📡 Free Space vs Two-Ray Ground Reflection Path Loss Models

This project simulates and compares two fundamental wireless propagation models:

• Free Space Path Loss (FSPL)
• Two-Ray Ground Reflection Model

It visualizes how the received power changes with distance using both models and marks the breakpoint distance, beyond which two-ray behavior dominates.

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📘 Theory Overview

1. Free Space Path Loss (FSPL)

The FSPL model assumes ideal line-of-sight propagation without obstacles or reflections.

Formula:

Where:

• P_r : Received power (W)
• P_t : Transmit power (W)
• G_t, G_r: Antenna gains (unitless)
• λ : Wavelength (m)
• d : Distance between transmitter and receiver (m)

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2. Two-Ray Ground Reflection Model

This model accounts for both the direct and ground-reflected signals, better modeling propagation over longer distances.

Formula:

Where:

• h_t, h_r : Transmit and receive antenna heights (m)

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3. Breakpoint Distance

The breakpoint distance marks where the model shifts from FSPL behavior to two-ray model behavior.

Formula:

Beyond d_break , the received power drops off faster (∝ (1/d^4)) compared to FSPL (∝ (1/d^2)).

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🧮 Simulation Parameters

Parameter	Value
Frequency	2.4 GHz
Transmit Power	1 W
Antenna Gains	1 (unitless)
Transmit Height	50 m
Receive Height	2 m
Distance Range	1 m – 5000 m

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📊 Output

The program plots both FSPL and Two-Ray received power versus distance on a logarithmic scale and marks the breakpoint distance.

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📂 How to Run

1. Install required Python packages:
   numpy, matplotlib

2. Run the Python script in your IDE or notebook.

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🔍 Applications

• Wireless communication systems
• Signal coverage estimation
• Antenna design and placement
• Network simulation and planning (e.g., WiFi, 5G, IoT)

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📈 Sample Output

🤝 Contributing

Feel free to fork, improve the logic (e.g., include terrain/obstacle loss), or extend it for other propagation models.