Iterative Multiuser Detection for
Convolutionally Coded
Asynchronous DS-CDMA
9th IEEE International Symposium on
Personal, Indoor, and Mobile Radio Communications
Boston, MA
September 9, 1998
VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY
Matthew Valenti and Brian D. Woerner
Mobile and Portable Radio Research Group
Virginia Tech
Blacksburg, Virginia
Virginia
Tech
MPRG
MOBILE & PORTABLE RADIO RESEARCH GROUP
1872
VIRGINIA POLYTECHNIC INSTITUTE
AND STATE UNIVERSITY
Introduction

Performance of multiple access systems can be
improved by multiuser detection (MUD).
Introduction





Suboptimal approximations
• Decorrelator, MMSE,DFE, PIC, SIC, etc.
Most studies on MUD concentrate on the uncoded
performance.


9/9/98
Verdu, Trans. Info. Theory ‘86.
Implemented with Viterbi algorithm, complexity O(2K).
Optimal MUD is too complex for large K.

Here we consider the effects of coding.
We propose a receiver structure that approximates joint MUD
and FEC-decoding.
The algorithm allows for asynchronous users and fading.
MUD for Coded DS-CDMA

Practical DS-CDMA systems use error correction
coding (convolutional codes).

Introduction



If MUD and FEC are to be used,the interface should
be improved.

9/9/98
Soft-decision decoding outperforms hard-decision decoding
(by about 2.5dB).
However, the optimal MUD passes hard-decisions to the
channel decoder!
Therefore it is possible for the coded performance of a
system with MUD to be worse than the coded performance
without the MUD.

The decoder for turbo codes gives insight on how to
improve this interface.
Use soft-decisions and feedback.
Relation to Other Work

T. Giallorenzi and S. Wilson

Optimal joint MUD/FEC-decoding
Background




Suboptimal approaches.





9/9/98
Trans. Comm. Aug. 1996
Uses a “super-trellis”.
High complexity: O(2WK)
Trans Comm. Sept. 1996
Separate MUD and Channel decoding.
Soft values passed from MUD to channel decoder.
No feedback used.
See also P. Hoeher’s paper at ICUPC ‘93.
Relation to Other Work

M. Reed, C. Schlegel, et al

Feedback from FEC-decoder to MUD
Background


Synchronous DS-CDMA


PIMRC ‘97
Close to single-user bound for K=5 users and spreading
gain of N=7.

9/9/98
Turbo Code Symp ‘97, ICUPC ‘97
Turbo codes


“One-shot” detector.
Convolutional codes


Similar to the decoder for turbo codes.
AWGN channel
Relation to Other Work

M. Moher

Background

Feedback from FEC-decoder to MUD.
Multiuser systems with high signal correlation.



Random interleaving.
Synchronous systems


Comm. Letters, Aug. 1998
Close to single user bound for K=5,10 and =0.6,0.75


9/9/98
Trans. Comm., July 1998
Asynchronous systems


FDMA with overlapping signals.
K-symmetric channel.
AWGN
Turbo Codes and Iterative
Decoding
Turbo Processing

9/9/98
A turbo code is the parallel concatenation of two
convolutional codes.


An interleaver separates the code.
Recursive Systematic Convolutional (RSC) codes are
typically used.
RSC
Encode
r
#1
Data
interleaver
RSC
Encode
r
#1
Output
Turbo Decoding
Turbo Processing

A turbo decoder consists of two elementary
decoders that work cooperatively.

Soft-in soft-out (SISO) decoders.


Feedback.


Received
Data
9/9/98
Implemented with Log-MAP algorithm
Each decoder produces a posteriori information, which is used
as a priori information by the other decoder.
Iterative
A priori probability
SISO
Decoder
#1
A priori
probability
SISO
Decoder
#2
Estimated
Data
Serial Concatenated Codes
Turbo Processing

The turbo decoder can also be used to decode
serially concatenated codes.

Data
Typically two convolutional codes.
Outer
Convolutional
Encoder
interleaver
Inner
Convolutional
Encoder
n(t)
AWGN
Turbo
Decoder
interleaver
APP
Inner
SISO
Decoder
9/9/98
deinterleaver
Outer
SISO
Decoder
Estimated
Data
Turbo Equalization
Turbo Processing

The “inner code” of a serial concatenation could be
an Intersymbol Interference (ISI) channel.

Data
ISI channel can be interpreted as a rate 1 code defined
over the field of real numbers.
(Outer)
Convolutional
Encoder
interleaver
n(t)
AWGN
ISI
Channel
Turbo
Equalizer
interleaver
APP
SISO
Equalizer
9/9/98
deinterleaver
(Outer)
SISO
Decoder
Estimated
Data
Turbo Multiuser Detection

The “inner code” of a serial concatenation could be
a MAI channel.
Turbo MUD

9/9/98


MAI channel can be thought of as a time varying ISI
channel.
MAI channel is a rate 1 code with time-varying coeficients
over the field of real numbers.
The input to the MAI channel consists of the encoded and
interleaved sequences of all K users.
System Diagram
d1
“multiuser interleaver”
Convolutional
Encoder
#1
interleaver #1
b1
Turbo MUD
MUX
dK
Convolutional
Encoder
#K
interleaver #K
y
9/9/98
SISO
MUD
MAI
Channel
n(t)
AWGN
bK
Λ (q )
APP
b
Ψ (q )
multiuser
interleaver
multiuser
deinterleaver
Turbo
MUD
Λ (q ')
Ψ(q ')
Bank of
K SISO
Decoders
dˆ ( q )
Estimated
Data
MAI Channel Model

Received Signal:
K
r (t )   sk (t )  n(t )
k 1
System Model
L
sk (t )   Pk [i ]bk [i ]ak (t  iT   k )e jk
i 1

Where:




ak is the signature waveform of user k.
k is a random delay (i.e. asynchronous) of user k.
Pk[i] is received power of user k’s ith bit (fading ampltiude).
Matched Filter Output:



yk [i ]    r (t )ak (t  iT   k )e  jk dt

9/9/98
Optimal Multiuser Detection
Algorithm: Setup

MUD

Place y and b into vectors:
y   y1[1], , yK [1], , y1[ L], , yK [ L]
b  b1[1], , bK [1], , b1[ L], , bK [ L]
Place the fading amplitudes into a vector:
c


P1[1],, Pk [1],, P1[ L],, PK [ L]

Compute cross-correlation matrix:

 1
 cos(i  j   j )  ai  j (t   i  j )a j (t   j  T )dt ,
 T

Gij  

1
 cos(
i  j  K   j )  ai  j  K (t   i  j  K ) a j (t   j ) dt ,
T

9/9/98
if i  j  K
if i  j  K
Optimal MUD: Execution

Run Viterbi algorithm with branch metric:
K 1


n
i (b) 
ln p(bi )  bi ci 2 yi  bi ci  2 bi  j ci d GK  j , (i ) 
Eb N o
j 1


 where
MUD
i mod K
 (i)  
 K


9/9/98
if (i mod K )  0
Note that most derivations of the optimal MUD drop
the p(b) term.


if (i mod K )  0
Here we keep it.
The channel decoder will provide this value.
The algorithm produces hard bit decisions.

Not suitable for soft-decision channel decoding.
Soft-Output MUD


Several algorithms can be used to produce softoutputs (preferably log-likelihood ratio).
Trellis-based.

MAP algorithm
MUD



SOVA algorithm


Hagenauer & Hoeher, Globecom ‘89
Non-trellis-based.


9/9/98
Log-MAP, Robertson et al, ICC ‘95
OSOME, Hafeez & Stark, VTC ‘97

Suboptimal, reduced complexity.
Linear: decorrelator, MMSE.
Subtractive (nonlinear): DFE, SIC, PIC.
Simulation Parameters

K=5 users


Example


Convolutional Code



24 by 22 block interleaver (L=528).
Log-MAP decoding.

9/9/98
Constraint length 3.
Rate 1/2.
Interleaving


Power controlled (same average power).
N=7 (processing gain), code-on-pulse.
Random spreading codes.

Both MUD and channel decoder.
3 iterations.
Simulation Results:
AWGN Channel
1
10

Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Single User Bound
0
10
-1
10
After the second iteration,
performance is close to
single-user bound for BER
greater than 10-4.

-2
BER
10

-3
10
-4
10

-5
10
Only a slight incremental
gain by performing a third
iteration.

-6
10
0
1
2
3
4
Eb/No in dB
5
6
7
For BER less than 10-4, the
curves diverge.
This behavior is similar to
the “BER floor” in turbo
codes.
The extra processing for the
third iteration is not worth it.
Simulation Results:
Rayleigh Flat-Fading Channel
1
10

Matched Filter
Turbo-MUD: iter 1
Turbo-MUD: iter 2
Turbo-MUD: iter 3
Single User Bound
0
10
Fully-interleaved Rayleigh
flat-fading.

-1
10

-2
BER
10
i.e. fades are independent
from symbol to symbol.
After second iteration,
performance is close to the
single-user bound.
-3
10

-4
10

The curves do not diverge
as they did for AWGN.
Why?

-5
10
-6
10
0
2
4
6
8
E b/No in dB
10
12
14
16

The instantaneous
received power is different
for the different users.
Therefore the MUD has
one more parameter it can
use to separate signals.
Conclusion

A strategy for iterative MUD/FEC-decoding is
proposed.

Conclusion




independently faded signals
code and bit asynchronism.
Proposed strategy was illustrated by simulation
example.


9/9/98
Based on the concept of turbo processing.
Similar to other researchers’ work, but the algorithm is
generalized to allow:
Significant performance gain by performing 2 iterations.
When signals are independently faded, the algorithm
exploits the differences in instantaneous signal power.
Future Work

The study assumes perfect channel estimates.

Conclusion


The proposed strategy is still very complex



O(2W+2K) per iteration.
Future work should consider the use of reduced complexity
multiuser detectors.
This structure could also be used for TDMA systems.



9/9/98
The effect of channel estimation should be considered.
The estimator could be incorporated into the feedback loop.

TDMA: only a few strong interferers, small K.
Highly correlated signals, can take advantage of this system.
Can use observations from multiple base stations.
See our work at VTC, ICUPC, and Globecom CTMC.