Beamforming at the Transmitter
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I'm interested in implementing a narrowband phase shift beamformer at a tx ULA antenna array. The example https://www.mathworks.com/help/phased/ref/phased.phaseshiftbeamformer-system-object.html only shows the beamformer after signal collection. However, a tx will be radiating a signal instead so I'm wondering how exactly to apply the beamformer when transmitting a signal via antenna array.
Answers (1)
To implement a narrowband phase shift beamformer on a transmit uniform linear array (ULA), the key idea is to apply the appropriate steering vector to the baseband signal before transmission. This pre-weighting ensures that the signals constructively interfere in the desired direction when radiated from the antenna elements.
The beamformed transmit signal across all antennas can be expressed as:
x(t)=a(θ)⋅s(t)
were
- ‘a(θ)’ represents the steering vector for the desired direction
- ‘s(t)’ represents the baseband signal
- ‘x(t)’ represents the signal sent from each antenna
In a transmit ULA; to steer a narrowband signal toward a desired direction ‘θ’, the key idea is to multiply the baseband signal by a steering vector. This phase shift across elements causes constructive interference in the target direction.
Therefore, after applying the steering vector to the baseband signal, it will give you full control over how signals are radiated from each antenna element in the ULA.
I wrote a minimal code to ensure this workflow:
% Parameters
fc = 2.5e9; % Carrier frequency
c = physconst('LightSpeed');
lambda = c/fc;
N = 8; % Number of elements
d = lambda/2;
% Define ULA
array = phased.ULA('NumElements', N, 'ElementSpacing', d);
% Generate steering vector for desired transmit angle
angle_deg = 30;
steervec = phased.SteeringVector('SensorArray', array, 'IncludeElementResponse', false);
a_theta = steervec(fc, angle_deg); % Nx1 complex weights
% Baseband signal to transmit (using a sinusoid as an example)
t = (0:1e-8:1e-6);
s = sin(2*pi*1e6*t);
s = s(:);
tx_signals = a_theta * s.'
Each row of ‘tx_signals’ represents the time-domain waveform that should be transmitted by one element of the array. These signals can be passed into RF front ends or used in simulation as-is.
Hope this helps.
For additional information, please consult the following official documentation from MATLAB:
- Steering Vector: https://www.mathworks.com/help/releases/R2024b/phased/ref/phased.steeringvector-system-object.html
- Uniform Linear Array (ULA): https://www.mathworks.com/help/releases/R2024b/phased/ug/uniform-linear-array.html
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on 22 Feb 2021
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