Transcript WCDMA system

Multi-user CDMA
Enhancing capacity of wireless
cellular CDMA
Characterizing asynchronous CDMA system

Normalize power for each user:
1 t 2
0 si (t )dt  1, i  1, 2, U
tm
m
U

ˆ (tm )  m jj   mij  n j
Integrate and dump yields at the decision time: m

Intended signal for the j:th user:

1 t
User interference (MAI): mij  0
tm
i 1
i j
2(35)
m jj 
m
1 t
0
tm
m
Pj s j (t )v j (t )dt  Pj
Ps
(t )v j (t )dt  Pi ij
i i
Timo O. Korhonen, Helsinki University of Technology
Characterizing asynchronous CDMA system (cont.)

The AWGN component is at the the decision time
nj 


1 t
0 n(t )v j (t )dt
tm
m
Sum effect of user interference is a function of (1) applied codes
crosscorrelation, (2) modulation method, (3) user power balance,
(4) code synchronization, (5) channel characteristics
The j:th user experiences the SNR:
( SNR) j 
( SNR ) j 
3(35)

m 2jj
E   mij  n j 
i

2

Pj
2


 

E    mij    2 E    mij n j    E n 2j 
 

 i
 i
Timo O. Korhonen, Helsinki University of Technology
Evaluating different interference and noise
components for multiple access

The background noise power is filtered by the code matched filter
or correlator:

E n 2j  

2

2
Gn ( f ) Vi ( f ) df
tm
N
N 1
  0  2 vi2 (t )dt  0
2tm
 2  tm



0

The crossproduct component 2E    mij n j   is averaged into zero.

i

The user interference assuming equal rates and code
autocorrelations:
2
 

E    mij 

  i
where
E[ ij2 ] 
4(35)
U
 U U
 ij2 
   E  mij mkj    PE
i
i 1
 i 1 k 1
i j k  j
i j
2
2
2
R
(

)
d


s
tm 0
tm 0
t1
t1
2
 
2 t1
1

d


 t
3 tm

1
Timo O. Korhonen, Helsinki University of Technology
SNR for the asynchronous CDMA

The user crosscorrelation power can be expressed by using the
effective bandwidth:
2

1 

Beff   G( f )df /  G 2 ( f )df

2
that evaluates for the code matched filter as
Beff 
and finally
E[ ij2 ] 

3
4t1
1
2tm Beff
Therefore the j:th user experiences SNR of
( SNR ) j 
Pj
 1  N0
Pi 


2
t
B
i 1
 m eff  2tm
U
i j

Received power
2tm Beff Pj
U
N 0 Beff   Pi
i 1
i j
MAI component
AWGN component
5(35)
Timo O. Korhonen, Helsinki University of Technology
Perfect power control
U


Equal received powers for U users means that
 P  (U  1)P
i 1
i j
i
r
2tm Beff Pr
Therefore ( SNR)O 
N0 Beff  (U  1) Pr
and the number of users is

 1
1 
U  1   2tm Beff 

 ,
(
SNR
)
(
SNR
)

O
1 

2t P
where SNR1  m j  2 Eb
N0
N0


Example: SNRO = 11.5 dB
R=30 kb/s
Note that there exist the limit for
the maximum number of users
that is not a function of Eb/N0
6(35)
Timo O. Korhonen, Helsinki University of Technology
Unequal received powers and the near-far -effect

Assume all users apply the same power but their distance to the
receiving node is different. Hence the power from the i:th node is
Pi  P0 / dia

where d is the distance, and a: propagation attenuation
coefficient, a = 2 for free space. In multipath environment in UHF
range (300 MHz… 3 GHz), a = 3 … 4.
Express the power ratio of the i:th and j:th node at the common
reception point
a
a
d j 
Pi  d j 

 Pi  Pj  
Pj  di 
 di 
 ( SNR)O 
2tm Beff Pj
a
 dj 
N 0 Beff     Pj
i 1  d i 
U
i j
7(35)
Timo O. Korhonen, Helsinki University of Technology
The near-far effect in asynchronous CDMA

In order to have the required (SNR)0 it is therefore required that
a
dj 

 d   2tm Beff
i 1  i 
U
i j



 1
1 



 ( SNR)0 ( SNR)1 
SNR1 
2tm Pj 2 Eb

N0
N0
Note that the near-far -effect is manifested here because just one
sum term on the left side of this equation is adequate to fulfill the
condition
Example: Assume that all but one transmitter have the same
distance to the receiving node di  d j , i  j and i  1 . The one
transmitter has the distance d1  d j / 2.5
Assume further a=3.68, SNR=11.5 dB, Rb = 30 kb/s, Beff = 20
MHz and received Eb/N0 = 12.5, now
a
 dj 
3.68

 d   2.5  U  2  U  14
i 1  i 
U
i j
8(35)
Timo O. Korhonen, Helsinki University of Technology
Near-far effect (example cont.)

By using perfect power control the number of users is

U  1  int  2tm Beff



 1
1 


  42
 ( SNR)0 ( SNR)1 
Hence the presence of this single user so near has dropped the
number of users into almost 1/3 part of the maximum number
If this user comes closer than
d1  d j / 2.78

all the other users will be rejected, e.g. they can not communicate
in the system in the required SNR level. This illustrates the nearfar effect.
To minimize the near-far effect efficient power control is realized
in asynchronous CDMA-systems. (Closed and open loop power
control.)
9(35)
Timo O. Korhonen, Helsinki University of Technology
Multiple Access Interference (MAI)




For multiple access codes often have relatively good
crosscorrelations as Gold codes (asynchronous usage) or
Walsh codes (synchronous usage)
Quite often, however, correlation properties destroyed by
multipath (as happens in wireless communications)
Also Near-far-effect has a tendency to increase MAI into
harmful levels
Hence compensation of MAI would yields additional
capacity. This can be achieved by
 Code waveform design
 Power control
 FEC codes
 Adaptivity: - spatial - frequency - time
 Multiuser detection
10(35)
Timo O. Korhonen, Helsinki University of Technology
Multi-user CDMA






The conventional detector
Mitigating the effect of MAI
Multi-user detection (MUD) limitations and potential
benefits
Matrix-vector notations
Synchronous and asynchronous channels
Detector classification and properties
 Maximum likelihood sequence detection
 Linear detectors
 Decorrelating detector
 Minimum mean-square error detector
 Polynomial expansion detector
 Subtractive interference cancellation
 Serial and parallel cancellation techniques
 Zero-forcing decision feedback detector
11(35)
Timo O. Korhonen, Helsinki University of Technology
Background





CDMA capacity is in great deal limited by multiple access
interference (MAI)
MAI is introduced by
 breaking down code orthogonality due to
 code design
 always by multipath propagation
 other cells build up interference
Multiuser detection is a method by which MAI can be
suppressed
Multiuser detection is computationally demanding, thus it
has become applicable quite lately
WCDMA-system has a provision for using multiuser
detection at base stations
12(35)
Timo O. Korhonen, Helsinki University of Technology
Received signal


Assume
 single path AWGN channel
 perfect carrier synchronization
 BPSK
Received signal is therefore
K
r (t )   Ak (t ) g k (t )d k (t )  n(t )
k 1
where for K users
Ak (t ) is the amplitude
g k (t ) is the signature code waveform
d k (t ) is the modulation of the k:th user
n(t ) is the AWGN with N0/2 PSD

Note that there are PG chips/bit (PG:processing gain)
13(35)
Timo O. Korhonen, Helsinki University of Technology
Conventional detection

The conventional BS receiver for K users consists of K
matched filters or correlators:
r (t )
Tb
0
x(t )dx
decision
g1 (t )
Tb
0
x(t )dx
decision
dˆ1
dˆ2
g2 (t )
Tb
0
x(t )dx
decision
dˆK
gK (t )

Assumed that background noise is Gaussian, each user is
detected without considering deterministic noise of the
other users
14(35)
Timo O. Korhonen, Helsinki University of Technology
Output for the K:th user without MUD



Detection quality depends on code cross- and
1
autocorrelation
i ,k   gi (t ) g k (t )dt
Tb Tb
Hence we require a large autocorrelation and small
crosscorrelation
 i ,k  1, i  k

0  i ,k  1, i  k
The output for the K:th user consist of the signal, MAI and
filtered Gaussian noise terms
1
yk  T r (t ) g k (t )dt
Tb
b
yk  Ak d k   i 1 i ,k Ai d i 
K
ik
1
n(t ) g k (t )dt

T
Tb
b
yk  Ak d k  MAI k  zk
15(35)
Timo O. Korhonen, Helsinki University of Technology
MAI versus ISI (Inter-Symbolic Interference)


Multiuser detection main classification:
 linear
 subtractive
Note that there exist a strong parallelism between the
problem of MAI and that of ISI:
Asynchronous K-user channel can be
modeled with a single user ISI
channel with memory of K-1

For this reason a number of multiuser detectors have
their equalizer counter parts as:
 maximum likelihood
 zero-forcing
 minimum mean square
 decision feedback
16(35)
Timo O. Korhonen, Helsinki University of Technology
Zero forcing equalizer for ISI cancellation



Classical technique to combat ISI is to use zero-forcing
equalizer (ZFE)
Principle used also in decorrelating MUD
ZFE is a time domain linear filter (or convolver) whose
discrete convolution sum can be required
 to yield zero values outside of sampling instances
 to be maximized at the sampling instant
17(35)
Timo O. Korhonen, Helsinki University of Technology
18(35)
Timo O. Korhonen, Helsinki University of Technology
19(35)
Timo O. Korhonen, Helsinki University of Technology
Benefits and limitations of multiuser detection
PROS:




Significant capacity improvement - usually signals of the
own cell are included
More efficient uplink spectrum utilization - hence for
downlink a wider spectrum may be allocated
Reduced MAI and near-far effect - reduced precision
requirements for power control
More efficient power utilization because near-far effect is
reduced
CONS:


If the neighboring cells are not included interference
cancellation efficiency is greatly reduced
Interference cancellation is very difficult to implement in
downlink where, however, largest capacity requirements
exist
20(35)
Timo O. Korhonen, Helsinki University of Technology
Matrix-vector notation

Assume a three user synchronous system with the
outputs
 y1  A1d1   2,1 A2 d 2  3,1 A3d3  z1

 y2  1,2 A1d1  A2 d 2  3,2 A3 d3  z2
y   Ad   A d  A d  z
1,3 1 1
2,3 2 2
3 3
3
 3
 y1   1
 y   
 2   1,2
 y3   1,3
 2,1
1
 2,3
3,1   A1
3,2   0

1   0
0
A2
0
0   d1   z1 
0   d 2    z2 
   
A3   d3   z3 
that is expressed by the matrix-vector notation as
y  RAd  z
matched filter outputs
correlations between
each pair of codes
21(35)
noise
data
received amplitudes
Timo O. Korhonen, Helsinki University of Technology
The data-term and the MAI-term

Matrix R can be partitioned into two parts by setting
R  IQ
and therefore MF outputs y  RAd  z can be expressed
as
y  Ad  QAd  z



Note that hence Q contains off-diagonal elements or R (or
the crosscorrelations)
Therefore the term Ad contains decoupled data and QAd
represents the MAI
Objective of all MUD schemes is to cancel out the MAIterm as effectively as possible (with respect of HW and
computational efficiency)
22(35)
Timo O. Korhonen, Helsinki University of Technology
Asynchronous and synchronous channel


In synchronous detection decisions can be made bit-by-bit
In asynchronous detection bits overlap and multiuser
detection is based on taking all the bits into account
K
r (t )   Ak (t ) g k (t )d k (t   k )  n(t )
k 1
User 1
User 2
1
3
2
5
4
 1  2 Tb  1

6
User 1
1
3
5
User 2
2
4
6
3Tb   2
3Tb  1
Tb  1
The matrix R contains now the partial correlations that
exist between every pair of the NK code words (K users,
N bits)
23(35)
1
Timo O. Korhonen, Helsinki University of Technology
Asynchronous channel correlation matrix

In this example the correlation matrix extends to 6x6
dimension:
y  RAd  z
 1

 1,2
 0
R
 0
 0

 0


 2,1
0
0
0
1
3,2
0
 2,3
1
 4,3
0
0
0
0
3,4
1
5,4
0
 4,5
1
0
0
0
5,6
0 
0 

0 
0 
 6,5 

1 
Note that the resulting matrix is sparse because most of
the bits do not overlap
Sparse matrix can be utilized to alleviate computational
difficulties
24(35)
Timo O. Korhonen, Helsinki University of Technology
Maximum-likelihood sequence detection

Optimum multiuser detection uses maximum-likelihood
principle:
Considering the whole received sequence
find the sequence estimate that has the
minimum distance to the received
sequence

The ML principle
 has the optimum performance
 has severe computational difficulties - In exhaustive
search 2NK vectors to consider! (K users, N bits)
 can be implemented by using Viterbi-decoder that
reduces computations approximately to 215xN
 requires estimation of received amplitudes and phases
that takes still more computational power
25(35)
Timo O. Korhonen, Helsinki University of Technology
Decorrelating detector

The decorrelation detector applies the inverse of the
correlation matrix
Ldec  R1
and the data estimate is therefore
dˆ dec  R 1y
 R 1 ( Ad  QAd  z )
RAd
 Ad  R 1z  Ad  z dec



We note therefore that the decorrelating detector
completely eliminates the MAI
Note that the noise is filtered by the inverse of correlation
matrix - This results in noise enhancement
Mathematically decorrelating detector is similar to zero
forcing equalizer used to compensate ISI
26(35)
Timo O. Korhonen, Helsinki University of Technology
Decorrelating detector properties summarized








Provides substantial performance improvement over
conventional detector under most conditions
Does not need received amplitude estimation
Has computational complexity substantially lower that the
ML detector (linear with respect of number of users)
Corresponds ML detection when the energies of the users
are not know at the receiver
Has probability of error independent of the signal energies
Optimal near-far resistance metric
Noise enhancement
High computational complexity in inverting R
27(35)
Timo O. Korhonen, Helsinki University of Technology
Minimum mean-square error (MMSE) detector






Based on solving MMSE optimization problem where
2
E[ d  Ly ]
should be minimized
This leads into solution
ˆd  LMMSE y  R  ( N0 / 2)A2  1 y


One notes that under high SNR this solution is the same
as decorrelating receiver
This multiuser technique is exactly equal to MMSE linear
equalizer used to combat ISI
Pros: Provides improved noise behavior with respect of
decorrelating detector
Cons:
 Requires estimation of received amplitudes
 Performance depends on powers of interfering users
28(35)
Timo O. Korhonen, Helsinki University of Technology
r (t )
MF
user 1
Aˆ1 (t  Tb )
decision
Tb





r (t  Tb )
dˆ1
g1 (t  1  Tb )
- sˆ1 (t  Tb )
+
r1 (t )
To the next stage
Successive interference cancellation (SIC)
Each stage detects, regenerates and cancels out a user
First the strongest user is cancelled because
 it is easiest to synchronize and demodulate
 this gives the highest benefit for canceling out the
other users
Note that the strongest user has therefore no use for this
MAI canceling scheme!
Pros: minimal HW and significant performance
improvement when compared to conventional detector
Cons: Processing delay, signal reordered if their powers
changes, in low SNR:s performance suddenly drops
29(35)
Timo O. Korhonen, Helsinki University of Technology
Parallel interference cancellation (PIC)
r (t  Tb )
sˆ1 (t  Tb )
dˆ1 (0)
dˆ2 (0)
dˆK (0)
Aˆ1 (t  Tb )
sˆ2 (t  Tb )
Aˆ2 (t  Tb )
spreader
sˆK (t  Tb )
amplitude
estimation

i 1
 sˆi (t ) i2
 sˆ (t ) i K
AˆK (t  Tb )

s
(
t
)
ˆ
i
i
dˆ1 (1)
+
matched
filter
bank
ˆ
decisions d2 (1)
and
stage
weights dˆK (1)
parallel
summer
With equal weights for all stages the data estimates for
each state are
dˆ (m  1)  y  QAdˆ (m) y  Ad  QAd  z
 Ad  QA(d  dˆ (m))  z
Number of stages determined by required accuracy
(Stage-by-stage decision variance can be monitored)
30(35)
Timo O. Korhonen, Helsinki University of Technology
PIC variations



PIC variations


SIC performs better in non-power controlled channels
PIC performs better in power balanced channels
Using decorrelating detector as the first stage
 improving first estimates improves total performance
 simplifies system analysis
Linearly combining the soft-decision outputs of different
stages of the PIC detector
 noise correlations between stages can be used to
cancel out each other improving performance greatly
Doing a partial MAI cancellation at each stage with the
amount of cancellation increasing for each successive
stage
 tentative decisions of the earlier stages are less
reliable - hence they should have a lower weight
 very large performance improvements have achieved
by this method
 probably the most promising suboptimal MUD
31(35)
Timo O. Korhonen, Helsinki University of Technology
Zero-forcing decision-feedback (ZF-DF) detector
dec*
r (t )
dˆ1 (1)
K 1
dˆk (n  1)  yw,k   i 0 Fk ,i Ai dˆi (n)
A1 F2,1
matched
filter
bank
(F
F )
T 11
T
A1 F3,1
A1FK ,1


-
dˆ2 (1)
dec
A2 F3,2
-
A2 FK ,2
-
dec
AK FK , K
-
-
dec
dˆK (1)
An enhanced SIC technique consisting of
 pre-whitening that removes noise correlations and
partially removes signal correlations
 SIC performed in the descending order of signal power
T
The pre-whitening is realized by decomposing R  F F
where after y w  FAd  ( N0 / 2)I
32(35)
*decision device
Timo O. Korhonen, Helsinki University of Technology
Some properties of ZF-DF detector





Pre-whitening can be shown to cause the first detected bit
to contain no MAI
Under the assumption that all past decisions are correct,
the ZF-DF eliminates all MAI and maximizes SNR.
ZF-DF principle can be used also to combat ISI
An important difficulty is is to calculate the whitening filter
(FT)-1. This can be simplified similar techniques than the
Polynomial expansion (PE) detector (next slide)
ZF-DF needs the estimates of received amplitudes
 If the soft output of the decorrelating detector are used
for amplitude estimation, ZF-DF performance equals
decorrelating detector
 If still improved amplitude estimates exists, ZF-DF
performance can be even higher
33(35)
Timo O. Korhonen, Helsinki University of Technology
Polynomial expansion (PE) detector

Many MUD techniques require inversion of R. This can be
obtained efficiently by PE
NS
L PE   wi R i  R 1
i 0

dˆ PE  LPE y
For finite length message a finite length PE series can
synthesize R-1 exactly. However, in practice a truncated
series must be used for continuous signaling
dˆ PE  LPE y
y
r (t )
matched
filter
bank
Weight
multiplication
Ry
R
y
R2 y
R
Ry
34(35)
Weight
multiplication
Weight
multiplication
R
R2 y
Timo O. Korhonen, Helsinki University of Technology
Summary of MUD techniques




MAI limits significantly performance of CDMA systems and
enhances near-far effect
MAI can be compensated by using MUD-techniques
MUD is especially applicable in cellular uplink
Optimum MUD (maximum likelihood) is too complicated to
realize, hence suboptimum techniques developed:
 Linear
 MMSE
 PE
 Subtractive
 SIC
 PIC
 ZF-DF
35(35)
Timo O. Korhonen, Helsinki University of Technology