Multiuser Detection in CDMA
A. Chockalingam
Assistant Professor
Indian Institute of Science, Bangalore-12
achockal@ece.iisc.ernet.in
http://ece.iisc.ernet.in/~achockal
Outline
 Near-Far
Effect in CDMA
 CDMA
System Model
 Conventional MF Detector
 Optimum Multiuser Detector
 Sub-optimum Multiuser Detectors
– Linear Detectors
» MMSE, Decorrelator
– Nonlinear Detectors
» Subtractive Interference cancellers (SIC, PIC)
» Decision Feedback Detectors
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
2
DS-CDMA
 Efficient
means of sharing a given RF spectrum
by different users
 User
data is spread by a PN code before
transmission
 Base
station Rx distinguishes different users
based on different PN codes assigned to them
 All
CDMA users simultaneously can occupy
the entire spectrum
» So system is Interference limited
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
3
DS-SS
 DS-SS
signal is obtained by multiplying the
information bits with a wideband PN signal
Information
Bits
Carrier
Modulation
Tb
PN Signal
Information
Bits
Tb = N Tc
N : Processing Gain
Dr. A. Chockalingam
t
Tc
PN Signal
t
Dept of ECE, IISc, Bangalore
4
Processing Gain
 Ratio
of RF BW (W) to information rate (R)
Gp 
W
(e.g., In IS-95A, W = 1.25 MHz, R = 9.6 Kbps
R
1 . 25 X 10
 System
K 
i.e.,
Gp 
9 . 6 X 10
3
 133  21 dB )
Capacity (K) proportional to G p
G pG vG A
( E b / I o )G f
G v  2 . 67 (voice activity gain)
G A  2 . 4 (sectorization gain)
G f  1 .6
(other cell interference loss)
E b / I o  6 dB
Dr. A. Chockalingam
6
Dept of ECE, IISc, Bangalore
(typically required)
5
Near-Far Effect in DS-CDMA
 Assume K
users in the system.
 Let Ps be the average Rx power of each signal.
 Model interference from K  1 users as AWGN.
E
Ps T
 SNR at the desired user is b 
I0
N 0  ( K  1) Ps T c
 Let
one user is near to BS establishes a stronger
Rx signal equal to aPs , a  1
 SNR
then becomes
Eb
I0
 When a

Ps T
N 0  aP s T c  ( K  2 ) Ps T c
is large, SNR degrades drastically.
 To maintain same SNR, K  2 has to be reduced
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore i.e., loss in capacity.
6

Near-Far Effect

Factors causing near-far effect (unequal Rx Signal
powers from different users) in cellular CDMA
– Distance loss
– Shadow loss
– Multipath fading (Most detrimental. Dynamic range of
fade power variations: about 60 dB)

Two common approaches to combat near-far effect
– Transmit Power Control
– Near-far Resistant Multiuser Detectors
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
7
CDMA System Model
Data of User 1
Chip shaping
filter
1
Spreading Sequence
of user 1
Data of User 1
AWGN
Chip shaping
filter
2
Chip shaping
filter
K
Spreading Sequence
of user 2
Data of User 1
r (t )
To
Demod/
Detector
Spreading Sequence
of user K
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
8
Matched Filter Detector (MFD)
^
nT
r1
MF
User 1
^
nT
^
nT
rK
MF
User K
rk 
E k bk 

E jbj
jk
b 2 (n )
r2
MF
User 2
r (t )
b1 (n )
b K (n )
r  RA b  n
 nk
jk
E [ nn ]   R
T
Dr. A. Chockalingam
2
R:
Correlation Matrix
A  diag
Dept of ECE, IISc, Bangalore

E1 ,
E 2 ,...,
EK

9
MFD Performance: Near-Far Scenario
2-User system:
NFR 
Interferin
Desired
0.4
g User' s Rx Power
User' s Rx Power
NFR = 20 dB
0.1
NFR = 10 dB
Bit
Error Rate
NFR = 5 dB
NFR = 0 dB
E/b/No (dB)
• Problem with MF Detector: Treats other user interference
(MAI) as merely noise
• But MAI has a structure which can be exploited in the
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
detection process 10
Optimum Multiuser Detector
 Jointly
detect all users data bits
 Optimum
Multiuser Detector
– Maximum Likelihood Sequence Detector
 Selects
the mostly likely sequences of data bits
given the observations
 Needs
knowledge of side information such as
– received powers of all users
– relative delays of all users
– spreading sequences of all users
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
11
Optimum Multiuser Detector

Optimum ML detector computes the likelihood fn
 (b ) 

T
0

 r (t ) 

2

E k b k c k ( t )  dt

K

k 1
the sequence bk ,1  k

 K  that
and selects
minimizes
 (b )
The above function can be expressed in the form
T
c(r , b)  B r  B R B
where
r  r1 , r2 ,..., rK

T
B 
T

 and
T
E 1 b1 ,
E 2 b 2 ,...,
E K bK
is the correlation matrix with elements
T
where
 ij ( ) 
c
i
( t ) c j ( t   ) dt
0
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
12
Optimum Multiuser Detector
results in 2 K choices of the bits
of the K users
 { b1 , b 2 ,..., b K }

Thus Optimum Multiuser Detector is highly complex
– complexity grows exponentially with number of users
– Impractical even for moderate number of users
 Need
to know the received signal energies of all
the users
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
13
Suboptimum Detectors
 Prefer
– Better near-far resistance than Matched Filter Detector
– Lesser complexity (linear complexity) than Optimum
Detector

Linear suboptimum detectors
– Decorrelating detector
– MMSE detector
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
14
Decorrelating Detector
r1
r2
Linear Transformation
and Detector
Decision
1
^
R r
b  sgn()
rK
p
For the case of 2 users
(k )
and p e

 Q


Dr. A. Chockalingam
R 
2
E k (1   ) 



1
xx

(k )
e

 Q


Ek
R 
1
kk




1
1 
2
Dept of ECE, IISc, Bangalore
15
Decorrelating Detector
 For
the case of 2 users
and
R
1
 1

2 
1    
1
1
R  



1
 

1 


1
R r  



E 1 b1
E 2 b2
n1   n 2 
2

1 

n 2   n1 
2

1 

– R  1 r operation has completely eliminated MAI
components at the output (.e., no NF effect)
– Noise got enhanced (variance increased by a factor of
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
1
1 
16
2
)
Decorrelating Detector
 Alternate
representation of Decorrelating detector
^
T

b1
0
r (t )
c1 ( t )   c 2 ( t )
^
T

b2
0
c1 ( t )   c 2 ( t )
– By correlating the received signal with the modified signature
waveforms, the MAI is tuned out (decorrelated)
– Hence the name decorrelating detector
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
17
MMSE Detector
• Choose the linear transformation that minimizes
the mean square error between the MF outputs
and the transmitted data vector b
r1
r2
Linear Transformation
and Detector
1
A r
rK
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
Decision
^
b  sgn()
18
MMSE Detector
0
• Choose the linear transformation b  A r
where A is determined so as to minimize the
mean square error (MSE)
J ( b )  E [( b  A r ) ( b  A r )]
T
• Optimum choice of A that minimizes J (b ) is

A  R  I
0
Dr. A. Chockalingam
2

1
Dept of ECE, IISc, Bangalore
19
MMSE Detector
r1
r2
Linear Transformation
and Detector
R   I 
2
1
r
rK
Decision
^
b  sgn()
• When  2 is small compared to the diagonal
elements of R MMSE performance approaches
Decorrelating detector performance
• When  2 is large A 0 becomes  2 I (i.e., AWGN
becomes dominant)
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
20
Adaptive MMSE
Estimate of the
data bits
Linear
Transversal
Filter
Adaptive
Algorithm
 Several
Re()


Training bits
adaptation algorithms
– LMS
– RLS
 Blind
techniques
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
21
Performance Measures

Bit Error Rate
 Asymptotic
k 
Lt
efficiency: Ratio of SNRs with and
without interference

  0 
 Asymptotic
Dr. A. Chockalingam
ke
k
represents loss due to multiuser
interference
efficiency easy to compute than BER
Dept of ECE, IISc, Bangalore
22
Performance Measures
Optimum Detector
DC
1.0
MMSE
k
MF Detector
0.0
-20.0
Dr. A. Chockalingam
-10.0
0.0
Dept of ECE, IISc, Bangalore
10.0
20.0
 E2

 E
1




 dB
23
Subtractive Interference Cancellation
 Multistage
interference Cancellation approaches
– Serial (or successive) Interference Canceller (SIC)
» sequentially recovers users (recover one user per stage)
» data estimate in each stage is used to regenerate the
interfering signal which is then subtracted from the original
received signal
» Detects and removes the strongest user first
– Parallel Interference Canceller (PIC)
» Similar to SIC except that cancellations are done in
parallel
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
24
SIC
^
^
b1
bm
MF
Detector
MF
Detector
r (t )
Matched
Filter
Remodulate
& Cancel
e2
em
Stage-1
Dr. A. Chockalingam
e m 1
Remodulate
& Cancel
Stage-m
Dept of ECE, IISc, Bangalore
25
m-th Stage in SIC
MF Detector
MF
User m
^
em
bm
Select
Strongest
User
MF
User K
cm
^

Remodulate
& Cancel
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
Em
e m 1
26
Performance of SIC
 Good
near-far resistance
 Most performance gain in achieved using
just 2 to 3 stages
 High
NFR can result in good performance!
– Provided accurate estimates of amptitude and timing
are available
 Sensitive
to amplitude and timing estimation errors
– increased loss in performance for amplitude estimation
errors > 20 %
 Some
amount of power control may be required to
compensate for the near-far resistance loss due to
imperfect estimates and low NFR
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
27
PIC
MF
User 1
(1 )
1
r
^ (1 )
b1
r

r (t )

^ ( j)
( j)
1
^ ( j 1 )
K

b1
1i
Ei bi
i 1
i 1
MF
User K
r
(1 )
K
^ (1 )
bK
( j)
rK

Stage 1


Dept of ECE, IISc, Bangalore
bK
^ ( j 1 )
K
i 1
i K
Dr. A. Chockalingam
^ ( j)
Ki
Ei bi
Stage j
28
Performance of PIC
Performance of PIC
 Good
near-far resistance
 Similar
performance observations as in SIC
 Performance
of PIC depends more heavily
on the relative amplitude levels than on the
cross-correlations of the user spreading codes
 Hybrid
SIC/PIC architectures
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
29
DFE Detector
Tc
T  1
^
MF
User 1
b1
FFF
Centralized
Decision
Feedback
^
bK
Tc
T K
MF
User K
FFF
• Feedback current data decisions of the stronger users as well
• DFE multiuser detectors outperform linear adaptive receivers
• Complexity, error propagation issues
Dr. A. Chockalingam
Dept of ECE, IISc, Bangalore
30