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Array Antenna and LMS Algorithm

Shivi Jain 10BEC0338

Slot - C1

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Array Antenna

• Multiple antenna elements• Isotropic radiators• Current of different amplitude and phase• Array pattern can be changed• Total pattern is the sum of individual radiation

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Array Antenna

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Types of Array Antenna

• Active and passive array antenna• Linear array antenna• Planar array antenna• Cylindrical array antenna• Conical array antenna• Digital array antenna• Multibeam array antenna

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Types of Array Antenna

• Multifaced array antenna• Multifrequency array antenna• Adaptive array antenna

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Active and Passive Array

• Active – active element like oscillator connected to the path of radiator

• Classified as receiving, transmitting and tranceiving antenna

• Radiated power increased• Thermal loss decreased• Reliability increased• Use transmit/receive (T/R) module

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Active and Passive Array

• Passive – has central transmitter and receiver • Phase shifter located at each radiating

element• All elements excited by common oscillator or

connected to common receiver• Feed network is the main part connecting

elements

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Active and Passive Array

• Classified as receiving, transmitting and transceiving antenna

• Used in variable purpose radars• Cheapest phased array• Less number and cost of components

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Active and Passive Array

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Linear Array

• Consists of group of identical elements• Elements placed in 1-D• Elements placed in specified direction in a

straight line• Spacing between element may be equal or not• Used in analysis of directional properties of

arrays• Building blocks for forming array of elements

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Linear Array

• Design of antenna is practical and simpler• Easy fabrication• Individual elements may be wire dipoles,

loops apertures or any other type• Total field = vector superposition of field

radiated by individual elements• AFn(normalized) = 1/n[sin(nψ/2) / sin(ψ/2)]

where Afn is the normalized array factor.

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Linear Array

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Planar Array

• All elements in a single plane• Elements occupy a definite area• Configurations – rectangular, triangular, square,

hexagonal.• Provides large aperture• Used in directional beam control by varying

relative phase of each element• Each radiating element has its own phase

shifter

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Planar Array

• The elements are in the form of matrix• It is two dimensional• Beam steering in two planes is possible• Digital beamforming can be done• Arrangement of elements is complicated• More electronically controlled phase shifters

are required• Cost is more

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Planar Array

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Cylindrical Array

• Radiators positioned on a cylindrical surface• Radiators used – wire and slot dipoles, open

ended waveguides and horns, spiral and dielectric rod antennas

• Selection of radiator depends on wavelength and required bandwidth

• Narrow bandwidth – 10000 elements• Used where azimuthal scanning with constant

beam shape and gain is required

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Cylindrical Array

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Conical Array

• Radiators positioned on a conical surface• Wavelength less than 0.5λ should be used for

the array element spacing• To use radiators efficiently – beam axis

pointed to the required direction to have maximum gain

• Narrow bandwidth – around 10000 elements• Maintains high gain and EIRP in forward

hemisphere

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Conical Array

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Digital Array

• Is a phased array• Signal is converted into digital code• Further processing, formation of antenna

pattern and signal processing performed in a digital computer

• The computer performs digital beamforming• Instantaneous shaping of array pattern in any

direction

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Digital Array

• Can generate adaptive array patterns of arbitrary shape

• Error is minimized• Complex hardware and software• Fast and efficient algorithms required to

reduce complexity

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Digital Array

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Multibeam Array

• Supports generation of several beams• Multibeam feed is used for above• Beams are used for surveillance of a sector• Each beam has a separate input channel• Uses multiple beam forming network• This network has quadrature directional

couplers and fixed phase shifters

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Multibeam Array

• Provide high quality of service• SDMA is used to design the antenna• SDMA provides high user capacity in a limited

frequency spectrum• Used in radar applications, satellite

communication and mobile communication• Interference is minimized

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Multibeam Array

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Multi-faced Array

• System of planar arrays• Arrays arranged in a form of a regular

polyhedron• Performance increases as the coverage range

becomes wider• No clear improvement gained by using more

than 10 faces

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Multi-faced Array

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Multifrequency Array

• Operates over several frequency bands• Can be formed by many techniques• By using convex multifrequency arrays with

distributed multifrequency radiators positioned on convex, curvilinear surfaces

• By using multifrequency or wideband radiators and frequency separation filters

• By the merging of one array into another

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Adaptive Array

• Consists of N element array• Appropriate choice of weighting coefficients• Weights placed between antenna elements

and a combining network• Weight should be capable of changing the

amplitude and phase of received signal from each element

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Adaptive Array

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Adaptive Array

• Interference can be reduced by:• Maximization of SINR at output of array• Minimum mean square deviation of received

signal from a reference level at output of array• Minimum interference power at array output• Maximum probability of detection of the

desired target signal

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Advantages of Array Antennas

• Increase in the overall gain • Provides diversity reception• Cancels out interference from a particular set

of directions• Steer the array such that it is more sensitive in

a particular direction• Used to determine the direction of arrival of

incoming signal

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Advantages of Array Antennas

• To maximize the signal to interference noise ratio (SINR)

• Provide high array gain by using simple antenna elements

• Provide a diversity gain in multipath signal reception

• Enabling of array signal processing• Provide capability of steerable beam as in

smart antennas

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Adaptive Array and LMS Algorithm

• Adaptive antenna – multibeam adaptive array• Gain pattern adjusted dynamically• Used to mitigate interference and improve

spectral efficiency in mobile systems• Digital beamforming antennas (DBF) are

developing as advanced phase array antennas

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Adaptive Array and LMS Algorithm

Adaptive array configuration

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Adaptive Array and LMS Algorithm

• LMS (Least Mean Square) error algorithm is used to cancel interference

• It was developed by Widrow et al• Further work was done by Frost and Griffiths• They worked to ensure that the desired signals

were not filtered out along with the unwanted signals

• LMS algorithm uses continuous adaptation

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Adaptive Array and LMS Algorithm

• Interference rejection achieved by optimally determining the array weights

• The LMS algorithm takes advantage of the following two points:

• The MSE when plotted against the filter coefficients is a quadratic, bowl-shaped one with a unique minimum

• The gradient of a function always points towards the maximum of the function

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Adaptive Array and LMS Algorithm

Example MSE surface for N = 2

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Adaptive Array and LMS Algorithm

The Adaptive Processor

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Adaptive Array and LMS Algorithm

• In the Steepest Descent Optimization method, the weight vector is made to “evolve” in the direction of the negative gradient

• Disadvantage - complex computation involved in finding the values of the r and R matrices

• R - auto correlation matrix of received signal• r – cross correlation vector between the

desired signal and the received signal

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Adaptive Array and LMS Algorithm

• LMS algorithm - simplification of the Method of Steepest Descent

• Instantaneous values of R and r are used instead of their actual values

• Simple expression for weight adaptation

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LMS Algorithm Steps

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LMS Algorithm Steps

• We assume that the signals involved are real-valued

• The LMS algorithm changes (adapts) the filter tap weights so that e(n) is minimized in the mean-square sense

• LMS algorithm is simplified form of steepest descent algorithm and replaces the cost function by its instantaneous coarse estimate

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LMS Algorithm Steps

• E{e2[n]} changes to e2[n]• e2[n]is the mean square error between the

beam-former output y(n) and the reference signal

• Substituting the above value in the steepest descent recursion, we obtain w[n + 1] = w[n] -μ[ {e▼ 2[n]}]

• µ is the step-size parameter and controls the convergence characteristics of the LMS algorithm

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LMS Algorithm Steps

• Now {e▼ 2[n]} = -2e(n)x(n)• Finally we get the LMS recursive function as:

w[n + 1] = w[n] + 2μx[n]e[n]• Therefore the summary can be given as:• Weight vector : w[n]• Input vector : x[n]• Desired output : d[n]• Filter output : y[n]

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LMS Algorithm Steps

• Weight vector updated : w[n+1]• Output : y[n] = wt[n]x[n]• Error : e [n] = d[n] − y[n]• Weight : w[n + 1] = w[n] + 2μx[n]e[n]• LMS is simple in implementation• Stable and robust performance against

different signal conditions

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References

• ‘LMS and SMI algorithms for spatial adaptive interference rejection’ by Vijaya Chandran Ramasami; March 16, 2001.

• ‘GPS interference mitigation for small UAV applications’ by Joy Li; School of Electrical and Electronic Engineering; The University of Adelaide; Adelaide, South Australia; March 2009.

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References

• ‘Theory and Analysis of Adaptive Cylindrical Array Antenna for Ultrawideband Wireless Communications’ by Malek G. Hussain, Senior Member, IEEE; IEEE Transactions on Wireless Communications, Volume 4; November 6, 2005.

• ‘Passive Phased Arrays for Radar Antennas’ by EMS Technologies, Inc.; Space and Technology – Atlanta; December 2005.

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References

• ‘Adaptive Array Antenna for Mobile Communication’ by Isamu Chiba, Rumiko Yonezawa and Kazunari Kihira; Mitsubishi Electronics Corporation, Japan; IEEE 2000.

• ‘An Overview of Adaptive Antenna Systems’ bu Hafeth Hourani; Helsinki University of Technology Communications Lab; Postgraduate course in Radio Communications (2004/2005).

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References

• ‘Interference Rejection of Adaptive Array Antennas by using LMS and SMI algorithms’ by Kerim Guney, Bilal Babayigit and Ali Akdagli; Turkey.

• http://www.antennatheory.com/arrays/main.php

• http://www.radartheory.8m.com/antenna15.html

• http://cwww.ee.nctu.edu.tw/course/asp/ASP04.pdf

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References

• http://en.wikipedia.org/wiki/Antenna_array• http://personal.ee.surrey.ac.uk/Personal/D.Je

fferies/antarray.html• http://en.wikipedia.org/wiki/Phased_array#Ac

tive_Phase_Array

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