Digital Communication Model
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 convert that
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 digital^{ }sequence
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 5bit
blocks. Since there are 32 distinct 5bit blocks, each letter may be mapped
into a distinct 5bit block with a few blocks left over for control or other
symbols. Similarly, uppercase letters, lowercase letters, and a great many
special symbols may be converted into 8bit 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 variablelength 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
pointtopoint communication systems and in networks. They are often treated in
an ad hoc way in pointtopoint 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 sample from 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 shorttime 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 noiselike signal is used to produce
consonants. ..or unvoiced sounds.
B. Linear Prediction
Model
In this section, an allpole 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 LevinsonDurbin
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 is is 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
waveforms M → ∞ provided
that the SNR per 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 discreteinput, 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 discretetime binary input
sequence and a discretetime 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
discretetime channel which is represented by the diagram shown in Fig 4.1.
This binaryinput, binaryoutput, 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 discreteinput, discreteoutput 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
inputoutput 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 bandlimited 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 onetoone mapping. In fact, each input information bit is ‘convolved’
with K1 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 K1 bits. Similarly, since it is involved in the
encoding of K1 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 Shiftkeying (ASK), Frequency
Shiftkeying(FSK),Phase Shiftkeying(PSK), Binary Phase Shiftkeying (BPSK) and
Quadrature Phase Shiftkeying(QPSK). We then talk about Quadrature Phase Shiftkeying(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 shiftkeying 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
shiftkeying is illustrated in figure below:
Figure 5.1: an ASK signal (below) and the
message (above)
In
order to generate an amplitude shiftkeyed (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 Shiftkeying
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 shiftkeyed signal is decoded by means of a
phaselocked loop (PLL) detector. The detector follows changes in frequency in
the FSK signal, and generates an output voltage proportional to the signal
ferquency.
The
phaselocked loop’s output also contains components at the two carrier
frequencies; a lowpass 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
for PSK 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 constant level. 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 shiftkeyed signal is decoded by means of a
squaring loop detector. This PSK Demodulator is shown in figure below:
5.4 BINARY PHASESHIFT 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 timevarying
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 wellknown 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 adjustedthat 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<N1}. 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 ≤ N1
r_{xx}(k)= 0 ≤
k ≤ N1
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 ≤
N1
and,
hence
rxx(km)=rdx(m), 0
≤ k ≤ N1
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 (steepestdescent)
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 ≤ N1,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)=hn1(k)+
Δ.e(n).x(nk), 0 ≤ k ≤
N1, n=0,1,…..
where Δ is
called the step size parameter, x(nk) is the sample of the input signal
located at the kth tap of the filter at time n, and e(n).x(nk) 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(nD), which are contained in x(n) and x(nD) 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)=hn1(k)+
Δ.e(n).x(nkD), k=0,1,…..N1


DEMODULAITON
Function
of receiver consists of two parts:
A.
Demodulation
B. Detection
Demodulation is the act of extracting the original
informationbearing 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–coherent
demodulation is envelope detection. Envelope detection is a technique
that does not require a coherent carrier reference and can be used if
sufficient carrier power is transmitted.
Although the structure of a noncoherent receiver is
simpler than is a coherent receiver, it is generally thought that the
performance of coherent is superior to noncoherent 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 phaselocked 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 phaselocked 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 lowpass filtered and used to drive
a voltagecontrolled 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 highfrequency 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 67 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 b