Transcript Partial Parallel Interference Cancellation Multiuser

Partial Parallel Interference
Cancellation
Based on Hebb Learning Rule
Taiyuan University of Technology
Yanping Li
Content
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Background
Hebb Learning Rule
CDMA System Model
PIC
PPIC
Hebb-PPIC
Simulations and Conclusion
References
Background (1)

Multiuser Detection
–
–
In CDMA systems MAI (Multiple-access
Interference) will be the main factor of damaging
system performance when the number of users is
relatively large. The methods of rejecting MAI
mainly include improving the design of spreading
code, power control, space filtering and multiuser
detection [1, 2].
Multiuser detection applies the correlation
between the expected user and interference
users to MAI cancellation.
Background (2)

Parallel Interference Cancellation (PIC)
–
–
PIC is one of nonlinear multiuser detection
approaches, and it can obtain obvious
performance improvement at the cost of low
computing complexity and short processing delay.
The PIC process is shown in the next page.
Background (3)

Partial Parallel Interference Cancellation
(PPIC)
–
–
In PIC process, due to the correlation between
the spreading codes of each user, MAI is
introduced into the decision variables after
matched filtering, which will impact the decision of
each user’s information bits.
To solve this problem more efficiently, we multiply
the regenerated interference signals by ICF
(Interference Cancellation Factors). Such is PPIC.
Hebb Learning Rule (1)

Hebb Learning Rule
–
–
Hebb learning rule is one of the neural network
learning rules widely used. It was proposed by
Donald Hebb in 1949 as a potential mechanism
for the brain to adjust its neuron synapse and
from then on it has been used in training artificial
neural network [3].
Hebb learning rule is based on Hebb assumption.
Hebb Learning Rule (2)

Hebb Assumption [4]
–
–
When an axon of cell A is near enough to excite a
cell B and repeatedly or persistently takes part in
firing it, some growth process or metabolic
change takes place in one or both cells such that
A’s efficiency, as one of the cells firing B, is
increased.
Hebb assumption means that if a positive input p j
results in a positive output a i , w ij should be
increased.
Hebb Learning Rule (3)
–
Such is a kind of mathematics explanation for it:
new
w ij
–
 w ij
old
also simplified as
new
w ij
–
  f i ( a iq ) g j ( p jq )
 w ij
old
  a iq p jq
where p jq is the jth element of the qth input
vector p q , a iq is the ith element of network output
when the qth input vector is entered into the
network and  is a positive constant called as
learning rate.
Hebb Learning Rule (4)
–
It should be noticed that Hebb assumption can be
expanded as follows: the variation of weights is
proportional to the product of active values from
each side of synapse. Therefore, weights will
increase not only when p j and a i are both positive
but also when they are both negative. Besides,
Hebb rule will decrease weights as long as p j and a i
have opposite signs.
CDMA System Model (1)

Synchronous DS-CDMA System Model
–
Consider a DS-CDMA system where K users
transmit their information synchronously over a
common additive white Gaussian noise (AWGN)
channel. The received signal at the base station
can be modeled as [5]
K
r (i ) 
Ab
j
j 1
j
(i )s j  n (i )
CDMA System Model (2)
–
–
–
–
–
where
A j is received amplitude of the jth user,
b j  i  is transmitted symbol (±1) of the jth user,
s j is signature vector of the jth user,
and n ( i ) is an AWGN vector.
CDMA System Model (3)

MC-CDMA System Model
–
In a MC-CDMA system where K users transmit
their information synchronously over a common
AWGN channel, the received nth chip of the ith bit
at the base station can be described in discretetime form
K
yi ( n ) 
N 1
h
j 1 l  0
j ,i
( l ) s j ,i ( n  l )  z i ( n )
CDMA System Model (4)
–
where h j ,i ( l ) is channel impulse response, z i ( n ) is
the AWGN vector with zero mean and a two-sided
power spectral density of  2 W/Hz
N 1
and s j ,i ( n )  A j  c j , k ,i e j 2  nk / N , where A j is received
k 0
amplitude of the jth user, N is spreading gain (as
same as the number of carriers) and c j , k ,i  b j ,i a j ,k ,
where b j ,i and a j , k are the ith bit and kth chip of the
jth user respectively.
PIC (1)
–
The decision variable at stage 1 (output of MF
(Matched Filter)) in conventional PIC is [5]
K
ri
(1)
 Ai b i 

 ik Ak b k  n i , i  1,
,K
k 1, k  i
–
–
where  ik is the correlation coefficient between
spreading codes of the ith user and kth user.
The output after decision is
(1)
(1)
bˆi  sgn[ ri ], i  1,
,K
PIC (2)
–
The decision variables of the following stages
(interference cancellation stages) are
K
ri
(m )
 Ai b i 

 ik Ak ( b k  bˆk
( m 1)
)  ni ,
k 1, k  i
i  1,
–
, K , m  2, 3,
,
and the corresponding decision outputs are
(m )
(m)
bˆi  sgn[ ri ], i  1,
,K.
PIC (3)
PPIC (1)
–
The decision variables at interference
cancellation stages in PPIC with ICF are
K
ri
(m )
 Ai b i 

 ik Ak ( b k  w i bˆk
( m 1)
(m )
)  ni ,
k 1, k  i
i  1,
–
, K , m  2, 3,
,
where w i( m ) is the ICF of the ith user at stage m.
PPIC (2)
Hebb-PPIC (1)
–
Apply recurrent neural network based on Hebb
learning rule to adjusting w i( m ) :
(m )
wi
( m 1)
 satlin{ w i
i  1,
–
( m 1)
( m 1)
[1   (1  bˆi
 bi
)]},
, K , m  2, 3,
,
where w i(1)  1, i  1, , K ,   (0,1) is the learning
rate and saturated linear function satlin is used to
assure the convergence of learning process.
Hebb-PPIC (2)
Hebb-PPIC (3)
Simulations and Conclusion (1)

Based on the analysis above several
computer simulations are presented in the
conditions of ideal power control and “nearfar” scenario to compare the performance of
Hebb-PPIC with that of PIC or MF (namely
DEC (decorrelation) in MC-CDMA system)
detection.
Simulations and Conclusion (2)

Ideal Power Control
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–
Simulation 1 (in DS-CDMA system) :
number of users K = 5 ; number of stages m=5;
noise power spectral density  2  1 ; the
processing gain N = 32 ;number of test
bits N b  1000 ;   1 / 20 . The BER curves of MF
detector, PIC and Hebb-PPIC detectors (at stage
3) versus SNR are given below:
Simulations and Conclusion (3)
Ideal Power Control
0.12
MF
PIC
Hebb-PPIC
0.1
BER of Stage 3
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
SNR(dB)
6
7
8
9
10
Simulations and Conclusion (4)
–
From this figure we can see that the BER
decreases all along with increasing of SNR and
moreover, the BER curve of Hebb-PPIC is under
those of MF and PIC all the time. Especially when
SNR is low (not exceeding 4dB), the BER of
Hebb-PPIC is 1 to 2 percentage points lower than
MF and 0.5 to 1 percentage points than PIC in [5],
which indicates that Hebb-PPIC performs better in
noisy communication environment.
Simulations and Conclusion (5)
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–
Simulation 2 (in MC-CDMA system) :
amplitude of users Ai  1, i  1, , K ; m=5;  2  1 ;
N = 32 ; N b  1000 ;   1 / 200 . The BER curves of
PIC and Hebb-PPIC detectors versus stage are
shown in the next figure.
Simulations and Conclusion (6)
Ideal Power Control
0.03
PIC
Hebb-PPIC
0.025
BER
0.02
0.015
0.01
0.005
0
1
1.5
2
2.5
3
Stage
3.5
4
4.5
5
Simulations and Conclusion (7)
–
From the figure above we can find that the BERs
of both PIC and Hebb-PPIC decrease along with
stage and especially from stage 1 to stage 2 they
decrease very obviously and tend to be stable
from stage 2 on. On the other hand, the BER
curve of Hebb-PPIC is under that of PIC all the
while from stage 1 to stage 5, which indicates that
on the basis of PIC structure Hebb-PPIC
improves the reception performance of system
further, i.e., weakens the effect resulted from error
cancellation in PIC.
Simulations and Conclusion (8)

“Near-Far” Scenario
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–
Simulation 3 (in DS-CDMA system) :
K=10; As / Aw  5 db , As and Aw denote amplitude of
the strong users and weak users respectively;
m=5;  2  1 ; N=32; N b  1000 ;   1 / 20 . BER
curves of weak user group and strong user group
versus SNR are presented as follows:
Simulations and Conclusion (9)
Near-Far Scenario
0.18
PIC
Hebb-PPIC
BER of the weak user group at stage 3
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
SNR(dB)
6
7
8
9
10
Simulations and Conclusion (10)
Near-Far Scenario
0.14
PIC
Hebb-PPIC
BER of the strong user group at stage 3
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
SNR(dB)
6
7
8
9
10
Simulations and Conclusion (11)
–
From the two figures we observe that the BER of
Hebb-PPIC and PIC is decreasing all the time
when SNR is increasing and the corresponding
curves of Hebb-PPIC is under those of PIC in [5]
all along for both user groups. Especially for weak
users the BER of Hebb-PPIC is 4 to 6 percentage
points lower than PIC while it is 0.5 to 2
percentage points for strong users, which shows
that Hebb-PPIC detection can be able to reject
“near-far” effect more efficiently.
Simulations and Conclusion (12)
–
–
Simulation 4 (in MC-CDMA system) :
K=10; As / Aw  5 db , As and Aw denote amplitude of
the strong users and weak users respectively;
m=5;  2  1 ; N=32; N b  1000 ;   1 / 50 . BER
curves of weak user group and strong user group
versus SNR are presented as follows:
Simulations and Conclusion (13)
Near-Far Scenario
0.18
DEC
PIC
Hebb-PPIC
0.16
BER of the weak user group
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
SNR(dB)
6
7
8
9
10
Simulations and Conclusion (14)
–
In this figure it can be easily seen that for weak
users the BER level of PIC and Hebb-PPIC is far
lower than that of DEC and even with the biggest
SNR (10 dB) the BER of DEC (12%) is higher
than that of PIC and Hebb-PPIC (about 11.5%)
with the smallest SNR (0 dB). Although becoming
nearer to the BER curve of PIC along with
increasing of SNR, that of Hebb-PPIC is still
under it.
Simulations and Conclusion (15)
Near-Far Scenario
0.14
DEC
PIC
Hebb-PPIC
BER of the strong user group
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
SNR(dB)
6
7
8
9
10
Simulations and Conclusion (16)
–
From this figure we notice that compared with
weak user group the distances between the three
BER curves are not too large in the case of strong
user group, and when SNR is relatively small
(0~2 dB) the BER of DEC is even lower than that
of PIC, which is because that small SNR means
serious interference while this will result in error
decision and cancellation which will influence the
veracity of decisions at the next stage. But with
SNR increasing (bigger than 2 dB), the advantage
of PIC will emerge that its BER is 1 to 2
percentage points lower than DEC’s.
Simulations and Conclusion (17)
–
Comparing these two figures we can find that
when the user signals are weak PIC, especially
Hebb-PPIC, will play an important role in
improving reception performance and rejecting
“near-far” effects.
Simulations and Conclusion (18)

The Hebb-PPIC algorithm is simulated in two
conditions of idea power control and “nearfar” scenario. Simulation results indicate that
no matter which parameter changes among
stage number, SNR and number of active
users, the BER performance of Hebb-PPIC is
generally better than conventional PIC.
Simulations and Conclusion (19)

On the other hand, compared with most of
the PPIC algorithms proposed by now, HebbPPIC has the advantage of small computing
quantity, low complexity and easy
implementation and it can adjust ICF at any
moment of channel variation, so it owns
practicability in engineering.
References
[1] S. Verdu, “Minimum probability of error for asynchronous
Gaussian multiple-access channels,” IEEE Trans. Inf. Theory,
vol. 32, no. 1, pp. 85-96, Jan. 1986.
[2] R. Lupas, and S. Verdu, “Linear multiuser detectors for
synchronous code-division multiple-access channels,” IEEE
Trans. Inf. Theory, vol. 35, no. 1, pp. 123-135, Jan. 1989.
[3] M. T. Hagan, H. B. Demuth, and M. H. Beale, Neural Network
Design, Beijing: China Machine Press, 2002.
[4] D. O. Hebb, The Organization of Behavior, Massachusetts: MIT
Press, 2000.
[5] G. B. Giannakis, Y. Hua, and P. Stoica, Signal Processing
Advances in Wireless and Mobile Communications, Beijing:
Posts & Telecommunications Press, 2002.
Thank you!