Linear-Antenna-Array-Simulation

MATLAB computational simulation analyzing beam steering, directivity, and Array Factor (AF) in N-element linear antenna arrays.

Linear Antenna Array Simulation

Overview

This repository contains a MATLAB computational simulation analyzing the behavior of N-element Uniform Linear Arrays (ULA). It mathematically models and visualizes two fundamental concepts in microwave engineering and antenna theory:

1. Electronic Beam Steering: Modifying the progressive phase shift to direct the main lobe.
2. Directivity and Beamwidth: Demonstrating how increasing the number of elements ($N$) narrows the main beam and increases overall directivity.

Mathematical Foundation

The simulation relies on the calculation of the Array Factor (AF). For an N-element linear array with uniform spacing and uniform amplitude, the normalized Array Factor is given by:

$$AF = \left| \frac{\sin(N \frac{\psi}{2})}{N \sin(\frac{\psi}{2})} \right|$$

Where the total phase $\psi$ is defined as:

$$\psi = \beta d \cos(\theta) + \alpha$$

• $\beta = \frac{2\pi}{\lambda}$ (Phase constant)
• $d$ = Element spacing
• $\theta$ = Observation angle
• $\alpha$ = Progressive phase shift between elements

To steer the main beam to a desired angle ($\theta_0$), the required progressive phase shift $\alpha$ is calculated as:

$$\alpha = -\beta d \cos(90^\circ - \theta_0)$$

Note: The limit where $\psi \to 0$ results in a $0/0$ mathematical condition, which theoretically evaluates to $1$. The MATLAB script programmatically handles this limit using AF(isnan(AF)) = 1.

Simulation Parameters

The computational script utilizes the following default parameters, modeling a standard Wi-Fi/Bluetooth ISM band scenario:

• Operating Frequency ($f$): $2.4\text{ GHz}$
• Speed of Light ($c$): $3 \times 10^8\text{ m/s}$
• Element Spacing ($d$): $\frac{\lambda}{2}$ (Half-wavelength spacing to avoid grating lobes)

Visual Outputs

1. Proof of Beam Steering ($N = 8$)

The script applies the phase shift equations to steer a fixed 8-element array to $-45^\circ$, $0^\circ$ (broadside), and $50^\circ$, generating comparative polar plots.

Beam Steering Patterns

2. Effect of Element Count on Directivity

The script fixes the steering angle at $30^\circ$ and compares the radiation pattern of a 4-element array against a 16-element array, visually proving the relationship between element count and beamwidth narrowing.

Directivity Comparison

Usage

1. Clone this repository to your local machine.
2. Open the .m script in MATLAB.
3. Run the script. The figures will generate automatically.
4. You can freely modify the freq, angles, and N_values arrays in the script to explore different array configurations.

License

This project is open-source and available under the MIT License.