An Optimal Soft-Output Multiuser Detection Algorithm and its Applications Matthew C. Valenti...
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Transcript of An Optimal Soft-Output Multiuser Detection Algorithm and its Applications Matthew C. Valenti...
An Optimal Soft-OutputMultiuser Detection Algorithm
and its Applications
Matthew C. Valenti
Assistant ProfessorComp. Sci. & Elect. Eng.West Virginia University
Morgantown, WVU.S.A.
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
sio
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.