To BEam or Not to BEam !

In my previous articles about Smart antenna and beamforming http://www.techplayon.com/smart-antennas-and-beamforming-understanding-with-gnu-part-2/ and http://www.techplayon.com/smart-antennas-beam-forming-understanding-gnu-part-3/

I talked about

  • The relationship between height of the antenna ans its ability to detect useful signal that is fainted due to propagation. A big antenna collects a lot of electromagnetic waves just like a big bucket collects a lot of rain. However, this solution of increasing height of the antenna or having a very big bucket to collect rain water is not practical.
  • Another approach to collect a lot of rain is to use many buckets rather than one large bucket. The advantage is that the buckets can be easily carried one at a time. Collecting electromagnetic waves works in a similar manner. “Many antennas can also be used to collect electromagnetic waves. If the output from these antennas is combined to enhance the total received signal, then the antenna is known as an antenna array. ”
  • Will it make difference in total collected water if many small buckets are arranged in a linear way or circular way ? will the distance between buckets make any difference ? Maybe not, but in case of antenna arrays, Geometry of antenna array, spacing between them matters.
  • A Smart system of collecting rain water is the one that changes as per the environment conditions. On similar lines, Smart antenna sytems are designed to adapt to a changing signal environment in order to optimize a given algorithm.

Antenna pattern consists of main-lobe, side-lobe and nulls. As shown in figure below:

The main-lobe is that portion of the pattern which has maximum intended radiation. The side-lobes are generally unintended radiation directions. This blog is an attempt to understand how to suppress side-lobes.

Recall that an Array factor can be represented in vector terms as follows:

One of the easiest way to suppress the side-lobes is to add weighting to array elements. Array weights can be chosen to minimize the side-lobes, to shape the side-lobes or placing a null at a specific angle.

Windows functions can provide array weights that can be used with linear arrays. Let’s see this from following octave example:

N = 8; % Number of array Elements
d = 0.5; % Array Element spacing
theta = -pi/2:.01:pi/2;
ang = theta*180/pi;

test = diag(rot90(pascal(N)));
wB = flipud(test(1:N/2));  wB = wB/max(wB);

% Weighted Array Factor
AF = 0;
tot = sum(wB);
for i = 1:N/2
AF = AF + wB(i)*cos((2*i-1)*pi*d*(sin(theta)));
end

% Normalised Array Factor
AFn = sin(N*pi*d*sin(theta))./(N*pi*d</em>sin(theta));

%----- Plot Results -----%
figure, plot(ang,abs(AF)/tot,'r', ang,abs(AFn),'k:')
xlabel('\theta (deg)'), ylabel('|AF|')
title('Binomial Weighted Array Factor vs. Angle')
axis([-90 90 0 1.1]), grid on
set(gca,'xTick',[-90:30:90])

Suppressed side-lobe can be seen in red plot corresponding to weighted array factor. Also, price paid to suppress the side-lobe was to broadening of main lobes.

Ref:

  1. Book-1: “Smart Antennas for Wireless Communications ” Frank B. Gross, PhD
  2. Book-2: ” “Antenna Arrays : A computational Approach by Randy L. Haupat” ”

~Cheers

Dheeraj

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