Design and Implementation of Efficient Analysis and Synthesis QMF Bank for Multicarrier Cognitive Radio Communication

TELKOMNIKA, Vol.15, No.2, June 2017, pp. 636~645
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v15i2.4746  636
Received January 5, 2017; Revised March 8, 2017; Accepted April 1, 2017
Design and Implementation of Efficient Analysis and
Synthesis QMF Bank for Multicarrier Cognitive Radio
Communication
A. S. Kang*, Renu Vig
Department ECE, UIET, Panjab University Chandigarh, India
*Corresponding author, e-mail: askang_85@yahoo.co.in
Abstract
The present section deals with a new type of technique for designing an efficient two channel
Quadrature Mirror Filter Bank with constant phase in frequency. For achieving the Perfect Reconstruction
Condition in Filter bank, an attempt has been made to design the low pass prototype filter with its impulse
response and frequency response in three regions namely pass band, stop band and transition band
region. With the error in terms of Reconstruction and the attenuation in the stop band as seen in the
prototype filter response, one can evaluate the performance of the introduced filter with the help of filter
coefficients generated in the design examples that affects the quality of filter bank design under the
constraints of Near Perfect Reconstruction Conditions.
Keywords: analysis filter bank, synthesis filter bank, quadrature mirror filter, cognitive radio
Copyright © 2017 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
The Sensing of the available spectrum is a gigantic task in the cognitive radio systems
because of Interference mitigation among different primary and secondary users is only possible
by making a sacrifice of a portion from transmission bandwidth. Filter Bank Multicarrier
approach can serve as a near optimal tool for spectrum analysis in cognitive radio systems with
increased bandwidth efficiency attainable and decreased hardware complexity as well. Some
researchers in the past have made an attempt to develop an efficient two channel Quadrature
Mirror Filter banks by taking into consideration their magnitude and frequency responses in the
passband, stopband and transition band regions [1]. Even, the joint effect of filters and symbols
introduce various characteristics in different multicarrier schemes. The survey on wireless
multicarrier communications suggests a framework to design and realize newer waveforms that
not only lay the basis for further enhancements in wireless radio access techniques but also, it
provides a information and ways to address different practical issues involved in the frequency
domain synchronization for FBMC based Transmission. Better Spectral Containment is crucial
to avoid distortion from asynchronous signals in the bands which are adjacent to each other.
Also, higher spectrum is necessary while doing spectrum sensing, that is the fundamental thing
in cognitive radio terminology [2].
2. FBMC System
In OFDM approach, the frequency selective channel can be converted into a number of
subcarrier channels by using cyclic prefix and as a result, each of these subcarrier channels can
be modeled as flat fading channel with constant gain. On the receiver side, the unwanted
distortion and ISI can be reduced in each subcarrier band by using the concept of equalization
as this holds true in case of Filter Bank based multicarrier communication systems. It has been
found that out of all the multicarrier methodologies which are existing, OFDM-OQAM (i.e.
FBMC) achieves the highest stop band attenuation [2].The higher attenuation in the stop band
of Filter Bank allows the channel selection filtering along with Narrowband Interference
attenuation at the analysis bank in receiver, with no pre-processing except for anti-aliasing filter
estimated by the sampling rate at input in analysis filter bank. As the Filter Bank gives good
frequency selection for the required spectral components, it is genuine to think of an overall

TELKOMNIKA ISSN: 1693-6930 
Design and Implementation of Efficient Analysis and Synthesis QMF Bank… (A.S. Kang)
637
receiver architecture where all the signal processing functions at the baseband are performed in
the frequency [1]. FBMC Prototype Filter Design (frequency domain optimized) is an interesting
direction of the future studies to investigate the overall system performance. In FBMC system,
the pulses that are transmitted are localized in both time and frequency domain. A multicarrier
system can be described by a synthesis-analysis filter bank called Trans multiplexer
Structure [3]. The synthesis filter bank comprises of parallel transmit filters and analysis filter
bank comprises of all the matched receive filters. FBMC waveforms use an advanced filter
design to better localize the different subcarriers. The impulse response of the prototype filter is
expressed by the following equation.
h(t)=GP(0)+2∑(-1)
k
Gp (k) cos([2πk/KN](t+1)) (1)
where Gp=[1,0.97195983,0.707,1-Gp(1)
2
] for Overlapping factor K=4,6,8,10;N is the number of
carriers. The higher the overlapping factor is, the more localized the signal is in frequency. In
fact, the fragmented spectrum can be observed as the consequence of extension to channel
aggregation for mobile communication systems [4].
Here a program is given to design a prototype filter for use in a Quadrature Mirror Filter
bank. Here a two-channel filter bank has four filters, each based on a low pass prototype (𝑧).
The analysis filters are 𝐻 𝐿(𝑧), 𝐻 𝐻(𝑧) while the synthesis filters are 𝐺 𝐿(𝑧), 𝐺 𝐻(z), 𝐻 𝐿(𝑧)=𝐻(𝑧);
𝐻 𝐻(𝑧)=𝐻(−𝑧); 𝐺 𝐿(𝑧)=𝐺 𝐿(𝑧); 𝐺 𝐻(𝑧)=−2𝐻(−𝑧) respectively.
The design procedure reduces the ripple energy and the stop band energy of the low
pass filter. The design procedure is adopted by Jain-Crochiere [5] and is based on iterative
cautious update optimization algorithm. When the configuration of analysis-synthesis filters is
done, the overall system has an impulse response with a unit coefficient at a delay of 𝑁−1
samples. The process explained here is changed to apply a cautious update during the iteration
process. This procedure uses Plot Filter command to plot the frequency responses [1].
3. Earlier Related Work Done
Two channesl QMF bank is a multirate filter structure which consists of two decimators
in the signal analysis section and two interpolators in the signal synthesis section [5]. QMF
banks find applications in automated methods for scoring tissue microarray spots [6], image
coding [7], multicarrier modulation systems [8], two dimensional and three dimensional short
time spectral analysis of short perfect reconstruction filters [9], antenna systems and MIMO [10],
sampling theory techniques [11], biomedical electronics [12], wideband beam forming for sonar
and radar [13] and in solving various co-existence problems of wireless communication systems
[14, 15]. The earlier related work on the design of Nearly Perfect Reconstruction two channel
QMF banks [16-31] can be categorized in different ways.Least Squares [16-18] and Weighted
Least Squares [19-21] techniques had been applied for the filter design. Eigen value-Eigen
vector approach has been proposed to find the optimum filter coefficients in time [17-18]. Lee
and Chan [18] proposed a WLS method on the basis of the linearization of objective function to
get optimal filter tapping weights. Several iterative methods [21-26] and genetic algorithm based
techniques [27-31] have been suggested for design of two channel QMF banks. In [22], authors
have presented a technique by taking into consideration the responses of filter in pass
band,stop band and in transition band regions for QMF bank. In the two channel analysis and
synthesis section of QMF bank, the discrete input signal x(n) is split into two sub band signals
with equal bandwidth using low pass and high pass analysis filters H1(z) and H2(z). The
subband signals are downsampled by a factor of 2 to attain signal compression for reducing the
complexity during processing. The outcomes of synthesis filters are added to attain the
reconstructed signal x(n) which suffers from Aliasing Distortion and Phase Distortion. Hence,the
main focus of attention while designing the prototype filter for two channel QMF is the removal
of these errors to obtain a Near Perfect Reconstruction [18-23]. In QMF banks,the high pass
and low pass analysis filters are linked to each other by the mirror image symmetry i.e
H2(z)=H1(-z), around quadrature frequency π/2.Due to this symmetry, the amplitude distortion
can be reduced by optimizing the filter tapping weights of the low pass prototype filter. In the
present section, we discuss an algorithm to design the two channel QMF bank with no matrix
inversion which influences the performance of the optimization method used.

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TELKOMNIKA Vol. 15, No. 2, June 2017 : 636 – 645
638
4. QMF Bank Design Methodology
The mathematical expression for the overall system function or distortion transfer
function of the alias free two channel QMF bank is expressed as [21-29].
T(z)=1/2[H1
2
(z)-H1
2
(-z)] (2)
where for alias cancellation,synthesis filters are defined as:
F1(z)=H2(-z)andF2(z)=-H1(-z) (3)
To obtain the perfect reconstruction QMF bank, the overall transfer function T(z) must be a pure
delay.i.e.
T(z)=(1/2)[H1
2
(z)-H1
2
(-z)]=cz
-n
0.or.x(n)=cx(n-n0) (4)
This equation shows that if the prototype filter H1(z) is chosen to be linear phase FIR with nil
phase distortion, then to ensure linear phase FIR constraint, the impulse response h1[n] of low
pass prototype filter H1(z) must be symmetrical .i.e. h1[n]=h1[N-1-n],0<n<N-1 where N is the filter
length [17]. The corresponding frequency response is given by [5] as:
H1(e
jω
)=A(ω)e
-jω(N-1)/2
(5)
where A(ω)= H1(e
jω
) is the amplitude function.If the prototype flter H1(z) characteristics are
assumed ideal in pass band and stop band regions then the exact reconstruction condition is
satisfied for 0<ω<ωp and ωs<ω<π. Here ωp and ωs are the passband and stopband edge
frequencies. The constraint comes in the transition band(ωp<ω< ωs) where Amplitude Distortion
needs to be controlled. It means our motive is to optimize the coefficients of H1(z) such that the
exact reconstruction condition is approximately nearly satisfied.
Design Implementation: A Matlab code has been run to implement the design part of
prototype LPF and inference has been drawn on the basis of CPU processing time taken to run
that event.The entire process here involves three steps mainly (1). Design Specification for
Efficient Two Channel QMF Bank(2). Implementation of Two Channel QMF (3). Evaluation of
Designed QMF results.
Case Study (Design Example): We have designed the QMF here for
N=24,32,42,48,64,128 with Stopband Frequency Fsb=0.359 for Alpha constant lying between 0
and 1(0.22),ωs=0.6π,ωp=0.4π. A Matlab code has been written which implements the design
procedure for prototype low pass filter described and tested on a laptop equipped with an Intel
Core i5-2410M Processor 2.30GHz with Turbo Boost upto 2.90 GHz with 4GB RAM on
Windows 7 (64-bit) Operating system. This section presents a design example to check the
effectiveness of the proposed algorithm.The main parameters which govern the performance of
the algorithm are First lobe Stop band attenuation,Stop band edge attenuation, As=-
20log10(H1(ωs), Maximum Overall Ripple/Passband-Ripple), Prototype QMF Length N,
Stopband-Frequency(Fsb),Roll off factor Alpha, Measure of Reconstruction
Error(dB)=max(10log(T(e
jω
))-min(10log(T(e
jω
)).
The Design Specification: N-Number of coefficients for the lowpass prototype. fsb-
Normalized stop band edge frequency for the low pass prototype, where 0.25 < fsb < 0.5. Alpha-
Relative weighting between the stop band energy and the ripple in the overall response. An
increase in alpha will lead to greater stop band attenuation in the low pass prototype. A sample
filter has been designed with QMF Design (32, 0.3, 1). The performance of the designed
algorithm can be analysed through a set of observations in terms of Magnitude w.r.t. Normalized
Frequency (π radians/sample), Phase w.r.t. Normalized Frequency plots which also reveal the
Phase Distortion occuring at values of Normalized Frequency. The results of the used algorithm
have been compared to the results obtainable in case of Jain-Crochiere [5] and S.K. Aggarwal-
O.P.Sahu [31]. The following set of filter coefficients have been obtained for (0< n< N/2-1) in
case of Filter (Jain & Crochiere) and subsequent set of filter coefficients obtained for O.P.Sahu
et al and that obtained in case of our proposed algorithm given in Table 1-4.

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Table 1. QMF coefficients generated [Jain & Crochiere]
Optimized Filter Tap Weights in QMF design By Jain and Croichere [N=32]at fsb=0.3;α=1
Table 2. QMF coefficients generated {Sahu et al]
Optimized Filter Tap Weights in QMF design By O.P.Sahu et al [N=24;fsb=0.3;α=1]
h1(0)=0.0034 h1(1)= -0.0074
h1(2)=-0.0022 h1(3)= 0.0163
h1(4)= -0.0020 h1(5)= -0.0301
h1(6)= 0.0124 h1(7)= 0.0525
h1(8)= -0.0375 h1(9)= -0.1000
h1(10)= 0.1272 h1(11)= 0.4672
Table 3. QMF coefficients generated [Kang& Vig-Proposed Algorithm]
Optimized Filter Tap Weights in QMF design by Kang-Vig [N=24;fsb=0.3;α=0.22]
h1(0)=0.0036 h1(1)=-0.0072
h1(2)=-0.0023 h1(3)= 0.0161
h1(4)= -0.0018 h1(5)= -0.0300
h1(6)= 0.0122 h1(7)= 0.0524
h1(8)= -0.0373 h1(9)= -0.1000
h1(10)= 0.1270 h1(11)= 0.4673
Table 4. QMF coefficients generated [Vig& Kang-Proposed Algorithm]
Optimized Filter Tap Weights in QMF design by Vig-Kang [N=32;fsb=0.3;α=0.22]
Figure 1. N=32;Fsb=0.3;Alpha=1 [Jain & Croicere] Figure 2. N=64;Fsb=0.3;Alpha=1
h1(0)=0.46513280 h1(1)= 0.13063700
h1(2)=-0.99656700E-1 h1(3)= -0.41773659E-1
h1(4)= 0.53938050E-1 h1(5)= 0.16805820E-1
h1(6)= -0.33077250E-1 h1(7)= -0.58240110E-2
h1(8)= 0.20216010E-1 h1(9)= 0.71798260E-3
h1(10)= -0.11586330E-1 h1(11)= 0.12928400E-2
h1(12)= 0.58649780E-2 h1(13)= -0.16349580E-2
h1(14)= -0.23388170E-2 h1(15)= 0.12488120E-2
h1(0)=0.0013 h1(1)= -0.0023
h1(2)=-0.0016 h1(3)= 0.0058
h1(4)= 0.0013 h1(5)= -0.0115
h1(6)= 0.0006 h1(7)= 0.0201
h1(8)= -0.0057 h1(9)= -0.0330
h1(10)= 0.0167 h1(11)= 0.0539
h1(12)= -0.0417 h1(13)= -0.0997
h1(14)= 0.1305 h1(15)= 0.4652

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Figure 3. N=128;Fsb=0.3;Alpha=1 Figure 4. N=42;Fsb=0.3;Alpha=1
Figure 5. N=24;Fsb=0.3;Alpha=1 [Sahu] Figure 6. N=24;Fsb=0.3;Alpha=0.22
Figure 7. N=48;Fsb=0.3;Alpha=0.22 Figure 8. N=32;Fsb=0.3;Alpha=0.22
Figure 9. N=64;Fsb=0.3;Alpha=0.22 Figure.10 N=128;Fsb=0.3;Alpha=0.22

641
Figure 11. N=24,Fsb=0.3,Alpha=1 [O.P.Sahu et al]
Figure 12. Magnitude wrt Frequency Plot for (a) Gaussian Noise Input (b) Gaussian Noise
Output(c)Gaussian Noise Intermediate Signal U0(d) Gaussian Noise Intermediate Signal U1 (Filter Length
N=78)
Figure 13. Magnitude wrt Frequency Plot for, (a) Gaussian Noise Input, (b) Gaussian Noise Output, (c)
Gaussian Noise Intermediate Signal U0, (d) Gaussian Noise Intermediate Signal U1 (Filter Length N=24)

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5. Results and Discussion
Table 5 shows the Performance Evaluation of Proposed Method for QMF design w.r.t
QMF design by Earlier workers namely Jain & Croichere [5], Sahu et al [31]. An attempt has
been made to minimize the phase distortion occurring w.r.t normalized frequency and the level
of stopband attenuation occurring at different instants with variable N, Fsb and Roll off factor α.
Beyond N=128 with roll off factor 1, the first lobe attenuation comes around 137.784 with
passband ripple of 8.1dB and phase distortion occurring at a normalized frequency of 0.60.
Table 5. Comparatative Performance Evaluation of QMF for Design Specification
N=24,32,42,48,64,128 with Stopband Frequency Fsb=0.359 for Alpha constant lying between 0
and 1(0.22),ωs=0.6π,ωp=0.4π
QMF Design
Method
Filter
Length
N
Stop
band
Freq
uency
Fsb
Roll Off
factor α
Magnitu
de w.r.t.
Norma
lized Fre
quency
Normalized
Freq value
(πradians/sa
mple)at
which
Minimum
Stopband
Attenuation
occurs
First lobe
Attenua
tion in dB
Stopband
Edge
Attenuation
= -
20log10(δs)
dB
Passband
Ripple/Max
Overall
Ripple (dB)
Phase
Response wrt
Normalized
Frequency
Norma
lized
Frequency
at which
Phase
Distortion
starts
occuring
Sahu et al 24 0.3 1.0 -80dB 0.62 34.723 0.30575 0.0334359 Linear N.A.
Proposed
App I
24 0.3 0.22 -63dB 0.83 44.1946 0.30325 0.015315 0 to -1250
degrees
0.63
Jain &
Crochiere
32 0.3 1.0 -100dB 0.62 44.1946 0.30325 0.015315 0 to -1650
degrees
0.62
Proposed
App II
48 0.3 0.22 -70dB 0.75 61.2333 0.3025 0.0061505
5
0 to -2600
degrees
0.62
Proposed
App III
32 0.3 0.22 -62dB 0.62 44.4244 0.3035 0.0142484 0 to -1700
degrees
0.63
Proposed
AppIV
64 0.3 0.22 -75dB 0.86 67.1736 0.30125 0.0008103
18
0 to -3400
degrees
0.60
Proposed
App V
128 0.3 0.22 -165dB 0.63 137.71 0.30025 0.0001306
43
0 to -6800
degrees
0.58
Proposed
App VI
24 0.3 1 -93dB 0.64 34.7233 0.30575 0.0334359 0 to -1250
degrees
0.63
Proposed
App VII
42 0.3 1 -72dB 0.86 55.0136 0.302 0.0067590
1
0 to -2200
degrees
0.61
Proposed
App VIII
64 0.3 1 -75dB 1 70.7027 0.301 0.0013292
9
0 to -3400
degrees
0.61
Proposed
App IX
128 0.3 1 -155dB 0.62 137.784 0.30025 8.13492e-
05
0 to -6700
degrees
0.60
Figure 14. Magnitude wrt Frequency Plot for
(a)Gaussian Noise Input(b)Gaussian Noise
Output(c)Gaussian Noise Intermediate Signal
U0(d)Gaussian Noise Intermediate Signal U1
(Filter Length N=32)
Figure 15. Magnitude wrt Frequency Plot for
(a)Gaussian Noise Input(b)Gaussian Noise
Output(c)Gaussian Noise Intermediate Signal
U0(d)Gaussian Noise Intermediate Signal U1

643
Table 6. Comparison of the Proposed Algorithm with existing optimization algorithms based on
computational complexities
Technique
Filter
Length
N
Any
Matrix
Inversio
n
in.each
Iteration
Comp
utatio
nal
Compl
exity
Reduc
ed
Selectio
n of
h1(n)
Ripple
Compu
tation
Phase
Res
ponse
Per
fect
Recon
structi
on
Achiev
ed
Alia
sing
Distor
tion
Reduc
ed
Amplitude
Distortion
Minimized
Eigen
Value
Evalua
tion in
each
Itera
tion
Phase
Distort
ion
Elimin
ated
CPU
time
(sec)
Sahu[31] 24 Yes Yes
Assu
med
3.19056
e-06
Linear
Yes,
PR
Yes Eliminated No Yes 0.66
Jain &
Croichere
[5]
32 Yes Yes
Assu
med
5.34059
e-07
Linear/
Non
Linear
NPR Yes Eliminated Yes Yes 1.68
Proposed
Method I
24 Yes Yes
Assu
med
3.19056
e-06
Non
Linear
NPR Yes Minimized Yes Yes 0.62
Proposed
Method II
48 Yes Yes
Assu
med
7.23799
e-08
Non
Linear
Proposed
Method
III
32 Yes Yes
Assu
med
4.79034
e-07
Non
Linear
Proposed
Method
IV
64 Yes Yes
Assu
med
1.74207
e-09
Non
Linear
Proposed
Method V
128 Yes No
Assu
med
4.62215
e-11
Non
Linear
Proposed
Method
VI
24 Yes Yes
Assu
med
3.19056
e-06
Non
Linear
Proposed
Method
VII
42 Yes Yes
Assu
med
1.76966
e-07
Non
Linear
Proposed
Method
VIII
64 Yes Yes
Assu
med
4.90713
e-09
Non
Linear
Proposed
Method
IX
128 Yes Yes
Assu
med
1.71327
e-11
Non
Linear
Figure 16. Magnitude wrt Frequency Plot for (a)Gaussian Noise Input(b)Gaussian Noise
Output(c)Gaussian Noise Intermediate Signal U0(d)Gaussian Noise Intermediate Signal U1
6. Conclusion
The present study on the Design and Implementation of Efficient QMF bank for Cognitive
Radio Wireless Communication highlights how the different aspects such as Aliasing Distortion,
Computational Complexity, affect the Two Channel QMF bank with Analysis and Synthesis
Filters as the discrete input signal x(n) gets split up into two sub-band signals with equal
Bandwidth using analysis filters H0(z) and H1(z).These filters have been designed to have Near
Perfect Reconstruction conditions satisfied. These subband signals are downsampled by a
factor of two to achieve signal compression. The decimated signals are coded and then
transmitted. At the receiver, the two subband signals are decoded and then interpolated by a

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factor of two and ultimately passed through low pass and high pass synthesis filters. The
outputs of synthesis filters are combined to obtain the reconstructed signal y(n)=x(n). The
reconstructed signal suffers from errors such as Aliasing Distortion, Amplitude Distortion and
Phase Distortion because of the fact that these filters are not ideal. So here, the Amplitude
distortion has been minimized by optimizing the filter tap weights of low pass analysis filter. The
proposed algorithm presents improved performance in terms of reduced computation time when
compared to Sahu, Jain.
7. Impact of Study
The present research work has its strong impact on the design of Multirate Filter banks
for cognitive radio communication under ubiquitous, pervasive domain. The study can be
extended to the wireless networks through the application of efficient filter banks which can be
further helpful for analysis and design of future wireless radio technologies [32-35].
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