Transcript Multi-user CDMA Enhancing capacity cellular CDMA

Multi-user CDMA
Enhancing capacity of wireless
cellular CDMA
Topics Today


Dealing without multi-user reception:
asynchronous CDMA
 SNR
 power balance - near-far effect
Multi-user detection (MUD) classification and properties
 The conventional detector (non-MUD, denotations)
 Maximum likelihood sequence detection
 Linear detectors
 Decorrelating detector
 Minimum mean-square error detector
 Polynomial expansion detector
 Subtractive interference cancellation
 Serial and parallel cancellation techniques
Timo O. Korhonen, Helsinki University of Technology
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s1 (t ) 2 P1
Asynchronous CDMA
s2 (t ) 2 P2
voltage at the I&D*
at the decision instant
U
mˆ j (tm )  m jj   mij  n j
sU (t ) 2 PU
i 1
i j
mˆ j (tm )
signal
voltage
v j (t )

ISI & noise voltage
signal power for the j:th user
The j:th user experiences the SNR:
SNR j 
m 2jj
 

E    mij  n j 

 i i, jj
2




m 2jj
2
2
 
 
 
 
E    mij    2E    mij n j    E n 2j 
 
  ii, j j  
  i , j
0
MAI
channel noise
*Integrate and dump receiver
Timo O. Korhonen, Helsinki University of Technology
3
Practical CDMA receiver
from channel

LPF
tm
0
u (t )
local code
Effective BW
is defined by:
decision
phasing of
sampling
Beff 
Lc Pj  WPj / R
SNR j 
m
U
P
i 1
i j

V 2 ( f )df
V( f )
S0
f
BN
B S 
 N 0
Beff
BN S
2
0
2
 BN
Lc Pj
U
P  N B
i 1
i j
Timo O. Korhonen, Helsinki University of Technology
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for rectangular
spectra:
i
Hence, SNR upper bound for the j:th user is SNR j 


0
2
jj
2
2
 
 
 
 
E    mij    2E    mij n j    E n 2j 
 
 
  i , j
  i , j
N 0 Beff  PN
0
  V ( f )df 
 0

i
0
eff
4
Perfect power control
U

Equal received powers for U users means that
Pi  (U  1)Pr

i 1
i j

Therefore the j:th user SNR equals
( SNR)0 
Lc Pj
N 0 Beff  (U  1) Pr
and the number of users is
 1
1 
U  1  Lc 


SNR
SNR
o
1


where* (for BPSK)
SNR1  Lc

U max

 1
1 
L
U max  lim 1  Lc 

 1 c


SNR1 
SNR0
 SNRo SNR1 

Pr
PW 2 E
 r  b
Beff N 0 PN R N o
Number of users is
determined by
 channel AWGN level N0
 processing gain Lc
 received power Pr
SNR0 / 2
AWGN level decreases
Eb/No
(=SNR1/2)
*SNR1: received SNR without multiple access interference
Timo O. Korhonen, Helsinki University of Technology
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Unequal received powers - 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 / d ia


where d is the distance, and a is the propagation attenuation
coefficient (a = 2 for free space, in urban area a = 3…5 )
Express the power ratio of the i:th and j:th user at the common
reception point
a
d
 j
a
a
Po  Pd

P
d

P

P
i i
j j
i
j

d
 i
Therefore, the SNR of the j:th user is
SNR j 
Lc Pj
U
N 0 Beff   Pi
i 1
i j
Timo O. Korhonen, Helsinki University of Technology
 SNR j 
Lc Pj
a
 dj 
N 0 Beff  Pj   
i 1  d i 
U
i j
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The near-far effect in asynchronous CDMA

Grouping the previous yields condition
a
 dj 
 1
1 

L

 U 1

c 
 

i 1  d i 
 SNR0 SNR1 
U
i j



Multiple-access interference (MAI) power should not be larger
than what the receiver sensitivity can accommodate
Note the manifestation of near-far -effect because just one larger
sum term on the left side of the equation voids it
Example: Assume that all but one transmitter have the same
distance to the receiving node. The one transmitter has the
distance d1=dj /2.5 and a=3.68, SNR0=14, SNR1=25,
Rb = 30 kb/s, Beff = 20 MHz, then
a
dj 
3.68

(2.5)
U  2 

 
i 1  d i 
U
i j
Lc , BPSK  (2 / Tc ) /(1/ Tb )  2Tb / Tc  2Tb Beff
Timo O. Korhonen, Helsinki University of Technology

 1
1 
3.68
(2.5)

U

2

L


c 


 SNR0 SNR1 

U  2  2.53.68  L  1  1   14
c 


SNR
SNR
0
1


7

By using the perfect power balance the number of users is
 1
1 
U  1  Lc 

  42
 ( SNR )0 ( SNR )1 


Hence the presence of a 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 should be
adaptively realized in asynchronous CDMA-systems
Timo O. Korhonen, Helsinki University of Technology
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Fighting against Multiple Access
Interference



CDMA system can be realized by spreading codes having
low cross -correlation as Gold codes (asynchronous
usage) or Walsh codes (synchronous usage)
Multipath channel with large delay spread can destroy
code cross-correlation properties
 a remedy: asynchronous systems with large code gain
assume other users to behave as Gaussian noise (as
just analyzed!)
Additional compensation of MAI yields further capacity
(increases receiver sensitivity). This can be achieved by
 Code waveform design (BW-rate/trade-off)
 Power control (minimizes near-far effect)
 FEC- and ARQ-systems
 Diversity-systems: - Spatial - Frequency - Time
 multi-user detection
Timo O. Korhonen, Helsinki University of Technology
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MAI versus ISI (Inter-Symbolic
Interference)

Note that there exists a strong parallelism between the
problem of MAI and that of ISI:
Asynchronous channel of K-users behaves the same
way as a single user channel having ISI with *memory
depth of K-1


Hence, a number of multi-user detectors have their
equalizer counter parts as:
 maximum likelihood
 zero-forcing
 minimum mean square
 decision feedback
General classification of multi-user detectors:
 linear
 subtractive
*This could be generated for instance by a multipath
channel having K-1 taps
Timo O. Korhonen, Helsinki University of Technology
10
Maximum-likelihood sequence detection

Optimum multi-user detection applies maximum-likelihood
principle:
Considering the whole received sequence, find the
estimate for the received sequence that has the
minimum distance to the allowed sequences


The ML principle
 has the optimum performance
 has large computational complexity - In exhaustive
search 2NK vectors to be considered! (K users, N bits)
 requires estimation of received amplitudes and phases
that takes still more computational power
 can be implemented by using Viterbi-decoder that is
‘practically optimum’ ML-detection scheme to reduce
computational complexity by surviving path selections
We discuss first the conventional detector (by following
the approach we already had to familiarize to denotations)
Timo O. Korhonen, Helsinki University of Technology
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Formulation: Received signal


Assume
 single path AWGN channel
 perfect carrier synchronization
 BPSK modulation
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 spreading code waveform
d k (t ) is the data modulation of the k:th user
n(t ) is the AWGN with N0/2 PSD

Note that there are Lc chips/bit (Lc : processing gain)
Timo O. Korhonen, Helsinki University of Technology
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Conventional detection (without MUD)
for multiple access

The conventional BS receiver for K users consists of K
matched filters or correlators:
r (t )
Tb
0
x(t )dx
decision
x(t )dx
decision
g1 (t )
Tb
0
d̂1
d̂2
g2 (t )
Tb
0
x(t )dx
decision
dˆK
gK (t )

Each user is detected without considering background
noise (generated by the spreading codes of the other
users) to be deterministic (Assumed to be genuine
AWGN)
Timo O. Korhonen, Helsinki University of Technology
13
Output for the K:th user without MUD

Detection quality depends on code cross- and
autocorrelation
1
i ,k   gi (t ) g k (t )dt
Tb T
Hence we require a large autocorrelation and small
crosscorrelation
i ,k  1, i  k


0  i ,k  1, i  k
b


The output for the K:th user consist of the signal, MAI and
filtered Gaussian noise terms (as discussed earlier)
1
yk  T r (t ) g k (t )dt
Tb
b
yk  Ak d k   i 1 i ,k Ai di 
K
ik
1
n(t ) g k (t )dt

T
Tb
b
yk  Ak d k  MAI k  zk

Received SNR of this was considered earlier in this
lecture
Timo O. Korhonen, Helsinki University of Technology
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Matrix notations to consider
detection for multiple access

Assume a three user synchronous system with
a matched filter receiver
 y1  A1d1   2,1 A2 d 2  3,1 A3 d3  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
Timo O. Korhonen, Helsinki University of Technology
noise
data
received amplitudes
15
The data-term and the MAI-term

Matrix R can be partitioned into two parts by setting
y  RAd  z with R  I  Q



Note that hence Q contains off-diagonal elements or R
(or the crosscorrelations)
and therefore MF outputs y  RAd  z can be expressed
as
y  (I  Q) Ad  z  Ad  QAd  z
Therefore the term Ad contains the decoupled data and
QAd represents the MAI
Objective of all MUD schemes is to cancel out the MAIterm as effectively as possible (constraints to
hardware/software complexity and computational
efficiency)
Timo O. Korhonen, Helsinki University of Technology
16
Asynchronous and synchronous channel


In synchronous detection decisions can be made bit-by-bit
In asynchronous detection bits overlap and multi-user
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
asynchronous ch.
User 1
User 2
1
3
2
5
4
 1  2 Tb  1

synchronous ch.
6
User 1
1
3
5
User 2
2
4
6
3Tb   2
1
Tb  1
3Tb  1
The matrix R contains now partial correlations that exist
between every pair of the NK code words (K users, N bits)
Timo O. Korhonen, Helsinki University of Technology
17
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
1
3,2
0
0
 2,3
1
 4,3
0
0
0
0
0
0
3,4
1
5,4
0
0
 4,5
1
0
5,6






 6,5 

1 
0
0
0
0
Note that the resulting matrix is sparse because most of
the bits do not overlap
Sparse matrix - algorithms can be utilized to reduce
computational difficulties (memory size & computational
time)
Timo O. Korhonen, Helsinki University of Technology
18
Decorrelating detector

The decorrelating detector applies the inverse of the
correlation matrix to suppress MAI
L dec  R 1
and the data estimate is therefore
dˆ dec  R 1y
 R 1 ( Ad  Q A d  z )
RAd
 Ad  R 1z  Ad  z dec



We note that the decorrelating detector eliminates
the MAI completely!
However, channel noise is filtered by the inverse of
correlation matrix - This results in noise enhancement!
Decorrelating detector is mathematically similar to zero
forcing equalizer as applied to compensate ISI
Timo O. Korhonen, Helsinki University of Technology
19
Decorrelating detector properties
summarized






PROS:
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



CONS:
Noise enhancement
High computational complexity in inverting matrix R
Timo O. Korhonen, Helsinki University of Technology
20
Polynomial expansion (PE) detector

Many MUD techniques require inversion of R. This can be
obtained efficiently by PE
N
L   w R i  R 1 dˆ PE  L PE y
S
PE
NS
i 0
i
dˆ PE   wi R i y  w0 R 0 y w1R1 y...  wN S R N S y
i 0

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  L PE y
y
r (t )
Weight
multiplication
matched
filter
bank
y
Timo O. Korhonen, Helsinki University of Technology
Ry
Weight
multiplication
R2 y
Weight
multiplication
R
R
R
w0
w1
 w2
Ry
R2 y
21
Mathcad-example
NS
R   wi R i
1
i 0
R 1 
= series expansion
of R-1 (to 2. degree)
 wi
 R2
Timo O. Korhonen, Helsinki University of Technology
22
Minimum mean-square error (MMSE)
detector






Based on solving MMSE optimization problem with
2
E[ d  Ly ]
that should be minimized
This leads into the solution
ˆd  L MMSE y   R  ( N 0 / 2) A 2  1 y


One notes that under high SNR this solution is the same
as decorrelating receiver
This multi-user technique is 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 and
noise level
 Performance depends also on powers of
interfering users
Timo O. Korhonen, Helsinki University of Technology
23
r (t )
MF
user 1
decision
Tb





d̂1
r (t  Tb )
Aˆ1 (t  Tb )
1
g1 (t  1  Tb )
- sˆ1 (t  Tb )
+
r1 (t )
To the next stage
Successive interference cancellation
d̂
(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: Small HW requirements and large performance
improvement when compared to conventional detector
CONS: Processing delay, signal reordered if their powers
changes, in low SNR:s performance suddenly drops
Timo O. Korhonen, Helsinki University of Technology
24
Parallel interference cancellation (PIC)
r (t  Tb )
sˆ1 (t  Tb )
dˆ1 (0)
Aˆ1 (t  Tb )
dˆ2 (0)
sˆ2 (t  Tb )
Aˆ2 (t  Tb )
dˆK (0)
spreader
sˆK (t  Tb )
s
(
t
)
ˆ
i
i 1
 sˆi (t ) i2
 sˆ (t ) i K
Aˆ K (t  Tb )
amplitude
estimation
dˆ1 (1)
+
matched
filter
bank
ˆ
decisions d 2 (1)
and
stage
weights dˆK (1)
i
parallel
summer
y  (I  Q) Ad  z
 Ad  QAd  z
With equal weights for all stages the data estimates for
each stages are
dˆ (m  1)  y  QAdˆ (m) y  Ad  QAd  z
 Ad  QA(d  dˆ (m))  z
minimization tends to cancel MAI
initial
data
estimates


Number of stages determined by required accuracy
(Stage-by-stage decision-variance can be monitored)
Timo O. Korhonen, Helsinki University of Technology
25
PIC properties


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
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
Timo O. Korhonen, Helsinki University of Technology
26
Benefits and limitations of multi-user
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 reception where, however, larger capacity
requirements exist (DL traffic tends to be larger)
Timo O. Korhonen, Helsinki University of Technology
27