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The Physical Layer The Physical Layer
Curt Schurgers
Sources:
- Mani Srivastava, http://nesl.ee.ucla.edu/courses/ee206a/2002s/
2 ECEECE 284284
Wireless Communication System Wireless Communication System
Source coding
Source coding
Multiple access
Modulation & baseband
Wireless channel
Channel coding
RF
Source decoding
Source decoding (^) Multiple
access
Demodulation & baseband
Channel decoding
RF
0 1 0 1 1 1 0 0 1 0 1 0
V, I
E H
r r ,
Information
Electrical waveform
Electro-magnetic waveform
Multi- plexing
Demulti- plexing
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Bits versus Symbols Bits versus Symbols
Modulation: information is grouped together into waveforms
Demodulation: inverse process (best effort)
● If M → ∝ the ‘performance’ goes up, but at a cost of complexity
(Shannon limit)
1 bit/symbol
2 bits/symbol
b bits/symbol = M possible waveforms
b = log 2 (M)
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Signal Space Representation Signal Space Representation
The basic idea is that information can be transmitted in parallel over a
set of orthogonal waveforms with respect to the symbol intervalT. The inverse of this interval is called the symbol rate:Rs = 1/T.
ij
T
t
∫ s t ⋅ s t dt =^ δ
= 0 1 2
T
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Information Mapping Examples Information Mapping Examples
s 2
s 1
s 2
s 1
s 2
s 1
s 2
s 1
Send either s 1 or s 2. Send s (^) 1, s 2 , both or none of them.
Send ± s 1 or ± s 2. Send any of these combinations.
Y
X
x 1 y (^1) x 2 y (^1)
y (^3)
Y
x 3
X
X Y
Y
X
M = 4
M = 2 M = 4
M = 8
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Some Basic Modulation Schemes Some Basic Modulation Schemes
f (^2)
f (^1)
FSK
(Frequency Shift Keying)
Baseband PAM
(Pulse Amplitude Modulation) s 1
f (^1)
Passband PAM
(Pulse Amplitude Modulation)
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Some Basic Modulation Schemes Some Basic Modulation Schemes
4-QAM 16-QAM^ 64-QAM
4-PSK 8-PSK^ 16-PSK
QAM (Quadrature Amplitude Modulation)
PSK (Phase Shift Keying)
The two orthogonal dimensions are sin and cos waves at the carrier frequency
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Signal Space for Sinusoids Signal Space for Sinusoids
s i ( t )= ai ⋅ g ( t )⋅cos( 2 π⋅ fc ⋅ t )− bi ⋅ g ( t ).sin( 2 π⋅ fc ⋅ t )
si ( t )=Re[ g ( t )⋅( ai + j ⋅ bi )⋅ ej ⋅^2 π⋅ fc ⋅ t ]
Q
I
ai + j·b i
r i
θ i
si ( t )=Re[ g ( t )⋅ ( r i ⋅ ej θ^ i^ )⋅ ej ⋅^2 π⋅ fc ⋅ t ]
( )
si ( t )= Re[ g ( t )⋅ ri ⋅ ej ⋅^2 π^ ⋅ fc^ ⋅ t +^ θ i ]
si ( t )= g ( t )⋅ ri ⋅cos ( 2 π ⋅ fc ⋅ t + θ i )
2
Ei ∝ r i
=
M
i
S RMS ri
M
E r
1
The average energy when each 2 1 2
symbol is transmitted with an equal probability
Energy in symbol i
(in-phase)
(quadrature)
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Effect of Increasing Constellation Size Effect of Increasing Constellation Size
Data rate:
● Higher constellation sizeM results in a higher bit rateRb (bits/s)
● Define bandwidth efficiency as (bits/s/Hz)
Error rate: error performance depends on constellation size
4-QAM 16-QAM^ 64-QAM
4-QAM 16-QAM^ 64-QAM
(1) ES the same Same SNR increases SER
(2) ES increases Same noise results in similar SER
log( )
R 2 M
T
R S
b
b =^ = ⋅^ RS T
W
Rb
η b =
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Example: Performance QAM Example: Performance QAM
η b =log 2 ( M )
R S
T
W ≈ =
Data rate Error rate
log 2 ( )
0 0
M
N
E
N
E
N
P
SNR = R^ = S = b ⋅
N 0
E b
SER
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Comparison Comparison
SER = 10 -
Source: http://www.mhhe.com/e ngcs/electrical/proakis/s tudent/images.mhtml
FSK
W
Rb η b =
log 2 ( 1 )
N
S
C = W ⋅ +
S = C ⋅ E b N = W ⋅ N 0
log( 1 )
0
2 W
C
N
E
W
C b
→ 0 ( W →∞ )
W
C
log()
0 2
dB
N e
E b
Shannon capacity
● C is maximum data rate achievable with arbitrarily low error probability
● For infinite bandwidth, there is a minimum required energy for reliable communications
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Other Issues Other Issues
Coherent versus non-coherent receiver
● Coherent: carrier phase is needed. E.g. QAM, PSK, …
● Non-coherent or envelope detection. E.g. DPSK, FSK (could also be
coherent), …
Constant envelope or not
● If constant envelope, efficient amplifier can be used. E.g. PSK, FSK
Implementation complexity
Resilience against Interference
Out-of-band radiation
Effect of frequency offset, fading, time-variations, etc.
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CDMA CDMA
Spreading code 1^ Spreading code 2
CDMA (Code Division Multiple Access) uses DSSS as a multi-access technique.
Transmissions with different spreading codes to not interfere.
However, the number of correlators in the receiver is limited (so the number
of simultaneous receptions).
Spreading codes need good cross-correlation properties (for all different
shifts).
Graceful degradation: the performance worsens gradually as more users are
added to the system.
Near-far problem: even with good cross-correlation, a nearby interferer can
swamp the reception of a far away transmitter.
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CDMA versus FDMA CDMA versus FDMA
FDMA: frequency division multiple access
● Users have different frequency bands (possible use DSSS)
CDMA: code division multiple access
● Users occupy the same frequency band, but use orthogonal codes
Time
Frequency
User k
Code
CDMA
User k…
Time
Frequency
FDMA
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Code Properties Code Properties
Walsh-Hadamard codes
● Perfectly orthogonality between two codes
● Needs to be time-synchronized
E.g. row 2 and 3-shifted
Autocorrelation
● Try different shifts to synchronize
Cross-correlation
● Low value for different shifts
● Not zero: multi-user interference
Example: Gold codes
1 -
1 1
1 -
1 1
1 -
1 1
1 -
1 1
-1 1
H 1 -H (^1) -1 -
H H^1 H^1 2 =^ =
H 1 =
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Frequency Hopped Spread Spectrum Frequency Hopped Spread Spectrum
(FHSS)(FHSS)
Jump around between frequency bands in a pseudo random fashion.
Avoids being stuck in a bad frequency band.
As a multi-access technique, transmissions can collide, but
occurrences are infrequent.
Fast FHSS: jump multiple times during one symbol
Slow FHSS: multiple symbols per jump
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Data Transmission Sequence Data Transmission Sequence
NT
frequency
T
frequency
frequency
IFFT
T
NT^ time
time
i = 1 i = 2 i = 3
i = 1
i = 2
i = 3
Data is grouped into blocks and each block is treated sequentially Each blocki consists ofN symbols which are transformed intoN time samples using the IFFT
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Upconverting and Multiplexing Upconverting and Multiplexing
j ft j NTk^ t
ck e e
= ⋅^2 π⋅^ k ⋅= ⋅^2 π⋅^ ⋅
−
=
⋅ ⋅ + ⋅
1
0
N
k
j f Ft k
s t x t e^ π k
−
=
⋅ ⋅⋅ ⋅ ⋅ ⋅
1
0
2 2
N
k
j ft k
j Ft k
e x t e
π π
−
=
⋅ ⋅⋅ ⋅ ⋅ ⋅
1
0
2 2
N
k
t NT
j k k
j Ft
e x t e
π^ π
2 *
e p t
j Ft
⋅π⋅⋅
c 0
x (^0) ck
x (^) k
cN-
x (^) N-
ej.2π.F.t
s *
p *
NT
k
f k =
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Fast Fourier Transform Fast Fourier Transform
−
=
⋅ ⋅ ⋅
1
0
N
k
t NT
j k
p t xk t e
π
−
=
⋅ ⋅ ⋅
1
0
N
k
nT NT
k j
p nT xk nT e
π
−
=
⋅ ⋅⋅
1
0
2
N
k
N
j kn
xk nT e
π
= N ⋅ IFFT [ x k ]
c 0
x (^0) ck
x (^) k
cN-
x (^) N-
p *
x (^0)
x (^) k
x (^) N-
N-IFFT
(^0 )
p *
p *^ ( nT )
p *^ (( N − 1 ) T )
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Single Carrier versus Multicarrier Single Carrier versusMulticarrier
Single carrier and multicarrier both ● sendN symbols inNT, or 1/T symbols/second ● have a total single sided bandwidth of about 1/T
T
time
T
frequency
Single carrier
T
frequency
time
NT
Multicarrier
=
N
k 1
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OFDM System View OFDM System View
Typically QAM (quadrature amplitude modulation) is used to modulate the bits onto symbols, but any modulation is possible
K = N ⋅ b (^ N C )
K
R
R S = b ⋅ +
16-QAM
b = 4 bits/symbol
4-QAM
b = 2 bits/symbol
64-QAM
b = 6 bits/symbol
Concentrator (^) N -IFFT Cyclic prefix insertion
Radio front-end
R (^) b bits/s
Modulator
K bits/block (^) b bits/symbol N symbols/block
R (^) b / K blocks/s R^ b / b^ symbols/s^ R^ b / b^ symbols/s
(N+C) symbols/block
R (^) S symbols/s
freq time
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Equalizing OFDM Equalizing OFDM
=
N
k
av bk
N
b
1
Without adaptive loading With adaptive loading
x k y k
α k n^ αˆ k
From x ˆ k modulator
To
demodulator Channel Equalizer at receiver is 1-tap for each k
b (^) k = b (^) av
freq
α k
b (^) k = f(α k )
freq
α k
1-tap equalizer, channels with small αk may be treated as erasures at the receiver Adaptive loading takes channel info into account at the sender
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Adaptive Loading Adaptive Loading
BER
SNR (dB)
N = 256 (uncorrelated) b (^) av = 4
AWGN
Loaded
Unloaded
Assignb (^) i andPi such thatPtot is minimized Send more information when channel is good Channel needs to be estimated (as for equalization)
Normalized channel response (dB) Subcarrier
N = 256
bav = 4
b (^) i bits/symbol
Loading information needs to be fed back to the transmitter The channel must remain quasi- stationary between estimation updates (low Doppler rate)
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OFDM Considerations OFDM Considerations
Dynamic range at output of IFFT is much larger than at input (or single carrier systems): large peak-to-average ratio (PAR) Very good frequency synchronization is crucial to maintain orthogonality (otherwise ISI) Example: use OFDMA as multiple access technique
ISI
ISI
OFDMA downlink OFDMA uplink
Sync problem !!!
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UWB Properties UWB Properties
Operating conditions
● Limited power to reduce interference with existing systems: -41.3 dBm/MHz
● Limited range: few 10s of meters
Benefits
● High data rate possible (up to Gbps) over short distances
● Simple radio design: mostly digital
● Reuse spectrum
● Inherent security: hard to detect
● Position determination: Aetherwire
Source: http://dessr2m.adm-eu.uvsq.fr/pdfsportesouvertes/Presentation_Ultra-Wideband.pdf
Research:
● Aetherwire, Time Domain, Intel, TI,
XtremeSpectrum, etc.
● IEEE 802.15.3a
http://www.ieee802.org/15/pub/TG3a.html
● IEEE 802.15.4a
http://www.ieee802.org/15/pub/TG4a.html
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Smart AntennasSmart Antennas
Sectorized antennas
● Current cellular systems: 120º sectors with different frequencies
Switched beam antennas
● M beams provide an M-fold gain
● Improve capacity by limiting interferers: space division multiplexing (SDMA)
Adaptive arrays
● Signals from the M antennas are weighted and combined
Reference: [Win98]
● Line-of-sight environment
Steer antenna beam
Can create M-1 nulls to cancel
out M-1 interferers
● Multipath environment
Consider signal space
Cancel N interferers and provide
(M-N) fold diversity gain
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MIMO MIMO
MIMO: multi-input multi-output system: 2 types
Space time diversity coding
● Provide diversity gain
Spatial multiplexing: e.g. BLAST
● Data is split in parallel streams
● The channel itself provides the decorrelation (orthogonalization)
● Capacity proportional to min(Tx-antennas, Rx-antennas)
Reference: [Wol98]
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RF ID Tag RF ID Tag
Battery-less communication system
● Energy is provided by a reader
module in the form of an RF signal
● Short distances (under 2 meter)
Applications: factory automation,
security, life stock management,
wakeup radio, etc.
Reference: [Kai95]
