communication system design

Practical multitone architectures

Lecture 4

Vladimir Stojanović

6.973 Communication System Design – Spring 2006

Massachusetts Institute of Technology

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].

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 ( ) � ε ( ) −ε (b − β )e b b

⎛ e b g ( ) ⎞ n 2 ⎜

n n n⎟b = log 1 +

⎝ Γ ⎠

n n n n n n

bit increment

� Efficiency of bit distribution� Can’t move a bit from one channel to another and reduce the

total energy

6.973 Communication System Design 2



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




Efficientizing example

� 1+0.9D-1 channel (Pe=10-6, gap=8.8dB, PAM/QAM) � PAM and single-sideband � QAM

bn

b +1n




Rate adaptive solution

Need also to satisfy the energy constraint�

� E-tightness (ET) � Can’t add another bit without violating the E constraint

6.973 Communication System Design

If energy constraint violated subtract the most costly bit

If energy less than max add the bit that costs the least to add

5



LC - Rate adaptive algorithm

� ET example (continue from EF example) � Start from efficient distribution that blows up the energy

constraint = 8 1 8Nε ⋅ = x

� Margin Nε 8x = =1.8dBε 5.32

� Levin-Campello Rate Adaptive algorithm � Choose any bit distribution � Make it efficient using (EF algorithm) � Make it energy tight using (ET algorithm)




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




Channel partitioning� Divide the channel into a set of parallel,

independent channels

� Generalized Nyquist criterion � No interference between symbols � No interference between sub-channels




Figure by MIT OpenCourseWare.

.

.

.

...

.

.

.

X1,k

X2,k

h(t) y(t)

n(t)x(t)

h*(T-t)

XN-1,k

XN,k

X1,k n2,k

nN,k

n1,ky1,k

y2,k

yN,k

X2,k

XN,k

Qk(MIMO)

x

ϕ1(t)

ϕ2(t)

ϕ∗1(T-t)

ϕ∗2(T-t)

ϕ∗N-1(T-t)t=T

t=T

t=T

t=T

yN-1,k

y1,k

y2,k

yN,kϕ∗N(-t)

ϕN-1(t)

ϕN(t)

++

+

+

+

(lower case yindicates normalizing||p|| factors included)

n=1

n=1k

x(t)

x(t)

=

=

h(t) * x(t) =

=

=

xn . ϕn(t)

xn,k . ϕn(t - kT)

xn,k . ϕn(t - kT) * h(t) =

xn,k . pn(t - kT)

N

N

n=1k

N

n=1k

N

pm(t) * pn(-t)||pm|| . ||pn||

*

Qk = Q(kT)

Qk = Iδk

qn,m (t)∆

Modal modulation

� Transmission with eigen-functions

9

Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 20MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.



06.

r(t) = h(t) * h*(-t) (-TH / 2, TH / 2)

ρn ϕn (t) =.

.

.

....

∫T / 2

-T / 2r(t - τ)ϕn(τ)dτ n = 1,..., , t [-(T - TH) / 2, (T + TH) / 2)]

X1,k

X2,k

h(t) y(t)

n(t)x(t)

h*(T-t)

XN-1,k

XN,k

n=1n=1

n=1

x

ϕ1(t)

ϕ2(t)

ϕ∗1(T-t)

ϕ∗2(T-t)

ϕ∗N-1(T-t)t=T

x(t)y(t)

==

=y(t)

t=T

t=T

t=T

yN-1,k

y1,k

y2,k

yN,kϕ∗N(-t)

xnϕn(t)

xn . [r(t) *

ϕN-1(t)

ϕN(t)

++

NN

N

. ϕn (t)

ϕn (t)] + n(t)~

(ρnxn)

Per-channel MAP is optimalProblem is vector AWGN

eigenfunctions (channel dependent)

ϕk (t ) Channel


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

is also a valid eigen-function for inf symbol period � Eigen-functions are not unique

�

� 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

10




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




Discrete time channel partitioning

� Digital realization




X0

X1

XN-2

XN-1

m0

m1

mN-2

mN-1

+ +x

1/T 1/T

DAC

DA

C

x(t)

(t) (-t)(t)h

(t)n

*

(LPF) y(t) (LPF)

y = Px + n

f *N-1

f *N-2

f *1

f *0 Y0

Y1

YN-1

YN-2

yN-1

yN-2

y0

=

p0

p0

p0

p1

p1

py

py

pypy-1

0

0

00 0

0

0

0

xN-1

x0

x-y

x-1+

nN-1nN-1

n0

y


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




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 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].


DMT and OFDM

� Discrete multitone (DMT) and Orthogonal frequency Division Multiplexing (OFDM)

� DMT used on slowly time-varying channels � Optimize bn and En per sub-channel

� OFDM uses same channel partitioning as DMT � 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




DMT/OFDM channel partitioning

� Make channel “look” circular � Repeat the tail of the symbol at its beginning

� Add cyclic prefix to each transmitted symbol CP

DMT 0 ...x 1...N Nx xν− −1...N Nx xν− − VC 0 ...x 1...N Nx xν− −0...0

2 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




IDFT and DFT as orthogonal transformations

� DMT and OFDM use IDFT and DFT as eigen-vectors

DFT IDFT

� Proof channel gain at tone n

qn is eigen-vector of P #




DMT/OFDM implementation

/(� Data rate penalty N N +ν )

18




XN-i = Xi if x(t)is real

XN-1

XN-2

X1

X0

.

.

.IDFT

.

.

.DFT

Y0

Y1

YN-2

YN-1

serial toparallel& cyclic

prefixremover

parallelto serial& cyclic

prefixinsert

Forces P to be cyclic matrix

DAC

ADC

(LPF)(LPF) y(t)

ϕ(t) h(t) ϕ (-t)

n(t)

+

1 N+v=

x(t)

1 N+v=Γ T TΓ


One-tap frequency equalizer� Need to compensate for channel attenuation

� To recover the original constellation distance





Rx/Tx WindowingRectangular windowRaised cosine 5% Raised cosine 25%

Can overlap as long as sum is constant




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




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




Asymmetric digital subscriber line (ADSL)

� Symbol rate T=250us � Nd=256, 4.3125kHz wide

� 1/T’=2.208 MHz (CP = 40 samples) � Each time domain symbol 2*256+40=552 samples

� 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




video switch

ADSL

ADSL

Split

Telco CO

POTS

UpDown

0 H

z

10 k

Hz

138

kHz

1.1

MH

z

frequency

12 Mbps

1.5 Mbps

psd

ADSL

ADSLAccessMux

(DSLAM)

SplitADSL

internet

POTS(or ISDN)

Switch

UPDown


802.11a Wireless LAN example� Up to 54Mbps symmetrically (<100m) � 1-3 Tx power levels � Complex baseband

� unlike ADSL which is real baseband � N=64 (-31 … 31) (so 128 dimensions)

� Symbol length = 80 samples, CP=16 � Symbol rate 250kHz (T=4uS, T’=50ns), CPguard=0.8us

� FCC demands flat spectrum so no energy-allocation � The only knob is data rate selection

� Broadcast channel – can’t optimize bit allocation

not used

4 pilots 48 data tones




R (Mbps) constellation code rate bn bbn

69

121824364854

BPSKBPSK

64QAM64QAM16QAM16QAM

4QAM4QAM

1/21/2

1/2 1/2

1/2

1/2

3/4

3/4

3/4

3/4

3/4

3/4

3/41/4

3/23/2

3/2

9/49/2

3/81

12

3

2436487296

144192216

40 mW

5.15 GHz 5.25 GHz20 MHz

5.35 GHz 5.725 GHz 5.825 GHz

200 mW 800 mW

52 carriers total, each ~ 300 kHz

20 MHz



High-level system view




Data link control layer (DLC)

Physical radio layer (PHY)

Digital

Viterbidecoder +

descrambler

Demodulation+

deinterleaver

Guard interval

extraction +FFT

Scrambler +forward error

correction (FEC) coder

Interleaver+

modulation

IFFT +guard

intervalinsertion

Synchronization

Ana

log

front

-end

D/A

A/D

Analog


Transceiver architecture

[2]


FFT/IFFT

Cyclic prefix

Window

ing

DA

C

Upconvert

Synchronizer

Rem

ove prefix

AG

C&

AD

C

LNA

& D

ownconvert

Channel estim

atorP

ilot insertion

Mapper

Encoder

Interleaver

Descram

bler

Viterbi decoder

Deinterleaver

Dem

apper

Scram

bler



Transmitter architecture detail




MACData

ScramblerConvolutional

EncoderPuncturer

SignalMapper

Preamble

Interleaver

CyclicExtendIFFT

Modulation&

Upconvert

D/A

RF

Transmitter (Digital Components) Transmitter (Analog Components)


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?




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




Convolutional Encoder� Rate 1/2 convolutional encoder

� Punctured to obtain 2/3 and 3/4 rate � Omit some of the coded bits

Source Data

Encoded Data

Bit Stolen Data(sent/received data)

Bit Inserted Data

Decoded Data

Inserted Dummy Bit

Stolen Bit

Punctured Coding (r = 3/4)

Output Data B

Input Data

Output Data AX X X X X X X X X

A

A A A A A

B B B B B B1

A1 A4

6

A60

43

A3

7

A7

1 2 5 6 80 43 7

2

B2

5

B5

6

B6

8

B8

0

B0

3

B3

A A A A AA A A

B B B B B B B B B1 5 6 80

A0

43 7

1 2 5 6 80 43 7

y y y y y y y y y0 1 2 3 4 5 6 7 8

Tb Tb Tb Tb Tb Tb

B4

A5A2

B1

A8

B7

A2

g0=1338

g1=1718

� 64-state (constraint length K=7) code � Viterbi algorithm applied in the decoder





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




Pilot insertion and FFT/IFFT

� Pilot insertion � Pilots BPSK, prbs modulated

� FFT and IFFT shared � Just flip the Re and Im inputs




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)

Typical Signal Spectrum(an example)

-20 dBr

-28 dBr

-40 dBr

-30 -20 -11 -9 30209 11fcFrequency (MHz)

Transmit spectrum mask


Receiver architecture




I and Q fromanalog

front-endADC FIR

RemoveDC

of fsetRotate FFT

Channel

FIR

Rx gainto analogfront-end Signal

detectand AGC

Auto-correlate

Frequencylock

Symboltiming

Pipelinecontrol

Channelestimate

andtracking

Deinterleave Viterbi

Rx datato MAC

correct


Pilot tracking and channel correction

� OFDM packet structure




8 + 8 = 16 µs

Signal Detect,AGC, DiversitySelection

Coarse Freq.Offset EstimationTiming Synchronize

Channel and Fine FrequencyOffset Estimation

RATELENGTH

SERVICE + DATA DATA

Data 1 Data 2

0.8 + 3.2 = 4.0 µs 0.8 + 3.2 = 4.0 µs 0.8 + 3.2 = 4.0 µs10 x 0.8 = 8 µs 2 x 0.8 + 2 x 3.2 = 8.0 µs

t1 T1 T2t2 t3 t4 t5 t6 t7 t8 t9t10 SIGNALGI GI GIGI2

angle adjust

to de-interleaver

compositechannel correctiondata

long2 training

long1 trainingfrom fft

fir complexinverse

pilotmagnitudemultiply

magnitudeadjust

training symbol pilots

to timing controlsymbol

timing adjust

pilots

+

channelcorrectionmultiply

pilottracking

core

rotate



Synchronizer

36




ProcessingData Path

NCO FFT

crosscorrelator

OutputSymbols

InputData

Tracking Data Path

MovingAverage

(16)Jc(k)

JF(k)

CombineIg.1(.)

IP

α

MovingAverage

βε

IJ*

Z-16 Z-49

PlateauDetector


Channel estimator




Estimation Buffer

(Circular Buffer)

Pilot SignCorrection

DelayBuffer

(D)

ReferenceSign

Correction

Sync. + FFTResidual

PhaseCorrection

SoftDemapper Deinterleaver Soft

Viterbi

Channel Estimator

MapperZero Forcing

Equalizer

HREF (k)

Y(i-D,k)Interleaver Conv. Encoder

X(i,k) =Y(i,k)

H(i-D,k)

H(i-D,k)

X(i-D,k)

Y(i-D,k)H(i-D,k) =

X(i-D,k)

X(i,k)


First 802.11a chip

[1]




Image removed due to copyright restrictions.

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 200MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.


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