Mobile Computing (CS6242)

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UNIVERSITY OF MANCHESTER Department of Computer
Science CS6242 Mobile Computing Principles of
digital transmission - physical layer Barry
Cheetham Section 3 Multiple access for
wireless communications and digital
transmission by multi-carrier modulation (OFDM)
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• 3.1. Multiple user access for wireless
  communications
• Allow many users to share given amount of radio
  bandwidth.
• Three main techniques are
• Frequency division multiple access (FDMA)
• Time-division multiple access (TDMA)
• Code division multiple access (CDMA)
• (type of "spread spectrum
  multiple access" technique).
• To these add
• Space division multiple access (SDMA)
• (same
  band-width is re-used in different places)
• Packet radio (PR) is a form of time division
  multiplexing
• (e.g.'CSMA/CA' as used by IEEE802.11).

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• Narrow-band systems bandwidth used by a single
  channel
• lower
  than coherence bandwidth BC.
• Wide-band systems have bandwidth gtgt BC.
• BC is range of frequencies over which fading can
  be considered flat
• i.e. all
  frequencies have same attenuation delay.
• Sine-waves with freq separation gtgt BC Hz
  affected differently.
• If BC lt 30 kHz, analogue mobile phone system
  with 30 kHz
  channels works without
  equaliser.
• 900 MHz GSM with 200 kHz bandwidths requires
  equalisation.

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• FDMA divides available frequency range into
  sub-bands.
• AMPS uses 824-894 MHz band divided into 1664
  channels, each 30 kHz with 10 kHz guard-bands.
• Narrow-band channels so equalisation not needed
• TDMA uses available frequency range by
  transmitting high frequency
  bit-stream containing data from many users.
• Each user allocated cyclically repeating
  time-slot.
• GSM divides 890-960 MHz into 200kHz channels by
  FDMA.
• Transmits ?271 kb/s in each channel by binary
  GMSK.
• 
  (eight 25 kb/s speech channels)
• Adaptive equalisation needed as 200 kHz gt BC

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• SSMA spread transmissions over wide bandwidth by
  using pseudo-
  random signals as
  carriers.
• Different users have different pseudo random
  carriers .
• Frequency hopping-SSMA
• Varies frequency of sine-wav carrier in
  pseudo-random fashion.
• Fast slow hopping possible.
• Provides security immunity to effects of
  fading.
• Direct sequence SSMA (CDMA)
• Base-band modulates a spreading signal.
• Pseudo-random sequence of bits
• High bit-rate called "chip-rate".
• Soft capacity limit
• Effects of multi-path reduced but power control
  is a difficulty.

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Hedy Lamarr (died 2000) Patented spread spectrum
in early 1940s. Austrian born. First nude
actress appeared nude in Czech film
Ecstasy. Before leaving advance of Nazi Germany
Adolf Hitler, married an Austrian arms
merchant. Invented frequency hopping for secure
radio communication based on frequencies of
piano notes.
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• 3.2. Orthog Frequency Division Multiplexing
  (OFDM)
• Relatively new multi-carrier modulation
  scheme.
• Used for DAB, ADSL wireless LANs (IEEE
  802.11a).
• Many, say 64 or 1024, carrier frequencies evenly
  spaced out over
  a range of
  frequencies.
• Used in IEEE802.11g/a/e with 64 carrier
  frequencies.
• High bandwidth efficiency robust to freq.
  selective fading.
• First a few preliminaries

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3.2.1 Quadrature amplitude modulation_QAM

• QPSK combined with multi-level ASK
• With QPSK, ?A applied to cos sin carriers
• With QAM, 0, ?A, ?2A applied
• Nicely represented by constellations

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Constellation for QPSK
b(t) q(t)
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16-QAM _ symbol allocation table Bit1 bit2
bit3 bit4 VI VQ Bit1 bit2 bit3 bit4
VI VQ 0 0 0 0 A A
1 0 0 0 3A A 0 0
0 1 A -A 1 0 0
1 3A -A 0 0 1 0 A
3A 1 0 1 0 3A 3A 0
0 1 1 A -3A 1 0
1 1 3A -3A 0 1 0 0
-A A 1 1 0 0 -3A A
0 1 0 1 -A -A 1
1 0 1 -3A -A 0 1 1
0 -A 3A 1 1 1 0
-3A 3A 0 1 1 1 -A -3A
1 1 1 1 -3A -3A
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16_QAM constellation
Imag
(0010)
3A
(0000)
(0100)
A
Real
A
3A
-A
-A
(0001)
-3A
(0011)
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3.2.2 Vector-modulator
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Vector modulator in complex notation Take b(t)
jq(t) as a complex b-b signal. cos(2?fCt).b(t)
sin(2?fCt). q(t) real ( b(t) jq(t) )
exp(-2?jfCt)
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A slight variation cos(2?fCt).b(t) ? sin(2?fCt).
q(t) real ( b(t) jq(t) ) exp(2?jfCt)
Instead of sin we modulate -sin no real
difference
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A slight variation (continued)
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3.2.3 Fast Fourier Transform FFT xn0,N-1
??? Xk0,N-1
xn
n
k
N
0
Time-domain
Frequency domain
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Implementation of FFT The FFT is fast in that
it can be programmed or implemented in hardware
very efficiently especially when N is a power of
2, e.g. 64, 256, 512, 1024,
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Inverse Fast Fourier Transform IFFT Xk0,N-1
??? xn0,N-1
Xk
xn
n
k
2N
N
0
N
N/2
0
fS
Time-domain
fS/2
0
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End of preliminaries
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3.2.4 Multi-carrier modulation

• Take 64 carrier frequencies over range fC to fC
  20 MHz
• fC 0, fC fD, fC 2fD,
  , fC 63fD
• with fD 20MHz / 64 312.5
  kHz.

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Multi-carrier modulation
01001
Map
Mult
XN-1(t)
11001
11110
exp(2?j(fC(N-1)fD)t)
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Do multi-carrier modulation in two stages Stage
1 Apply PSK, QPSK, QAM (or other) to obtain
X0(t), X1(t), ..., XN-1(t)
which remain constant for a symbol period T.
(With QPSK we could represent 2N bits per
symbol period). Then vector-modulate complex
'sub-carriers' of frequencies
0 , fD, 2fD , , (N-1)fD Stage 2
Vector-modulate exp(2?jfC) with sum of modulated
sub-carriers.
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Stage 1
10110
Map
X0(t)
11011
01001
Map
Mult
XN-1(t)
11001
11110
exp(2?j((N-1)fD)t)
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Stage 2
(complex but need only real part)
(complex)
exp(2?jfC)
Note that this is complex multiplication.
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The 64 modulating signals X0(t) B0(t)
jQ0(t) modulating 0 Hz X1(t) B1(t)
jQ1(t) modulating fD X2(t) B2(t)
jQ2(t) modulating 2fD .
X63(t) B63(t) jQ63(t). modulating
63fD With QPSK, each Xi represents 2
bits. (IEE802.11a makes X0-X5 X58-X63 all
zero uses 4 others for
"pilot tones", leaving 48 to use.).
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• Adding these together we obtain
• 63
• x(t) ? Xk(t) exp (2?jkfD t ) -?lttlt?.
• k0
• With symbol period T, assume sample x(t) at ?
  T/64 and denote the samples by xn
• 63
• x(n?) xn ? Xk(n?) exp (2?jk fD n? )
• k0
• Make Xkn? Xk constant for 0ltnlt63, i.e. for 1
  symbol period
• 63
• xn ? Xk exp(jk(2?/N)n) 0ltnlt63
• k0
• Generates a set x0, x1, , x63 of complex
  numbers.

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This formula 63 xn ? Xk
exp(jk(2?/N)n) 0ltnlt63
k0 takes 64 complex numbers X0, X1, , X63
representing one symbol and generates a set
x0, x1, , x63 of complex numbers. It is
inverse FFT formula (apart from a factor 1/64).
Generates 64 complx samples of a time-domain
waveform a pulse. Repeat for next set of X0,
X1, ..., X63to get another pulse so on.
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With IEEE802.11, symbol period T 4 ?s, i.e. 250
k symbols/s. For each symbol we get 64 complex
samples hence 16 M sample/s These 64 samples
could form a single symbol capable of
representing up to 128 bits with QPSK. The
inverse FFT takes N frequency-domain samples
produces N time-domain samples. Here N64. But
what if we evaluated xn for n outside range 0
to 63 ? Samples 0 to 63 are repeated as 64 to 127
etc as shown next.
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Real(xn
n
-64
-128
63
127
Similarly for imaginary part.
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• Instead of taking n from 0 to 63, we take n from
  0 to 79 or sometimes from -16 to 63.
• Taking n from -16 to 63 generates a cyclic
  prefix before n0.
• From n -16 to -1 we 16 extra samples which are a
  copy of x48 to x63.
• Generates a set 80 time-domain complex numbers
  for each set X0, X1, ..., X63 rather than 64.
• If T remains at 4 us, we get 250 x 80 20 Mb/s
  for the time-domain waveform.
• Samples from -16 to -1 form the cyclic prefix.

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Real(xn
n
-64
-128
63
127
-16
Similarly for imaginary part.
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OFDM Scheme described is OFDM as used by
IEEE802.11. Time-domain OFDM "symbol" lasting
4us. Shape of pulse tell us the
information. With QPSK on 48 carriers, 296 ? 8 x
10 28 different symbol shapes. 250,000 such
symbols strung together per second
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• Up-conversion
• Applying these complex samples to a
  vector-modulator with carrier exp(2?jfC),
  taking real part we obtain required multi-carrier
  signal.
• To do this digitally (or in simulation) must
  up-sample to a sampling rate suitable for fC
  carrier. Could up-sample by a factor of 10 say by
  repeating each sample 10 times digitally
  low-pass filtering result to one tenth of the new
  sampling frequency.
• If modulation in analogue form, real imag
  parts of symbol stream must first be D to A
  converted. Again this may be best done by
  up-sampling first to simplify analogue filtering.

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• xn is inverse FFT of X0, X1, ., X63 .
• Normally generates complex sequence x0, x1,
  ., x63
• With 63 samples, x0, x1, ., x63, no
  information lost.
• xn0,63 contains all the information in
  Xk0,63 .
• DFT of xn0,63 gets back exactly to X0, X1,
  ., X63.
• OFDM demodulator is FFT followed by detectors

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But we calculate x0, x1, , x63, x64, ,
x79 x64 to x79 is the "cyclic
extension". Or we could calculate x-16, ,
x63 have cyclic prefix Not much difference
in reality. The extra samples may be thought of
as a guard interval" between one symbol the
next. But they are much more useful than just
that. Useful for carrier and symbol
synchronisation at receiver. Due to cyclic
extension cyclic nature of DFT its inverse,
even if exact synchronisation is not achieved at
receiver, exact data can still be recovered with
a phase shift.
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Simulation of simplified OFDM trasmitter
receiver Generate 8 random bits use these to
generate 1 OFDM symbol. Each symbol requires 4
complex numbers X0 to X3 which are transformed to
time-domain xn0,3 by 4-point inverse FFT.
Take X0 to X3 to be complex numbers representing
the I and Q channels of 4 QPSK modulators.
Extend complex time-domain symbol to 6 samples
xn0,6 by cyclic extension vector-modulate a
28 MHz carrier by the samples of x. Produce and
plot the transmitted waveform. Show how original
data can be recovered by 4-point FFT.
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Example Assume data is 00 01 10 11 Then X0
1j, X1 1- j, X2 -1j, X3 -1-j X
1j 1-j -1j -1-j xifft(X) This
generates the required symbol 0 0.5 0.5j
j 0.5 - 0.5j Including the cyclic
extension, this becomes j 0.5 - 0.5 j
0 0.5 0.5j j 0.5 - 0.5j
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With 64 26 sub-carrier frequencies, inverse DFT
can be carried out very efficiently by FFT. OFDM
works because of orthogonality of the 64
carriers. Good for channels affected by frequency
selective fading because (1) info can be spread
out across sub-carriers in intelligent ways so
that when some are lost, others will
compensate . (2) guard-band allows for ISI if
4us OFDM symbol rings on, it only affects
beginning of next symbol, repeated at end.
(Can have cyclic "prefix"). So no pulse-shaping
necessary! (3) equalisation much easier than
with single carrier systems. OFDM
equalisation done by multiplication in
frequency-domain after FFT. Easier than
adaptive filtering used for single carrier.
Works because of cyclic extension.
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• Disadvantage of OFMD is "peak to mean" ratio of
  symbols which can be very large by nature of FFT
  its inverse.
• Shape of each OFDM symbol ( there are 1014 of
  them) is very complex must be sent received
  accurately.
• Amplitudes can become very large in comparison to
  the mean. Definitely not "constant envelope".
• Transmitter receiver must be linear to preserve
  shape.
• Need class A amplifiers less power efficient
  than those for constant envelope
  transmissions.
• Lot of power lost in the amplifiers.
• Not ideal for mobile phones, but fine for mobile
  computers with bigger batteries that are not
  sending data continuously.

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Some details about IEEE 802.11a/g OFDM With
IEEE802.11a and g, OFDM symbols transmitted in 4
?s giving maximum of 250 k symbols/second. Each
symbol can carry up to 6 bits per carrier (using
64-QAM). Normally reduced to 4.5 bits per carrier
by ¾ rate FEC. As there are 48 carriers
carrying data, maximum bit-rate is
48 x 4.5 x 250 kb/s 54
Mb/s. Distances over which this bit-rate
achievable will be restricted. Lower bit-rates
(48, 36, 24, 18, 12, 9 and 6Mb/s) available. Two
lowest bit-rates (9 6Mb/s) use binary PSK 3/4
or 1/2 rate FEC to achieve 48 x (3/4) x 250kb/s
9 kb/s or 48 x (1/2) x
250 kb/s 6 Mb/s. For 18 Mb/s 12 Mb/s,
QPSK is used on each of 48 data carriers.
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Forward error control Within each IEEE802.11 data
packet is a mac protocol data unit (MPDU) with
format
It contains 256 control bits, the body and a
CRC check (FCS). The cyclic redundancy check
CRC consists of 32 parity checks over selected
combinations of bits so that bit-errors can be
detected if they occur during transmission. A
parity check simply tells us whether the selected
number of bits should contain an even or an odd
number of 1s. If the MPDU fails this parity
check at receiver, it is discarded
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MPDU preceded by SIGNAL sub-frame a PLCP
preamble consisting of 12 training symbols
SIGNAL block separately FEC coded always sent
at 6Mb/s.
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• MPDU is applied to a convolutional coder before
  transmission.
• Allows some bit-errors to be corrected.
• At 6 Mb/s, half rate coder with input
  constraint-length 7 is used.
• Half rate means that it doubles the number of
  bits.
• Two coded bits for each input bit.
• Each pair based on the current input bit and 6
  previous bits.
• Scrambling interleaving randomizes the
  occurrence of any bit-errors and eliminates any
  periodicity arising from the use of OFDM over a
  frequency selectively fading radio channel.

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Receiver incorporates a soft-decision Viterbi
FEC decoder for both SIGNAL sub-frame coded
MPDU data sub-frame. Soft decision means that
instead of making a definite decision as to
whether a bit is 0 or 1, threshold detector at
receiver delivers a number between 0 1
indicating how certain it is about the decision.
This may be illustrated for unipolar Voltage
x Hard Soft decision
x ? 0.125 0 000 certain 0 0.125
lt x ? 0.25 0 001 probably 0 0.25 lt x ?
0.375 0 010 likely 0 0.375 lt x ?
0.5 0 011 maybe 0 0 .5 lt x ?
0.625 1 100 maybe 1 . 0.625 lt x ? 0
.75 1 101 likely 1 0.75 lt x ?
0.875 1 110 probably 1 0.875 lt
x 1 111 certain 1
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The confidence of the decision is taken into
account by the Viterbi decoder when it attempts
to correct it-errors. Soft decision gains us
about 2 dB is SNR over hard. If there are too
many bit-errors in the received coded MPDU data
sub-frame to be corrected by the Viterbi decoder,
failure to correct these errors will mean that
the CRC check based on the 32-bit FCS, will
likely fail.
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Voice multimedia (interactive telephony)
Converged enterprise networks currently of
much interest. Voice data share same
links. Dedicated IP links between premises of a
large company. Integrated services reservation
of transmission capacity. Differentiated
services priority for certain traffic. Quality
of service (QoS) issues Contention mode not
ideal TCP normally not possible because of
latency. IEEE 802.11e is new QoS standard.