adaptive beam forming and space time adaptive processing

8/3/2019 Adaptive Beam Forming and Space Time Adaptive Processing

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In this Presentation

Fundamentals of Antenna Arrays Linear Arrays Planar Arrays Phased Arrays Adaptive Arrays

Beamforming (Spatial Filtering) Signal Models

Conventional Beamforming Optimal Beamforming MATLAB Illustration

Space-Time Adaptive Processing


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Fundamentals of Antenna Arrays Many applications require radiation characteristics (like

gain, directivity) that may not be achievable by a singleelement

Antenna array is a geometric arrangement of antennaelements

Resulting radiation pattern is a vector sum of individualpatterns

Antenna arrays provide more directivity by thephenomena of wave interference

Directive Gain in a given direction is a measure of abilityof an antenna/array to radiate power in that given

direction


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Fundamentals of Antenna Arrays

As the length of the antenna aperture increases, beamwidth decreasesAs the number of antenna elements increase, directive gain increases


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Linear Arrays

Linear array is a lineararrangement of antenna elementswith equal spacing d betweensuccessive elements

Uniform LA is LA with equalcurrent excitation and uniformprogressive phased shift betweenelements

The electric field at a far observation point is (assumingisotropic elements) is independent of


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Radiation Pattern of an 8-Element UniformLinear Array with d = 0.5

Polar Plot E(sin) vs direction cosine (sin)


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Array Controls


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Increasing Array Sizeby Adding Elements

S


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Increasing Array Sizeby Separating Elements


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Amplitude Tapering (Windowing) and Phase Quantization

In Antenna Arrays the current exitations (aperture distribution) are tapered i.emultiplied by a window sequence to reduce the side lobe level. Reduction of SideLobe Level is obtained at the cost of increase in beamwidth

In practice phase shifters are implemented as part of TR modules, using finitenumber of bits

Due to quantization error (difference between desired phase and actualquantized phase) the sidelobe levels are affected


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Planar Arrays Planar Arrays have antenna elements

placed on a plane according to somegrid configuration (rectangular, circular)

Planar arrays can control thebeamshape in both planes (, ) andform pencil beams whereas linear array

only controls the pattern in one plane

Total electric field at a far fieldobservation point is given by


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Radiation pattern of an 8 8-element uniform-amplitude and spaced square planar array

Spherical Radiation Pattern

Radiation Pattern Translation fromSpherical coordinates into U,V space


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Phased Array Antennas

Array antennas synthesize narrow directive beams thatmay be steered mechanically or electronically

Electronic steering is achieved by controlling the phaseof the electric current feeding the array elements, thus

the name phased array

Phase relation is maintained using a network of powerdividers and phase shifters

Direction is selected by adjusting the phase differenceprovided by each phase shifter (usually done using amicroprocessor)

Li Ph d A


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Linear Phased ArrayScanned Every 30deg, N=15, d=/4


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Adaptive Arrays

An adaptive array not only steers the beamsbut also the nulls

Nulls are steered towards the direction ofjammers and nullify their detrimental effects

Adaptive arrays first sample the environmentto estimate the interferences

Next a weight vector is calculated to modify

the sidelobes for effective null steering andsupression of interferences


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Signal Models In spatial array processing there are three types of signals

desired target signal

jammer signal noise signal

Thus the total signal received by the array is

x = xs + xj + xn Jammer and Noise are classified as interference. The

undesired interference signal is

xu = xj + xn Both jammer and noise are characterized as zero mean

normally distributed. Hence the covariance matrix of thisundesired signal would be

Ru = E[xuxuH] = Rn + Rj


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Signal Models Desired Target Signal

Signal is narrowband x(t) = e j2ft

Antenna Array has receiverbehind each element. These

receivers digitize the receivedsignal

The combined output of thereceivers is a N-dimensionalsignal

x is complex baseband signalreceived at left most element

V is spatial array vector


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Signal Models Noise Signal

In the receiver array each element produces thermal noise Modelled as zero mean Gaussian random process

The noise covariance matrix is Rn = n2I, n

2 =kTnB

Jamming Signal Jammers are modeled as spatial point sources that constantly

transmit high power omni-directional interference signal

The signal covariance matrix is equal to

Where j

2 jammer noise power

Vj is array manifold vector associated with jammer

direction of arrival If we are dealing with N jammers, then the covariance

matrices would add, because we assume jammers are

mutually uncorrelated


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Conventional Beamformer The beamformer output y of our

array is

The complex weights wi arechosen to control the sidelobe level to steer the main beam towards

an angle 0

However this data independentbeamformer may not providenulls in the direction of interferersand hence suboptimal SINR


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Optimal Beamformer (MVDR) A minimum variance distortionless response beamformer (MVDR) also

called an optimal beamformer accomplishes two objectives Minimize the array output interference power Get the target desired signal without any distortion

Controllable parameters are array weights wi (weight vector w) Array output in vector notation is

Output is a combination of desired signal and interference components

The interference output is the sum of noise and jammer outputs or

If we want to minimize the interference output power, then we mustminimize

subject to the constraint


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Optimal Beamformer (MVDR) The constrained minimum variance distortionless response can be

achieved with the weight vector

where is the desired target steering vector

The desired weight vector can be calculated to be

with


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Matlab Illustration(Both Jammers in Sidelobes, with No Weighting)

N=16 antennas elements are used

Desired target located at 00

Jammers located at 180 (with SNR of 50dB) and -330 (with SNR of 30dB)

Two dotted vertical lines indicate the angles of arrival of the two jammers

-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

Angle of Arrival (degrees)

NormalizedArrayResponse(dB)

Unadapted Array Pattern

-80 -60 -40 -20 0 20 40 60 80-60

-50

-40

-30

-20

-10

0

Angle of Arrival (degrees)

NormalizedArrayResponse(dB)

Distortionless Beamformer Array Pattern


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Adaptive Beamforming Optimal Beamforming only sounds good only in theory

Obtaining Rin (interference covariance matrix) requires

infinite number of samples. Hence we can onlyestimate it. A sampled interference covarianceestimation is

Various adaptive beamforming methods are based oncollecting data from which correlation matrix isestimated Block Adaptive Implementation

Uses block of data to estimate the adaptive beamforming weight vectorand is known as Sample Matrix Inversion (SMI)

Sample by Sample Adaptive Implementation RLS Algorithm Steepest Descent Method


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Training Data

Before the beamforming system can be used,it must be trained with target- free samples

Training Data are of two types Target Free training data xin = xn + xj Target in training data xin = xn + xj + xs

In applications like radar, target free trainingdata is always available by takingmeasurements at ranges shorter or longerthan the target


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Space-Time Adaptive Processing (STAP)

STAP is concerned with the two-dimensional processing ofsignals in both the spatial and temporal domains to optimallydiscriminate targets from both clutter and jamming

Detection of slowly moving targets by air- and spaceborneMTI radar (moving target indication) is heavily degraded bythe motion induced Doppler spread of clutter returns.

Space-time adaptive processing (STAP) can achieve optimumclutter rejection via implicit platform motion compensation.


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General STAP Architecture

Space TimeEnvironment issampled in spatialdomain by using

array of antennaelements

Also sampled in

temporal domain bytransmitting a seriesof pulses to obtaindoppler information


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Space-Time vs Spatial Processing Degrees of Freedom

In spatial array processing, thedegrees of freedom equals numberof antenna elements N

In STAP, every antenna transmits atrain of M pulse and applies a

complex weight on each echo afterreceiving them. Hence the degrees offreedom equals NM.

Progressive Phase Shift In spatial array processing only

progressive phase shift betweenantenna elements is used In STAP, progressive phase shift

between antenna elements andbetween successive pulses receivedfrom each antenna element is

exploited


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Signal Behavior in Space-Time Environment

Space Time Signal Environment

Receiver Noise has no structure inspace/frequency and thereforeappears as a uniform noise floor

Broadband Noise Jammers are

localized in AOA but spread acrossthe entire doppler spectrum

Appears as ridge of energylocalized in AOA but spreadacross all doppler shifts

Scatterers at an angle of w.r.tantenna boresight will have adoppler shift of


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Space Time Adaptive Processing

Angle doppler characteristics of the echo froma moving point target depend on both theradar platform motion and the target motion

If the target is stationary and directly on theboresight, the doppler shift will be zero andwill fold into the clutter

However if the target is moving it will separatefrom the clutter on the doppler axis andshown in the figure


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Optimal STAP Processing The spatial steering vector for a ULA of M sensors is

The temporal frequency steering vector assuming Ltransmitted/received pulses is

The two dimensional LM X 1 space time steering vector isgiven by

The optimal STAP weight vector is given by


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Thank You

Matlab Source Listing (beamformer m)


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Matlab Source Listing (beamformer.m)Input Section

close all

clear all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% User Input Section

lambda = 0.03; % wavelength

d = lambda/2; % element spacing

dl = d/lambda;

N = 16; % # of array elements

aoa_max = asin(1/2/dl); % maximum "real space" AOA (radians)

window_on = false; % true or false

Nangle = 1000; % # of angles for evaluating beam pattern

Nm1 = Nangle-1;

t_aoa = pi/180*(0); % target AOA (radians)

j_aoa1 = pi/180*(18); % jammer #1 AOA (radians)j_aoa2 = pi/180*(-33); % jammer #2 AOA (radians)

SNR = 0; % signal to noise ratio (dB)

JSR1 = +50; % jammer #1 to noise ratio (dB)

JSR2 = +30; % jammer #2 to noise ratio (dB)

% End user input section%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



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Matlab Source Listing (beamformer.m)Computing the Optimal Weight Vector

p_n = 1; % noise powerp_t = p_n*(10^(SNR/10)); % target powerp_j1 = p_t*(10^(JSR1/10)) ; % jammer powerp_j2 = p_t*(10^(JSR2/10)) ; % jammer power% compute signal vectorstarget = sqrt(p_t)*exp(j*2*pi*(0:N-1)'*d*sin(t_aoa)/lambda);if (window_on)

t = target.*taylorwin(length(target),4,-30);elset = target;endj1 = sqrt(p_j1)*exp(j*2*pi*(0:N-1)'*d*sin(j_aoa1)/lambda);j2 = sqrt(p_j2)*exp(j*2*pi*(0:N-1)'*d*sin(j_aoa2)/lambda);

% compute covariance matrix with and without jammersR = p_n*eye(N);Rj = p_n*eye(N) + p_j1*j1*(j1') + p_j2*j2*(j2');disp(['Covariance matrix rank with jammers = ',num2str(rank(R))]);% compute beamformer weight vector with and without jammersw = R\conj(t);wj = Rj\conj(t);



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Matlab Source Listing (beamformer.m)Plotting the Output Patterns

% compute and display beampatterntheta = -aoa_max + 2*aoa_max/Nm1*(0:Nm1);W = zeros(Nangle,1);Wj = zeros(Nangle,1);for p = 1:NangleW(p) = w.'*exp(-j*2*pi*(0:N-1)'*dl*sin(theta(p)));Wj(p) = wj.'*exp(-j*2*pi*(0:N-1)'*dl*sin(theta(p)));endWp = db(abs(W),'voltage');scale = 10*log10(N^2);% scale = 0;Wp = Wp - scale;Wjp = db(abs(Wj),'voltage') - scale;figure(1)plot(180/pi*theta,Wp)axis([-180*aoa_max/pi +180*aoa_max/pi -60 0])% gridxlabel('Angle of Arrival (degrees)');ylabel('Normalized Array Response (dB)')title('Unadapted Array Pattern')vline(180/pi*[j_aoa1, j_aoa2])

kappa = t'*transpose(inv(Rj))*conj(t);wj1 = wj/kappa;Wj1 = zeros(Nangle,1);for p = 1:NangleWj1(p) = wj1.'*exp(-j*2*pi*(0:N-1)'*dl*sin(theta(p)));endWjp1 = db(abs(Wj1),'voltage');figure(3)plot(180/pi*theta,Wjp1)axis([-180*aoa_max/pi +180*aoa_max/pi -60 0])% gridxlabel('Angle of Arrival (degrees)');ylabel('Normalized Array Response (dB)')title('Distortionless Beamformer Array Pattern')vline(180/pi*[j_aoa1, j_aoa2])

adaptive beam forming and space time adaptive processing

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