IRJET- A Novel Adaptive Sub-Band Filter Design with BD-VSS using Particle Swarm Optimization

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 10 | Oct 2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 925
A novel Adaptive Sub-Band Filter design with BD-VSS using Particle
Swarm Optimization
Yuvaraj V1
1Electronics and Communication Engineering, College of Engineering Guindy, Anna University, Chennai, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – A delayless Sign Subband Adaptive Filter
algorithm with Individual Weighting Factors (IWF-SSAF)and
Band-Dependent Variable Step-Sizes (BD-VSS) approach is
recently proposed to control noise for impulsive noise
environments. However, such approaches have slow
convergence rate and high computation complexity for real-
time applications. To address these issues, Particle Swarm
Optimization (PSO) algorithm delayless closedloopIWF-SSAF
with BD-VSS is proposed. The proposed algorithm is applied
for Active Impulsive Noise Control (AINC) technique to
suppress the impulsive noise. The proposed algorithm attains
better convergence performance by employing the 1l -norm
minimization approach to sub-bands and decorrelating
properties of SSAF. Furthermore, the proposed algorithm has
achieved more computational efficiency with the aid of PSO
algorithm. The experimental result shows that the proposed
algorithm obtained better performancethantheconventional
SSAF algorithms in terms of computational complexity.
Key words – Sign Subband Adaptive Filter, Particle Swarm
Optimization, Active Impulsive Noise Control, Variable Step-
Sizes.
Normalized Least Mean Square (NLMS) is one of the
fundamental approaches in adaptive filtering techniques
which has been broadly used in several real-time
applications including channel estimation, system
identification and Active noise cancellation (ANC) [1].
However, NLMS approach has the disadvantage of slow
converges for the colored input signals. An innovative
approach which is used in the Sub-band Adaptive Filter
(SAF) for resolving the disadvantage of NLMS approach [2].
It splits the coloured input signal into the equally divided
multiple sub-band signals, where each sub-band signal is
almost white.Then,theNormalizedSub-bandAdaptive Filter
(NSAF) approach is introduced which converges the NLMS
for the coloured input signals owing to the inherent
decorrelating features of SAF in a faster manner [3], [4].
In addition, NSAF approach has the same computational
complexity of the NLMS approach for the applications of
echo cancellation [5]. Also, the traditional NLMS approach
and NSAF approach has a trade-off between the rate of
convergence and steady-state error for the selection step
size. Then, more variable step size NSAF approaches were
established to attain both low steady-state error and fast
convergence rate [6]. However, these approaches may
deviate for the presence of impulsive noises. A Sign Sub-
band Adaptive Filter (SSAF) approach is developed for
reducing the L1-norm of the a posteriori error vectorofSub-
band filter to mitigate the impulsive interferences [7]. Also,
Variable Regularization Parameter with SSAF is presented
for lower the steady-state error of the SSAF [8].
Then, some variable step size SSAF approaches were
presented from diverse principles of the step size update to
alleviate the trade-off problem of the SSAF [9]. But, these
convergence rates of several variable step size SSAF
approaches are not reasonable [8]. To address this concern,
a novel SAF approach is developed from Huber’s cost
function using the gradient descent technique [10]. This
approach offersanautomaticschemetoadjustment between
the NSAF and SSAF approaches by iteratively updating the
cut-off metrics and provides good robustness to the
impulsive noises. Hence, this approachiscalledastherobust
variable step size NSAF (RVSS-NSAF) [11].
Moreover, SSAF approach withIndividual WeightingFactors
(IWF-SSAF) approach is presented to improve the
convergence rate of SSAF approach [12], [13]. An improved
proportionate IWF-SSAF is proposed for sparse system to
further improve the convergence rate of the IWF-SSAF
algorithm. Two delaylessstructuresforNSAFwereproposed
to alleviate the concern of undesirable signal path delay
since this is essential for the different real-time applications
such as AEC and ANC [14]. SSAF approaches have an
inherent signal path delay issue for real-time systems.
Hence, a delayless IWF-SSAF with band-dependent variable
step-sizes (BD-VSS) algorithm is developed which offers
more robustness under impulsive noise conditions [14].
M-Estimator based approach is developed to control the
context of active impulse noise where M-Estimator aims to
minimize the effect of outliers [15], [20]. This result proved
the better efficiency of the M-Estimator than the existing
algorithms basedonnoisecontrol performance.However, its
complexity is lower than the otherconventional approaches.
A BD-VSS based SSAF is presented using the concept of
mean-square deviation (MSD) minimization [10].Inthis, the
filter performance is improved based on the assign of
different step size to each band. From the results, this
approach performs better than the conventional techniques
based on the steady-state estimation error and convergence
rate.
An active control of impulsive noisewithsymmetricα-stable
(SαS) distribution is developed ANC system [16]. A common
step-size normalized filtered-x Least Mean Square (FxLMS)
approach is derived based on the Gaussian distribution
1. INTRODUCTION
2. RELATED WORKS

function is used to regularize the step size. The results
demonstrate that the developed approach has good
performance for SαS impulsive noise attenuation. Then, the
filtered-x state-space recursive least square (FxSSRLS) is
presented for active noise control (ANC) [17]. From the
results, FxSSRLS approach is moreeffectivein exterminating
high-peaked impulses than other approaches for ANC
applications.
SAF approach is developed for reducing impulsive noises
using Huber’s cost function [12]. In general, this approach
operates in the normalized SAF mode and it performs like
SSAF approach. The sub-bandcut-offmetricsarederived ina
recursive manner for enhancing the robustness of the
approach against impulsive noises. For impulsive ANC, an
altered bi-normalized data-reusing (BNDR) based adaptive
approach is developed [18]. The approachisresultingfroma
adapted cost function and it is based on reusing the past and
present data samples. The results demonstrates the
effectiveness of the BNDR-based adaptive approach with a
rational increase in the complexity. Delayless SSAF
approaches were derived with IWF-SSAF and BD-VSS in
impulsive noise conditions for real-timeapplications[14].In
this, two delayless filter structures implemented for the ℓ2-
norm based SAF are appliedtogether withIWF-SSAF.Finally,
the performance of the approach is proved efficiency in
different impulsive interference situations.
3.1 Sign Subband Adaptive Filter Algorithms with
Individual Weighting Factors (IWF-SSAF)
Subband adaptive filter (SAF) isanattractiveoption
to minimize the computational complexity problem of the
Least Mean Squares (LMS). Fig.1 shows the structure of SAF
algorithm.
The desired signal ( )d n is expressed as (1),
( ) ( ) ( )T
optd n w u n v n  (1)
Where, ( )u n is the input signal that is represented
by ( ) [ ( ), ( 1), ( 2),..., ( 1)]T
u n u n u n u n u n L     , optw is
the weight vector of the unknown system with L-length
and ( )v n includes an impulsive noise ( )i n and the
background noise ( )b n .
The sub-band signals are represented by ( )id n and
( )iu n which are attained by filtering the ( )d n and
( )u n using filter examination  iH z for i=1,2,3,...,N is the
number sub-bands. In addition,  ,i Dd k is obtained by
decimating  id n by a factor of N, thedecimatedsequenceis
represented as k. The error vector of decimated sub-band
 De k is calculated as (2),
( ) ( ) ( ) ( )T
D De k d k U k w k  (2)
Where,  w k is the calculate of optw at k -number of
iterations,
1 2( ) [ ( ), ( ),..., ( )]NU k u k u k u k
1, 2, ,( ) [ ( ), ( ),..., ( )]T
D D D N Dd k d k d k d k
( ) [ ( ),..., ( 1)]T
i i iu k u kN u kN L  
The coefficient vector is attained by reducing the cost
function using a stochastic gradient decent [12]:
,
1
( ) ( )
N
i i D
i
J k e k

  (3)
Where,  ,i Dd k is the
th
i element of  De k in (2) and
i represents the weighting feature. Besides, the updated
equation for the coefficient vector derived as follows in the
IWF-SSAF,
,
1
( )
( 1) ( )
( )
= ( ) ( )sgn( ( ))
N
i i i D
i
J k
W k w k
w k
w k u k e k

 


  

 
(4)
Where,  sgn・ is denotes the sign functionand  is
a step-size to make sure that the coefficient vector does not
change rapidly and sgn(・) represents the sign function.
When  is derived as a small positiveconstanttokeepaway
from dividing by zero,
1
1
( ) ( )
i N
T
i i
i
u k u k





is
employed as the weighting feature in the original SSAF [5].
Also, the individual weighting feature i for IWF-SSAF is
considered in all sub-bands:
1
( ) ( )
i T
i iu k u k




, 1,2,...,i N (5)
Form the outcome, IWF-SSAF completely uses the
decorrelating possessions of SSAF and provides speedy
convergence. At last, the coefficient vector update in IWF-
SSAF is,
,
1
( )sgn( ( )
( 1) ( )
( ) ( )
N
i i D
T
i
i i
u k e k
w k w k
u k u k


  

 (6)
3. PRELIMINARIES

Fig.1 Sub-band adaptive filter structure [12].
3.2 Delayless IWF-SSAF
IWF-SSAF approach [12] enhancestheconvergencerate
of the conventional SSAF approach [5]. In [17], developed
two delayless IWF-SSAF namely-loop and closed-loop
designs by applying the new delayless configurations in the
NSAF. In the delayless open-loop based IWF-SSAF, the
obtained convergence performanceissameastheIWF-SSAF.
Besides, the error signal ( )e n in the proposed approach is
developed without delay and estimated in a supplementary
loop, although the signal path delay can be producedinIWF-
SSAF because it is recreated by the combination filter bank.
In addition, a delayless closed-loop based IWF-SSAF is
achieved based on configuration of closed-loop shown in
Fig.2. In this, sub-band error signal derived by d ( )e n using
the examination offilter ( )iH z .Then,bydecimatingitbased
on a factor of N and update the adaptive filter  w k .
Therefore, it is adjusted based on prior data of the error
signal due to the interruption of the analysis filters ( )iH z .
In delayless closed-loopIWF-SSAF,theresults showthat
the upper bound of the step size is reduced for fixed
convergence [19]. To address this drawback, the delayless
closed-loop structure is used in some beneficial application
called as active impulsive noise control (AINC) while only
the error signal is obtainable and it is considered as
impulsive interference.
Fig.2 Delayless closed-loop NSAF structure [14]
The delayless closed loop IWF-SSAF algorithm as
follows,
Algorithm: 1 Delayless Closed-Loop IWF-SSAFalgorithm
[14]
: ( )
:
1. 1,2,3,....,
2. ( ) ( ) ( ) ( )
3. ( ) (
, (
), 1,2,...,
) ,
(
4.
)
T
T
i i
input signal vector e n error signal
update equation for the coefficient vector w
Input u n
Output
For n
e n d n w k u k
u h n i N
k
n a
 

 
 
,
,
1
k 1,2,3,....,
5. ( ) ( ) 1,2,...,
6. ( ) ( ) ( )
( )sgn( ( ))
7. ( 1) ( )
( )
8.
9.
T
i D i
T
i i i
N
i i D
i i
For when n kN
e k h e kN i N
k u k u k
u k e k
w k w k
k
end
end



 
 

   
3.3 BD-VSS based delayless IWF-SSAF
Besides, a BD-VSSapproachisintroducedto enhancethe
open-loop convergence rate and closed-loop delayless IWF-
SSAF approach. In this,the 1l normalizationisintegratedinto
each subband of the delayless IWF-SSAF [9]. This provides
the robustness against impulsive interferences. Hence, to
achieve the expected convergence rate, variable step sizes
are arranged to be considered to corresponding subbands.
Some VSS subband approaches have been proposed [8].
Although, most of these algorithm needs the past
information which may be basically unavailable and a priori
knowledge is not required in ℓ1-norm based VSS approach.
The proposed IWF-SSAF with BD-VSS and Particle
Swarm optimization (PSO) [21] is assigned and its closed-
loop design is developed. Fig.3 shows the structure of
proposed approach with PSO for the AINC.
We proposed methodology incorporates AINC
technique into the Filteringtechniquetosuppressthenoises.
The posteriori error of
th
i sub-band is derived as,
, ,( ) ( ) ( ) ( 1)T
i p i D i ie k d k u k w k   (7)
Where,
,( )sgn( ( ))
( 1) ( ) ( )
( ) ( )
i i D
i i T
i i
u k e k
w k w k k
u k u k


  

,
( )i k is
The step size of the
th
i subband and , ( )i pe k is rewritten as
follows,
, ,( ) ( ) ( ) ( )i p i D i ie k e k u k g k  (8)
4. PROPOSED METHODOLOGY

Where,
,( ) ( )sgn( ( ))
( )
( ) ( )
T
i i i D
i T
i i
u k u k e k
g k
u k u k 


.
Also, the BD-VSS for 1,2,...,i N , optimum in the
1l -norm regularization control [8], is derived by minimizing
1l -norm of , ( )i pe k as,
,
( )
,
argmin ( ) ( ) ( )
( )
( )
i
i D i i
k
i sol
L i U
e k u k g k
k
subject to k


  
 

 
  
(9)
In (9), the positive constraints, the lower and upper
bounds for ( )iu k are represented as L and U
respectively. The U is chosen to be adjacent to zero
and U is considered as less than one for constancy of the
adjusted 1l -norm approach. Moreover, diverse numbers for
L and U are considered for every sub-band.
Nevertheless, the identical L and U are employed in
every sub-bands. From (9), we examine that the 1l -norm
regularization that is a one-dimensional linear curved
constraint. Therefore, the result of , ( )i sol k is expressed
from the 1l -norm regularization approach. This should be
derived as,
,
,
( )
( ) , 1,2,....,
( )
i D
i sol
i
e k
k i N
g k


 

(10)
Where,  is used to evade dividing by zero and
developing the convexity of 1l -norm, the optimum result (9)
is derived.
,
, ,
,
, if ( )
( ) , if ( )
( ), otherwise
U i sol U
i sol L i sol L
i sol
k
k k
k
  
   

 

 


(11)
Further, the convergence performance of the BD-
VSS approach is assuming the consequence of the impulsive
interference in step size control. However, from equation
(10), when the impulsive noise works on few sub-band
which controls the impulsive noise and the convergence
behaviour is weakened.
To prevent this, in the BD-VSS ( )i k isachievedby
applying the time average method as follows,
 ,( ) ( 1) (1 )min ( ), ( 1)i i i opt ik k k k         (12)
Where,  is the smoothing parameter that is expressed,
1
.
N
L



 and  1,2,...,10  is a variablewhichisbased
the input signal and coefficient vector ( )w k correlation.
Fig.3 The proposed structure of delayless closed-loop IWF-
SSAF approach with BDVSS and PSO for the AINC
The equation(12)expresses theBD-VSSapproachis
derived from the aforementionedstepsize ( 1)i k  where
the impulsive interferences influence the
th
i subband that
provides heftiness in contradiction of impulsive noise. Else,
the algorithm isperformedwiththetimenormalizedoptimal
step size as follows,
,( ) ( 1) (1 ) ( )i i i optk k k       (13)
Moreover, the computational complexity is
diminished using proposed approach with PSO.

In this, we present the results of computational
complexity and convergence operation of the proposed
algorithm. Initially, we have considered the input signal in
time domain which includes the noise signal Fig.4 showsthe
input signal in time domain representation.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
-1
0
1
Row 1 in the Time Domain
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
-1
0
1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
-1
0
1
Fig.4 Input signal in time domain
Then, the signal is switched into frequencydomainfrom
time domain using FFT transformation. Fig.5 illustrates the
input signal in frequency domain representation.
0 50 100 150 200 250 300 350 400 450 500
0
0.5
1
Row 1 in the Frequency Domain
0 50 100 150 200 250 300 350 400 450 500
0
0.5
1
0 50 100 150 200 250 300 350 400 450 500
0
0.5
1
Fig.5 Input signal in frequency domain
The analysis of IWF-SSAF with BD-VSS with PSO
approach was proved in ANIC, which is assigned as an
impulsive noise situation of the closed-loop structure.
0 500 1000 1500 2000 2500 3000
-10
-8
-6
-4
-2
0
2
ANIC Technique
Number of iterations, k
NoiseControl[dB]
Fig.6 Noise suppression using AINC technique
To analyze the performance enhancement by the
proposed closed-loop algorithm, this is better than without
optimization algorithm. Fig.6 showsthenoisesuppression of
proposed method. Simultaneously,theinputsignal isdivided
into multiples subband using Mexican Hat Wavelet
transformation. Fig.7 shows the Mexican Hat wavelet,
-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Mexican Hat Wavelet
Fig.7 Mexican Hat Wavelet
Now, there are two signals are achieved, one from
output of FFT and another from Mexican Wavelet result.
These signals are undergone with analysis of ROC and the
results are obtained. Then, the Machine learning algorithms
are incorporated to analyse on the best values of ROC in the
Mexican wavelet transformationandFFTandthebestvalues
are collected in a structured array. Moreover, the evaluation
factors are analysed to have an concept on the signal
accuracy and strength. This evaluation parameter gives an
idea on the extension of the signals.
In Fig.8 show that the Averaged Noise Reduction
(ANR) performances achieved by the proposed approach
with Particle Swarm Optimization (PSO) algorithm. This
demonstrates the approach produced the effective ANR
operation.
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
30
Iterations
Averagednoisereduction(db)
Fig.8 ANR performance of proposed algorithm
The closed-loop 1l -norm achieved a effective
performance under the same environments and high
impulsive noise control compared to other existed
algorithms. In addition, the impulsive noises by all assigned
algorithms which prove that the algorithm accomplished a
efficient noise control than other approches.
5. RESULTS AND DISCUSSION

In this paper, BD-VSS based delayless closed-loop IWF-
SSAF approach is proposed. The impulsive noise is
successfully suppressedusingAINCtechnique.Theproposed
approach has better convergence performance based onthe
1l -norm minimization technique and decorrelating
properties of SSAF algorithm. PSO technique is applied
together with IWF-SSAF algorithm for reducing the
computational complication. The performance evaluation
verifies the proposed algorithm has improved convergence
rate with condensed complexity comparedtotheotherSSAF
algorithms.
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6. CONCLUSION

IRJET- A Novel Adaptive Sub-Band Filter Design with BD-VSS using Particle Swarm Optimization

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