🧠 Machine Learning for Symbol Decision in AWGN Channel

Course: Digital Communication Systems
Student: Panagiota Grosdouli
Language: Python 3.x (NumPy, Matplotlib)

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🎯 Objective

This project investigates the use of a neural network (MLP) for symbol decision in BPSK and QPSK modulation schemes under Additive White Gaussian Noise (AWGN).
The goal is to train a small MLP to learn the optimal decision rule and compare its Bit Error Rate (BER) to that of the classical maximum-likelihood detector.

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📘 Theoretical Background

For an AWGN channel:

y = s + n
n ~ N(0, σ²)

Relation between signal-to-noise ratio and noise variance:

Eb/N0 = γb
σ² = 1 / (2 * γb)

Theoretical BER for BPSK:

Pb = Q(sqrt(2 * Eb/N0))

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⚙️ Implementation Steps

1️⃣ Data Generation

• Generate random bits.
• Map them to BPSK or QPSK symbols.
• Add AWGN noise for selected Eb/N0 values.

2️⃣ MLP Training

• Architecture: [Input] → ReLU(16–24 neurons) → Sigmoid(Output)
• Loss function: Binary Cross Entropy
• Training SNR = 6 dB
• Evaluate generalization for 0–12 dB.

3️⃣ Evaluation

• Compute BER for both modulations.
• Compare MLP vs Optimal Detector.

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🧪 Execution

To run the project:

python ml_symbol_decision.py

Automatically generates:

• ml_vs_opt_ber.csv
• ml_vs_opt_ber.png
• qpsk_mlp_decisions_6dB.png

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📈 Results

BER Curves (MLP vs Optimal)

QPSK MLP Decisions @ 6 dB

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🧠 Discussion

• The MLP effectively learns the optimal decision boundary.
• In AWGN, its performance closely matches the maximum-likelihood detector.
• At low SNR, small deviations occur due to limited training data.

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🔮 Extensions

• Introduce Rayleigh fading:

y = h * s + n
h ~ CN(0,1)

• Train with pilot estimates (ĥ) as extra input.
• Explore CNN/LSTM architectures for sequence detection.

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📚 Conclusion

Neural networks offer a modern, data-driven approach to symbol detection,
capable of adapting to complex, non-ideal channel conditions.