‫دانشکده مهندس ی کامپیوتر‬
‫شبکه‌های‌بی‌سیم‌(‪)40-873‬‬
‫مخابرات بیسیم‬
‫‪1‬‬
‫نیمسال ّ‬
‫دوم ‪92-93‬‬
‫افشین ّ‬
‫همتیار‬
Digital Communication over Radio Channel
• Radio spectrum is shared in wireless network.
• Nodes share a radio spectrum of bandwidth W.
• Radio spectrum is centered at carrier frequency, fc.
• It is assumed that fc >> W.
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Simple Binary Modulation/Detection
• Digital communication is achieved over the given radio
spectrum by modulating a sequence of pulses by the given bit
pattern.
• Simple modulator:
• If bit is 1: each pulse in pulse train is multiplied by
• If bit is 0: each pulse in pulse train is multiplied by
.
.
• The energy of the modulated pulse becomes Es.
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Additive White Gaussian Noise
• As the modulated signal passes through the channel, it is
corrupted by noise.
• This is taken to be zero mean Additive White Gaussian Noise
(AWGN), which means that noise just adds to the signal and
is a Gaussian random process with a power spectrum that is
constant over the passband of the channel.
• The symbol-by-symbol channel model is:
Yk = Ck + Zk
where Yk is output sequence, Ck is source symbol sequence,
and Zk is a sequence of i.d.d. zero mean Gaussian random
variables with variance N0/2.
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Probability Density of Statistic Yk
• YK can be depicted under the two possible values of Ck that both of
them are Gaussian with variance N0/2.
• The detector concludes that the bit sent was “0” if the value of Yk is
smaller than the threshold, and “1” if the value of Yk is more than
the threshold.
• An error occurs if “1” is sent and Yk falls below the threshold, and
vice versa.
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Probability of Error and BER
• The probability of error if a “0” was sent is equal to the
probability of error if a “1” was sent and is given by:
where
.
• Hence the probability of error of the binary modulation
scheme is:
• Note that in this simple modulation, since each symbol is used
to send one bit, the error rate obtained is also the Bit Error
Rate (BER).
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Getting Higher Bit Rates
• In the simple binary modulation we have already
discussed, each pulse is modulated by one of two
possible symbols, and the symbol rate is 1/T.
• Hence the bit rate is 1/T bps.
• There are two possibilities for increasing the bit
rate:
• Increase the symbol rate; that is, decrease T.
• Increase the number of possible symbols, from 2
to M > 2.
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Increasing Symbol Rate
• If the pulse bandwidth is limited to W/2, half of
channel bandwidth, then the pulse duration will not
be time limited.
• Thus the received signal in a symbol interval will be
the sum of the pulse in that interval and parts of
pulses in neighboring intervals.
• The pulses therefore have to be appropriately
designed to take care of this effect.
• This leads to the so-called Nyquist criterion, which
limits the pulse rate to no more than W:
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Increasing Number of Symbols (1)
• (a) shows simple binary symbol set that is called
Pulse Amplitude Modulation (PAM).
• (b) shows the simplest possibility of increasing
number of symbol which is called 4-PAM.
• In 4-PAM, when transmitting the left-most and rightmost symbols, the symbol energy is 32 times larger
than that for two other symbols.
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Increasing Number of Symbols (2)
• Another alternative is to have two-dimensional symbols.
• (a) shows symbol set where all symbols have the same
amplitude but different phases. This is called Quadrature
Phase Shift Keying (QPSK).
• In fact, QPSK is the superposition of two orthogonal PAM
signals.
• (b) shows received symbols after corruption by noise. By
utilizing both dimensions, for a given probability of error, a
smaller symbol spacing can be used than of 4-PAM, Hence
given BER can be achieved with less average power.
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Channel Coding (1)
• Due to physical limitations, it is not always possible
to increase SNR so as to reach certain BER.
• Some applications might need a lower BER to
achieve reasonable performance.
• For packet length of L bits and BER of ɛ, the Packet
Error Rate is 1-(1-ɛ)L.
• Required BER can be reduced by channel coding.
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Channel Coding (2)
• In channel coding, blocks of the incoming bits of length K are
coded into code-words of length N (>K), thus introducing
redundancy.
• Since the number of possible code strings (2N) is larger than
the number of possible source strings (2K), the code-words
can be chosen so that there is sufficient spacing between
them.
• Hence, by using nearest code-word decoding, even if the
channel causes errors, the original source string can be
inferred with a small residual error probability.
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Channel Coding (3)
• Error performance is improved by increasing N, but this
reduces the information rate.
• Shannon’s noisy channel coding theorem states that there is
a number C, called the channel capacity, such that if R < C,
then, as the block length increases, an arbitrarily small BER
can be achieved (of course, at the cost of a large block coding
delay).
• If we attempt to use R > C, then the BER can’t be reduced to
zero.
• In two-level modulation, for bit error rates of 10-3, the Es/N0
values required were approximately 7dB.
• With a high quality rate ½ code, the required Es/N0 can be
reduced by 2dB.
• This reduction in Es/N0 is called coding gain.
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Inter-symbol Interference (1)
• Several signals may be detected by receiver from
different paths.
• The difference between the smallest signal delay and the
largest signal delay is called the delay spread (Td).
• When the delay spread is not very small compared to
the symbol time then the superposition of the signals
received over the variously delayed paths at the receiver
results in Inter-Symbol Interference (ISI).
• But if the symbol time is sufficiently bigger than delay
imposed by different paths, the symbols are still
separately discernible, except that each is multiplied by
a complex “attenuation”.
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Inter-symbol Interference (2)
• We can write the k-th received symbol after down
conversion as:
Yk = Gk Xk + Ik + Zk
where Xk is the k-th symbol, Gk is the random
attenuation of the k-th symbol, Ik is a complex random
variable that models the interference, and Zk is a
sequence of complex random variables that models the
additive noise.
• In this case, BER becomes a function of the Signal to
Interference plus Noise Ratio (SINR).
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Inter-symbol Interference (3)
• A channel may have memory, which extends over Jd
symbols:
Gk( j), 0 ≤ j ≤ Jd − 1, are complex random variables
that model channel attenuation and phase shift of
the transmitted symbols for every k.
• Gk( j) models the influence that the input j symbols
in the past has on the channel output at k.
• The channel gain at the k-th symbol could be a
function of the symbol index k showing that fading is
a time-varying phenomenon.
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Inter-symbol Interference (4)
• We can combat ISI by passing the received signal
through a channel equalizer which compensate for the
various channel delays, making the overall system
appear like a fixed delay channel.
• Channel equalizer needs to be adaptive in a mobile
wireless situation, because of owing mobility and
changing the path between transmitter and receiver.
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Fading (1)
• The delay spread (Td) is a time domain concept. It can
also be viewed in the frequency domain.
• Carrying symbols Xk over the RF spectrum:
• multiplying them with a (baseband) pulse of
bandwidth approximately W/2 (e.g., 100 KHz)
• and up-converting the resulting signal to the carrier
frequency (e.g., 900 MHz).
• Some of the frequency components in the pulses can get
selectively attenuated, resulting in the corruption of the
symbols they carry.
• This is called frequency selective fading.
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Fading (2)
• If Td << 1/W , then the pulse would be passed through
with only an overall attenuation that called flat fading.
• The reciprocal of the delay spread is called the
coherence bandwidth (Wc).
• If Wc >> W then all the frequencies fade together and
we have flat fading.
• The assumption of flat fading is reasonable for a
narrowband system .
• The available radio spectrum is channelized, each bit
stream occupies one channel so symbol duration
becomes larger than the delay spread.
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Channel Capacity
• Capacity of AWGN channel (without fading) is:
C = B log2(1+S/N) bps
or
C = log2(1+S/N) bps/Hz
• If average power is Pav and Power Spectral Density
(PSD) of Noise is N0 (W/Hz) then:
C = B log2(1+Pav/N0B) bps
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Diversity (1)
• If the receiver has multiple antennas, and if the
antennas are spaced sufficiently far apart (at least half
of the carrier wavelength), then for the same
transmitted signal, the signals received at the different
antennas fade approximately independently.
• If the paths can be resolved, by combining the received
signals over multiple paths, the bit error probability
performance can be improved.
• So, we have diversity gain.
• Such a receiver is said to exploit multipath diversity.
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Diversity (2)
• The channel fade process, Gk, is correlated over periods
called the channel coherence time, which depends on
the speed of movement of the mobile device.
• Interleaving is a way to obtain an uncorrelated fade
process from a correlated one.
• We say that interleaving exploits time diversity.
• Interleaving fails if the fading is very slow.
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Diversity (3)
• Parallel channels between a transmitter-receiver pair can
arise, if the system bandwidth is partitioned into several
orthogonal channels.
• The multiple transmit antenna system and multiple receive
antenna system (also called a Multiple-Input-MultipleOutput (MIMO) system)
is equivalent to several parallel channels.
• For an M×M MIMO system the capacity
scales as:
.
• This is called multiplexing gain.
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Diversity (4)
• In Summary, multiple antenna system might used to:
• Obtain diversity gain
• Increase channel capacity
• For an N transmit antenna, and M receive antenna system,
the diversity gain is bounded by M × N, whereas the
multiplexing gain is limited to min{M,N}.
• We assumed that the channel gains are unknown at the
transmitter.
• If channel gain estimates could be provided to the
transmitter, then it could judiciously choose the transmitted
symbols and their powers, so that the better of the parallel
spatial channels are assigned the larger transmit powers.
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Wideband systems
• Unlike the narrow-band digital modulation used in
FDM-TDMA (Frequnecy Division Multiplexing – Time
Division Multiple Access) systems, in CDMA (Code
Division Multiple Access) and OFDMA (Orthogonal
Frequency Division Multiple Access) the available
spectrum is not partitioned, but all of it is dynamically
shared among all the users.
• The simplest viewpoint is to think of CDMA in the time
domain and OFDMA in the frequency domain.
• In a wideband system, user’s symbol rate is much
smaller than the symbol rate that the channel can carry
.
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CDMA (1)
• In CDMA a user’s symbol, which is of duration L channel
symbols (also called chips), is multiplied by a spreading code
of length L chips.
• Because of multiplication by the high rate spreading code,
the signal spectrum being spread out to cover the system
bandwidth, which is called Direct Sequence Spread
Spectrum (DSSS).
• Spreading factor is L= Rc/R (>1), where R is user’s bit rate
and Rc is chip rate (>R)
• Spreading codes take values in the set {-1,+1}L
• Each code is approximately orthogonal to all the time shifts
of the other codes, and also to its own time shifts.
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CDMA (2)
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CDMA (3)
• If the receiver can lock into any of paths, then the transmitted
symbol can be decoded
• If the paths fade independently, then we can exploit multipath
diversity.
• The orthogonality property at the receiver, the multiplication of
the received signal by various shifts of the spreading code, and
appropriate linear combination of the results, yields a detection
statistic that is the sum of several faded copies of the user symbol.
• Since these shifts correspond to different paths from the
transmitter to the receiver, this is called multipath resolution.
• In the context of CDMA systems this is achieved by the Rake
receiver.
• Rake receiver permits a desired BER to be achieved with a smaller
SINR.
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OFDMA (1)
• OFDMA is based on OFDM (Orthogonal Frequency Division
Multiplexing), which cab be viewed as statically partitioning
the available spectrum into several subchannels, each of
bandwidth B << 1/Td. Thus a flat fading model can be used
for each subchannel.
• The term orthogonal in OFDM
refers to the fact that
the center frequencies
of the subchannels are
separated by the
reciprocal of the
OFDM block time, T.
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OFDMA (2)
• In OFDMA, the system bandwidth, W, is partitioned into
overlapping subchannels, each of bandwidth B, with
their center frequencies spaced apart by 1/T, where T is
the OFDMA symbol duration.
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OFDMA (3)
• It can be shown that fading is uncorrelated between
subcarriers that are spaced apart by more than the
coherence bandwidth, Wc, which related roughly reciprocally
to the delay spread, Td.
• As time diversity is exploited in TDM systems, frequency
diversity can be exploited in OFDM systems.
• Depending on the rate requirement of each user, a certain
number of subchannels can be dynamically allocated to each
of the users.
• We note that, unlike static allocation on FDM-TDMA systems,
the resource allocation decisions in OFDMA can vary from
frame to frame, depending on channel conditions and traffic
demands
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