Practical multitone architectures
Lecture 4
Vladimir Stojanović
6.973 Communication System Design – Spring 2006
Massachusetts Institute of Technology
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Loading with discrete information units
‰
‰
Chow’s algorithm (rounding of waterfilling results)
Levin-Campello algorithm (greedy optimization)
„
„
Each additional bit placed on subchannel that requires
the least incremental energy for its transport
Incremental energy en (bn ) ε n (bn ) − ε n (bn − β )
⎛ e (b ) g ⎞
bn = log 2 ⎜1 +
n n n ⎟
Γ
⎠
⎝
„
bit increment
Efficiency of bit distribution
„
Can’t move a bit from one channel to another and reduce the
total energy
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Levin-Campello (LC) algorithm- components
‰
Efficientizing (EF) – finding energy-efficient bit
distribution
„
Always replace a bit distribution with a more efficient –
exhaustively search all single information unit changes
at each step
Smallest energy to add a new bit
Largest energy to subtract the bit
Subtract bits from costly sub-channels
and add to least costly sub-channels
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Efficientizing example
‰
1+0.9D-1 channel (Pe=10-6, gap=8.8dB, PAM/QAM)
„
„
PAM and single-sideband
QAM
bn
bn +1
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Rate adaptive solution
‰
Need also to satisfy the energy constraint
‰
E-tightness (ET)
„
Can’t add another bit without violating the E constraint
If energy constraint violated
subtract the most costly bit
If energy less than max add
the bit that costs the least to add
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LC - Rate adaptive algorithm
‰
ET example (continue from EF example)
„
Start from efficient distribution that blows up the energy
constraint
N ε = 8 ⋅1 = 8
x
„
Margin
Nε x
ε
‰
=
8
= 1.8 dB
5.32
Levin-Campello Rate Adaptive algorithm
„
„
„
Choose any bit distribution
Make it efficient using (EF algorithm)
Make it energy tight using (ET algorithm)
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Dynamic rate adaptation
‰
‰
‰
Change the loading when channel changes
LC is a natural candidate
Keep the ET bit distribution and perturb based on
channel changes
„
‰
Bit is moved from channel n to m
Tightly coupled with channel and noise estimation
„
Will cover in later lectures
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Channel partitioning
‰
Divide the channel into a set of parallel,
independent channels
X2,k
ϕ2(t)
x
XN-1,k
XN,k
ϕ∗1(T-t)
ϕ1(t)
X1,k
.
.
.
ϕ∗2(T-t)
n(t)
+
x(t)
h(t) +
h*(T-t)
.
.
.
y(t)
ϕ∗N-1(T-t)
ϕN(t)
ϕ∗N(-t)
t=T
.
Qk
(MIMO)
+
y1,k
+
y2,k
+
yN,k
n2,k
nN,k
x(t) =
y1,k
y2,k
yN-1,k
yN,k
(lower case y
indicates normalizing
||p|| factors included)
=
x(t)
h(t) * x(t) =
n1,k
X1,k
XN,k
t=T
t=T
ϕN-1(t)
X2,k
t=T
N
n=1
N
k n=1
N
k n=1
xn,k . ϕn(t - kT)
xn,k . ϕn(t - kT) * h(t) =
N
=
xn . ϕn(t)
xn,k . pn(t - kT)
k n=1
p
∆ m(t) * p*n(-t)
qn,m (t) =
||pm|| . ||pn||
Qk = Q(kT)
Qk = Iδk
Figure by MIT OpenCourseWare.
‰
Generalized Nyquist criterion
„
„
No interference between symbols
No interference between sub-channels
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Modal modulation
‰
Transmission with eigen-functions
(-TH / 2, TH / 2)
r(t) = h(t) * h*(-t)
ρn . ϕn (t) =
T/2
ò -T / 2 r(t - τ)ϕ (τ)dτ n = 1,...,
,
n
t
[-(T - TH) / 2, (T + TH) / 2)]
X1,k
ϕ1(t)
ϕ∗1(T-t)
X2,k
ϕ2(t)
ϕ∗2(T-t)
.
.
.
x
XN-1,k
y(t) =
+
x(t)
h(t) +
h*(T-t)
y(t)
.
.
.
ϕN-1(t)
ϕ∗N-1(T-t)
ϕN(t)
ϕ∗N(-t)
XN,k
x(t) =
n(t)
N
n=1
N
t=T
t=T
t=T
t=T
y1,k
y2,k
Per-channel MAP is optimal
Problem is vector AWGN
yN-1,k
yN,k
ϕk (t ) Channel eigenfunctions (channel dependent)
xnϕn(t)
y(t) =
~
xn . [r(t) * ϕn (t)] + n(t)
N
n=1
(ρnxn) . ϕn (t)
n=1
Figure by MIT OpenCourseWare.
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Convergence of multitone to modal modulation
‰
Modal modulation is optimal for finite symbol time
„
‰
Eigenfunctions hard to compute and channel dependent
Multitone converges to Modal modulation
„
As both N->inf and [-T/2, T/2]->(-inf,+inf)
„
„
„
Set of eigenvalues of any autocorrelation function is unique
„ This set determines the performance of MM through SNR
„ Eigen-functions are not unique
is also a valid eigen-function for inf symbol period
„ Corresponding eigenvalues are R(2πn/T)
„ No ISI on any tone since symbol period is infinite
„ Each tone is AWGN channel
„ SBS detector is MAP optimal
If channel is periodic (does not exist in practice)
„
„
are then eigen-functions even on finite [-T/2,T/2]
Can use extra bandwidth in the design to make the channel “look” periodic
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Finite symbol duration effects
‰
ISI corrupts the neighboring symbol
„
„
Need to leave the guardband
Can try to create a more sinc-looking symbols in
time by filtering the tones in frequency domain
„
Need excess bandwidth for filter roll-off
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Discrete time channel partitioning
‰
Digital realization
X0
m0
X1
m1
1/T
x
+
XN-2
XN-1
D
A
C
1/T
n (t)
x(t)
(t)
(LPF)
mN-2
*(-t)
+
h (t)
y(t) (LPF)
A
D
C
y = Px + n
f1*
Y1
*
fN-2
YN-2
*
fN-1
yN-1
y0
Y0
y
mN-1
yN-2
f0*
=
0
p0
p1
py
0
0
p0
py-1
py
0
p0
p1
0
py
0
0
0
xN-1
x0
x-1
+
YN-1
nN-1
nN-1
n0
x-y
Figure by MIT OpenCourseWare.
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Vector coding
‰
Creates a set of parallel channels by using SVD
singular-value decomposition of P
discrete transmitter waveforms
discrete matched filters
since F is unitary N is also AWGN
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VC example
‰
1+0.9D-1, N=8
„
Need one sample guardband
„
„
„
„
„
„
„
„
„
Etot=(N+1)*E_dim=(8+1)*1=9
SVD on
Gives singular values
Sub-channel SNRs
Waterfilling shows only 7 dimensions can be used
Sub-channel energies
SNRs are then
Total SNR
VC capacity
„
Would get 1.55bits/dim if N-> inf
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DMT and OFDM
‰
‰
Discrete multitone (DMT) and Orthogonal
frequency Division Multiplexing (OFDM)
DMT used on slowly time-varying channels
„
‰
OFDM uses same channel partitioning as DMT
„
„
‰
Optimize bn and En per sub-channel
But uses same bn and En on all channels
Used on one-way broadcast channels
Forms of vector coding with added restrictions
„
„
In vector coding, M,F channel dependent
Make the channel circular and make M,F channel
independent - simplify hardware implementation
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DMT/OFDM channel partitioning
‰
Make channel “look” circular
„
Repeat the tail of the symbol at its beginning
CP
„
Add cyclic prefix to each transmitted symbol
DMT
xN −ν ... xN −1 x0 ...
2
xN −ν ... xN −1
VC
0...0
x0 ...
xN −ν ... xN −1
2
„
SVD can be replaced by eigen-decomposition (spectral
factorization)
„ A discrete form of modal modulation
„ While SNRs are unique, many choices for M and F
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IDFT and DFT as orthogonal transformations
‰
DMT and OFDM use IDFT and DFT as eigen-vectors
IDFT
DFT
‰
Proof
channel gain at tone n
#
qn is eigen-vector of P
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DMT/OFDM implementation
X0
Y0
X1
.
.
.
IDFT
parallel
to serial
& cyclic
prefix
insert
1 = N+v
Γ
T
D
A
C
n(t)
x(t)
ϕ(t)
(LPF)
1 = N+v
Γ
T
h(t)
+
ϕ (-t)
y(t)
(LPF)
A
D
C
serial to
parallel
& cyclic
prefix
remover
Y1
DFT
XN-2
.
.
.
YN-2
XN-1
YN-1
Forces P to be cyclic matrix
XN-i = Xi if x(t)is real
Figure by MIT OpenCourseWare.
‰
Data rate penalty N /( N +ν )
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One-tap frequency equalizer
‰
Need to compensate for channel attenuation
„
To recover the original constellation distance
Figure by MIT OpenCourseWare.
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Rx/Tx Windowing
Rectangular window
Raised cosine 5%
Raised cosine 25%
Can overlap as long as sum is constant
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1+0.9D-1 DMT example
‰
N=8
‰
Waterfilling with Etot=8
„
Waste one unit on CP
lower than VC (8.1dB)
„
For N=16 quickly reaches max of 8.8dB
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Complexity of DFE, VC, DMT
‰
Example 1+0.9D-1 channel
‰
MMSE-DFE, SNR=7.6 dB, 3ff, 1fb tap, 4 mac/sample
‰
VC, N=8, SNR=8.1 dB, 7*8/9=6.2MAC/sample
‰
DMT, N=8, SNR=7.6 dB, 8pt FFT/IFFT,
2.7MAC/sample
„
„
N=16, 3.8MAC/sample, SNR=8.8 dB
DFE needs 10FF taps, 1FB tap, SNR=8.4 dB, 11MAC/sample
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Asymmetric digital subscriber line (ADSL)
video switch
12 Mbps
ADSL ADSL
Access ADSL
Mux
(DSLAM) ADSL
Split
POTS
(or ISDN)
Switch
1.5 Mbps
Split
ADSL
Telco CO
internet
„
„
„
„
138 kHz
Down
Down
frequency
1.1 MHz
psd
1/T’=2.208 MHz (CP = 40 samples)
Each time domain symbol 2*256+40=552 samples
„
‰
UP
Up
10 kHz
‰
Symbol rate T=250us
Nd=256, 4.3125kHz wide
0 Hz
‰
POTS
Figure by MIT OpenCourseWare.
Hermitian symmetry creates real signal transmitted from 0-1.1MHz
First 2-3 tones near DC not used – avoid interference with voice
Tone 256 also not used, 64 reserved for pilot
Nup=32, CP=5, each symbol 2*32+5=69 samples
„
Exactly 1/8 of downstream
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802.11a Wireless LAN example
‰
‰
‰
Up to 54Mbps symmetrically (<100m)
1-3 Tx power levels
Complex baseband
„
‰
unlike ADSL which is real baseband
5.25 GHz
20 MHz
5.35 GHz
„
4 pilots
Figure by MIT OpenCourseWare.
R (Mbps) constellation code rate
48 data tones
6
9
12
18
24
36
48
54
BPSK
BPSK
4QAM
4QAM
16QAM
16QAM
64QAM
64QAM
Broadcast channel – can’t optimize bit allocation
„
„
5.825 GHz
20 MHz
Symbol length = 80 samples, CP=16
Symbol rate 250kHz (T=4uS, T’=50ns), CPguard=0.8us
not used
5.725 GHz
52 carriers total, each ~ 300 kHz
N=64 (-31 … 31) (so 128 dimensions)
„
‰
5.15 GHz
800 mW
200 mW
40 mW
1/2
3/4
1/2
3/4
1/2
3/4
1/2
3/4
bn
bn
b
1/2
3/4
1
3/2
2
3/2
3
9/2
1/4
3/8
1/2
3/4
1
3/4
3/2
9/4
24
36
48
72
96
144
192
216
Figure by MIT OpenCourseWare.
FCC demands flat spectrum so no energy-allocation
The only knob is data rate selection
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High-level system view
Data link control layer (DLC)
Physical radio layer (PHY)
Guard
Viterbi
Demodulation
interval
decoder +
+
descrambler deinterleaver extraction +
FFT
Scrambler +
forward error
correction
(FEC) coder
Interleaver
+
modulation
IFFT +
guard
interval
insertion
A/D
D/A
Analog front-end
Analog
Digital
Synchronization
Figure by MIT OpenCourseWare.
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Transceiver architecture
DAC
Upconvert
AGC& ADC
LNA & Downconvert
Channel estimator
Remove prefix
Pilot insertion
Demapper
Windowing
Mapper
Deinterleaver
Synchronizer
Interleaver
Viterbi decoder
Cyclic prefix
Encoder
Descrambler
FFT/IFFT
Scrambler
[2]
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Transmitter architecture detail
Data
MAC
Scrambler
Convolutional
Encoder
Signal
Mapper
Puncturer
IFFT
Interleaver
Cyclic
Extend
Preamble
Modulation
&
Upconvert
RF
D/A
Transmitter (Digital Components)
Transmitter (Analog Components)
Figure by MIT OpenCourseWare.
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Scrambling
Need to randomize incoming data
‰ Enables a number of tracking algorithms in
the receiver
‰ Provides flat spectrum in the given band
‰
pseudo-random bit sequence (prbs) generator
What is the period of this pseudo-random sequence?
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Interleaver
‰
‰
Protects the code from overload by burst errors
Block interleaver
„
„
„
Block size is the #of coded bits in OFDM symbol (NCBPS)
Two-step permutation
Adjacent coded bits mapped
„
„
Onto nonadjacent sub-carriers
Alternate between less and more significant bits in the constellation – avoid long runs of low reliability LSBs
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Convolutional Encoder
‰
Rate 1/2 convolutional encoder
„
Punctured to obtain 2/3 and 3/4 rate
„
Omit some of the coded bits
Punctured Coding (r = 3/4)
g0=1338
Source Data
Encoded Data
Input Data
Tb
Tb
Tb
Tb
Tb
Tb
‰
‰
A0 A1 A2 A3 A4 A5 A6 A7 A8
B0 B1 B2 B3 B4 B5 B6 B7 B8
Stolen Bit
Bit Stolen Data
A0 B0 A1 B2 A3 B3A4 B5 A6 B6 A7 B8
(sent/received data)
Bit Inserted Data
g1=1718
X0 X1 X2 X3 X4 X5 X6 X7 X8
Output Data A
A0 A1 A2 A3 A4 A5 A6 A7 A8
B0 B1 B2 B3 B4 B5 B6 B7 B8
Inserted Dummy Bit
Output Data B
Decoded Data
y0 y1 y2 y3 y4 y5 y6 y7 y8
64-state (constraint length K=7) code
Viterbi algorithm applied in the decoder
Figure by MIT OpenCourseWare.
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Signal mapper
‰
BPSK, QPSK, 16-QAM, 64-QAM
„
Data divided into groups of (1,2,4,6) bits and mapped
to a constellation point (i.e. a complex number)
Gray-coded constellation mapings
„
Need the same average power for all mappings
„
„
Scale the output by KMOD
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Pilot insertion and FFT/IFFT
‰
Pilot insertion
„
‰
Pilots BPSK, prbs modulated
FFT and IFFT shared
„
Just flip the Re and Im inputs
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Spectral mask
‰
‰
Cannot use last 5 tones on each side
Does not use extra windowing
Power Spectral Density (dB)
Transmit Spectrum Mask
(not to scale)
-20 dBr
Typical Signal Spectrum
(an example)
-28 dBr
-40 dBr
-30
-20
-11 -9
fc
9 11
20
30
Frequency (MHz)
Transmit spectrum mask
Figure by MIT OpenCourseWare.
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Receiver architecture
I and Q from
analog
front-end
ADC
Remove
DC
of fset
FIR
FIR
Rx gain
to analog
front-end
Rotate
Frequency
lock
FFT
Channel
correct
Deinterleave
Viterbi
Rx data
to MAC
Channel
estimate
and
tracking
Autocorrelate
Signal
detect
and AGC
Symbol
timing
Pipeline
control
Figure by MIT OpenCourseWare.
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Pilot tracking and channel correction
‰
OFDM packet structure
8 + 8 = 16 µs
10 x 0.8 = 8 µs
2 x 0.8 + 2 x 3.2 = 8.0 µs
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2
T1
0.8 + 3.2 = 4.0 µs 0.8 + 3.2 = 4.0 µs 0.8 + 3.2 = 4.0 µs
T2
GI SIGNAL GI Data 1 GI Data 2
Signal Detect,
Coarse Freq. Channel and Fine Frequency RATE
AGC, Diversity Offset Estimation
Offset Estimation
LENGTH
Selection
Timing Synchronize
SERVICE + DATA
DATA
Figure by MIT OpenCourseWare.
to timing control
symbol
timing adjust
training symbol pilots
pilots
long2 training
data
angle adjust
magnitude
adjust
long1 training
from fft
pilot
tracking
core
+
fir
complex
inverse
pilot
magnitude
multiply
rotate
composite
channel correction
channel to de-interleaver
correction
multiply
Figure by MIT OpenCourseWare.
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
35
Synchronizer
Processing
Data Path
crosscorrelator
NCO
Input
Data
Z-16
FFT
Output
Symbols
Z-49
IJ*
Moving
Average
JF(k)
IP
Plateau
Detector
α
Tracking Data Path
Moving
Average
(16)
Combine
Ig.1(.)
Jc(k)
ε
β
Figure by MIT OpenCourseWare.
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design
36
Channel estimator
Equalizer
Sync. + FFT
X(i,k) =
Reference
Sign
Correction
Residual
Phase
Correction
Y(i,k)
H(i-D,k)
Soft
Demapper
Deinterleaver
Soft
Viterbi
X(i,k)
H(i-D,k)
Channel Estimator
Delay
Buffer
(D)
Estimation
Buffer
(Circular Buffer)
HREF (k)
Pilot Sign
Correction
Y(i-D,k)
Zero Forcing
Y(i-D,k)
H(i-D,k) =
X(i-D,k)
Mapper
Interleaver
Conv. Encoder
X(i-D,k)
Figure by MIT OpenCourseWare.
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
37
First 802.11a chip
Image removed due to copyright restrictions.
[1]
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design
38
References
‰
‰
‰
‰
[1] T.H. Meng, B. McFarland, D. Su and J. Thomson "Design and implementation of an all-CMOS 802.11a
wireless LAN chipset," Communications Magazine, IEEE vol. 41, no. 8 SN - 0163-6804, pp. 160-168, 2003
[2] M. Krstic, K. Maharatna, A. Troya, E. Grass and U. Jagdhold "Implementation of an IEEE 802.11a
compliant low-power baseband processor," Telecommunications in Modern Satellite, Cable and
Broadcasting Service, 2003. TELSIKS 2003. 6th International Conference on vol. 1, no. SN -, pp. 97-100
vol.1, 2003.
[3] J. Thomson, B. Baas, E.M. Cooper, J.M. Gilbert, G. Hsieh, P. Husted, A. Lokanathan, J.S. Kuskin, D.
McCracken, B. McFarland, T.H. Meng, D. Nakahira, S. Ng, M. Rattehalli, J.L. Smith, R. Subramanian, L.
Thon, Y.-H. Wang and R. Yu "An integrated 802.11a baseband and MAC processor," Solid-State Circuits
Conference, 2002. Digest of Technical Papers. ISSCC. 2002 IEEE International vol. 1, no. SN -, pp. 126
451 vol.1, 2002.
[4] E. Grass, K. Tittelbach-Helmrich, U. Jagdhold, A. Troya, G. Lippert, O. Kruger, J. Lehmann, K.
Maharatna, K.F. Dombrowski, N. Fiebig, R. Kraemer and P. Mahonen "On the single-chip implementation
of a Hiperlan/2 and IEEE 802.11a capable modem," Personal Communications, IEEE [see also IEEE
Wireless Communications] vol. 8, no. 6 SN - 1070-9916, pp. 48-57, 2001.
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design
39