**1.0 Introduction**

In this chapter, we describe the basic digital

communication system and channel model which is use in this thesis. The model

is a simple model of digital communication system. The model is broken into its constituent

functions or modules, and each of these is in turn described in terms of its

affects on the data and the system. Since this model comprises the entire

system, both the source coding and channel equalization are briefly described.

In chapters 3 through 8, these two areas will be covered in detail, and the

specific algorithms and methods used in the software implementation will be

addressed in detail.

We organize this chapter as follows. First, we review

some basic notions from digital communications. We present one basic model of

digital communication system. We then talk about source encoding and decoding, channel encoding and

decoding, modulation, digital interface and channel

effects.

**2.1 DIGITAL COMMUNICATION**

Communication systems that

first convert the source output into a binary sequence and then convertthat

binary sequence into a form suitable for transmission over particular

physical media such as cable, twisted wire pair, optical fiber, or

electromagnetic radiation through space.

Digital communication systems, by definition,are communication

systems that use such a digitalsequence

as an interface between the source and the channel input (and similarly between

the channel output and final destination).

**Figure 2.1: Digital Communication
Model**

Figure 2.1 in the basic digital communication model the first three blocks of the diagram

(source encoder, channel encoder, and modulator) together comprise the

transmitter .The source represents the message to be transmitted which includes

speech, video, image, or text data among others. If the information has been

acquired in analog form, it must be converted into digitized form to make our

communication easier.This analog to

digital conversion (ADC) is accomplished in the source encoder block. Placing a binary interface between source

and channel. The source encoder converts the source output to a binary sequence

and the channel encoder (often called a modulator) processes the binary

sequence for transmission over the channel.

The last three blocks consisting of detector/demodulator,

channel decoder, and source decoder form the receiver. The destination

represents the client waiting for the information. This might include a human

or a storage device or another processing station. In any case, the source

decoder’s responsibility is to recover the information from the channel decoder

and to transform it into a form suitable for the destination.

This transformation includes digital to analog conversion (DAC) if the destination

is a human waiting to hem or view the information or if it is an analog storage

device. If the destination is a digital storage device, the information will be

kept in its digital state without DAC. The channel decoder (demodulator) recreates the incoming binary

sequence (hopefully reliably), and the source decoder recreates the source

output.

**2.2 SOURCE ****ENCODING AND ECODING**

The source encoder and

decoder in Figure 2.1 have the function of converting the input from its

original form into a sequence of bits. As discussed before, the major reasons

for this almost universal conversion to a bit sequence are as follows:

inexpensive digital hardware, standardized interfaces, layering, and the

source/channel separation theorem.

The simplest source coding

techniques apply to discrete sources and simply involve representing each successive

source symbol by a sequence of binary digits. For example, letters from the

27symbol English alphabet (including a space symbol) may be encoded into 5-bit

blocks. Since there are 32 distinct 5-bit blocks, each letter may be mapped

into a distinct 5-bit block with a few blocks left over for control or other

symbols. Similarly, upper-case letters, lower-case letters, and a great many

special symbols may be converted into 8-bit blocks (“bytes”) using the standard

ASCII code.

For example the input

symbols might first be segmented into m – tupelos, which are then mapped into

blocks of binary digits. More generally yet, the blocks of binary digits can be

generalized into variable-length sequences of binary digits. We shall find that

any given discrete source, characterized by its alphabet and probabilistic

description, has a quantity called entropy associated with it. Shannon showed

that this source entropy is equal to the minimum number of binary digits per

source symbol required to map the source output into binary digits in such a

way that the source symbols may be retrieved from the encoded sequence.

Some

discrete sources generate finite segments of symbols, such as email messages,

that are statistically unrelated to other finite segments that might be

generated at other times. Other discrete sources, such as the output from a

digital sensor, generate a virtually unending sequence of symbols with a given

statistical characterization. The simpler models of Chapter 2 will correspond

to the latter type of source, but the discussion of universal source coding is

sufficiently general to cover both types of sources, and virtually any other

kind of source.

The most straight forward approach to analog source coding is

called analog to digital (A/D) conversion.

**2.3 CHANNEL ENCODING AND DECODING**

The channel encoder and decoder box in Figure 2.1 has the

function of mapping the binary sequence at the source/channel interface into a

channel waveform.

One of the advantages of digital communications over analog

communications is its robustness during transmission. Due to the two state

nature of binary data (i.e. either a 1 or a 0), it is not as susceptible to

noise or distortion as analog data. While even the slightest noise will corrupt

an analog signal, small mounts of noise will generally not be enough to change

the state of a digital signal from I to 0 or vice versa and will in fact be

‘ignored’ at the receiver while the correct information is accurately recovered.

Nevertheless, larger amounts of noise and interference can

cause a signal to be demodulated incorrectly resulting in a bit stream with

errors at the destination. Unlike an analog system, a digital system can reduce

the effect of noise by employing an error control mechanism which is used prior

to modulation. The channel encoder performs this error control by

systematically introducing redundancy into the information bit stream after it

has been source encoded but prior to its transmission. This redundancy can then

be used by the receiver to resolve errors that might occur during transmission

due to noise or interference.

The channel decoder performs the task of decoding the received

coded bit stream by means of a decoding algorithm tailored for the encoding

scheme. Error control of this variety that allows a receiver to resolve errors

in a bit stream by decoding redundant information introduced at the transmitter

is known as Forward Error Correction (FEC). The price paid for employing FEC is

the increased bit rate and complexity of the transmitter and receiver.

**2.4 MODULATION**

The digital modulator serves as an interface between the

transmitter and the channel. It serves the purpose of mapping the binary

digital information it receives into waveforms compatible with the channel. In

baseband modulation, the output waveforms we simple voltage pulses which take

predefined values corresponding to a 1 or 0. However, many channels, such as a

satellite channel, are not suited for backhand communication and require the

incoming data to be modulated to a higher frequency, referred to as the carrier

frequency, so it can be converted to an electromagnetic wave that will

propagate through space to its destination ( a satellite or a ,round station)

This type of modulation, known as band pass modulation, varies one of the

following three parameters of the carrier frequency based on the incoming

digital bit stream: amplitude, frequency or phase. These modulation types are

commonly known as Amplitude Shift Keying (ASK). Frequency Shift Keying (FSK)

and Phase Shift Keying (PSK) respectively.

The digital detector/demodulator reverses the process and

extracts the binary baseband information from the received modulated signal

which has been subjected to noise, interference, loss, and other distortions.

The demodulator produces a sequence of binary values which are estimates of the

transmitted data and passes it on to the channel decoder.

**2.5 DIGITAL INTERFACE**

The interface between the source coding

layer and the channel coding layer is a sequence of bits. However, this simple

characterization does not tell the whole story. The major complicating factors

are as follows:

–Unequal rates: The rate at which bits leave the source encoder is often not

perfectly matched to the rate at which bits enter the channel encoder.

–Errors: Source decoders are usually designed to decode an exact replica of

the encoded sequence, but the channel decoder makes occasional errors.

–Networks: Encoded source outputs are often sent over networks, traveling

serially over several channels; each channel in the network typically also

carries the output from a number of different source encoders.

The first two factors above appear both in

point-to-point communication systems and in networks. They are often treated in

an ad hoc way in point-to-point systems, whereas they must be treated in a

standardized way in networks. The third factor, of course, must also be treated

in a standardized way in networks.

**2.6 CHANNEL EFFECTS**

During transmission, the signal undergoes various degrading

and distortion effects as it passes through the medium from the transmitter to

the receiver. This medium is commonly referred to as the channel. Channel

effects include, but are not limited to, noise, interference, linear and non‑linear

distortion and attenuation. These effects are contributed by a wide variety of

sources including solar radiation, weather and signals front adjacent channels.

But many of the prominent effects originate from the components in the receiver.

While many of the effects can be greatly reduced by good system design, careful

choice of filter parameters, and coordination of frequency spectrum usage with

other users, noise and attenuation generally cannot be avoided and are the

largest contributors to signal distortion.

In digital communication systems, a common quantity used to

determinate whether a signal will be detected correctly is the ratio of energy

per bit to spectral noise power density, E_{b }/ N_{o},

measured at the detector. The higher the E_{b,} the lower the resulting

bit error rate (BER),the probability of

bit error, P_{b} Unfortunately, a high E_{b} demands greater

power consumption at the transmitter; in some cases, it may be unfeasible to

obtain a high E_{b} due to transmitter size or power limitations as in

the case of satellite transmission.

The digital communication system described consists of an

ordered grouping of various modules which operate on an input data sequence. In

practice, these modules or resources are not dedicated to a single

source/destination, but they me shared by multiple sources and their

destinations to achieve optimum utilization.

In a digital system, the transmission bit rate is an important

system resource. A given information source of bandwidth B, sampled at 2B samples/second

using q bits per sample results in a data rate, R, of 2Bq bits per second. With

a compression ratio C, the data rate from the source encoder is R_{s }=

RIC bits per second. Channel coding by a factor n leads to a coded data rate of

R_{c} = R_{s }n bits per second; R, is the system transmission

bit rate. These bits we then used by the modulator to form the transmission

waveforms which have to be accommodated within the available bandwidth. At the

receiver these steps m performed in the reverse order to recover the

information sequence.

**SOURCE CODING**

In the digital communication system model described previously,

the source encoder is responsible for producing the digital information which

will be manipulated by the remainder of the system. After the digital signal is

acquired from the analog information, the source encoder subjects it to a wide

range of processing functions, the goals of which are to compactly represent

the information. Speech, image, and textual information each have their own unique

characteristics that require different source encoding techniques. Depending on

the information source, different digital signal processing functions are

implemented to remove the redundancies inherent in the given signal. The

specifics of the speech compression techniques used in this thesis are detailed

below.

In

this chapter we describe the source coding and then its related speech

compression, Linear predictive coding (LPC) and Code excited linear prediction

(CELP).The use of these in digital communication in source coding. And we also

describe the LPC in large as we use it in the source coding in our digital

communication thesis.

**3.1 SPEECH COMPRESSION**

Since the frequency content of spoken language is confined to

frequencies under 4000 Hz, it is reasonable to use a sampling frequency of 8000

Hz. Using 16 bit linear Pulse code modulation (PCM) as the quantization method

results in a bit rate of 128 kbps. Subsequent analysis, coding, and compression

of speech are performed on segments or frames of 20 to 30 ms duration.

There are two broad categories of speech coding/compression.

Both categories are concerned with representing the speech with the minimum

number of applicable parameters while also allowing the speech to be

intelligibly reproduced; both are loss in nature.

The first category deals with waveform coders which manipulate

quantities in the speech signal’s frequency representation. Typical analysis tools

of waveform coders are the Discrete Fourier Transform (DFT) and the Discrete Wavelet

Transform (DWT), both of which transform the time signal to its frequency

domain representation. In this case, compression might potentially be achieved

by retaining the frequency components with the largest magnitudes.

The second category of speech compression

deals with voice coders, or vocoders for short. Vocoders attempt to represent

speech as the output of a linear system driven by either periodic or random

excitation sequences as shown in Figure 3.1.

**Figure 3.1: Basic Model of a Vocoder**

A periodic impulse train or a white

noise sequence, representing voiced or unvoiced speech, drives an all pole

digital filter to produce the speech output. The all pole filter digital filter

models the vocal tract.

Additionally, estimates of the pitch period and gain

parameters are necessary for accurate reproduction of the speech. Due to the

slowly changing shape of the vocal tract over time, vocoders successfully

reproduce speech by modeling the vocal tract independently for each frame of

speech and driving it by an estimate of a separate input excitation sequence

for that frame. Most vocoders differ in performance principally based on their

methods of estimating the excitation sequences.

**3.2 LINEAR PREDICTIVE CODING (LPC)**

Linear

Predictive Coding (LPC) is one of the most powerful speech analysis techniques,

and one of the most useful methods for encoding good quality speech at a low

bit rate. It provides extremely accurate estimates of speech parameters, and is

relatively efficient for computation. This document describes the basic ideas

behind linear prediction, and discusses some of the issues involved in its use.

Linear prediction model speech waveforms are same by

estimating the current value from the previous values. The predicted value is a

linear combination of previous values. The linear predictor coefficients are

determined such that the coefficients minimize the error between the actual and

estimated signal. The basic equation of linear prediction is given as follows:

Where,is the estimated sampleof the actual samplefrom the linear combination of

p samples with the coefficients.

A prediction is useless if that prediction is

inaccurate. Thus, the purpose is to minimize the prediction error. That is, to

minimize in the Equation below:

Where E the short-time is

average prediction error and

is the individual

error.

LPC starts with the assumption that the speech signal is

produced by a buzzer at the end of a tube. The glottis (the space between the

vocal cords) produces the buzz, which is characterized by its intensity

(loudness) and frequency (pitch). The vocal tract (the throat and mouth) forms

the tube, which is characterized by its resonances, which are called formants. For more information about

speech production, see the Speech

Production OLT.

LPC analyzes the speech signal by estimating the formants,

removing their effects from the speech signal, and estimating the intensity and

frequency of the remaining buzz. The process of removing the formants is called

inverse filtering, and the

remaining signal is called the residue.

The

numbers which describe the formants and the residue can be stored or

transmitted somewhere else. LPC synthesizes the speech signal by reversing the

process: use the residue to create a source signal, use the formants to create

a filter (which represents the tube), and run the source through the filter,

resulting in speech.

Because

speech signals vary with time, this process is done on short chunks of the

speech signal, which are called frames.

Usually 30 to 50 frames per second give intelligible speech with good

compression.

**A.Speech Production**

When a person speaks, his or her lungs work like a

power supply of the speech production system. The glottis supplies the input

with the certain pitch frequency (F0).

The vocal tract, which consists of the pharynx and the mouth and nose cavities,

works like a musical instrument to produce a sound. In fact, different vocal

tract shape would generate a different sound. To form different vocal tract

shape, the mouth cavity plays the major role. To produce nasal sounds, nasal

cavity is often included in the vocal tract. The nasal cavity is connected in

parallel with the mouth cavity. The simplified vocal tract is shown in Fig 3.2.

**Figure
3.2: Simplified view of a Vocal Tract**

The glottal pulse generated by the glottis is used to

produce vowels or voiced sounds. And the noise-like signal is used to produce

consonants. ..or unvoiced sounds.

**B.Linear Prediction Model**

In this section, an all-pole system (or the linear

prediction system) is used to model a vocal tract as shown in Fig. 3.3.

**Figure 3.3: Simplified model of the speech production**

An efficient algorithm known as the Levinson-Durbin

algorithm is used to estimate the linear prediction coefficients from a given

speech waveform.

Assume that the present sample of the speech is predicted by the past M samples of the speech such that

Where the prediction of isis the k^{th}

step previous sample, and a_{k}

are called the linear prediction coefficients.

Once the linear prediction coefficients {a_{k}} are found, which can

be used to compute the error sequence ε(n).The implementation of Equation

here x(n) is the input and ε(n) is the output, is called the

analysis filter and shown in Figure 3.4.

**Figure 3.4: Speech Analysis Filter**

The transfer function is given by

Because ε(n), residual error, has less standard

deviation and less correlated than speech itself, smaller number of bits is

needed to quantize the residual error sequence. Equation can be rewritten as

the difference equation of a digital filter whose input is ε (n) and output is s (n) such

that

The implementation of the above equation is called the synthesis filter and is

shown in Figure 3.5.

**Figure 3.5: Speech Synthesis Filter**

If both the linear prediction coefficients and the

residual error sequence are available, the speech signal can be reconstructed

using the synthesis filter. In practical speech coders, linear prediction

coefficients and residual error samples need to be compressed before transmission.

Instead of quantizing the residual error, sample by sample, several important

parameters such as pitch period, code for a particular excitation, etc are

transmitted. At the receiver, the residual error is reconstructed from the

parameters.

**3.3 CODE‑EXCITED LINEAR PEDICTION (CELP)**

Although the data rate of plain LPC coders is low, the speech

reproduction, while generally intelligible, has a metallic quality, and the

vocoder artifacts are readily apparent in the unnatural characteristics of the

sound. The reason for this is because this algorithm does not attempt to encode

the excitation of the source with a high degree of accuracy. The CELP algorithm

attempts to resolve this issue while still maintaining a low data rate.

Speech frames in CELP are 30 ms in duration, corresponding to

240 samples per frame using a sampling frequency of 8000 Hz. They are further

partitioned into four 7.5 ms sub frames of 60 samples each. The bulk of the

speech analysis/synthesis is performed over each sub frame.

The CELP algorithm uses two indexed codebooks and three lookup

tables to access excitation sequences, gain parameters, and filter parameters.

The two excitation sequences are scaled add summed to form the input excitation

to a digital filter created from the LPC filter parameters. The codebooks

consist of sequences which are each 60 samples long, corresponding to the

length of a sub frame.

CELP is referred to as an analysis‑by‑synthcsis

technique.

**Figure 3.6: CELP Analyzer**

Figure 3.6 shows a schematic diagram of the CELP

analyzer/coder. The stochastic codebook is fixed containing 512 zero mean

Gaussian sequences. The adaptive codebook has 256 sequences formed from the

input sequences to the digital filter and updated every two sub frames. A code

from the stochastic codebook is scaled and summed with a gain scaled code from

the adaptive codebook.

The result is used as the input excitation sequence to an LPC

synthesis filter. The output of the filter is compared to the actual speech

signal, and the weighted error between the two is compared to the weighted

errors produced by using all of the other codewords in the two codebooks. The

codebook indices of the two codewords (one each from the stochastic add

adaptive codebooks), along with their respective gains, which minimize the

error are then coded for transmission along with the synthesis filter (LPC)

parameters. Because, the coder passes each of the adaptive and stochastic

codewords through the synthesis filter before selecting the optimal codewords.

**CHANNEL CODING**

We considered the problem of digital modulation by means of M=2^{k}

signal waveforms, where each waveform conveys k bits of information. We

observed that some modulation methods provide better performance than others.

In particular, we demonstrated that orthogonal signaling waveforms allow us to

make the probability of error arbitrarily mail by letting the number of

waveformsM → ∞ provided

that the SNRper bit γ_{b }≥

‑1.6 dB. Thus, we can operate at the capacity of the Additive White

Gaussian Noise channel in the limit as the bandwidth expansion factor B_{e}

=W/R→∞. This is a heavy price to pay, because B_{e} grows

exponentially with the block length k. Such inefficient use of channel

bandwidth is highly undesirable.

In this and the following chapter, we consider signal

waveforms generated from either binary or no binary sequences. The resulting

waveforms are generally characterized by a bandwidth expansion factor that

grows only linearly with k. Consequently, coded waveforms offer the potential

for greater bandwidth efficiency than orthogonal M‑ary waveforms. We

shall observe that. In general, coded waveforms offer performance advantages

not only in power limited applications where RIW<1, but also in bandwidth

limited systems where R/W > 1.

We begin by establishing several channel models that will be

used to evaluate the benefits of channel coding, and we shall introduce the

concept of channel capacity for the various channel models, then, we treat the

subject of code design for efficient communications.

**4.1 CHANNEL MODEL**

In the model of a digital communication system described in

chapter 2, we recall that the transmitter building block; consist of the

discrete input, discrete output channel encoder followed by the modulator. The

function of the discrete channel encoder is to introduce, in a controlled

manner, some redundancy in the binary information sequence, which can be used

at the receiver to overcome the effects of noise and interference encountered

in the transmission of the signal through the channel. The encoding process

generally involves taking k information bits at a time and mapping each k‑bit

sequence into a unique n‑bit sequence, called a code word. The amount of

redundancy introduced by the encoding of the data in this manner is measured by

the ratio n/k. The reciprocal of this ratio, namely k/n, is called the code

rate.

The binary sequence at the output of the channel encoder is

fed to the modulator, which serves as the interface to the communication

channel. As we have discussed, the modulator may simply map each binary digit

into one of two possible waveforms, i.e., a 0 is mapped into s_{1} (t)

and a 1 is mapped into S_{2} (t). Alternatively, the modulator may

transmit q‑bit blacks at a time by using M = 2^{q} possible

waveforms.

At the receiving end of the digital communication system, the

demodulator processes the channel‑crurrupted waveform and reduces each

waveform to a scalar or a vector that represents an estimate of the transmitted

data symbol (binary or M‑ary).The detector, which follows the demodulator,

may decide on whether the ‘transmitted bit is a 0 or a 1. In such a case, the

detector has made a hard decision.

If we view the decision process at the

detector as a form of quantization, we observe that a hard decision corresponds

to binary quantization of the demodulator output. More generally, we may

consider a detector that quantizes to Q > 2 levels, i.e. a Q‑ary

detector. If M‑ary signals are used then Q ≥ M. In the extreme case

when no quantization is performed, Q = M. In the case where Q > M, we say

that the detector has made a soft decision.

**A.Binary Symmetric Channel**

**Figure 4.1: A composite discrete-input, discrete output channel**

Let us consider an additive noise channel and let the

modulator and the demodulator/detector be included as parts of the channel. If

the modulator employs binary waveforms and the detector makes hard decisions,

then the composite channel, shown in Fig. 4.1, has a discrete-time binary input

sequence and a discrete-time binary output sequence. Such a composite channel

is characterized by the set X = {0, 1} of possible inputs, the set of Y= {0, 1} of possible outputs, and a set of

conditional probabilities that relate the possible outputs to the possible

inputs. If the channel noise and other disturbances mum statistically

independent errors in the transmitted binary sequence with average probability

P then,

P(Y = 0 / x = 1) = P(Y = 1 / x = 0) =

P

P(Y = 1 / x = 1) = P(Y = 0 / X = 0) = 1- P

Thus, we have reduced the cascade of the binary modulator, the

waveform channel, and the binary demodulator and detector into an equivalent

discrete-time channel which is represented by the diagram shown in Fig 4.1.

This binary-input, binary-output, symmetric channel is simply called a binary

symmetric channel (BSC).

**B. Discrete Memory Less Channel**

The BSC is a special can of a more

general discrete-input, discrete-output channel. Suppose that the output form

the channel encoder are q‑ary symbols, i.e., X={x_{0}, x_{1,}…,x_{q
-1}) and the output of the decoder consists of q‑ary symbols, where

Q ≥M =2^{q}.

**Figure 4.2: Binary symmetric channels**

If the channel and the modulation are memory less, then the

input-output characteristics of the composite channel, shown in Fig. 4.1, are

described by a set of qQ conditional probabilities.

**C. Waveform Channels**

We may separate the modulator and demodulator from the

physical channel, and consider a channel model in which the inputs are

waveforms and the outputs are waveforms. Let us assume that such a channel has

a given bandwidth W, with ideal frequency response C(f) =1 within the bandwidth

W, and the signal at its output is corrupted by additive white Gaussian noise.

Suppose that x (t) is a band-limited input to such a channel and y (t) is the

corresponding output, then,

y(t) = x(t) + n(t)

Where n(t) represents a sample function of the additive noise

process.

**4.2 CONVOLUTIONAL CODES**

For (n,1) convolution codes, each bit of the information

sequence into the encoder results in an output of n bits. However, unlike block

codes, the relationship between information bits and output bits is not a

simple one-to-one mapping. In fact, each input information bit is ‘convolved’

with K-1 other information bits to form the output n‑bit sequence. The

value K is known as the constraint length of the code and is directly related

to its encoding and decoding complexity as described below in a brief

explanation of the encoding process.

For each time step, an incoming bit is stored in a K stage

shift register, and bits at predetermined locations in the register are passed

to n modulo‑2 adders to yield the n output bits. Each input bit enters

the first stage of the register, and the K bits already in the register are

each shifted over one stage with the last bit being discarded from the last

stage.

The n output bits produced by the entry of each input bit have

a dependency on the preceding K-1 bits. Similarly, since it is involved in the

encoding of K-1 input bits in addition to itself, each input bit is encoded in

nK output bits. It is in this relationship that convolutional coding derives

its power. For larger values of K, the dependencies among the bits increased

the ability to correct more errors rises correspondingly. But the complexity of

the encoder and especially of the decoder also becomes greater.

**Figure 4.3: K = 3, r = 1/2
Convolutional Code Encoder**

Shown in Figure 4.3 is the schematic for a (2,1) encoder with

constraint length K= 3 which will serve as the model for the remainder of the

development of convolutional coding. In the coder shown, the n = 2 output bits

are formed by modulo‑2 addition of the bits in stages one and three and

the addition of bits in stages one, two, and three of the shift register.

**MODULATION**

In this chapter, we describe the basic

Modulation Technique and emphasis on QPSK Modulation which is use in this

thesis. We are trying to show how QPSK Modulation is used in digital

communication system. In digital transmission systems, the

data sequence from the channel encoder is partitioned

into L bit words, and each word is mapped to one of M corresponding waveforms according to some predetermined rule, where M = 2^{L}.

We shall see later, in a QPSK modulation system, the incoming sequence is separated into words of L = 2 bits each and mapped to

M = 2^{2} = 4 different waveforms. During transmission, the channel

causes attenuation and introduces noise to the signal. The net result is the

formation of a version of the original signal which may not be detected

correctly by the receiver. If the errors are too numerous, the channel decoder

may not be able to resolve the information correctly. Baseband modulation using

the simple binary symmetric channel model is briefly discussed, and the details of QPSK modulation are then presented.

We organize this chapter as follows. First, we

review some basic from Modulation Technique. We present basic modulation of

Amplitude Shift-keying (ASK), Frequency

Shift-keying(FSK),Phase Shift-keying(PSK), Binary Phase Shift-keying (BPSK) and

Quadrature Phase Shift-keying(QPSK). We then talk about Quadrature Phase Shift-keying(QPSK) in detail and try

to show the use of QPSK in digital communication

system.

**5.1 AMPLITUDE SHIFT KEYING (ASK)**

In many situations, for example in radio frequency transmission, data cannot be

transmitted directly, but must be used to modulate a higher frequency sinewave

carrier. The simplest way of modulating a carrier with a data stream is to

change the amplitude of the carrier every time the data changes. This technique

is known as amplitude shift -keying.

The

simplest form of amplitude shift-keying is on- off keying, where the

transmitter outputs the sinewave carrier whenever the data bit is a ‘1’, and

totally suppresses the carrier when the data bit is ‘0’. In other words, the

carrier is turned ‘on’ for a ‘1’, and ‘off ‘ for a ‘0’.This form of amplitude

shift-keying is illustrated in figure below:

**Figure 5.1: an ASK signal (below) and the message (above)**

In order to generate an amplitude shift-keyed (ASK) wave form at the Transmitter a

balanced modulator circuit is used (also known as a linear multiplier). This

device simply multiplies together the signals at its two inputs, the output

voltage at any instant in time being the product of the two input voltages. One

of the inputs is a.c. coupled; this is known as the carrier input. The other is

d.c. coupled and is known as the modulation (or signal) input.

In order to generate the ASK waveform, all that is necessary is to connect the

sine wave carrier to the carrier input, and the digital data stream to the

modulation input, as shown in figure below:

**Figure 5.2: ASK generation method**

The data stream applied to the modulator’s modulation input is unipolar, i.e. its

‘0’ and ‘1’ levels are 0 volts and +5volts respectively. Consequently.

(1)When the current data bit is a ‘1’ , the

carrier is multiplied by a constant, positive voltage, causing the carrier to

appear, unchanged in phase, at the modulator’s output.

(2)When the current data bit is a ‘0’, the

carrier is multiplied by 0 volts, giving 0 volt as at the modulators output.

At

the Receiver, the circuitry required to demodulate the amplitude shift- keyed

wave form is minimal.The filter’s output appears as a very rounded version of

the original data stream, and is still unsuitable for use by the

“Receiver’s digital circuits. To overcome this, the filter’s output wave

form is squared up by a voltage comparator.

**5.2 Frequency Shift-keying**

In

frequency shift -keying, the signal at the Transmitter’s output is switched

from one frequency to another every time there is a change in the level of the

modulating data stream For example, if the higher frequency is used to

represent a data ‘1’ and the lower ferquency a data ‘0’, the reasulting

Frequency shift keyed (FSK) waveform might appear as shown in Figure below:

**Figure 5.3 An ASK waveform**

The generations of a FSK waveform at the Transmitter can be acheived by generating

two ASK waveforms and adding them together with a summing amplifier.

At the Receiver, the frequency shift-keyed signal is decoded by means of a

phase-locked loop (PLL) detector. The detector follows changes in frequency in

the FSK signal, and generates an output voltage proportional to the signal

ferquency.

The phase-locked loop’s output also contains components at the two carrier

frequencies; a low-pass fillter is used to filter these components out.

The filter’s output appears as a very rounded version of the original data stream,

and is still unsuitable for use by the Receiver’s digital circuits. To overcome

this, the filter’s output waveform is squared up by a voltage comparator.

Figure below shows the functional blocks required in order to demodulate the

FSK waveform at the Receiver.

**5.3 Phase Shift keying (PSK) **

In phase shift keying the phase of the carrier sinewave at the transmitter’s

output is switched between 0 º and 180 º, in sympathy with the data to be

transmitted as shown in figure below:

**Figure 5.3: phase shift keying**

The functional biocks required in order to generate the PSK signal are similar to

those required to generate an ASK signal. Again a balanced modulator is used,

with a sinewave carrier applied to its carrier input. In contscast to ASK

generation, however, the digital signal applied to the madulation input

forPSK generation is bipolar, rather

than unipolar, that is it has equal positive and negative voltage levels.

When

the modulation input is positive, the modulator multiplies the carier input by

this constantlevel. so that the

modulator’s output signal is a sinewave which is in phase with the carrier input.

When

the modulation input is negative, the modulator multiplies the carrier input by

this constant level, so that the modulatior’s autput signal is a sinewave which

is 180 º out of phase with the carier input.

At

the Receiver, the frequency shift-keyed signal is decoded by means of a

squaring loop detector. This PSK Demodulator is shown in figure below:

**5.4 BINARY PHASE-SHIFT KEYING (BPSK)**

In

binary phase shift keying (BPSK), the transmitted signal is a sinusoid of fixed

amplitude it has one fixed phase when the data is at one level and when the

data is at the other level the phase is different by 180 º . If the sinusoid is

of Amplitude A it has a power :

P_{s} = 1/2 A_{2}

A = Root over (2 P_{s})

BPSK(t) = Root over (2 P_{s})

Cos (ω_{0}t)

BPSK(t) = Root over (2 P_{s}) Cos

(ω_{0}t+π )

= – Root over (2 P_{s}) Cos (ω_{0}t)

In

BPSK the data b(+) is a stream of binary digits with voltage levels which, we

take to be at +1V and – 1 V.When b(+)

=1V we say it is at logic 1 and when b(+)= -1V we say it is logic 0. Hence,

BPSK(t)can be written as:

BPSK(t) =

b(t) Root over (2 Ps) Cos (w_{0}t)

In

practice a BPSK signal is generated by applying the waveform Coswo as a carrier

to a balanced modulator and applying the baseband signal b(+) as the modulating

signal. In this sense BPSK can be thought of as an AM signal similar as PSK

signal.

**5.5 Quadrature Phase Shift Keying (QPSK)**

In this section the topics of QPSK modulation of digital

signals including their transmission, demodulation, and detection, are

developed. The material in this section and the related coding of this system

are both based on transmission using an AWGN channel model which is covered at

the end of this section. Some of the techniques discussed below are specifically

designed for robustness under these conditions.

Because this is a digital implementation of a digital system,

it is important to note that the only places where analog quantities occur are

after the DAC, prior to the actual transmission of the signal, and before the

ADC at the receiver. All signal values between the source encoder input and

modulator output are purely digital. This also holds for all quantities between

the demodulator and the source decoder.

**A. Background**

QPSK modulation is a specific example of the more general M‑ary

PSK. For M‑ary PSK, M different binary words of length L = log_{2 }M

bits are assigned to M different waveforms. The waveforms we at the same

frequency but separated by multiples of φ = 2π/M in phase from each

other and can be represented as follows:

with i = 1, 2, … M. The carrier frequency and sampling

frequency are denoted by f_{c} and f_{s }respectively.

Since an M‑ary PSK system uses L bits to generate a

waveform for transmission, its symbol or baud rate is 1IL times its bit rate.

For QPSK, there we M = 4 waveforms separated by multiples of (= ) radians and assigned to four binary words of

length L = 2 bits. Because QPSK requires two incoming bits before it can

generate a waveform, its symbol or baud rate, D, is one‑half of its bit

rate, R.

**B.Transmitter**

Figure 5.2 illustrates the method of QPSK generation. The

first step in the formation of a QPSK signal is the separation of the incoming

binary data sequence, b, into an in‑phase bit stream, b_{1}, and

a quadratic phase bits ream, b_{Q}, as follows. If the incoming data is

given by b = b_{o}, b_{1}, b_{2}, b_{3}, b_{4}….

where b_{i} are the individual bits in the sequence, then, b_{I}

= b_{o}, b_{2}, b_{4 }……(even bits of b) and b_{Q}=

b_{1}, b_{3}, b_{5} …… (odd bits). The digital QPSK

signal is created by summing a cosine function modulated with the b_{I},

stream and a sine function modulated by the b_{Q} stream. Both

sinusoids oscillate at the same digital frequency, ω_{0}=2π f_{c}

/ f_{s} radians. The QPSK signal is subsequently filtered by a band

pass filter, which will be described later, and sent to a DAC before it is

finally transmitted by a power amplifier.

**Figure 5.4 QPSK Modulator**

**B.1 Signal Constellation**

It is often helpful to represent the modulation technique with

its signal space representation in the I‑Q plane as shown in Figure 5.3.

The two axes, I and Q, represent the two orthogonal sinusoidal components,

cosine and sine, respectively, which are added together to form the QPSK signal

as shown in Figure 5.2. The four points in the plane represent the four

possible QPSK waveforms and me separated by multiples of n/2 radians from each

other. By each signal point is located the input bit pan which produces the

respective waveform.

The actual I and Q coordinates of each bit pair are the

contributions of the respective sinusoid to the waveform. For example, the

input bits (0, 1) in the second quadrant correspond to the (I,Q) coordinates, (‑1,1).

This yields the output waveform ‑ I + Q = ‑ cos (ω_{0}n)

+ sin (ω_{0}n). Because all of the waveforms of a QPSK have the

same amplitude, all four points are equidistant from the origin. Although the

two basis sinusoids shown in Figure 5.2 are given by cos (ω_{0}n)

and sin (ω_{0}n), the sinusoids can be my two functions that are

orthogonal.

**Figure 5.3 Signal
Constellation of QPSK**

**B.2 Filtering**

The QPSK signal created by the addition of the two sinusoids

has significant energy in frequencies above and below the carrier frequency.

This is due to the frequency contributions incurred during transitions between

symbols which are either 90 degrees or 180 degrees out of phase with each

other. It is common to limit the out of band power by using a digital band pass

filter (BPF) centered at ω_{o}. The filter has a flat pass band

and a bandwidth which is 1.2 to 2 times the symbol rate.

**C.Receiver**

The receiver’s function consists of two steps: demodulation

and detection. Demodulation entails separating the received signal into its

constituent components. For a QPSK signal, these are the cosine and sine

waveforms carrying the bit information. Detection is the process of determining

the sequence of ones and zeros those sinusoids represent.

**C.1 Demodulator**

The demodulation procedure is illustrated below in Figure 5.4.

The first step is to multiply the incoming signal by locally generated

sinusoids. Since the incommoding signal is a sum of sinusoids, and the receiver

is a linear system, the processing of the signal can be treated individually

for both components and summed upon completion.

**Figure 5.4: QPSK Demodulator and
Detector**

Assuming the received

signal is of the form

r(n) =

A_{I }cos(ω_{0}

n) + A_{Q }sin (ω_{0}n)

where A_{I }and A_{Q }are scaled versions of

the b_{I} and b_{Q} bitstreams used to modulate the signal at

the transmitter. The contributions through the upper and lower arms of the

demodulator due to the cos(ω_{0}

n) input alone are

r_{ci} = A_{I }cos(ω_{0}n) cos (ω_{0}

n+ ө)

r_{cQ} = A_{I }cos(ω_{0}n) sin (ω_{0}

n+ ө)

where ө is the phase difference

between the incoming signal and locally generated sinusoids. These equations

can be expanded using trigonometric identities to yield.

**C.2 Detection**

After the signal r(n) has been demodulated into the bitstreams

dj(n) and dQ(n), the corresponding bit information must be recovered. The

commonly used technique is to use a matched filter at the output of each LPF as

shown in Figure 5.4. The matched filter is an optimum receiver under AWGN

channel conditions and is designed to produce a maximum output when the input

signal is a min‑or image of the impulse response of the filter. The

outputs of the two matched filters are the detected bitstreams bdj and bdO, and

they are recombined to form the received data bitstream. The development of the

matched filter and its statistical properties as an optimum receiver under AWGN

conditions can be found in various texts.

**5.6 AWGN Channel**

The previously introduced BSC channel modeled all of the

channel effects with one parameter, namely the BER; however, this model is not

very useful when attempting to more accurately model a communication system’s

behavior. The biggest drawback is the lack of emphasis given to the noise which

significantly corrupts all systems.

The most commonly used channel model to deal with this noise

is the additive white Gaussian noise (AWGN) channel model. The time results

because the noise is simply added to the signal while the term ‘white’ is used

because the frequency content is equal across the entire spectrum. In reality,

this type of noise does not exist and is confined to a finite spectrum, but it

is sufficiently useful for systems whose bandwidths are small when compared to

the noise power spectrum.

**CHANNEL EQUALIZATION**

Equalization is partitioned into two broad categories. The first category, maximum likelihood

sequence estimation (MLSE), entails making measurements of impulse response and

then providing a means for adjusting the receiver to the transmission

environment. The goal of such adjustment is to enable the detector to make good

estimates from the demodulated distorted pulse sequence. With an MLSE receiver,

the distorted samples are not reshaped or directly compensated in any way;

instead, the mitigating techniques for MLSE receiver is to adjust itself in

such a way that it can better deal with the distorted samples such as Viterbi

equalization.

The second

category, equalization with filters, uses filters to compensate the distorted

pulses. In this second category, the detector is presented with a sequence of

demodulated samples that the equalizer has modified or cleaned up from the

effects of ISI. The filters can be distorted as to whether they are linear

devices that contain only feed forward elements (transversal equalizer), or

whether they are nonlinear devices that contain both feed for ward and feedback

elements (decision feedback equalizer) the can be grouped according to the

automatic nature of their operation, which may either be preset or adaptive.

They are also

grouped according to the filter’s resolution or update rate.

**Symbol spaced**

Pre detection

samples provided only on symbol boundaries, that is, one sample per symbol. If

so, the condition is known.

**Fractionally spaced**

Multiple samples

provided for each symbol. If so, this condition is known.

**6.1 ADAPTIVE EQUALIZATION**

An adaptive

equalizer is an equalization filter that automatically adapts to time-varying

properties of the communication channel. It is frequently used with coherent modulations

such as phase shift keying, mitigating the effects of multipath propagation and

Doppler spreading. Many adaptation strategies exist. A well-known example is

the decision feedback equalizer, a filter that uses feedback of detected

symbols in addition to conventional equalization of future symbols. Some

systems use predefined training sequences to provide reference points for the

adaptation process.

Adaptive

equalization is capable of tracking a slow time varying channel response. It

can be implemented to perform tap weight adjustments periodically or

continually. Periodic adjustments are accomplished by periodically transmitting

a preamble or short training sequence of digital data that is known in advance

by the receiver. The receiver also detects the preamble to detect start of

transmission, to set the automatic gain control level, and to align internal

clocks and local oscillator with the received signal. Continual adjustments are

accomplished by replacing the known training sequence with a sequence of data

symbol estimated from the equalizer output and treated as known data.

When

performed continually and automatically in this way, the adaptive procedure is

referred to as decision directed. Decision directed only addresses how filter

tap weights are adjusted-that is with the help of signal from the detector.

DFE, however, refers to the fact that there exists an additional filter that

operates on the detector output and recursively feed back a signal to detector

input. Thus with DFE there are two filters, a feed forward filter and a feed

back filter that processes the data and help mitigate the ISI.

Adaptive equalizer

particularly decision directed adaptive equalizer, successfully cancels ISI

when the initial probability of error exceeds one percent. If probability of

error exceeds one percent, the decision directed equalizer might not converge.

A common solution to this problem is to initialize the equalizer with an

alternate process, such as a preamble to provide good channel error

performance, and then switch to the decision directed mode. To avoid the

overhead represented by a preamble many systems designed to operate in a

continuous broadcast mode use blind equalization algorithms to form initial

channel estimates. These algorithms adjust filter coefficients in response to

sample statistics rather than in response to sample decisions.

Automatic

equalizer use iterative techniques to estimate the optimum coefficients. The

simultaneous equations do not include the effects of channel noise. To obtain a

stable solution to the filter weights, it is necessary that the data are

average to obtain, stable signal statistics or the noisy solution obtained from

the noisy data must be averaged considerations of algorithm complexity and

numerical stability most often lead to algorithms that average noisy solutions.

The most robust of this class of algorithm is the least mean square algorithm.

**6.2 LMS ALGORITHM FOR OEFICIENT
ADJUSTMENT**

Suppose we have an

FIR filter with adjustable coefficient {h(k),0<k<N-1}. Let x(n) denote

the input sequence to the filter, and let the corresponding output be {y(n)},

where

y(n) = n=0,….M

Suppose we also

have a desired sequence d(n) with which we can compare the FIR filter output.

Then we can form the error sequence e(n) by taking the difference between d(n)

and y(n). That is,

e(n)=d(n)-y(n),n=0,….M

The coefficient of

FIR filter will be selected to minimize the sum of squared errors.

Thus we have

where, by

definition,

r_{dx}(k)=0 ≤

k ≤ N-1

r_{xx}(k)=0 ≤

k ≤ N-1

We call rdx(k) the

cross correlation between the desired output sequence d(n) and the input

sequence x(n), and rxx(k) is the auto correlation sequence of x(n).

The sum of squared

errors ε is a quadratic function of the FIR filter coefficient.

Consequently, the minimization of ε with respect to filter coefficient

h(k) result in a set of linear equations. By differentiating ε with

respect to each of the filter coefficients, we obtain,

∂ε

/∂h(m)=0,0 ≤ m ≤

N-1

and,

hence

rxx(k-m)=rdx(m),0

≤ k ≤ N-1

This is the set of

linear equations that yield the optimum filter coefficients.

To solve the set

of linear equations directly, we must first compare the autocorrelation

sequence rxx(k) of the input signal and cross correlation sequence rdx(k)

between the desired sequence d(n) and input sequence x(n).

The LMS provides

an alternative computational method for determining the optimum filter

coefficients h(k) without explicitly computing the correlation sequences rxx(k)

and rdx(k). The algorithm is basically a recursive gradient (steepest-descent)

method that finds the minimum of ε and thus yields the optimum filter

coefficients.

We begin with the

arbitrary choice for initial values of h(k), say h0(k). For example we may

begin with h0(k)=0, 0 ≤ k ≤ N-1,then after each new input sample x(n)

enters the adaptive FIR filter, we compute the corresponding output, say y(n),

from the error signal e(n)=d(n)-y(n), and update the filter coefficients

according to the equation

hn(k)=hn-1(k)+

Δ.e(n).x(n-k), 0 ≤ k ≤

N-1,n=0,1,…..

where Δ is

called the step size parameter, x(n-k) is the sample of the input signal

located at the kth tap of the filter at time n, and e(n).x(n-k) is an

approximation (estimate) of the negative of the gradient for the kth filter

coefficient. This is the LMS recursive algorithm for adjusting the filter

coefficients adaptively so as to minimize the sum of squared errors ε.

The step size

parameter Δ controls the rate of convergence of the algorithm to the

optimum solution. A large value of Δ leads to a large step size adjustments

and thus to rapid convergence, while a small value of Δ leads to slower

convergence. However if Δ is made too large the algorithm becomes

unstable. To ensure stability, Δ must be chosen to be in the range

0<

Δ < 1/10NPx

Where N is length

of adaptive FIR filter and Px is the power in the input signal, which can be

approximated by

Px

≈ 1/(1+M)

**Figure 6.1:
LMS ALGORITHM FOR OEFICIENT ADJUSTMENT**

**6.3
ADAPTIVE FILTER FOR ESTIMATING AND SUPPRESSING AWGN INTERFERENCE**

Let us assume that

we have a signal sequence x(n) that consists of a desired signal sequence, say

w(n), computed by an AWGN interference sequence s(n). The two sequences are

uncorrelated

The

characteristics of interference allow us to estimate s(n) from past samples of

the sequence x(n)=s(n)+w(n) and to subtract the estimate from x(n).

The general

configuration of the interference suppression system is shown in the entire

block diagram of the system. The signal x(n) is delayed by D samples, where

delay is chosen sufficiently large so that the signal components w(n) and

w(n-D), which are contained in x(n) and x(n-D) respectively, are uncorrelated.

The out put of the adaptive FIR filter is the estimate

s(n)

=

The error signal

that is used in optimizing the FIR filter coefficients is e(n)=x(n)-s(n). The

minimization of the sum of squared errors again leads to asset of linear

equations for determining the optimum coefficients. Due to the delay D, the LMS

algorithm for adjusting the coefficients recursively becomes,

hn(k)=hn-1(k)+

Δ.e(n).x(n-k-D),k=0,1,…..N-1

**DEMODULAITON**

Function

of receiver consists of two parts:

A.

Demodulation

B.Detection

Demodulation is the act of extracting the original

information-bearing signal from a modulated carrier wave. A demodulator is an electronic circuit

used to recover the information content from the modulated carrier wave. *Coherent
Demodulation* is accomplished by demodulating using a local oscillator (LO)

which is at the same frequency and in phase with the original carrier. The

simplest form of

*non*

**–**is envelope detection. Envelope detection is a technique

*coherent*

demodulationdemodulation

that does not require a coherent carrier reference and can be used if

sufficient carrier power is transmitted.

Although the structure of a non-coherent receiver is

simpler than is a coherent receiver, it is generally thought that the

performance of coherent is superior to non-coherent in a typical additive white

Gaussian noise environment. Demodulation entails separating the received signal

into its constituent components. For a QPSK signal, these are cosine and sine

waveforms carrying the bit information. Detection is the process of determining

the sequence of ones and zeros those sinusoids represent.

**7.1 DEMODULATION**

The

first step is to multiply the incoming signal by locally generated sinusoids.

Since the incoming signal is a sum of sinusoids, and the receiver is a linear

system, the processing of the signal can be treated individually for both

components summed upon completion. Assuming the received signal is of the form

r(n)=A_{i}

cos(ω_{0}n)+A_{q} sin(ω_{0}n)

where

A_{i} and A_{q} are scaled versions of the b_{i} and b_{q}

bit stream used to modulate the signal at the transmitter. Due to cos(ω_{0}n)

input alone,

r_{ci}(n)= A_{i} cos(ω_{0}n)

cos(ω_{0}n+Ө)

and

r_{cq} (n)= A_{i} cos(ω_{0}n)

sin(ω_{0}n+Ө)

where Ө is the phase difference between incoming

signal and locally generated sinusoids. Similarly for sin(ω_{0}n)

portion of the input r(n),

r_{si}(n)= A_{i} sin(ω_{0}n)

cos(ω_{0}n+Ө)……….7.1

and

r_{sq}(n)= A_{i} sin(ω_{0}n)

sin(ω_{0}n+Ө)………..7.2

**7.2
SYNCHRONIZATION**

For

the received data to be interpreted and detected correctly there needs to be

coordination between the receiver and transmitter. Since they are not

physically connected, the receiver has no means of knowing the state of the

transmitter. This state includes both the phase argument of the modulator and

the bit timing of the transmitted data sequence. The receiver must therefore

extract the desired information from the received digital signal to achieve

synchronization. A common means of accomplishing synchronization is with a PLL.

A phase-locked loop or phase lock loop (PLL) is a control

system that generates a signal that has a fixed relation to the phase of a

“reference” signal. A phase-locked loop circuit responds to both the

frequency and the phase of the input signals, automatically raising or lowering

the frequency of a controlled oscillator until it is matched to the reference

in both frequency and phase.

PLL compares the frequencies of two signals and

produces an error signal which is proportional to the difference between the

input frequencies. The error signal is then low-pass filtered and used to drive

a voltage-controlled oscillator (VCO) which creates an output frequency. The

output frequency is fed through a frequency divider back to the input of the

system, producing a negative feedback loop. If the output frequency drifts, the

error signal will increase, driving the frequency in the opposite direction so

as to reduce the error. Thus the output is locked to the frequency at the other

input. This input is called the reference and is often derived from a crystal

oscillator, which is very stable in frequency. At first the received signal is

raised to 4^{th} power. Then it is passed through a 4^{th}

order band pass filter and frequency divider. Thus the two sinusoid outputs

used to demodulate the received signal are produced.

**7.3
DETECTION**

The

signals [equation (7.1) and (7.2)] are passed through corresponding envelop

detector and threshold comparator to obtain I data and Q data. An envelope detector is an electronic

circuit that takes a high-frequency signal as input, and provides an output

which is the “envelope” of the original signal. The capacitor in the

circuit stores up charge on the rising edge, and releases it slowly through the

resistor when the signal falls. The diode in series ensures current does not

flow backward to the input to the circuit. Then threshold comparators compare

the signals with their values and generate the I data and Q data. These are

recombined by switching device to form received bit stream.

**Figure 7.1:
DETECTION**

**7.4
AWGN Channel**

During

transmission, the signal undergoes various degrading and distortion effects as

it passes through the medium from transmitter to receiver.This medium is commonly referred to as the

channel. Channel effects include but are not limited to noise, interference,

linear and non linear distortion and attenuation. These effects are contributed

by a wide verity of sources including solar radiation, weather and signal from

adjacent channels. But many of the prominent effects originate from the

components in the receiver. While many of the effects can be greatly reduced by

good system design, careful choice of filter parameters and coordination of

frequency parameter usage with other users, noise and attenuation generally can

not be avoided and are the largest contributors to signal distortion.

The

most commonly used channel model to deal with noise is the additive white

Gaussian noise (AWGN) channel model. The name results because the noise is

simply added to the signal while the term white is used because the frequency

content is equal across the entire spectrum. In reality this type of noise does

not exists and is confined to a finite spectrum, but it is sufficiently useful

for systems whose bandwidth are small compared to the noise power spectrum.

When modeling a system across an AWGN channel, the noise must first be filtered

to the channel prior to addition.

**RESULTS**

**8.1
SIMULATION**

The

section describes the performance of QPSK Modulation for speech.The simulation

was done using MATLAB 7 platform.

All

codes for this chapter are contained in Appendix A. An adaptive filter is used

in these routines. All of the repeatedly used values such as cosine and sine

are retrieved from look up tables to reduce computation load.

**8.2
TRANSMITTER**

A

speech signal is transmitted through the entire system. In each case speech

signals are obtained from the internet. These are short segments of speech data

of 6-7 seconds. From the speech signal 30874 samples are taken.

These samples are then quantized. Here 4 bit PCM is used (as 8 bit or higher PCM

takes longer time during the simulation) to obtain a total of 123496 bits from

30874 samples.

The bits are divided into even bits and odd bits using flip flop.Here for simplicity and for the purpose of

better understanding only 8 bits are shown on the figure instead of 123496

bits. Consider that the bit sequence is 11000110.

The even bits (1010) are modulated using a carrier

signal (sine wave) and odd bits (1001) are modulated using the same carrier

signal with 90 degree phase shift (cosine wave). The modulation process is

explained explicitly in the previous sections. In the case of odd data cosine

wave represents 1 while cosine wave with 180 degree phase shift represents 0.

On the other hand in the case of even data sine wave represents 1 and sine wave

with 180 degree phase shift represents 0. The odd data and even data are

modulated separately in this way and then added using a linear adder to obtain

QPSK modulated signal. This signal is passed through a band pass filter and transmitted

through the channel

**8.3
Channel and receiver**

In

this system AWGN channel is considered. As the signal passes through the

channel it is corrupted by AWGN noise. AWGN command in MATLAB is used to

generate this noise. Here SNR is taken sufficiently large to avoid possibility

of bit errors. Bit error rate and the performance of the system depend highly

on the SNR which is discussed later in this chapter. To remove this AWGN

interference sequence from the received signal the signal is passed through an

adaptive filter. The adaptive filter uses LMS algorithm which is explained

explicitly in the previous sections. Then the desired signal is obtained.

This desired signal is then passed through the demodulation process. At first it is

passed through a PLL to obtain necessary carrier signal. Here for simplicity

the angle generated by PLL is considered zero. At one side this desired signal

is demodulated with sine wave to obtain even data while on the other side it is

demodulated by cosine wave to obtain odd data.

Then these signals are passed through corresponding envelop detector and threshold

comparator to obtain odd data and even data. When data is greater than .75 then

it detected as 1 on the other hand when data is less than .75 then it is

detected as 0. After that a switching device is used to combine odd data and

even data.

Then this bit stream is passed through the decoder and the received speech signal is

obtained. This received signal can be heard using soundsc command

Here theoretical E_{b}/N_{0}

vs. BER curve for QPSK is shown

**CONCLUSION**

In this project

the details of a digital communication system implementation using QPSK

modulation and adaptive equalization have been discussed. Pulse-code modulation (PCM)

is a digital representation of an analog signal where the magnitude of the

signal is sampled regularly at uniform intervals, then quantized to a series of

symbols in a numeric (usually binary) code. PCM** **can facilitate accurate reception even with

severe noise or interference. An adaptive

equalizer is an equalization filter that automatically adapts to

time-varying properties of the communication channel. It is frequently used

with coherent modulations. It is useful for estimating and suppressing AWGN

interference. Lastly,

QPSK is an efficient modulation scheme currently used by modem satellite

communication links.

We studied QPSK

modulation technique through out the project. Instead of using other modulation

techniques such MSK, 8-QPSK, 16-QPSK etc we used 4-QPSK in this project. QPSK

is a quaternary modulation method, while MSK is a binary modulation method. In QPSK, the I and Q

components may change simultaneously, allowing transitions through the origin.

In a hypothetical system with infinite bandwidth, these transitions occur

instantaneously; however, in a practical band-limited system (in particular, a

system using a Nyquist filter) these transitions take a finite amount of time.

This results in a signal with a non-constant envelope. MSK performed in such a

way that the transitions occur around the unit circle in the complex plane,

resulting in a true constant-envelope signal. Using 8-QPSK and 16-QPSK

techniques higher data rate and higher spectral efficiency can be achieved but

BER also increases. The performance of MSK,

8-QPSK, 16-QPSK techniques is better but implementation of these techniques is complex.

4-QPSK is simpler and easy to implement. Its spectral efficiency is not higher

than that of 8-QPSK, 16-QPSK but it

provides lower BER. In this project we performed the simulation of 4-QPSK

modulation technique using MATLAB platform accurately and without any error.

The system is flexible enough in accommodating any speech signal or analog

signal. Digital communication systems can be implemented using QPSK modulation.