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8/9/2019 A Pod is at Ion

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Project on Non-linear Apodisation

Techniques

for

Sidelobe Suppression

Submitted by

Satam Choudhury

Electronics and Communication Engg.

National Institute of Technology, Silchar


2/13

Acknowledgement

I would like to express my heartfelt gratitude for my supervisor, Dr. Amit Kumar

Mishra, Dept. of Electronics and Communications Engg., Indian Institute of Technology,

Guwahati, for guiding me through my summer project on Non-linear Apodisation

Techniques for Sidelobe Suppression. My special thanks to Mr. Rajiv Panigrahi, Dept. of

Electronics and Communications Engg., Indian Institute of Technology, Guwahati ,for

constantly clarifying my doubts and also guiding my project work.

I am beholden to the Ms. Jharana Rabha of System Simulation Laboratory for

providing me with the necessary facilities for accomplishing the project.


3/13

We have considered a sinusoidal signal comprising of 3 components, 2, 2.5 and 5 kHz

and the signal is sampled at a rate 1.5 times the Nyquist rate. The spectrum analysis is done

using the following techniques:

Dual Apodisation

fig.1

fig.2


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The two versions of the image are the IPRs shown in Fig 1. and Fig 2. (Hanning). The

resultant dual-apodized IPR, shown below has the narrow mainlobe of the sinc IPR and the

small sidelobes of the Hanning IPR. The combination of a uniformly weighted image with a

normalized version of the same image computed with any weighting function chosen to

produce low sidelobes is the basic principle behind Dual apodisation. The combination

technique uses a min function applied to the detected image on a pixel-by-pixel basis.

Applied to complicated images, DA results in an effective weighting function that can differ

from sample to sample in the image. Thus it results in a weighting function and an IPR that

are both nonlinear and spatially varying.


5/13

Complex Dual Apodisation

To make use of the complex values we operate on the real (I or in-phase) and

imaginary (Q or quadrature) components of the undetected images separately. If the value

of a component has a sign that is different for the sinc IPR than for the Hanning IPR, then

there must be some weighting function intermediate between uniform weighting and

Hanning weighting for which the value of the component would be zero.

CDA provides significantly lower sidelobes than DA for the one-dimensional case (1-D).

SVA

We shall now discuss spatially variant apodization (SVA), which allows each pixel in an

image to receive its own frequency domain aperture amplitude weighting function from a

continuum of possible weighting functions. SVA effectively eliminates finite-aperture induced


6/13

sidelobes from uniformly weighted SAR data while retaining nearly all of the good mainlobe

resolution and clutter texture of the unweighted SAR image.

(simulated at 2-times Nyquist frequency)


7/13

(simulated at 1.5 times Nyquist frequency)

We observe that for non-integer multiples of Nyquist sampling frequency, the

resolution is not accurate and the sidelobe suppression is not complete.

There is another important limitation of Spatially Variant Apodisation. At higher

smapling rates, the mainlobe resolution is not good and the sidelobes are not suppressed as

well.


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9/13

However the proposed algorithm intends to address this problem of sidelobe

suppression at non-integer multiples of Nyquist sampling frequency.

1. At first, the zero crossing points are determined. For every three consecutive zerocrossing points, there is a maxima( appositive maxima) and a minima(a negative

minima). These maxima are determined for a uniform weighting function. The same

process is carried out for two or more windowed-weighted functions and the points of

maxima are determined. The maxima points are compared and those points which

occur in the all the weighted functions are retained while other maxima( the

sidelobes) are ignored.

2. A particular case may occur when two closely placed frequency components overlapeach other. This may be illustrated as follows:

The following signal is composed of 6 frequency components: 2, 2.9, 3.5,3.8,4, 5 kHz


10/13

In this case we observe that there is overlap of two closely spaced frequencycomponents. It is obvious that in between zero-crossing points there is more than 1 maxima.

So we need to determine the total positive minima in that interval and subdivide the interval

into [zero-crossing point 1, 1st

+ve minima], (1st

+ve minima, 2nd

+ve minima](nth +ve

minima, zero crossing point 2]. The same process is repeated for other weighted window

functions and the maxima are compared. This process can help us in considerably resolving

closely spaced frequency components.

Program for Uniform Weighting, Hanning weighting and Dual apodisation

clc;

clear all;

close all;

N= 256;

l = 64;%length of seq

t=sqrt(-1);

n = 0:1:l-1;

eps=power(10,-10);

%frequency components

F1 = 5000;%in Hz

F2 = 2000;

F3= 2500;

Fs = 3*F1; %sampling freq

f1 = F1/Fs;

f2= F2/Fs;

f3= F3/Fs;

%given signal

x = sin(2*pi*f1*n)+sin(2*pi*f2*n)+sin(2*pi*f3*n);

f= (-Fs/2):(Fs/N):(Fs/2-(Fs/N));%range

x1= [x zeros(1,N-l)];%zero padding

y1= fftshift(fft(x1));


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m1= abs(y1); figure(1);

plot(f,m1);grid on;title('Uniform weighting'); ylabel('Amplitude');

%windoww= (hann(l))';

x2= x.*w;

x3= [x2 zeros(1,N-l)];

%fft of x1 and x2


m3= abs(y3);

figure(2);plot(f,m3);grid on;title('Hanning Weighting'); xlabel('frequency in

Hz');ylabel('Amplitude');

%DA

for k= 1:N

mag1(k)=min(m1(k),m3(k));end

figure(3);plot(f,mag1);grid on;title('DA'); xlabel('frequency in

Hz');ylabel('Amplitude');

Program for Complex Dual Apodisation

clc;

clear all;

close all;

N= 256;

l = 64;%length of seq

t=sqrt(-1);

n = 0:1:l-1;

eps=power(10,-10);

%frequency components

F1 = 5000;%in Hz

F2 = 2000;

F3= 2500;

Fs = 3*F1; %sampling freq

f1 = F1/Fs;

f2= F2/Fs;f3= F3/Fs;

%given signal

x = sin(2*pi*f1*n)+sin(2*pi*f2*n)+sin(2*pi*f3*n);


x1= [x zeros(1,N-l)];


m1= abs(y1);

w= (hann(l))';


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x2= x.*w;

x2= [x2 zeros(1,N-l)];


m2= abs(y2);

I1=real(y1);

I2=real(y2);

Q1=imag(y1);

Q2=imag(y2);

I=zeros(1,N);

Q=zeros(1,N);

%I-Q indepenent comparison

for k = 1:N

if(sign(I1(k))~=sign(I2(k)))

I(k)=0;

else

I(k)=min(abs(I1(k)),abs(I2(k)));end

if(sign(Q1(k))~=sign(Q2(k)))

Q(k)=0;

else

Q(k)=min(abs(Q1(k)),abs(Q2(k)));

end

end

mag=I+t*Q;

figure(3);plot(f,abs(mag),'r');grid on;title('CDA'); xlabel('frequency in Hz');

Program for Spatially Variant Apodisation

clc;clear all

close allN= 256;l = 64; %length of seqt=sqrt(-1);n = 0:1:l-1;

%frequency componentsF1 = 2000;F2 = 5000;

F3= 3000;

Fs = 4*F2; %sampling freqf1 = F1/Fs;f2 = F2/Fs;f3= F3/Fs;

xn = sin(2*pi*f1*n)+sin(2*pi*f2*n);



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x1= [xn zeros(1,N-l)];%zero paddingy= fftshift(fft(x1));

p=sign(angle(y));

y1=p.*y;I1=real(y);Q1=imag(y1);n1=length(y1);I=zeros(1,N);Q=zeros(1,N);w1= zeros(1,N);w2=zeros(1,N);

for k=3:N-2w1(k)=-I1(k)/(I1(k-2)+I1(k+2)+eps);

if(w1(k)

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