Phase conjugation is used in beamforming and retro-directive antennas to focus waves in a particular direction or to a point. It takes the complex conjugate of the received signal’s phase and retransmits it, which causes the wave to focus back on the source.
The phase conjugation can be computed using “conj” function in MATLAB.
Follow the steps below to create a phase conjugation in MATLAB:
1.Define Parameters
freq = 2.4e9; % Carrier frequency (2.4 GHz)
c = physconst('LightSpeed');
lambda = c/freq;
N = 8; % Number of antenna elements
d = lambda/2; % Element spacing
theta_source = 30; % Source direction (degrees)
2. Create Uniform Linear Array (ULA) using “phased.ULA”
array = phased.ULA(N, d);
3. Generate steering vector for the source direction and apply complex conjugate “conj” to the steering vector for phase conjugation.
steerVec = phased.SteeringVector('SensorArray', array, 'PropagationSpeed', c);
w_conj = conj(steerVec(freq, theta_source));
4. Plot array pattern
pattern(array, freq, 'PropagationSpeed', c, 'Type', 'powerdb', ...
'Weights', w_conj, 'CoordinateSystem', 'rectangular');
title('Phase Conjugate Beam Pattern');
To create a phase conjugation antenna in Simulink, use the following blocks from “Phased Array Toolbox”:
1. Signal Source (e.g., Sine Wave): Generates the baseband signal intended for transmission.
2. Transmitter Block: Upconverts the baseband signal to a radio frequency (RF) signal with a carrier.
3. Antenna Array: Use the "phased.ULA" block configured with N elements and an element spacing of d to model the physical antenna array.
4. Source and Target Placement: Define the spatial positions, for example, place the signal source at coordinates [1000; 0; 0]
5. Phase Conjugation: Insert a MATLAB Function block with the code y = conj(u); to apply phase conjugation to the received signal.
6. Simulation and Verification: Run the simulation and use a Scope block to verify that the transmitted energy is beamformed and focused back toward the original source location.
You can refer to the following documentation pages for more information:
- “conj”: https://www.mathworks.com/help/releases/R2024a/matlab/ref/conj.html
- “phased.ULA”: https://www.mathworks.com/help/releases/R2024a/phased/ref/phased.ula-system-object.html
Hope you find this helpful.
