Download ber performance over fading channels diversity

BER PERFORMANCE OVER FADING CHANNELS
DIVERSITY COMBINING AND QAM TECHNIQUES
AyushKaushik(student)
Mrs.DeeptiSharma(Lecturer)
Dimple Tanwar(student)
Electronics and Communication Department
Ambuj Mani Chaudhary(student)
Inderprastha engineering college
FarheenBano(student)
Ghaziabad, India.
Electronics and Communication Department
INDERPRASTHA ENGINEERING COLLEGE
Abstract-In order to choose the most suitable
modulation, several criteria such as power efficiency,
bandwidth efficiency, and bit error rate are used for
evaluation. This paper focuses on error performance
of phase modulation schemesin different channel
conditions and on the method to reduce bit error rates
with the help of convolutional coding which is
extensively used in GSM cellular system's encoder. A
brief description of theoretical aspects of phase
modulation schemes commonly used in satellite
communications such as BPSK is given here along
with simulations carried out with the help of Matlab.
I.INTRODUCTION
In any phase modulation scheme the information is
expressed in terms of phase of the carrier. Phase of
the carrier signal is shifted according to the input
binary data. Two-state phase shift keying (PSK) is
called BPSK where the phase of the radio carrier is
set to 0 or π according to the value of the incoming
bit. Each bit of the digital signal produces a transmit
symbol with duration Ts, which is equal to the bit
duration Tb. Bit error rate (BER) of a communication
system is defined as the ratio of number of error bits
and total number of bits transmitted during a specific
period. It is the likelihood that a single error bit will
occur within received bits, independent of rate of
transmission. There are many ways of reducing BER.
Here, we focus on channel coding techniques.
A channel in mobile communications can be
simulated in many different ways. The main
considerations include the effect of multipath
scattering, fading and Doppler shift that arise
from the relative motion between the transmitter and
the receiver. In our simulations, we have considered
the two most commonly used channels: the Additive
White Gaussian Noise (AWGN) channel where the
noise gets spread over the whole spectrum of
frequencies and the Rayleigh fading channel.
Ghaziabad, India.
2.1 Factors affecting BER
• channel noise
• interference
• distortion
• bit synchronization problems
• attenuation
• Wireless multipath fading, etc
2.2 Analysis of 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:
analysis of
decoding error probability in case of non bursty bit
error on the transmission channel)
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%. In a noisy channel, the BER is often
expressed as a function of the normalized carrier-tonoise 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:
Returning to BER, we have the likelihood of a bit
misinterpretation
.
where is the threshold of decision, set to 0 when
We can use the average energy of the signal
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 bitinsertions 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.
II.MATHEMATICAL MODEL
The BER is the likelihood of a bit
misinterpretation due to electrical noise w(t).
Considering a x1(t)=A+w(t)
to find the final expression :
III. FADING
Fading is the term used to describe the rapid
fluctuations in the amplitude of the received radio
signal over a short period of time. Fading is a
common phenomenon in Mobile Communication
Channels, where it is caused due to the interference
between two or more versions of the transmitted
signals which arrive at the receiver at slightly
different times. The resultant received signal can vary
widely in amplitude and phase, depending on various
factors such as the intensity, relative propagation
time of the waves, bandwidth of the transmitted
signal etc.
A fading channel is a communication channel in
which deviation of the attenuation affecting a signal
over certain propagation media. In wireless systems
fading may either be due to multipath propagation
shadowing from obstacles affecting the wave
propagation.
bipolar NRZ transmission, we have
for a "1" and x0(t)= -A+w(t) for a "0". Each of
x1(t) and x0(t) has a period of T.
Knowing that the noise has a bilateral spectral
density of No/2 ,
A common example of multipath fading is the
experience of stopping at a traffic light and hearing
an FM broadcast degenerate into static, while the
signal is re-acquired if the vehicle moves only a
fraction of a meter. The loss of the broadcast is
caused by the vehicle stopping at a point where the
signal experienced severe destructive interference.
Cellular phones can also exhibit similar momentary
fades.
SLELCTION DIVERSITY
IV. RAYLEIGH FADING
Rayleigh fading is a statistical model for the
effect of a propagation environment on a radio signal,
such as that used by wireless devices.
Rayleigh fading models assume that the
magnitude of a signal that has passed through such a
transmission medium (also called a communications
channel) will vary randomly, or fade according to a
Rayleigh distribution — the radial component of the
sum of two uncorrelated Gaussian random variables.
Of the N received signals, the strongest signal is
selected. When the N signals are independent and
Rayleigh distributed, the expected diversity gain has
been shown to be , expressed as a power ratio.
Therefore, any additional gain diminishes rapidly
with the increasing number of channels. This is a
more efficient technique than selection combining.
Sometimes more than one combining technique is
used – for example, lucky imaging uses selection
combining to choose (typically) the best 10% images,
followed by equal-gain combining of the selected
images.
Zk = (Z1k, if |Z1k| > |Z2k|
Z2k, if |Z2k| > |Z1k|
V.DIVERSITY
One of the most efficient and simple
techniques to overcome the destructive effects of
fading is Diversity. Diversity is an efficient technique
to exploit the random nature of radio propagation by
finding methods to generate and extract independent
signal paths for communication. The concept behind
diversity is relatively simple if one signal path
undergoes a deep fade at a particular point of time,
another independent path may have a strong signal.
By having more than one path to select from, both the
instantaneous and average SNR can be improved in
the receiver by a large amount. There are various
types of diversity used in communication systems
operating over fading channels. They are:• Space Diversity.
• Frequency Diversity.
• Time Diversity.
• Polarization Diversity.
• Multipath Diversity.
EQUAL GAIN COMBINING
In Equal Gain Combining (EGC), all the received
signals are co-phased at the receiver and added
together without any weighting. The performance of
EGC
is only marginally inferior to the optimal maximal
ratio combiner. In case of a two-fold diversity
scheme, the combining equation is given by:
Zk = Z1k + Z2k
Whatever be
the
diversity
technique
employed, the receiver has to process the
diversity
signals obtained in a fashion that
maximizes the power efficiency of the system. There
are several possible diversity reception methods
employed in communication receivers. The most
common techniques are:
•Selection Diversity.
•Equal Gain Combining (EGC).
•Maximal Ratio Combining (MRC).
MAXIMAL RATIO COMBINING
In Maximal Ratio Combining (MRC), the signal
all the branches are co-phased and individually
weighed to provide the optimal SNR at the output.It
can be shown that the output SNR is maximized
when the signals in each of the diversity branches are
weighed by their own envelopes. In case of a twofold diversity scheme, the combining equation is
given by:
Zk = r1kZ1k + r2kZ2k
protection channel for automatic use by any faded
channel. Later examples include:
•
OFDM modulation in combination with
subcarrier inter leaving and forward error correction
•
Spread spectrum, for example frequency
hoping
Where, r1k and r2k represent the instantaneous
envelopes of the signals received at each of the
diversity branches.
TIME DIVERSITY
SPACE DIVERSITY
The signal is transmitted over several different
propagation paths. In the case of wired transmission,
this can be achieved by transmitting via multiple
wires. In the case of wireless transmission, it can be
achieved by antenna diversity using multiple
transmitter antennas (transmit diversity) and/or
multiple receiving antennas (reception diversity). In
the latter case, a diversity combining technique is
applied before further signal processing takes place.
If the antennas are far apart, for example at different
cellular base station sites or WLAN access points,
this is called macro diversity or site diversity. If the
antennas are at a distance in the order of
one wavelength, this is called micro diversity (STC).
FREQUENCY DIVERSITY
The signal is transmitted using several frequency
channels or spread over a wide spectrum that is
affected by frequency-selective fading. Middle-late
20th century microwave radio delay lines often used
several regular wide bands radio channels, and one
Multiple versions of the same signal are
transmitted at different time instants. Alternatively, a
redundant forward error correction code is added and
the message is spread in time by means of bitinterleaving before it is transmitted. Thus error
bits are avoided, which simplifies the error
correction.
POLARIZATION DIVERSITY
Multiple versions of a signal are transmitted and
received via antennas with different polarization.
A diversity combining technique is applied on the
receiver side.
MULTIPATH DIVERSITY
Multiuser diversity is obtained by opportunistic
user scheduling at either the transmitter or the
receiver. Opportunistic user scheduling is as follows:
at any given time, the transmitter selects the best user
among candidate receivers according to the qualities
of each channel between the transmitter and each
receiver. A receiver must feed back the channel
quality information to the transmitter using limited
levels of resolution, in order for the transmitter to
implement
Multiuser
diversity.
VI.QUADRATURE AMPLITUDE
MODULATION
Quadrature amplitude modulation (QAM) is both an
analog and a digital modulation scheme. It conveys
two analog message signals, or two digital bit
streams, by changing (modulating) the amplitudes of
two carrier waves, using the amplitude-shift keying
(ASK) digital modulation scheme or amplitude
modulation (AM) analog modulation scheme. The
two carrier waves, usually sinusoids, are out of phase
with each other by 90° and are thus called quadrature
carriers or quadrature components. The modulated
waves are summed, and the resulting waveform is a
combination of both phase-shift keying (PSK) and
amplitude-shift keying (ASK), or (in the analog case)
of phase modulation (PM) and amplitude modulation.
QAM Transmitter
Output using BPSK Modulation
First the flow of bits to be transmitted is split into
two equal parts: this process generates two
independent signals to be transmitted. They are
encoded separately just like they were in
an amplitude shift keying (ASK) modulator. The sent
signal can be expressed in the form:
where and are the voltages applied in response to
the symbol to the cosine and sine waves respectively.
Output using Diversity in BPSK Modulation
QAM Receiver
The receiver simply performs the inverse process
of the transmitter. Its ideal structure is shown in the
picture below with the receive filter's frequency
response :
Multiplying by a cosine (or a sine) and by a lowpass filter it is possible to extract the component in
phase (or in quadrature). Then there is only
an ASK demodulator and the two flows of data are
merged back.
Output using QAM Modulation
Output using 64 QAM
Output using 128 QAM
Comparing Outputs of BPSK and QAM
CONCLUSION
Output using 16 QAM
We have studied the effect of fading amplitude
and diversity combining techniques on the BPSK
over flat Rayleigh fading channels. The results
areobtained by averaging the conditional BER over
the jointdistribution of the fading and its estimate.
The exact BERexpressions are given by finite-range
integrals. Thus by diversity technique we can
improve our signal to noise ratio by three techniques
which one is suited the best.
We find that for 16-QAM and 64-QAM,
amplitude estimation error yields degradation in
average SNR, and combined amplitudephaseestimation error yields a greater degradation for
the systemparameters. Our results allow the designers
ofM-QAM to easily choose system parameters
tomeet their performance requirements under
reasonable channel conditions.
We have also found out various future aspects to
find out new techniques and device ways for better
communication.These techniques has shown us the
path for a lot more better communication methods
with an excellent accuracy and better efficiency.
Thus it has opened new ways for finding more
efficient techniques that will change the course of
future.
VII. REFERENCES
[1] D. Brennan, "Linear diversity combining
techniques", Proc. IRE, vol. 47, no. 6, pp.1075 1102 1959 .
[2] R.Price and P. E. Green, "A communication
technique for multipath channels", Proc. IEEE, vol.
46.
[3] G. L. Stu&uml,ber, Principles of Mobile
Communications, 1996 :Kluwer .
[4] J. W. Craig, "A new, simple, and exact result
for calculating the probability of error for twodimensional signal constellations", Proc. IEEE Milit.
Commun. Conf. MILCOM',91, pp.571 -575 1991.
[5] G. L. Turin, "Communication through noisy,
random-multipath channels", IRE Nat. Conv. Rec.,
pp.154 -166 1956 .