An Optimal Soft-OutputMultiuser Detection Algorithm

and its Applications

Matthew C. Valenti

Assistant ProfessorComp. Sci. & Elect. Eng.West Virginia University

Morgantown, WVU.S.A.

mvalenti@wvu.edu

Intr

od

ucti

on

Outline of Talk

Turbo multiuser detection.• Related work.

System model.

The optimal SISO MUD algorithm

Applications of SISO MUD• Turbo multiuser detection.• Antenna arrays• Distributed multiuser detection.

Intr

od

ucti

on

Turbo Multiuser Detection

FECEncoder

#K

n(t)AWGN

SISOMUD

Bank ofK SISO

DecodersEstimated

Data

TurboMUD

interleaver #K

multiuserdeinterleaver

multiuserinterleaver

MAIChannelModel

Extrinsic Info

FECEncoder

#1interleaver #1

Parallelto

Serial

“multiuser interleaver”

1b

b

y

1d

KbuKd

)(ˆ qd

Channel

Time-varying FIR filter

Intr

od

ucti

on

Some Developments in Turbo Multiuser Detection

Gialllorenzi and Wilson• 1996: Trans. Comm.• Hypertrellis approach. Not iterative. No interleaving.

Vojcic, Shama, Pickholtz• 1997: ISIT • Optimal Soft Output MAP. Asynchronous. Not iterative.• No noise whitening.

Reed, Schlegel, Alexander, Asenstorfer• 1997: Turbo Code Symposium, PIMRC.• Several Journal Papers (Trans. Comm., JSAC, ETT)• Early work considered synchronous, later asynchronous.

M. Moher• 1998: Trans. Comm. (synchronous), Comm. Letters.

(asynchronous)• Based on cross entropy minimization.

System Model

encoder interleaver modulator

transmitter 1

encoder interleaver modulator

transmitter K

bank of

matched

filters

bank of

matched

filters

receiver 1

receiver M

asynchronous channel

AWGN or

complex Rayleigh fading

Y(1)

Y( )M

Op

tim

al S

ISO

MU

D

Whitened Matched Filter Output

Matrix notation for output of matched filter at mth receiver

Cholesky decomposition

Whitened matched filter output

Y R A V N( ) ( ) ( ) ( )m m m m colored noise

transmitted symbols (round-robin)

channel gains (diagonal)

crosscorrelations

R F F( ) ( ) ( )m m T mc h

Y F Y

F A V N

( ) ( ) ( )

( ) ( ) ( )

m m T m

m m m

c h

white noise, variance = No/(2Es)

lower triangular, only K diagonals

Op

tim

al S

ISO

MU

D

Metric for Optimal SISO MUD Trellis representation:

Noiseless Reconstruction of the signal:

Branch metric:

Now, just use MAP algorithm.

s si i i i i K 1 1 1b g l qV V V, ,...,

f s sim

i i i i jm

j

K

i jm

i j( )

,( ) ( )

10

1b g F A V

i i i im

i i i i

im

im

i ii i o

s

s s P Y i s s P s s

f s sN

E

1 1 1

1

2

2

b gb g

ln | , ln( )

( ) ( )YZ V

Squared Euclidian distance

between received symbol and

noiseless reconstruction of signal Term incorporating

the extrinsic information Z

constant

ignore for LLR

Ap

plicati

on

s

Turbo MUD forDirect Sequence CDMA

CDMA: Code Division Multiple Access• The users are assigned distinct waveforms.

Spreading/signature sequences

• All users transmit at same time/frequency. Use a wide bandwidth signal

• Processing gain Ns

Ratio of bandwidth after spreading to bandwidth before MUD for CDMA

• The resolvable MAI originates from the same cell. Intracell interference.

• MUD uses observations from only one base station. M=1 case.

1

0, )()(

sN

jccjkk jTtptg

Performance of Turbo-MUD for CDMA in AWGN

K = 5 users Spreading gain Ns = 7 Convolutional code: Kc = 3, r=1/2

Eb/No = 5 dB 1 K 9

0 1 2 3 4 5 6 710

-5

10-4

10-3

10-2

10-1

100

Eb/N

o in dB

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Single User Bound

1 2 3 4 5 6 7 8 910

-5

10-4

10-3

10-2

10-1

100

Number of users

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3

0 2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o in dB

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Single User Bound

1 2 3 4 5 6 7 8 910

-6

10-5

10-4

10-3

10-2

10-1

100

Number of users

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3

Performance of Turbo-MUD for CDMA in Rayleigh Flat-fading

K = 5 users Fully-interleaved fading

Eb/No = 9 dB 1 K 9

Ap

plicati

on

s

Turbo MUD for TDMA TDMA: Time Division Multiple Access

• Users are assigned unique time slots• All users transmit at same frequency• All users have the same waveform, g(t)

TDMA can be considered a special case of CDMA, with gk(t) = g(t) for all cochannel k.

MUD for TDMA• Usually there is only one user per time-slot per cell.• The interference comes from nearby cells.

Intercell interference.• Observations from only one base station might not be

sufficient. Performance is improved by combining outputs from multiple

base stations.

Performance of Turbo-MUD for TDMA in AWGN

K = 3 users Convolutional code: Kc = 3, r=1/2 Observations at 1 base station

Eb/No = 5 dB 1 K 9

0 1 2 3 4 5 6 7 8 9 1010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No in dB

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound

1 2 3 4 5 6 7 8 910

-6

10-5

10-4

10-3

10-2

10-1

100

101

Number of users

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No in dB

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound

1 2 3 4 5 6 7 8 910

-6

10-5

10-4

10-3

10-2

10-1

100

Number of users

BE

R

Matched Filter Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4

Performance of Turbo-MUD for TDMA in Rayleigh Flat-Fading

K = 3 users Fully-interleaved fading

Eb/No = 9 dB 1 K 9

Ap

plicati

on

s

Antenna Arrays Consider an antenna array with M elements.

• In this case, M>1 Each element has its own multiuser detector. Can use the SISO MUD algorithm. Antenna elements should be far enough apart that the

signals are uncorrelated.

MultiuserDetector

#1

MultiuserDetector

#M

1y

My

)(ˆ qd

arrayelement

#1

arrayelement

#M

Ap

plicati

on

s

Distributed Multiuser Detection Why must the elements of an antenna array be located

at the same base station? We could synthesize an antenna array by using the

antennas of spatially separated base stations. A benefit is now signals will be uncorrelated.

MultiuserDetector

#1

MultiuserDetector

#M

1y

My

)(ˆ qd

basestation

#1

basestation

#M

F2

F1

F3

F4

F5

F6

F7

F2

F1

F3

F4

F5

F6

F7

F2

F1

F3

F4

F5

F6

F7

Cellular Network Topology

Conventional layout• Isotropic antennas in cell center• Frequency reuse factor 7

Alternative layout• 120 degree sectorized antennas

Located in 3 corners of cell

• Frequency reuse factor 3

1 2 3 4 5 6 7 8 910

-4

10-3

10-2

10-1

100

Number of users, K

BE

R

MF at closest BS MF with MRC MUD at closest BSDistributed MUD

Performance of Distributed MUD

Eb/No = 20 dB 1 K 9 For conventional receiver:

• Performance degrades quickly with increasing K.

• Only small benefit to using observations from multiple BS.

With multiuser detection:• Performance degrades very

slowly with increasing K. • Order of magnitude

decrease in BER by using multiple observations.

Now multiple cochannel users per cell are allowed.

Ap

plicati

on

s

Cooperative Decoding for the TDMA Uplink

Now consider the coded case. The outputs of the MUD’s are summed and passed

through a bank of decoders. The SISO decoder outputs are fed back to the multiuser

detectors to be used as a priori information.

MultiuserDetector

#1

MultiuserDetector

#M

Bank ofK SISOChannelDecoders

1y

My

)(ˆ qd

Extrinsic Info

EstimatedData

0 2 4 6 8 10 12 1410

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No in dB

BE

R Matched Filter MF w/ MRC Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4Single-user bound

Performance of Cooperative Decoding

K = 3 transmitters• Randomly placed in cell.

M = 3 receivers (BS’s)• Corners of cell• path loss ne = 3

Fully-interleaved Rayleigh flat-fading

Convolutional code• Kc = 3, r = 1/2

1 2 3 4 5 6 7 8 910

-6

10-5

10-4

10-3

10-2

10-1

100

Number of users

BE

R

Matched Filter MRC Turbo-MUD: iter 1Turbo-MUD: iter 2Turbo-MUD: iter 3Turbo-MUD: iter 4

Performance of Cooperative Decoding

Eb/No = 5 dB

1 K 9 • Randomly placed in cell.

M = 3 receivers For conventional receiver:

• Performance degrades quickly with increasing K.

• Only small benefit to using observations from multiple BS.

With multiuser detection:• Performance degrades

gracefully with increasing K. • No benefit after third iteration.

Could allow an increase in TDMA system capacity.

Con

clu

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n

Conclusion

An optimal SISO MUD algorithm has been derived.• Complexity is exponential in the number of users.

For many applications, the SISO MUD is too complex.• Traditional turbo-MUD for CDMA systems.

However, there are many applications where the SISO MUD is suitable.

• Turbo-MUD for TDMA, hybrid CDMA/TDMA, WCDMA• SISO MUD can be used to achieve distributed detection.

Future work.• Comparison against suboptimal approaches.• Other applications of SISO MUD algorithms.