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CHAPTER 1
INTRODUCTION
OFDM is of great interest by researchers and research laboratories all over the world.
It has already been accepted for the new wireless local area network standards IEEE
802.11a, High Performance LAN type 2 (HIPERLAN/2) and Mobile Multimedia
Access Communication (MMAC) Systems. Also, it is expected to be used for wireless
broadband multimedia communications.Data rate is really what broadband is about.
The new standard specify bit rates of up to 54 Mbps. Such high rate imposes large
bandwidth, thus pushing carriers for values higher than UHF band. For instance,
IEEE802.11a has frequencies allocated in the 5- and 17- GHz bands. This project is
oriented to the application of OFDM to the standard IEEE 802.11a, following the
parameters established for that case.
OFDM can be seen as either a modulation technique or a multiplexing technique. One
of the main reasons to use OFDM is to increase the robustness against frequency
selective fading or narrowband interference. In a single carrier system, a single fade or
interferer can cause the entire link to fail, but in a multicarrier system, only a small
percentage of the subcarriers will be affected. Error correction coding can then be used
to correct for the few erroneous subcarriers. The concept of using parallel data
transmission and frequency division multiplexing was published in the mid-1960s.
In a classical parallel data system, the total signal frequency band is divided into N
nonoverlapping frequency subchannels. Each subchannel is modulated with a separate
symbol and then the N subchannels are frequency-multiplexed.It seems good to avoid
spectral overlap of channels to eliminate interchannel interference. However, this leads
to inefficient use of the available spectrum.To cope with the inefficiency, the ideas
proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels, in which, each carrying a signaling rate b is spaced b apart in frequency
to avoid the use of high-speed equalization and to combat impulsive noise and
multipath distortion, as well as to fully use the available bandwidth.
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1.1 The Principles of OFDM
Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier
transmission technique, which divides the bandwidth into many carriers; each one is
modulated by a low rate data stream. In term of multiple access technique, OFDM is
similar to FDMA in that the multiple user access is achieved by subdividing the
available bandwidth into multiple channels that are then allocated to users. However,
OFDM uses the spectrum much more efficiently by spacing the channels much closer
together. This is achieved by making all the carriers orthogonal to one another,
preventing interference between the closely spaced carriers.
Figure 1.1: Concept of OFDM signal: orthogonal multicarrier technique
versus conventional multicarrier technique
Pictorially it can be represented as shown in the figure (1) in the next page. The figure
shows the difference between the conventional non-overlapping multicarrier technique
and overlapping multicarrier modulation technique. As shown in figure 1, by using the
overlapping multicarrier modulation technique, we save almost 50% of bandwidth. To
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realize the overlapping multicarrier technique, however we need to reduce crosstalk
between subcarriers, which means that we want orthogonality between the different
modulated carriers. The orthogonality of the carriers means that each carrier has an
integer number of cycles over a symbol period. Due to this, the spectrum of each
carrier has a null at the center frequency of each of the other carriers in the system.
This results in no interference between the carriers, allowing then to be spaced as close
as theoretically possible. This overcomes the problem of overhead carrier spacing
required in FDMA. Each carrier in an OFDM signal has a very narrow bandwidth
(i.e.1kHz), thus the resulting symbol rate is low. This results in the signal having a
high tolerance to multipath delay spread, as the delay spread must be very long to
cause significant inter-symbol interference (e.g. > 500 sec).
1.2 OFDM Operation
1.2.1 Definition of Orthogonality Two periodic signals are orthogonal when
the integral of their product, over one period, is equal to zero. This is true of certain
sinusoids as illustrated in the equation( 1) and (2) below-
The carriers of an OFDM are sinusoids that meet this requirement because each one is
sa multiple of frequency. Each one has an integer number of cycles in the fundamental
period.
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1.2.2 Concept of DFT and FFT
When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency
domain results are a function of the time sampling period and the number of samples
as shown in Figure 2. 1 he fundamental frequency of the DFT is equal to 1/NT (1/total
n sample time). Each frequency represented in the DFT is an integer multiple of the
fundamental frequency. The maximum frequency that can be represented by a time
signal sampled at rate 1/T is fmax = 1/2T as given by the Nyquist sampling theorem.
This frequency is located in the center of the DFT points. All frequencies beyond that
point are images of the representative frequencies. The maximum frequency bin of the
DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT). The
IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the
DFT. It takes a signal defined by frequency components and converts them to a time
signal. The parameter mapping is the same as for the DFT. The time duration of the
IDFT time signal is equal to the number of DFT bins (N) times the sampling period
(T). It is perfectly valid to generate a signal in the frequency domain, and convert it to
a time domain equivalent for practical use. This is how modulation is applied in
OFDM. In practice FFT and IFFT are used in place of DFT and IDFT respectively as
they are faster than the later methods.
Figure 1.2:Parameter Mapping from Time to Frequency for the DFT
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1.3 Modulation
Modulation is the process of modifying some properties of the high frequency carrier
signal in accordance with the baseband signal. Binary data from the memory device or
from a digital processing stream is used as the modulating signal. The following steps
may be carried out in order to apply modulation to the carriers in OFDM:
Combine the binary data into symbols according to the number of bits/ symbols
selected.
Convert the serial symbols stream into parallel segments according to the
number of carrier and form the carrier symbol sequence.
Apply differential coding to each carrier symbol sequence.
Convert each symbol into complex phase representation.
Assign each carrier sequence to the appropriate IFFT bin, including complex
conjugate.
Take IFFT of the result.
Figure 1.3: OFDM modulator
1.4 Transmission and Reception
The key to the uniqueness and desirability of OFDM is the relationship between the
carrier frequencies and the symbol rate. Each carrier frequency is separated by a
multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT(symbols/sec).The
effect of the symbol rate on each OFDM carrier is to add a sin(x)/x shape to each
carriers spectrum. The nulls of the sin(x)/x (for each carrier) are at integer multiples
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of 1/NT [4] The peak (for each carrier) is at the carrier frequency k/NT. Therefore,
each carrier frequency is located at the nulls for all the other carriers. This means that
none of the carriers will interfere with each other during transmission, although their
spectrums overlap. The ability to space carriers so closely together is very bandwidth
efficient. In the process of transmission and reception it is essentially required to
linearly amplify the signals. This is a sort of disadvantage of the OFDM system.
1.5 Demodulation
This process is the juts reverse of the modulation process. It is carried out on the
receiver side of the system and is done in the frequency domain. The following steps
may be taken to demodulate the OFDM signal:
Partition the input stream into vectors representing each symbol period.
Take the FFT of each symbol period vector.
Extract the carrier FFT bins and calculate the phase of each.
Calculate the phase difference, from one symbol period to the next, for each
carrier.
Decode each phase into binary data.
Sort the data into appropriate order.
1.6 Guard Period
OFDM demodulation must be synchronized with the start and end of the transmitted
symbol period. If it is not, then ISI will occur (since information will be decoded and
combined for 2 adjacent symbol periods). ICI will also occur because orthogonality
will be lost (integrals of the carrier products will no longer be zero over the integration
period). To overcome this a guard period is inserted in the sequence such that the ISI
effect is eliminated. But still we have the problem of ICI because if the complete
period is not integrated then the orthogonality will be lost. As a result the guard
interval that is to be added should be the cyclic extension of the end of the symbol
transmitted during a period and it should be added in the front part of the next symbol.
The symbol length will increase but the integration can be done between anywhere in
the symbol since it is periodic extension only. Hence by this the ICI will also be
eliminated from the scene.
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CHAPTER 2
OFDM TRANSCEIVER
The block diagram of an OFDM transceiver is shown in Fig.(3) The basic component
will be discussed in the next few subsections.
2.1 OFDM Transmitter
The main components of OFDM transmitter are shown in Fig.(3). The randomizer is
used as random bit generator. The first three blocks are used for data coding and
interleaving. The coded bits will be mapped by the constellation modulator using Gray
codification, this way an + jbn values are obtained in the constellation of the
modulator. The serial to parallel converter converts the data bits from the serial form to
the parallel form. The Inverse Fast Fourier Transform (IFFT) transforms the signals
from the frequency domain to the time domain; an IFFT converts a number of complex
data points, of length that is power of 2, into the same number of points but in the time
domain. The number of subcarriers determines how many sub-bands the available
spectrum is split into . The Cyclic Prefix (CP) is a copy of the last N samples from the
IFFT, which are placed at the beginning of the OFDM frame to overcome ISI problem.
It is important to choose the minimum necessary CP to maximize the efficiency of the
system .
2.2 OFDM Receiver
The main blocks of OFDM receiver are observed in Fig.(3) The received signal goes
through the cyclic prefix removal and a serial-to-parallel converter. After that, the
signals are passed through an N-point fast Fourier transform to convert the signal to
frequency domain. The output of the FFT is formed from the first M samples of the
output. The demodulation can be made by DFT, or better, by FFT, that is it efficient
implementation that can be used reducing the time of processing and the used
hardware. FFT calculates DFT with a great reduction in the amount of operations,
leaving several existent redundancies in the direct calculation of DFT.
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Figure 2.1:OFDM Transceiver
2.3 Advantage and Disadvantage of OFDM:
After going through a discussion on OFDM in last few sections it is evident that
OFDM has certainly some advantage over the other multiple access techniques. The
OFDM scheme has following key advantages:
By allowing overlap of carriers it uses the spectrum very efficiently.
By dividing the channel into narrow band flat fading sub channels, OFDM is
more resistant to frequency selective fading than the single carrier system.
Eliminates ISI and ICI with the use of guard interval via cyclic prefix.
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Using adequate channel coding and interleaving one can recover symbols lost
due to frequency selectivity of the channel.
Channel equalization becomes simpler than single carrier system by using
adaptive equalization techniques.
In conjunction with differential modulation there is no need to implement a
channel estimator.
It is less sensitive to sample timing offset than the single carrier system.
Provides good protection against co-channel interference and impulsive
parasitic noise.Though the OFDM scheme has numerous advantages, there are
still some drawbacks in this scheme. They are indicated as below:
The OFDM signal has a high Peak to Average Power Ratio (PAPR)
It is more sensitive to carrier frequency offset and drift than the single carrier
systems dueto leakage in the DFT.
Phase noise and Image Rejection are also a problem in OFDM .
2.4 Application of OFDM
OFDM find application in many of the wireless LAN (WLAN)structures. It is a
general scheme used in the IEEE WLAN standards starting from 802.11a, 802.11b,
802.11g to even in 802.16 WLAN standards. Also HIPERLAN/2 wireless LAN
network uses this OFDM technique. Along with that they are mainly used in digital
audio broadcasting (DAB) and digital video broadcasting (DVB). These transmission
techniques combine with them advanced technology of high data compression and
efficient use of spectrum in transmission. Hence in these techniques OFDM plays a
very significant role.
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CHAPTER 3
SIGNAL-TO-NOISE RATIO
Signal-to-noise ratio (often abbreviated SNR or S/N) is a measure used in science and
engineering that compares the level of a desired signal to the level of
background noise. It is defined as the ratio of signal power to the noise power. A ratio
higher than 1:1 indicates more signal than noise. While SNR is commonly quoted for
electrical signals, it can be applied to any form of signal (such as isotope levels in
an ice core or biochemical signaling between cells).
The signal-to-noise ratio, the bandwidth, and the channel capacity of a communication
channel are connected by the ShannonHartley theorem.
Signal-to-noise ratio is sometimes used informally to refer to the ratio of
useful information to false or irrelevant data in a conversation or exchange. For
example, in online discussion forums and other online communities, off-topic posts
and spam are regarded as "noise" that interferes with the "signal" of appropriate
discussion.
3.1 Definition
Signal-to-noise ratio is defined as the power ratio between a signal (meaningful
information) and the background noise (unwanted signal):
where P is average power. Both signal and noise power must be measured at the same
or equivalent points in a system, and within the same system bandwidth. If the signal
and the noise are measured across the sameimpedance, then the SNR can be obtained
by calculating the square of the amplitude ratio:
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where A is root mean square (RMS) amplitude (for example, RMS voltage). Because
many signals have a very wide dynamic range, SNRs are often expressed using
the logarithmic decibel scale. In decibels, the SNR is defined as
S
which may equivalently be written using amplitude ratios as
The concepts of signal-to-noise ratio and dynamic range are closely related. Dynamic
range measures the ratio between the strongest un-distorted signal on a channel and the
minimum discernable signal, which for most purposes is the noise level. SNR
measures the ratio between an arbitrary signal level (not necessarily the most powerful
signal possible) and noise. Measuring signal-to-noise ratios requires the selection of a
representative orreference signal. In audio engineering, the reference signal is usually
a sine wave at a standardized nominal or alignment level, such as 1 kHz at
+4 dBu (1.228 VRMS).
SNR is usually taken to indicate an average signal-to-noise ratio, as it is possible that
(near) instantaneous signal-to-noise ratios will be considerably different. The concept
can be understood as normalizing the noise level to 1 (0 dB) and measuring how far
the signal 'stands out'.
3.2 Difference from conventional power
In Physics power (physics) of an ac signal is defined as
But in Signal Processing and Communication we usually assume that so
that usually we don't include that resistance term while measuring power or energy of
a signal. This usually causes some confusions among readers but the resistance term is
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not significant for operations performed in signal processing. Most of cases the power
of a signal would be
where 'A' is the amplitude of the ac signal. In some places people just use
as the constant term doesn't affect much during the calculations.
3.3 Alternative definition
An alternative definition of SNR is as the reciprocal of the coefficient of variation, i.e.,
the ratio of mean to standard deviation of a signal or measurement:
where is the signal mean or expected value and is the standard deviation of the
noise, or an estimate thereof. Notice that such an alternative definition is only useful
for variables that are always non-negative (such as photon counts and luminance).
Thus it is commonly used in image processing, where the SNR of an image is usually
calculated as the ratio of the mean pixel value to the standard deviation of the pixel
values over a given neighborhood. Sometimes SNR is defined as the square of the
alternative definition above.
The Rose criterion (named after Albert Rose) states that an SNR of at least 5 is needed
to be able to distinguish image features at 100% certainty. An SNR less than 5 means
less than 100% certainty in identifying image details.
Yet another alternative, very specific and distinct definition of SNR is employed to
characterize sensitivity of imaging systems; see signal to noise ratio (imaging).
Related measures are the "contrast ratio" and the "contrast-to-noise ratio".
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3.4 SNR for various modulation systems
3.4.1 Amplitude modulation
Channel signal-to-noise ratio is given by
where W is the bandwidth and ka is modulation index.
Output signal-to-noise ratio (of AM receiver) is given by
3.4.2 Frequency modulation
Channel signal-to-noise ratio is given by
Output signal-to-noise ratio is given by
3.5 Improving SNR
All real measurements are disturbed by noise. This includes electronic noise, but can
also include external events that affect the measured phenomenon wind, vibrations,
gravitational attraction of the moon, variations of temperature, variations of humidity,
etc.
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Figure 3.1: Recording of the noise of athermogravimetric analysis device
depending on what is measured and of the sensitivity of the device. It is often possible
to reduce the noise by controlling the environment. Otherwise, when the characteristics
of the noise are known and are different from the signals, it is possible to filter it or to
process the signal.
For example, it is sometimes possible to use a lock-in amplifier to modulate and
confine the signal within a very narrow bandwidth and then filter the detected signal to
the narrow band where it resides, thereby eliminating most of the broadband noise.
When the signal is constant or periodic and the noise is random, it is possible to
enhance the SNR by averaging the measurement. In this case the noise goes down as
the square root of the number of averaged samples.
3.6 Digital signals
When a measurement is digitised, the number of bits used to represent the
measurement determines the maximum possible signal-to-noise ratio. This is because
the minimum possible noise level is the error caused by thequantization of the signal,
sometimes called Quantization noise. This noise level is non-linear and signal-
dependent; different calculations exist for different signal models. Quantization noise
is modeled as an analog error signal summed with the signal before quantization
("additive noise").
This theoretical maximum SNR assumes a perfect input signal. If the input signal is
already noisy (as is usually the case), the signal's noise may be larger than the
quantization noise. Real analog-to-digital converters also have other sources of noise
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that further decrease the SNR compared to the theoretical maximum from the idealized
quantization noise, including the intentional addition of dither.
Although noise levels in a digital system can be expressed using SNR, it is more
common to use Eb/No, the energy per bit per noise power spectral density.
The modulation error ratio (MER) is a measure of the SNR in a digitally modulated
signal.
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CHAPTER 4
BIT ERROR RATE
In digital transmission, the number of bit errors is the number of received bits of
a data stream over a communication channel that have been altered due
to noise, interference, distortion or bit synchronization errors.
The bit error rate or bit error ratio (BER) is the number of bit errors divided by the
total number of transferred bits during a studied time interval. BER is a unitless
performance measure, often expressed as a percentage.
The bit error probability pe is the expectation value of the BER. The BER can be
considered as an approximate estimate of the bit error probability. This estimate is
accurate for a long time interval and a high number of bit errors.
Example:
As an example, assume this transmitted bit sequence:
0 1 1 0 0 0 1 0 1 1,
and the following received bit sequence:
0 0 1 0 1 0 1 0 0 1,
The number of bit errors (the underlined bits) is in this case 3. The BER is 3 incorrect
bits divided by 10 transferred bits, resulting in a BER of 0.3 or 30%.
4.1 Factors affecting the BER
In a communication system, the receiver side BER may be affected by transmission
channel noise, interference, distortion, bitsynchronization problems, attenuation,wirele
ss multipath fading, etc.
The BER may be improved by choosing a strong signal strength (unless this causes
cross-talk and more bit errors), by choosing a slow and robust modulation scheme
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or line coding scheme, and by applying channel codingschemes such as
redundant forward error correction codes.
The transmission BER is the number of detected bits that are incorrect before error
correction, divided by the total number of transferred bits (including redundant error
codes). The information BER, approximately equal to the decoding error probability,
is the number of decoded bits that remain incorrect after the error correction, divided
by the total number of decoded bits (the useful information). Normally the
transmission BER is larger than the information BER. The information BER is
affected by the strength of the forward error correction code.
4.2 Analysis of the BER
The BER may be analyzed using stochastic computer simulations. If a simple
transmission channel model and data source model is assumed, the BER may also be
calculated analytically. An example of such a data source model is
the Bernoulli source.
Examples of such simple channel models are:
Binary symmetric channel (used in analysis of decoding error probability in
case of non-bursty bit errors on the transmission channel)
Additive white gaussian noise (AWGN) channel without fading.
A worst case scenario is a completely random channel, where noise totally dominates
over the useful signal. This results in a transmission BER of 50% (provided that
a Bernoulli binary data source and a binary symmetrical channel are assumed, see
below).
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Figure 4.1: Bit-error rate curves for BPSK, QPSK, 8-PSK and 16-PSK, AWGN channel.
In a noisy channel, the BER is often expressed as a function of the normalized carrier-
to-noise ratio measure denoted Eb/N0, (energy per bit to noise power spectral density
ratio), or Es/N0 (energy per modulation symbol to noise spectral density). For
example, in the case of QPSK modulation and AWGN channel, the BER as function of
the Eb/N0 is given by: .
People usually plot the BER curves to describe the functionality of a digital
communication system. In optical communication, BER(dB) vs. Received
Power(dBm) is usually used; while in wireless communication, BER(dB) vs. SNR(dB)
is used. Measuring the bit error ratio helps people choose the appropriate forward error
correction codes. Since most such codes correct only bit-flips, but not bit-insertions or
bit-deletions, the Hamming distance metric is the appropriate way to measure the
number of bit errors. Many FEC coders also continuously measure the current BER.
A more general way of measuring the number of bit errors is the Levenshtein distance.
The Levenshtein distance measurement is more appropriate for measuring raw channel
performance before frame synchronization, and when using error correction codes
designed to correct bit-insertions and bit-deletions, such as Marker Codes and
Watermark Codes.
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4.3 Bit error rate tester
A bit error rate tester (BERT), also known as a bit error ratio tester or bit error rate test
solution (BERTs) is electronic test equipment used to test the quality of signal
transmission of single components or complete systems.
The main building blocks of a BERT are:
Pattern Generator, which transmits a defined test pattern to the DUT or test
system.
Error detector connected to the DUT or test system, to count the errors
generated by the DUT or test system.
Clock signal generator to synchronize the pattern generator and the error
detector.
Digital communication analyser is optional to display the transmitted or
received signal.
Electrical-optical converter and optical-electrical converter for testing optical
communication signals.
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CHAPTER 5
OFDM SIMULINK MODEL
Figure 5.1: OFDM simulink model
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5.1 Quadrature Amplitude Modulation
In general, QAM is superior to CPM when a linear amplifier is used. The spectral
efficiency of CPM is lower than that of linear modulation due to the loss of one degree
of freedom (amplitude). However, CPM systems can use power efficient nonlinear
amplifiers because of the constant envelope characteristic, while nonlinear
amplification greatly affects QAM. In this thesis, Monte Carlo methods are employed
to evaluate the performance of QAM and CPM systems over different channels. We
also compare QAM schemes' performance to CPM schemes in the presence of a
nonlinear amplifier.
Figure shows a block diagram of the QAM modulation system under con- sideration.
The key characteristics of the system are:
Turbo codes are used in the system.
It is a multihop system.
It can provide high speed data transmission over an AWGN channel and
frequency selective fading channels.
The synchronizer module provides symbol and carrier frequency
synchronization.
The details of each module in the QAM system will be discussed in the following
section. There is an additional difference between the QAM system and the CPM
system, namely, the CPM system does not have a baseband filter nor does it has a
synchronizer.
s
Figure 5.2: QAM transceiver system
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5.2 QAM Transmitter System
The block diagram of a QAM transmitter is shown in Figure. The information
sequence u is encoded into a code sequence c by the channel encoder. The coded bits c
are then interleaved at the bit level to produce the sequence v. The interleaved bits are
then modulated to produce 16-QAM or 32-QAM symbols. Physical hops are formed
by adding pilots in the middle of a block of data symbols. Finally, the hops are filtered
with a baseband filter to meet the requirements of the spectrum mask and amplified by
a nonlinear high power amplifier.
Figure 5.3 : QAM transmitter system
5.3 Bit Interleaver
The next stage in the modulation chain is the interleaving stage. The bit interleaver
spreads the coded bits so that bits that are close to each other after encoding are not
close during transmission. An S-random interleaver is used. The size of the bit
interleaver is 4108 bits (one turbo codeword) when the rate R is 1=2 or 5462 bits when
the rate R is 3=4.
5.4 Physical Hop
The QAM system is a multi-hop system, in which a turbo codeword is separated into 8
hops or 16 hops and each hop is transmitted on a different carrier frequency. The
physical hop format is illustrated in Figure 3.2.3. After the interleaver, some additional
zero bits are inserted at the end of the data bits to make each physical frame have the
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same number of QAM symbols and to insure that 8 or 16 physical hops make up a
single codeword. Code bits are grouped into binary 4-tuples or 5-tuples and are
modulated using 16-QAM or 32-QAM methods. The outputs of the modulator are
separated into 8 or 16 hops and a pilot sequence is inserted into the middle of each
hop.3 The pilots will be used in synchronization and channel estimation.
Figure 5.4: Physical Hop Structure
5.5 Baseband Filter
A 64th-order root raised cosine (RRC) filter with roll-off parameter 0:25 is used in the
simulation. The filter works at a sample rate of 4 * fsymbol, where fsymbol is the
symbol rate.
5.6 Receiver System Description
Figure 5.5: QAM Receiver Diagram
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A block diagram of the receiver is shown in Figure(10). The received signals are first
sampled at the sampling rate 4fsymbol. The synchronizer then filters the discrete time
signal r(nTs) with a bank of matched filters to recover the symbol timing. The channel
estimator estimates the channel impulse response H(n) using the pilot sequence. The
pilots are also used to estimate the carrier frequency. The matched filter output
y(kTsym) is equalized and demapped into log-likelihood ratios for each encoded bit.
Finally, the turbo decoder accepts the log-likelihood ratios and executes the iterative
decoding algorithm to produce an estimate of the data bits.
5.7 Synchronizer
Symbol timing synchronization is designed to recover data from a digitally modulated
waveform. In the system under evaluation, a polyphase filterbank is used for symbol
timing synchronization. The synchronizer filters the discrete time signal r(nTs) with a
bank of matched filters to recover the symbol timing.
5.8 Turbo Decoder
In the decoding module, the BCJR algorithm is used for each component decoder. In
one decoding iteration, the computational complexity is proportional to the number of
states of the component encoder. The component encoder of the 3GPP turbo code has
8 states. The component encoders of the multiple turbo code 3BNA4 and 3ACC-1FF
have 4 and 2 states, respectively. Since the encoders of multiple turbo codes have a
small number of states, decoding complexity is effectively reduced.
There are several choices for the decoding structure through which the constituent
decoders exchange information. We selected the extended serial structure (Fig), since
it yields the best performance for a given number of iterations. In the extended serial
structure, the most recent extrinsic information from all the other decoders are
combined to form the a priori information provided to the current decoder.
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Figure 5.6: Extended Serial Decoder Structure
5.9 CPM Transmitter
A block diagram of the CPM system is shown in Figure . We employ highly
bandwidth efficient CPM with the following key features.
Binary signaling is used, i.e., M = 2.
It uses rectangular pulse shaping, and the length of the shaping function is larger
than 1.So the schemes used in the simulation are partial response CPM.
A small modulation index is used to improve the spectral efficiency.
Figure 5.7: System Block Diagram
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CHAPTER 6
COMPARISON OF QAM AND CPM
The ultimate goal of modulation is to transport message signals through a radio
channel with the best possible quality while occupying minimum bandwidth in the
radio spectrum and requiring minimum signal power level. A desirable modulation
scheme should be spectrally efficient, provides low bit error rates (BER) at a low
power level, performs well under various types of channel impairments, and should be
easy and cost-effective to implement. However, it is practically impossible to find a
modulation scheme that can simultaneously satisfy all these requirements. For
example, frequency modulation (FM) is power efficient while amplitude modulation
(AM) is bandwidth efficient. There is an unavoidable tradeoff when selecting a
modulation scheme. The choice of an appropriate modulation scheme depends on the
requirements of the particular application, such as power and bandwidth limitations.
6.1 Choice of Digital Modulation
Power efficiency and spectral efficiency are two important measures used to evaluate
the performance of a modulation scheme. Given the hostile conditions that include
thermal noise, fading, and multipath in a mobile radio channel, it is often necessary to
increase the signal power to provide an acceptable data transmission. However, the
amount by which the signal power should be increased to obtain an acceptable bit error
probability depends on the particular type of modulation employed. Power efficiency
characterizes the ability of a modulation scheme to make the tradeoff between the BER
performance and the required signal power level.
Spectral efficiency reflects how efficiently a modulation scheme utilizes the allocated
bandwidth. In general, increasing the data rate implies decreasing the pulse width of a
digital symbol, which, in turn, increases the bandwidth of the signal. Nevertheless,
some modulation schemes perform better than others in making this tradeoff. For
example, linear modulation schemes are more spectral efficient then nonlinear
modulation schemes.
Besides power and bandwidth efficiency, other factors also affect the choice of a
modulation scheme. The issue of amplifier efficiency is essential in the design of a
portable terminal. Thus, constant envelope modulation schemes are favorable since
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they can use power efficient nonlinear amplifiers. The complexity of system
implementation is another important consideration. With more complicated systems,
come more power consumption and longer processing delay.
In the design of a communication system, there is always a tradeoff between power
and spectral efficiency. Different modulation schemes have different characteristics
that call for different levels of the tradeoff between power and spectral efficiency.
When using a linear power amplifier, QAM is always superior to CPM. However,
QAM will have performance degradation if a nonlinear amplifier is used; in contrast, a
CPM system will not be affected as much by amplifier nonlinearities. As a result, we
have to reduce the spectral efficiency to compensate for the loss in power efficiency
for a QAM system; in contrast, the energy efficiency of a CPM system can be
maximized while keeping the spectrum efficiency the same.
Figure 6.1: Bandwidth efficiency
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CHAPTER 7
OFDM Simulink Model Using 16 QAM Modulation
Figure 7.1: OFDM Simulink Model using 16 QAM Modulation technique
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7.1 Bernoulli Binary Generator
The Bernoulli Binary Generator block generates random binary numbers using a
Bernoulli distribution. The Bernoulli distribution with parameter p produces zero with
probability p and one with probability 1-p. The Bernoulli distribution has mean value
1-p and variance p(1-p). The Probability of a zero parameter specifies p, and can be
any real number between zero and one.
Figure 7.2 : Bernoulli Binary Generator
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7.2 Convolutional Encoder
The Convolutional Encoder block encodes a sequence of binary input vectors to
produce a sequence of binary output vectors. This block can process multiple symbols
at a time.
If the encoder takes k input bit streams (that is, it can receive 2k possible input
symbols), the block input vector length is L*k for some positive integer L. Similarly, if
the encoder produces n output bit streams (that is, it can produce 2n possible output
symbols), the block output vector length is L*n. This block accepts a column vector
input signal with any positive integer for L. For both its inputs and outputs for the data
ports, the block supports double, single, boolean, int8, uint8, int16, uint16, int32,
uint32, and ufix1. The port data types are inherited from the signals that drive the
block. The input reset port supports double and boolean typed signals.
Figure 7.3 : convolution encoder
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Specifying the Encoder -To define the convolutional encoder, use the Trellis
structure parameter. This parameter is a MATLAB structure whose format is described
in the Trellis Description of a Convolutional Encoder section of the Communications
Toolbox documentation. You can use this parameter field in two ways:
If you have a variable in the MATLAB workspace that contains the trellis
structure, enter its name in the Trellis structure parameter. This way is
preferable because it causes Simulink to spend less time updating the diagram
at the beginning of each simulation, compared to the usage described next.
If you want to specify the encoder using its constraint length, generator
polynomials, and possibly feedback connection polynomials, use a poly2trellis
command in the Trellis structure parameter. For example, to use an encoder
with a constraint length of 7, code generator polynomials of 171 and 133 (in
octal numbers), and a feedback connection of 171 (in octal), set the Trellis
structure parameter to poly2trellis(7,[171 133],171).
7.3 Matrix Interleaver
The Matrix Interleaver block performs block interleaving by filling a matrix with the
input symbols row by row and then sending the matrix contents to the output port
column by column.The Number of rows and Number of columns parameters are the
dimensions of the matrix that the block uses internally for its computations. This block
accepts a column vector input signal. The number of elements of the input vector must
be the product of Number of rows and Number of columns. The block accepts the
following data types: int8, uint8, int16, uint16, int32, uint32, boolean, single, double,
and fixed-point. The output signal inherits its data type from the input signal.
Number of rows :
The number of rows in the matrix that the block uses for its computations.
Number of columns :
The number of columns in the matrix that the block uses for its computations.
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Figure 7.4 : Matrix Interleaver
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7.4 General Block Interleaver
The General Block Interleaver block rearranges the elements of its input vector
without repeating or omitting any elements. If the input contains N elements, then the
Elements parameter is a column vector of length N. The column vector indicates the
indices, in order, of the input elements that form the length-N output vector; that is,
Output(k) = Input(Elements(k))
for each integer k between 1 and N. The contents of Elements must be integers
between 1 and N, and must have no repetitions. Both the input and the Elements
parameter must be column vector signals. This block accept the following data types:
int8, uint8, int16, uint16, int32, uint32, boolean, single, double, and fixed-point. The
output signal inherits its data type from the input signal.
Figure 7.5 : General Block Interleaver
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7.5 Rectangular QAM Modulator Baseband
The Rectangular QAM Modulator Baseband block modulates using M-ary quadrature
amplitude modulation with a constellation on a rectangular lattice. The output is a
baseband representation of the modulated signal. This block accepts a scalar or column
vector input signal. For information about the data types each block port supports, see
Supported Data Types.
M-ary number-:The number of points in the signal constellation. It must have
the form 2K for some positive integer K.
Input type: Indicates whether the input consists of integers or groups of bits.
Constellation ordering: Determines how the block maps each symbol to a
group of output bits or integer. Selecting User-defined displays the field
Constellation mapping, which allows for user-specified mapping.
Constellation mapping: This parameter is a row or column vector of size M
and must have unique integer values in the range [0, M-1]. The values must be
of data type double. The first element of this vector corresponds to the top-
leftmost point of the constellation, with subsequent elements running down
column-wise, from left to right. The last element corresponds to the bottom-
rightmost point. This field appears when User-defined is selected in the drop-
down list Constellation ordering.
Normalization method : Determines how the block scales the signal
constellation. Choices are Min. distance between symbols, Average Power, and
Peak Power.
Minimum distance : The distance between two nearest constellation points.
This field appears only when Normalization method is set to Min. distance
between symbols.
Average power, referenced to 1 ohm (watts) : The average power of the
symbols in the constellation, referenced to 1 ohm. This field appears only
when Normalization method is set to Average Power.
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Peak power, referenced to 1 ohm (watts) : The maximum power of the
symbols in the constellation, referenced to 1 ohm. This field appears only when
Normalization method is set to Peak Power.
Phase offset (rad) : The rotation of the signal constellation, in radians.
Output data type : The output data type can be set to double, single, Fixed-
point, User-defined, or Inherit via back propagation. Setting this parameter to
Fixed-point or User-defined enables fields in which you can further specify
details. Setting this parameter to Inherit via back propagation, sets the output
data type and scaling to match the following block.
Output word length : Specify the word length, in bits, of the fixed-point
output data type. This parameter is only visible when you select Fixed-point for
the Output data type parameter.
Figure 7.6 : Rectangular QAM Modulator Baseband
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7.6 NORMALIZE
Figure 7.7 : Normalize
7.7 OFDM Transmitter
Figure 7.8 : OFDM Transmitter
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7.8 AWGN Channel
The AWGN Channel block adds white Gaussian noise to a real or complex input
signal. When the input signal is real, this block adds real Gaussian noise and produces
a real output signal. When the input signal is complex, this block adds complex
Gaussian noise and produces a complex output signal. This block inherits its sample
time from the input signal. This block uses the Signal Processing Blockset Random
Source block to generate the noise. Random numbers are generated using the Ziggurat
method. The Initial seed parameter in this block initializes the noise generator. Initial
seed can be either a scalar or a vector whose length matches the number of channels in
the input signal. For details on Initial seed, see the Random Source block reference
page in the Signal Processing Blockset documentation set. This block accepts a scalar-
valued, vector, or matrix input signal with a data type of type single or double. The
output signal inherits port data types from the signals that drive the block.
Relationship Among Eb/No, Es/No, and SNR Modes
For complex input signals, the AWGN Channel block relates Eb/N0, Es/N0, and SNR
according to the following equations:
Es/N0 = (Tsym/Tsamp) SNR
Es/N0 = Eb/N0 + 10log10(k) in dB
where
Es = Signal energy (Joules)
Eb = Bit energy (Joules)
N0 = Noise power spectral density (Watts/Hz)
Tsym is the Symbol period parameter of the block in Es/No mode
k is the number of information bits per input symbol
Tsamp is the inherited sample time of the block, in seconds
For real signal inputs, the AWGN Channel block relates Es/N0 and SNR according to
the following equation:
Es/N0 = 0.5 (Tsym/Tsamp) SNR
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Note that the equation for the real case differs from the corresponding equation for the
complex case by a factor of 2. This is so because the block uses a noise power spectral
density of N0/2 Watts/Hz for real input signals, versus N0 Watts/Hz for complex
signals.
Figure 7.9 : AWGN Channel
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7.9 Spectrum Scope
Display mean-square spectrum or power spectral density of each input signal The
Spectrum Scope block computes and displays the mean-square spectrum or power
spectral density of each input signal. The input can be a vector or a matrix.
Figure 7.10 : Spectrum Scope
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7.10 OFDM Receiver Pilots
Figure 7.11 : OFDM Receiver Pilots
7.11 Rectangular QAM Demodulator Baseband
The Rectangular QAM Demodulator Baseband block demodulates a signal that was
modulated using quadrature amplitude modulation with a constellation on a
rectangular lattice. The signal constellation has M points, where M is the M-ary
number parameter. M must have the form 2K for some positive integer K. The block
scales the signal constellation based on how you set the Normalization method
parameter
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Figure 7.12 : Rectangular QAM Demodulator Baseband
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M-ary numbe: The number of points in the signal constellation. It must have
the form 2K for some positive integer K.
Normalization method :Determines how the block scales the signal
constellation. Choices are Min. distance between symbols, Average Power, and
Peak Power.
Minimum distance :This parameter appears when Normalization method is
set to Min. distance between symbols. The distance between two nearest
constellation point.
Average power, referenced to 1 ohm (watts) :The average power of the
symbols in the constellation, referenced to 1 ohm. This field appears only when
Normalization method is set to Average Power.
Peak power, referenced to 1 ohm (watts) :The maximum power of the
symbols in the constellation, referenced to 1 ohm. This field appears only when
Normalization method is set to Peak Power.
Phase offset (rad):The rotation of the signal constellation, in radians.
Constellation ordering:Determines how the block assigns binary words to
points of the signal constellation. More details are on the reference page for the
Rectangular QAM Modulator Baseband block.
7.12 General Block Deinterleaver
The General Block Deinterleaver block rearranges the elements of its input vector
without repeating or omitting any elements. If the input contains N elements, then the
Elements parameter is a column vector of length N. The column vector indicates the
indices, in order, of the output elements that came from the input vector. That is, for
each integer k between 1 and N,
Output(Elements(k)) = Input(k)
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The Elements parameter must contain unique integers between 1 and N.
Both the input and the Elements parameter must be column vector signals.
This block accept the following data types: int8, uint8, int16, uint16, int32, uint32,
boolean, single, double, and fixed-point. The output signal inherits its data type from
the input signal.
Figure 7.13 : General Block Deinterleaver
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7.13 Matrix Deinterleaver
The Matrix Deinterleaver block performs block deinterleaving by filling a matrix with
the input symbols column by column and then sending the matrix contents to the
output port row by row. The Number of rows and Number of columns parameters
are the dimensions of the matrix that the block uses internally for its computations.
This block accepts a column vector input signal. The length of the input vector must be
Number of rows times Number of columns.
The block accepts the following data types: int8, uint8, int16, uint16, int32, uint32,
boolean, single, double, and fixed-point. The output signal inherits its data type from
the input signal.
Figure 7.14 : Matrix Deinterleaver
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7.14 Viterbi Decoder
The Viterbi Decoder block decodes input symbols to produce binary output symbols.
This block can process several symbols at a time for faster performance. If the
convolutional code uses an alphabet of 2n possible symbols, this block's input vector
length is L*n for some positive integer L. Similarly, if the decoded data uses an
alphabet of 2k possible output symbols, this block's output vector length is L*k.
Figure 7.15 : Viterbi Decoder
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Trellis structure :MATLAB structure that contains the trellis description of
the convolutional encoder. Use the same value here and in the corresponding
Convolutional Encoder block.
Punctured code :Select this check box to specify a punctured input code. The
field, Punctured code, appears.
Puncture vector :Constant puncture pattern vector used at the transmitter
(encoder). The puncture vector is a pattern of 1s and 0s, where the 0s indicate
the punctured bits. This field appears when the check box Punctured code is
selected. Enable erasures input port :When you check this box, the decoder
opens an input port labeled Era. Through this port, you can specify an erasure
vector pattern of 1s and 0s, where the 1s indicate the erased bits. For these
erasures in the incoming data stream, the decoder does not update the branch
metric. The widths and the sample times of the erasure and the input data ports
must be the same. The erasure input port can be of data type double or
Boolean.
Decision type :Specifies the use of Unquantized, Hard Decision, or Soft
Decision for the branch metric calculation.Unquantized decision uses the
Euclidean distance to calculate the branch metrics. Soft Decision and Hard
Decision use the Hamming distance to calculate the branch metrics, where
Number of soft decision bits equals 1.
Number of soft decision bits :The number of soft decision bits used to
represent each input. This field is active only when Decision type is set to Soft
Decision.
Error if quantized input values are out of range :Check this box to throw an
error when quantized input values are out of range. This check box is active
only when Decision type is set to Soft Decision or Hard Decision.
Traceback depth :The number of trellis branches used to construct each
traceback path.
Operation mode :Method for transitioning between successive input frames:
Continuous, Terminated, and Truncated.
Enable reset input port :When you check this box, the decoder opens an input
port labeled Rst. Providing a nonzero input value to this port causes the block
to set its internal memory to the initial state before processing the input data.
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7.15 Error Rate Calculation
The Error Rate Calculation block compares input data from a transmitter with input
data from a receiver. It calculates the error rate as a running statistic, by dividing the
total number of unequal pairs of data elements by the total number of input data
elements from one source. Use this block to compute either symbol or bit error rate,
because it does not consider the magnitude of the difference between input data
elements. If the inputs are bits, then the block computes the bit error rate. If the inputs
are symbols, then it computes the symbol error rate.
Figure 7.16 : Error Rate Calculation
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Receive delay Number of samples by which the received data lags behind the
transmitted data. (If Tx or Rx is a vector, then each entry represents a sample.)
Computation delay :Number of samples that the block should ignore at the
beginning of the comparison.
Computation mode :Either Entire frame, Select samples from mask, or Select
samples from port, depending on whether the block should consider all or only
part of the input frames.
Selected samples from frame :A vector that lists the indices of the elements of
the Rx frame vector that the block should consider when making comparisons.
This field appears only if Computation mode is set to Select samples from
mask.
Output data :Either Workspace or Port, depending on where you want to send
the output data.
Variable name :Name of variable for the output data vector in the base
MATLAB workspace. This field appears only if Output data is set to
Workspace.
Reset port :If you check this box, then an additional input port appears, labeled
Rst.
Stop simulation :If you check this box, then the simulation runs only until this
block detects a specified number of errors or performs a specified number of
comparisons, whichever comes first.
Target number of errors :The simulation stops after detecting this number of
errors. This field is active only if Stop simulation is checked.
Maximum number of symbols :The simulation stops after making this
number of comparisons. This field is active only if Stop simulation is checked.
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CHAPTER 8
OFDM PLOTS
8.1 OFDM Transmitter Scatter plot
Figure 8.1 : OFDM Transmitter Scatter Plot
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8.2 OFDM Receiver Scatter Plot
Figure 8.2 : OFDM Receiver Scatter Plot
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8.3 Bandwidth Spectrum
Figure 8.3 : Bandwidth Spectrum
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8.4 BER VS SNR Graph of 16 QAM
Figure 8.4 : BER VS SNR Graph of 16 QAM
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8.5 Bit Error Rate Analysis Tool
Figure 8.5: Bit Error Rate Analysis Tool
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CHAPTER 9
RESULTS
Sample time = 4e-6/144
SNR value = 15 dB
The result is found after simulation
Error rate = 2.777e-006
Number of errors = 1
Number of bits = 3.601e + 005
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CHAPTER 10
CONCLUSION
Here we have analyzed the performance of different modulation schemes with OFDM
technique in Rayleigh fading channel with gray coded bit mapping and without gray
mapping. By using higher order modulation scheme (like 16- QAM, 64-QAM, 16-
PSK, 64-PSK) with OFDM technique in Rayleigh channel, we can transmit more data
rate. In both the cases we get better performance for QAM modulation scheme. So, at
this stage we can easily conclude that QAM has got better performance than PSK and
use of gray bit mapping enhances this performance even more.
M-ary modulation techniques provide better bandwidth efficiency than other low level
modulation Techniques . As the value of M i.e. number of bits in symbol increases
bandwidth utilization is increases. Also as communication range increases between a
transmitter & receiver lower order modulation techniques are preferred over higher
order modulation techniques . In this paper we have studied the error rate performance
of different MPSK modulation schemes in normal AWGN channel & multipath
Rayleigh fading channel with the help of MATLAB/Simulink, the most powerful and
user friendly tool for various communication systems, digital signal processing system,
control systems etc which provides easy simulation and observation of the model
before it is physically made.According to the various graphs provided in this paper we
can conclude that error rate is much higher in fading channel than normal AWGN
channel & the error rate is further increases with the value of M i.e. number of bits in
symbol increases in both AWGN & multipath fading channel. High level modulation
techniques are always preferred for high data rate. As error rate increases with the
value of M so low level of M-ary modulation techniques should be used for data
transmission over short distance and lower level of modulation technique like QPSK
should be preferred over longer distance. So to provide reliable communication along
with higher data rates there should be a tradeoff between error rate & data rate.
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56
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