Applications of Phased Array System Using MATLAB
Phased array systems are widely used in radar, communication, and medical imaging systems. This section explores their applications, concepts, and implementation using MATLAB with practical examples.
Introduction to Phased Array Systems
A phased array system consists of multiple antennas arranged in a specific configuration to achieve beamforming and beam steering. Using MATLAB, we can simulate and analyze such systems effectively.
Key Concepts
Phased arrays use constructive and destructive interference to steer beams in desired directions. This is mathematically modeled using phase shifts between antenna elements.
Basic Equations
The steering vector for a uniform linear array (ULA) is given as:
s(θ) = [1, exp(-j2πd sinθ/λ), ..., exp(-j2π(N-1)d sinθ/λ)]T
\[ s(\theta) = \begin{bmatrix} 1, \exp\left(-j \frac{2\pi d \sin\theta}{\lambda}\right), \ldots, \exp\left(-j \frac{2\pi (N-1) d \sin\theta}{\lambda}\right) \end{bmatrix}^T \]
where:
- θ: Steering angle
- λ: Wavelength
- d: Distance between elements
- N: Number of elements
Examples and Solutions
1. Beamforming in a Uniform Linear Array
% MATLAB example: Beamforming
N = 8; % Number of elements
d = 0.5; % Element spacing in wavelengths
theta = 30; % Desired steering angle in degrees
lambda = 1; % Wavelength
% Calculate steering vector
k = 2 * pi / lambda; % Wavenumber
angles = deg2rad(theta);
steeringVector = exp(-1j * k * d * (0:N-1)' * sin(angles));
disp(steeringVector);
2. Side Lobe Suppression
MATLAB provides windowing techniques to suppress side lobes in radiation patterns.
% Apply Hamming window to suppress side lobes
N = 8; % Number of elements
w = hamming(N); % Hamming window
disp(w);
3. Radar Cross Section (RCS) Analysis
Calculate and plot RCS patterns for a given array configuration.
% Radar Cross Section example
N = 4; % Number of elements
theta = -90:1:90; % Angle range in degrees
lambda = 1; % Wavelength
d = 0.5; % Element spacing in wavelengths
% Compute array factor
k = 2 * pi / lambda;
arrayFactor = abs(sin(N*k*d*sin(deg2rad(theta))/2)./sin(k*d*sin(deg2rad(theta))/2));
plot(theta, 20*log10(arrayFactor/max(arrayFactor)));
title('RCS Pattern');
xlabel('Angle (degrees)');
ylabel('Normalized Magnitude (dB)');
grid on;
4. Communication Link Analysis
Evaluate the impact of beamforming on communication links.
% MATLAB example: Link budget calculation with beamforming
Pt = 1; % Transmit power
Gt = 10; % Antenna gain
Gr = 10; % Receiver gain
R = 1000; % Distance in meters
% Free-space path loss
lambda = 0.3; % Wavelength in meters
FSPL = (4 * pi * R / lambda)^2;
Pr = Pt * Gt * Gr / FSPL; % Received power
disp(Pr);
Advanced Example Problems for Phased Array Systems Using MATLAB
These examples demonstrate advanced concepts in phased array systems, such as direction finding, adaptive beamforming, and interference suppression.
Example 5: Direction of Arrival (DOA) Estimation
Direction of arrival estimation is a critical task in radar and communication systems. The MUSIC (Multiple Signal Classification) algorithm is widely used for DOA estimation.
% MATLAB Example: MUSIC DOA Estimation
N = 8; % Number of elements
d = 0.5; % Spacing in wavelengths
fc = 1e9; % Frequency in Hz
angles = [-20, 30]; % Directions of arrival in degrees
% Create sensor array
array = phased.ULA('NumElements', N, 'ElementSpacing', d);
% Generate signals
Fs = 1e3; % Sampling frequency
t = (0:1/Fs:1)';
signal = [cos(2*pi*100*t), cos(2*pi*200*t)];
collector = phased.Collector('Sensor', array, 'OperatingFrequency', fc);
collectedSignal = collector(signal, angles);
% Estimate DOA using MUSIC
estimator = phased.MUSICEstimator('SensorArray', array, ...
'OperatingFrequency', fc, ...
'NumSignalsSource', 'Property', ...
'NumSignals', 2);
estimatedAngles = estimator(collectedSignal);
disp('Estimated DOA:');
disp(estimatedAngles);
Example 6: Adaptive Beamforming
Adaptive beamforming adjusts weights dynamically to optimize performance in the presence of interference.
% MATLAB Example: Adaptive Beamforming
N = 10; % Number of elements
d = 0.5; % Spacing in wavelengths
fc = 2.4e9; % Frequency in Hz
% Create sensor array
array = phased.ULA('NumElements', N, 'ElementSpacing', d);
steervec = phased.SteeringVector('SensorArray', array, 'OperatingFrequency', fc);
angles = [30, 60]; % Desired and interference angles
% Generate signals
signal = cos(2*pi*fc*(0:1e-6:1e-3));
interference = sin(2*pi*fc*(0:1e-6:1e-3));
collectedSignal = collector([signal; interference], angles);
% Apply adaptive beamforming
beamformer = phased.AdaptiveBeamformer('SensorArray', array, ...
'OperatingFrequency', fc);
output = beamformer(collectedSignal);
plot(abs(output));
title('Beamformed Output');
xlabel('Time (s)');
ylabel('Amplitude');
Example 7: Null Steering to Suppress Interference
Null steering involves directing nulls in the radiation pattern to suppress interference from specific directions.
% MATLAB Example: Null Steering
N = 8; % Number of elements
d = 0.5; % Element spacing in wavelengths
fc = 3e9; % Frequency in Hz
% Create sensor array
array = phased.ULA('NumElements', N, 'ElementSpacing', d);
nullAngles = [45, 120]; % Directions of interference
% Generate null steering weights
nullSteeringVector = phased.SteeringVector('SensorArray', array, ...
'OperatingFrequency', fc);
weights = zeros(N, 1);
for i = 1:length(nullAngles)
weights = weights - nullSteeringVector(nullAngles(i));
end
% Apply null steering weights
collector = phased.Collector('SensorArray', array, 'OperatingFrequency', fc);
output = collector(signal, nullAngles) .* weights;
plot(abs(output));
title('Null Steering Output');
xlabel('Time (s)');
ylabel('Amplitude');
Example 8: Range and Velocity Estimation in Radar
Phased arrays are used to estimate target range and velocity in radar systems.
% MATLAB Example: Range and Velocity Estimation
fc = 77e9; % Radar frequency in Hz
c = 3e8; % Speed of light in m/s
R = 100; % Target range in meters
v = 30; % Target velocity in m/s
% Create waveform
waveform = phased.FMCWWaveform('SweepBandwidth', 200e6, ...
'SweepTime', 1e-6, ...
'SampleRate', 1e6);
sig = waveform();
% Transmit and receive signals
transmitter = phased.Transmitter('PeakPower', 1e3);
receiver = phased.ReceiverPreamp('Gain', 40);
reflectedSignal = transmitter(sig) .* exp(-1j * 2 * pi * fc * R / c);
% Calculate range and velocity
beatFreq = abs(fft(reflectedSignal - sig));
rangeEst = c * beatFreq / (2 * fc);
velocityEst = (c / fc) * (beatFreq / waveform.SweepBandwidth);
disp('Estimated Range:');
disp(rangeEst);
disp('Estimated Velocity:');
disp(velocityEst);
5. Wideband Beamforming
Wideband beamforming is crucial for broadband communication systems.
% MATLAB Example: Wideband Beamforming
N = 16; % Number of elements
fc = [1e9, 2e9, 3e9]; % Wideband frequencies
% Create wideband array
array = phased.ULA('NumElements', N, 'ElementSpacing', 0.5);
steeringVector = phased.SteeringVector('SensorArray', array, 'OperatingFrequency', fc);
% Generate signal for each band
signals = cell(1, length(fc));
for i = 1:length(fc)
signals{i} = sin(2*pi*fc(i)*(0:1e-6:1e-3));
end
% Perform wideband beamforming
output = cellfun(@(s) sum(s .* steeringVector), signals, 'UniformOutput', false);
plot(abs(cell2mat(output)));
title('Wideband Beamforming Output');
xlabel('Time (s)');
ylabel('Amplitude');
Useful MATLAB Functions for Phased Array Systems
Practice Questions
Test Yourself
1. Create a ULA with 8 elements and simulate its beamforming at 45°.
2. Implement a Dolph-Chebyshev window for side lobe suppression in a 16-element array.
3. Simulate a communication link and calculate received power for a phased array system.
4. Implement DOA estimation for a 16-element ULA and compare results for different SNR levels.
5. Design a phased array to achieve simultaneous null steering and beamforming at 3 GHz.
6. Simulate a wideband beamforming system with 4 frequency bands and compare their performance.