3 2 Total

Symbols

10

Rx Data

Symbols

1 2 1 1 1 3 0 1 3 0 Error

Symbols

6

Channel

Matrix

(H)

0.379772440973511 + 0.851240453939351i

0.578727415914267 - 0.0541236602159802i

Addition

of Two

Noise

Matrices

and One

Channel

Matrix

Tx Data

Bits

1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 Total

Bits 20

Rx Data

Bits

0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 Error

Bits

9

SNR 0.75dB Fix

SER 0.600000000000000 (6/10)

BER 0.450000000000000 (9/20)


116

BER Performance of Single Input Multiple OutputAntenna Diversity Technique

0

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21SNR in dB

BER

Figure-3.17 BER vs. SNR for SIMO antenna system

It can be observed from the BER v/s SNR graph of Figure-3.17 as well as from the

calculation of the sample table that in case of receive diversity, i.e. using single

transmitting and two receiving antennas, the value of BER is improving at the same

channel SNR.

Initially at the lower end of SNR, the BER can be obtained around 0.06 and at higher

value of SNR, the achievable BER decreases around 0.005 for 21dB SNR. Also for 10

sample data, with SIMO the BER is 0.45 rather than 0.55 with SISO.

In this way, by using SIMO, the received signal quality gets enhanced by averaging over

multiple independent signals.

3.4.5 Software implementation of Multiple Input Single Output antenna diversity

technique

Here also in this case, the same sequence of defining no. of antennas along with

generation of random data streams with the modulation order specification would be

repeated again by taking multiple transmitter and single receiver antenna. The exact

algorithm for implementing the MATLAB code of MISO system is shown in Figure-

3.18. Now for the purpose of performance evaluation, the fixed range of signal to noise

ratio will be defined for which the data stream would be transmitted with the specific

channel scenario and at the receiver side the bit error rate will be calculated.


117

Figure-3.18 Designing of algorithm for MISO antenna system



Create Randomly generated bit pattern of transmitted data according tothe two Transmitting antennas

Generate two complex conjugate noise matrixes

Generate two Rayleigh Channel Matrixes by taking complex conjugatefor Alamouti coding scheme






Obtain Rx data by putting appropriate channel estimation detection



118

Then after the system is MISO i.e. it comprises of multiple input antennas; two for our

case and single output antenna, and Alamouti coding scheme can be explored with this

system as well, so the generation and realization of noise matrices and channel matrices

is crucial aspect. As a matter of fact, the Alamouti coding scheme is applicable where

transmitter diversity is deployed, so here with MISO system to realize logically the

Alamouti scheme, the complex conjugate of the data has to be taken and would be

transmitted with two different antennas. This task can be implemented with the

application of MATLAB commands for generating signal matrix, two complex conjugate

noise matrixes and two Rayleigh channel noise matrixes.

3.4.6 Simulation Results of MISO system (TX antenna = 2 and Rx antenna = 1)

Here also the simulation would be initiated by taking 10 symbols per transmitting

antennas as a sample data as shown in Table 3.3. As two transmitting antennas have been

utilized in the system, total 20 sample data symbols have been considered over which the

whole process of modulation, coding, transmission, decoding and demodulation have

been performed. The table shows the input and output of the simulation process for the

sample data.

As 20 symbols from both the antennas (10 symbols each) are transmitted through the

MISO condition i.e. through two channel and two noise matrices whose mathematical

equation is shown in form of transfer function, the same no. of output symbols would be

received with the effect of errors. At the fix value of SNR=075dB, 9 symbols (indicated

by red color) are getting corrupted out of 20 symbols leading to SER of 045dB while 12

bits (indicated by red color) are corrupted out of 40 bits leading to BER of 0.3. If these

two values are getting compared with the SISO system, then drastic improvement in

BER/SER can be observed because of the phenomenon of Alamouti coding of MISO

diversity. The same thing can be observed from the graph of BER v/s SNR, if this

simulation is integrated over 10,000 bits for real time scenario.


119

Table 3.3 Simulation results of MISO system with user define sample data

As can be seen from the Figure-3.19, in case of transmit diversity, i.e. using multiple

transmitting and one receiving antennas, initially the BER can be obtained around 0.048

at lower value of SNR, the achievable BER decreases around 0.001 for 21dB SNR. Here

the Alamouti scheme decouples the MISO channel into two virtually independent

channels with channel gain h2 and diversity gain d = 2. As two independent channels are

Tx Data

Symbols

2 1 1 1 0 0 2 1 3 2 Total

Symbols

202 1 1 1 0 0 2 1 3 2

Rx Data

Symbols

0 1 1 1 0 0 1 0 1 0 Error

Symbols

9

1 1 1 1 0 0 0 1 0 0

Channel

Matrix+

(H)

-1.04429266452263 - 0.0993077287635684i (-S1*)

-0.696253522655436 + 0.290063644892930i (S0)

-0.696253522655436 - 0.290063644892930i (S0*)

1.04429266452263 - 0.0993077287635684i (S1)

Alamouti

Coding

Technique

Tx Data

Bits

1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 Total Bits

401 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0

Rx Data

Bits

0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 Error Bits

120 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0

SNR 0.75dB Fix

SER 0.450000000000000 (9/20)

BER 0.300000000000000 (12/40)


120

BER performance of Multiple Input Single OutputAntenna Diversity Technique

0

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

SNR in dB

BER

defined, signal fades independently; making sure that reliable communication is possible

as long as one of the paths is strong and received signal quality gets enhanced.

Figure-3.19 BER vs. SNR for MISO antenna system

3.4.7 Software Implementation of Multiple Input Multiple Output Antenna diversity

technique

To develop this, same tradition will be followed i.e. several parameters of the antenna as

well as of the data stream have to be set such as two transmitting and two receiving

antennas elements, modulation order, range of signal to noise ratio, etc as shown in

Figure-3.20. After that as per the system specification, the logical realization of

transmission, reception and channel propagation would be performed with the application

of MATLAB commands. In this case also, as the transmission diversity is prevailing,

Alamouti coding will have to be realized. So signal matrix, four complex conjugate noise

matrixes for Alamouti coding scheme to represent four different combinations of

propagation paths from transmitter to receiver and two Rayleigh channel noise matrixes

have been created by taking complex conjugate for Alamouti coding scheme.


121

Figure-3.20 Designing of algorithm for MIMO antenna system



Create Randomly generated bit pattern of transmitted data according tothe two Transmitting antennas

Generate four complex conjugate noise matrixes

Generate two Rayleigh channel matrixes by taking complex conjugate forAlamouti coding scheme






Obtain Rx data by putting M.L. detection



122

This is how the better path from the multiple no. of paths can be chosen at the transmitter

side as well as the averaging can be performed at the receiver side so as to get the exact

analogy of actual physical MIMO system.

Finally the evaluation of errors due to propagation through the communication channel

will be calculated for the different values of signal to noise ratios and the performance of

the channel as well as transmitter-receiver system will be evaluated by plotting the graph

of BER v/s SNR.

3.4.8 Simulation Results of MIMO system (TX antenna = 2 and Rx antenna = 2)

Finally to achieve advantages of SIMO and MISO both, the MIMO system can be

developed where system capacity along with BER will be improved by utilizing transmit

as well as receive diversity. The proof has been given in two ways: first by performing

simulation over just samples of 20 user defined symbols or 40 bits and second applying

the same phenomenon to stream of 10,000 bits for taking real time transmission analogy.

As indicated in the Table 3.4, by transmitting 20 symbols (40 bits) by two antennas

through 4 noise matrices and 2 channel matrices, only 8 symbols (8 bits) are getting

corrupted which is the lowest no. in all four systems. The erroneous bits/symbols are

indicated by red color. Finally the lowest error rate i.e. SER=0.4dB and BER=0.2 can be

encountered among all that leads to the highest system performance.

The same mechanism of simulation is now applied to the stream of 10,000 bits for giving

it real time touch by taking 0dB to 21dB SNR range. The respective BERs have been

calculated to evaluate the system performance. With respect to the relationship between

BER and SNR of the table, graph has been plotted to justify the performance of MIMO

system that has been visualized by Figure-3.21.


123

Table 3.4 Simulation results of MIMO system with user define sample data

Tx Data

Symbols

2 1 1 1 0 0 2 1 3 2 Total

Symbols 20

2 1 1 1 0 0 2 1 3 2

Rx Data

Symbols

0 1 1 1 0 0 0 1 1 0 Error

Symbols

8

0 1 1 1 0 0 0 1 1 0

Channel

Matrix

(H)

1.09980602264884 - 0.852422471464323i (-S1*)

0.579729420304971 - 0.615471441657012i (S0)

0.579729420304971 + 0.615471441657012i (S0*)

-1.09980602264884 - 0.852422471464323i (S1)

0.0984368049147121 - 0.127313051276969i (-S1*)

0.637261486427597 - 0.481568123719595i (S0)

0.637261486427597 + 0.481568123719595i (S0*)

0.0984368049147121 - 0.127313051276969i (S1)

Alamouti

Coding

Technique

Tx Data

Bits

1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 Total Bits

401 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0

Rx Data

Bits

0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 Error Bits

80 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0

SNR 0.75dB Fix

SER 0.400000000000000 (8/20)

BER 0.200000000000000 (8/40)


124

BER Performance of Multiple Input MultipleOutput Antenna Diversity Technique

0

0.01

0.02

0.03

0.04

0.05

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21SNR in dB

BER

Figure-3.21 BER vs. SNR for MIMO antenna system

As can be seen from the above graph, in case of transmit and receive diversities, i.e. using

multiple transmitting and multiple receiving antennas, initially the BER can be obtained

around 0.04 which is lowest among all diversity techniques and at higher value of SNR,

the achievable BER decreases almost around 0.00001≈0 for 21dB SNR. With the

implementation of transmit diversity, signal fads independently making sure that reliable

communication is possible as long as one of the paths is strong, and with the

implementation of receive diversity, received signal quality gets enhanced by averaging

over multiple independent signals. In this way, MIMO technique exploits the advantages

of MISO and SIMO diversity techniques. This can be again clearly justified by the next

section of comparative analysis of antenna diversity techniques.

3.4.9 Comparative Analyses of Antenna Diversity Techniques

Figure-3.22 illustrates the comparative analysis of all diversity techniques. The main

objective of this research leads to just one task that is to implement the most efficient

antenna diversity technique in WiMAX system so as to achieve the lowest error

probability along with the highest system capacity. For that it’s most important to judge

the comparative behavior of various antenna diversity schemes.

It can be observed that with the implementation of receiving diversity (SIMO), BER

performance is improved compared to SISO antenna system. For example, at 5dB SNR,


125

SISO Vs. SIMO

0

0.02

0.04

0.06

0.08

0.1

0.12

1 3 5 7 9 11 13 15 17 19 21

SNR in dB

BER SISO

SIMO

the BER possessed by SISO is 0.08 while at the same point, the BER provided by SIMO

system is just around 0.04. It is due to the fact that by averaging over multiple

independent signal paths, the probability of error is decreased and BER is reduced for the

same value of SNR.

Figure-3.22 Comparative analysis of SISO vs. SIMO

It can be observed that with the implementation of transmit diversity (MISO), BER

performance is improved compared to SISO antenna system. For example, in Figure-

3.23, at 5dB SNR, the BER of SISO system is around 0.08 while the BER of MISO is

0.035. It is due to the fact that as two independent channels are defined, signal fades

independently; making sure that reliable communication is possible as long as one of the

paths is strong and received signal quality gets enhanced.


126

SISO Vs. MIMO

0

0.02

0.04

0.06

0.08

0.1

0.12

1 3 5 7 9 11 13 15 17 19 21

SNR in dB

BER SISO

MIMO

SISO Vs. MISO

0

0.02

0.04

0.06

0.08

0.1

0.12

1 3 5 7 9 11 13 15 17 19 21

SNR in dB

BER SISO

MISO

Figure-3.23 Comparative analysis of SISO vs. MISO

It can be observed that with the implementation of transmit diversity and received

diversity depicted by Figure-3.24, the lowest BERs are achieved and performance is

dramatically improved compared to SISO antenna system. It is due to the fact that MIMO

technique exploits the advantages of MISO and SIMO diversity techniques.

Figure-3.24 Comparative analysis of SISO vs. MIMO


127

SISO Vs. SIMO Vs. MISO Vs. MIMO

0

0.02

0.04

0.06

0.08

0.1

0.12

1 3 5 7 9 11 13 15 17 19 21

SNR in dB

BER

SISOSIMOMISOMIMO

It can be observed that MIMO antenna system along with Alamouti coding scheme

emphasis the lowest BER among all diversity techniques. Also as compare to MISO

technique, SIMO technique provides much better performance up-to some extent.

However MISO technique is common in the downlink of a cellular system since it is

often cheaper to have multiple antennas at the base station than to having multiple

antennas at every handset. But above all, the MIMO system offers the highest

improvement in BER that is lowest errors during transmission as compared to SISO,

SIMO and MISO. This analysis has been shown in Figure-3.25.

Figure-3.25 Comparative analysis of all diversity techniques

Now after analyzing the behavior of antenna diversity techniques, the following section

evaluates the effect of variation in modulation order and performance analysis of

effective wireless channels in the same.

3.5 Effect of Modulation Orders

The different simulation results of various antenna diversity scheme analyzed above are

by considering the effect of no. of transmitting and receiving antennas only for the

specific modulation scheme having fixed order of modulation. As shown in simulation

results of Figure-3.26, it can be observed that by changing the order of modulation


128

Effect of Variation in Modulation Order-M

00.020.040.060.080.1

0.120.140.160.18

1 3 5 7 9 11 13 15 17 19 21

SNR in dB

BER

M = 2M = 4M = 8

scheme, the BER of the system would be affected. As the modulation order M increases

in SISO system, the BER will also increase. For e.g. in Figure-3.26 in which the lower

order modulation scheme (M=2) has been applied, the BER is approximately 0.04 at SNR

= 1dB as compared to BER = 0.09 (for M=4) and around 0.15 (for M=8) at the same

value of SNR.

Figure-3.26 Effect of varying the modulation order M

This is due to the fact that for fixed number of transmitting and receiving antennas, as the

modulation order increases i.e. in turn the no. of bits per symbol increases for that

modulation scheme, due to the variation in their spatial position as well overlapping, the

loss of bits will be encountered which is the main cause behind the degradation of BER.

3.6 Critical Performance Analysis of Efficient Wireless Channels

In the previous section, it has been analyzed that with the use of various antenna diversity

techniques for the upcoming wireless systems, the system capacity along with bit error

rate can be improved by exploiting the advantage of fading through the wireless channel.

So as a further investigation, it is most critical to analyze the behavior of wireless channel

over the signals for the improvement in BER and system capacity of modern wireless

communication systems. To fulfill the above mentioned criteria, this section elaborates

the effects of different wireless channels along with various diversity techniques. As an


129

example here in this research work, two channels i.e. Rayleigh and AWGN channel with

certain specifications have been analyzed.

For the software implementation of Rayleigh and AWGN channels, same algorithm

(Algorithm of Single Input Single Output) can be used to describe the various channel

parameters as shown in Figure-3.27. In such a case, instead of Rayleigh channel matrix,

AWGN channel matrix is defined. For the implementation of MISO and MIMO

techniques, two AWGN channels are defined and outputs are combined to allow single

propagation path as AWGN channel allows only single propagation path for signal

transmission. For comparative analysis, the BER curve for Rayleigh and AWGN

channels are obtained.

An AWGN channel adds white Gaussian noise to the signal that passes through it. Radio

signal undergoes scattering on a local scale for each major path. Such local scattering is

typically characterized by a large number of reflections by objects near the mobile. These

irresolvable components combine at the receiver and give rise to the phenomenon known

as multi path fading. Due to this phenomenon, each major path behaves as a discrete

fading path. Typically, the fading process is characterized by a Rayleigh distribution for a

non-line-of-sight path and a Rician distribution for a line-of-sight path.

As a whole the comparative analysis for the single system can be done in which it can be

concluded that for the long distance communication, at the higher value of SNR, it is

appropriate to model wireless channel as AWGN channel because through this modeling

we can analyze the variations in SNR through which the BER can be calculated. While

for the small scale propagation, under the multi path environment, the modeling of

wireless channel as a Rayleigh channel will give the accurate analysis if no line of sight

component is present.


130

Figure-3.27 Algorithm for AWGN channel

By simulating the algorithm of system by selecting appropriate efficient channel, the

graph of BER v/s SNR can obtained which is shown in Figure-3.28



Create randomly generated bit pattern of transmitted dataaccording to no. of Transmitting antenna

Define single Rayleigh channel and single AWGN channel

Generate single noise matrix for Rayleigh and AWGN channels







Calculate BER from Received data


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Rayleigh Vs. AWGN

0

0.02

0.04

0.06

0.08

0.1

0.12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16SNR in dB

BER Rayleigh

AWGN

Figure-3.28 Comparative analysis of all diversity techniques

As shown in simulation results of Figure-3.28, AWGN channel gives the better response

for higher dB SNRs. This is due to the fact that as the PSK modulation technique is used,

Rayleigh fading channel directly affects on phase variation and AWGN channel directly

affects on magnitude variation. Therefore, at higher dB SNRs, these magnitude variations

are overcome. However for the Rayleigh channel, due to phase variation in PSK

technique, the BER values are higher compare to AWGN channel.

Now it has been already discussed in section 3.2 that total three types of diversities can

be broadly used in modern wireless systems to improve its performance; out of which

time diversity and antenna diversity has been discussed. This section of the chapter

describes the basic OFDM system which is as a whole frequency diversity technique. The

section discusses the basics of OFDM system, working principle, basic OFDM

transmitter and receiver arrangement along with its MATLAB simulation based on the

GUI designed.


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3.7 Simulation and Performance Analysis of OFDM Technique

This section basically elaborates the OFDM system which is the frequency diversity

technique. Besides this it is also forming the platform of physical layer of WiMAX

system which is the strong contender as a 4G wireless system. The performance analysis

of OFDM system has been done here by the illustration of basic principle and working of

the system. In the subsequent sections, the basic transceiver modeling of OFDM system

and its software implementation in MATLAB R2009a have been represented.

3.7.1 Principle of OFDM

The idea of OFDM comes from Multi Carrier Modulation (MCM) transmission

technique. The principle of MCM describes the division of input bit stream into several

parallel bit streams and then they are used to modulate several sub carriers as shown in

Figure-3.29. Each subcarrier is separated by a guard band to ensure that they do not

overlap with each other. In the receiver side, bandpass filters are used to separate the

spectrum of individual subcarriers. OFDM is a special form of spectrally efficient MCM

technique, which employs densely spaced orthogonal subcarriers and overlapping

spectrums. The uses of bandpass filters are not required in OFDM because of the

orthogonality nature of the subcarriers. The basic orthogoanlity property has been

discussed in detail in the next section. Here, the available bandwidth is used very

efficiently without causing the Inter Carrier Interference (ICI). In Figure-3.29, the effect

of this is seen as the required bandwidth is greatly reduced by removing guard band and

allowing subcarrier to overlap. It is still possible to recover the individual subcarrier

despite their overlapping spectrum provided that the orthogonality is maintained. The

Orthogonality is achieved by performing Fast Fourier Transform (FFT) on the input

stream [22]. Because of the combination of multiple low data rate subcarriers, OFDM

provides a composite high data rate with long symbol duration. Depending on the channel

coherence time, this reduces or completely eliminates the risk of Inter Symbol

Interference (ISI), which is a common phenomenon in multipath channel environment

with short symbol duration.


133

Figure-3.29 Bandwidth saving

Orthogonality

Earlier, the application of OFDM was not very practical. This was because at that point,

several banks of oscillators were needed to generate the carrier frequencies necessary for

sub-channel transmission. Since the scheme was difficult to implement at that time.

Orthogonal means right angles to each other. The term has been extended to general use,

meaning the characteristic of being independents (relative to something else). It also can

mean: non-redundant, non-overlapping, or irrelevant. Orthogonality is defined for both

real and complex valued functions. The functions and are said to be

orthogonal with respect to each other over the interval if they satisfy the

condition.

f2(t)dt=0, where f1 (3.22)

Based on the principle of orthogonality, the whole OFDM system functions and provides

frequency diversity mechanism. The following section, evaluates the structure of OFDM

technique in terms of transmitter and receiver.


134

3.7.2 OFDM Technique

Figure-3.30 shows the basic block diagram of OFDM system which figures out

transmitter and receiver of the system.

Figure-3.30 OFDM technique

The OFDM transmitter comprises of basic blocks of QAM, IFFT and addition of cyclic

prefix to evaluate the performance. The receiver possesses exactly opposite blocks of the

system. Basically the input signal stream which having single dimension would get multi

dimensional paths through serial to parallel converter block. This stream of data gets

modulated to get complex conjugates and these symbols are made to pass through IFFT

process. At last on the transmitter side, the cyclic prefix bit is added so as to improve the

system performance in the noisy condition [23].

After addition of guard band, the whole stream is passed through the wireless channel.

After receiving that data, total opposite processes of cyclic prefix removal, FFT, QAM

demodulation and parallel to serial conversion will take place. The forthcoming sections

elaborate the OFDM modulator and demodulator.


135

3.7.3 OFDM Modulation

In general, the OFDM signal can be represented as the sum of ‘N’ separately modulated

orthogonal sub-carriers.

(3.23)

Where gk(t),k=0,1,...,N-1,represent the ‘N’ carriers and are given by

In above equation, dn, k stands for the symbol that modulates the kth carrier in the

signaling interval and each signaling interval is of duration Ts. From this equation, ’N’

symbol are transmitted in Ts time interval. The symbol sequence dn, k is obtained by

converting a serial symbol sequence of rate N/Ts (symbol duration=Ts/N) into ‘N’

parallel symbol sequences of rate l/Ts (each with symbol duration Ts). Also the sub-

carrier frequencies satisfy the following requirement

+ , k=1,2,...,N-1 (3.24)

The signal transmitted in the ‘n’ signaling interval (of duration Ts) is defined as the nth

OFDM frame i.e.,

(3.25)

The nth OFDM frame Fn (t) consists of ’N’ symbols, each modulating one of the N

orthogonal sub-carriers and from equations (3.24), (3.25), it can be said that N

modulators and N demodulators are required at the receiver respectively. The number of

sub-carriers ‘N’ in OFDM systems is usually of the order of 100’S implying that the

transmitter and receiver blocks become bulky and expensive to build. Also the oscillators

(for generating the carrier frequencies) have temperature instability and other problems.


136

The Discrete Fourier Transform is used to solve the modulation and demodulation

complexities discussed above. The following discussion is modulation process can be

achieved by the IFFT operation.

The OFDM frame represented by equation (3.26) at a rate ‘N/Ts’, the resulting discrete-

time signal is

(3.26)

Expanding

Assume, fo=0 then the above equation reduces to

(3.27)

The equation 3.27 can be expressed in terms of the ITFFT as,

n,k) (3.28)

Applying the FFT operation on both sides of the equation 3.28,

( n,k)) n,k (3.29)

Thus the OFDM modulation and demodulation can be accomplished using the

computationally efficient operations IFFT and FFT respectively.

3.7.4 OFDM Demodulation

Since the carriers are orthogonal with each other, it follows that the scalar product

(k-i) (3.30)


137

Thus, the Orthogonality of the carriers can be used to demodulate each of the sub carriers

(without Inter-Carrier Interference) as follows

n,k= k(t)dt (3.31)

If there is zero inter frame interference, then the expression 3.31 reduces to

n,k= = n,k (3.32)

3.7.5 Cyclic Prefix Addition

The subcarrier orthogonality of an OFDM system can be jeopardized when passes

through a multipath channel. CP is used to combat ISI and ICI introduced by the

multipath channel. CP is a copy of the last part of OFDM symbol which is appended to

the front of transmitted OFDM symbol. The length of the CP (Tg) must be chosen as

longer than the maximum delay spread of the target multipath environment. Fig 3.31

depicts the benefits arise from CP addition, certain position within the cyclic prefix is

chosen as the sampling starting point at the receiver, which satisfies the criteria

tmax < Tx < Tg

where tmax is the maximum multipath spread.

Once the above condition is satisfied, there is no ISI since the previous symbol will only

have effect over samples within [0, tmax]. And it is also clear from the Figure-3.31 that

sampling period starting from Tx will encompass the contribution from all the multipath

components so that all the samples experience the same channel and there is no ICI.

Figure-3.31 Cyclic Prefix in OFDM


138

3.8 OFDM System Design Considerations

OFDM system design issues aim to decrease the data rate at the subcarriers, hence, the

symbol duration increases and as a result, the multipath effects are reduced effectively.

The insertion of higher valued CP will bring good results against combating multipath

effects but at the same time it will increase loss of energy. Thus, a tradeoff between these

two parameters must be done to obtain a reasonable system design. To achieve such

optimum design of OFDM system, certain design requirements are to be taken into

account which has been explained in the following section.

3.8.1 System Design Requirements

OFDM system depends on the following four requirements:

Available bandwidth: The bandwidth limit will play a significant role in the

selection of number of FFT subcarriers. Large amount of bandwidth will allow

obtaining a large number of sub-carriers with reasonable CP length.

Required bit rate: The system should be able to provide the data rate required for

the specific purpose.

Tolerable delay spread: A user environment specific maximum tolerable delay

spread should be known beforehand in determining the CP length.

Doppler values: The effect of Doppler shift due to user movement should be taken

into account.

By considering the above design requirements the complete optimized OFDM system can

be realized by choosing suitable design parameters which has been discussed in the next

section.

3.8.2 System Design Parameters

The design parameters are derived according to the system requirements. The design

parameters for an OFDM system are as follows.

Number of subcarriers: It has been stated earlier that the selection of large

number of subcarriers will help to combat multipath effects. But, at the same time,

this will increase the synchronization complexity at the receiver side.


139

Symbol duration and CP length: A perfect choice of ratio between the CP

length and symbol duration should be selected, so that multipath effects are

combated and not significant amount bandwidth is lost due to CP.

Subcarrier spacing: Subcarrier spacing will be depending on available

bandwidth and number of subcarriers used. But, this must be chosen at a level so

that synchronization is achievable.

Modulation type per subcarrier: The performance requirement will decide the

selection of modulation scheme. Adaptive modulation can be used to support the

performance requirements in changing environment.

FEC coding: A suitable selection of FEC coding will make sure the robustness of

the channel to the random errors.

3.8.3 Benefits and Drawbacks and Applications of OFDM

In the earlier section, it has been stated that how an OFDM system combats the ISI and

reduces the ICI. Besides those benefits, there are some other benefits as follows:

High spectral efficiency because of overlapping spectra

Simple implementation by fast Fourier Transform

Low receiver complexity as the transmitter combat the channel effect to some

Extents.

Suitable for high data rate transmission.

High flexibility in terms of link adaptation

It is possible to use maximum likelihood detection with reasonable complexity.

On the other side, few drawbacks of OFDM are listed as follows

An OFDM system is highly sensitive to timing and frequency offsets.

Demodulation of an OFDM signal with an offset in the frequency can lead to a

high bit error rate.

An OFDM system with large number of subcarriers will have a higher peak to

average power ratio (PAPR) compared to single carrier system. High PAPR of a

system makes the implementation of Digital to Analog and Analog to Digital

conversions extremely difficult.


140

Applications

OFDM has gained a big interest since the beginning of the 1990s as many of the

implementation difficulties have been overcome. OFDM has been in used or proposed for

a number of wired and wireless applications. Digital Audio Broadcasting was the first

commercial use of OFDM technology. OFDM has also been used for the Digital Video

Broadcasting [24]. OFDM under the acronym of Discrete Multi Tone has been selected

for asymmetric digital subscriber line. The specification for wireless LAN standard such

as IEEE 802.11a/g employed their physical layer architecture. IEEE 806.16 standard for

Fixed/Mobile BWA has also accepted OFDM for physical layer architecture [25].

Now by combining all the theoretical aspects logically, the software implementation of

optimized OFDM system has been performed over MATLAB in form of coding and GUI

which has been discussed in the following section.

3.9 Software Implementation of OFDM Technique

According to the basic structure of the OFDM system as discussed in the previous

section, the software implementation has been carried out whose algorithm has been

described in Figure-3.32. Now first of all to initiate the simulation, several designing

parameters suc as symbol rate (SR), No. of samples per symbol (NS), Range of symbols

(M), No. of data symbols per frame (Sdata), length of symbol (Slen), Guard band length

(GI), etc. have been defined and entered. Then after the random data stream would be

generated over which the process of OFDM is to be carried out.

As a next step, the randomly generated data stream would be processed by the MATLAB

command “MODMAP” to convert the analogue symbols into digital symbols so as to

realize the discrete frequency domain data.

This discrete frequency domain data would be converted into discrete time domain

through the MATLAB command “AMODCE” to get complex conjugate of the symbols

for achieving orthogonality. The central theme behind the OFDM system is orthogonality

only because of which the distance between the consecutive symbols can be reduced to

50% and hence the requirement of transmission bandwidth can also be reduced with

negligible effects of ISI.


141

Create the randomly generated bit pattern in form of Matrixusing RANDINT command in MATLAB

Map the digital symbols generated as Analog symbols usingMODMAP command in MATLAB

Converts the symbol into complex number by usingAMODCE command in MATLAB

Insert the Guard Interval

Take the IFFT of generated matrix using IFFT command inMATLAB

Generate the graphs of framing showing compression in Timedomain and in Frequency Domain

Take the FFT using FFT command in MATLAB

Finally, by considering specific length of the symbols and length of the guard interval,

IFFT of that stream is taken so as to convert the discrete frequency domain data into

discrete time domain for making it compatible for real time transmission through the

wireless channel.

Figure-3.32 OFDM Algorithm

With the simulation of MATLAB code as per algorithm discussed just now, the time

domain and frequency domain results has been obtained for the OFDM system which has

been analyzed in the next section of simulation results and discussion.


142

3.9.1 Simulation Results and Discussion

As per the algorithm discussed above, simulation would be performed over MATLAB for

the variable length of IFFT and as a result, the compression and expansion in the OFDM

spectrum in time as well as in frequency domain can be observed.

With OFDM, we can transmit the symbols within the same range of bandwidth due to

orthogonality principle because of which even the overlapped symbols can also be

transmitted without any mixing. Due to the overlapping of consecutive signal samples,

the bandwidth can be saved up to 50% and as the samples are orthogonal to one another,

the interference can be eliminated with maximum extent compared to ordinary

modulation techniques in which due to single carrier modulation, there would be

significant amount of inter symbol interference (ISI) and bit rate is also limited. Figure-

3.33 and 3.34 show the simulation results of time domain and frequency domain OFDM

related to symbols per frame equal to 64 and 32 respectively.

By considering 512 data symbols for the transmission and data symbols per frame of

IFFT equal to 64, once the simulation is performed the time and frequency domain graph

would be obtained as shown in the Figure 3.33. As shown in the time domain graph, the

OFDM symbols which are orthogonal in nature are adjusted very nearly to one another

that they occupy quite less space and still interference is also less.

This separation can still be reduced by reducing the data symbols per frame to 32 and

hence the required channel bandwidth can still be lowered down. The same thing can be

very well visualized through the following Figure-3.34.


143

Figure-3.33 OFDM G.U.I. representation of data symbol for IFFT = 64

Figure-3.34 OFDM G.U.I. representation of data symbol for IFFT = 32


144

From the two time domain and frequency domain results as shown in simulation results

of Figure-3.32 and 3.34, it can be observed that in case of OFDM, due to the overlapping

of consecutive signal samples, the higher amount of bandwidth can be saved and as the

samples are orthogonal to one another, the interference can be eliminated with maximum

extent compared to ordinary modulation techniques in which due to single carrier

modulation, there would be significant amount of ISI and bit rate is also limited. Further

by changing the size of FFT as well as symbols per frame, the amount of compression

can be varied.

At last, it can be stated that this chapter opens the main area to fulfill the research

objective. In the previous chapter, basic traditional WiMAX modeling has been analyzed

along with pros and cons. The main limitation in that was the SNR bound nature of

WiMAX system that its performance was totally dependant on channel SNR because of

single input output antenna system. In this chapter through the analysis of various types

of antenna diversity techniques and frequency diversity technique, how the overall

performance can be improved in terms of BER and system capacity has been proved.

Hence by taking reference of both these chapters, the next chapter of thesis has been

designed with the combination of diversity techniques in the WiMAX physical layer to

improve the system performance in terms of system capacity and BER improvement.

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