ML-Based Symbol Detection for BPSK & QPSK

Neural Receivers under AWGN & Rayleigh Fading Channels

This repository provides two NumPy-only implementations of neural symbol detectors for BPSK and QPSK modulation. The aim is to study whether small feedforward neural networks can learn (and sometimes surpass) classical communication-theory detectors under different channel conditions.

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🎯 Project Goals

• Learn the optimal detector in an AWGN channel using a compact MLP.
• Investigate whether a neural detector can outperform the mismatched classical detector under Rayleigh fading with imperfect CSI.
• Compare empirical BER curves against theoretical baselines.

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📂 Repository Structure

File	Description
ψηφιακατηλεπ.py	Simple MLP (1 hidden layer) trained with vanilla Gradient Descent
adam.py	Deeper MLP trained with the Adam optimizer (more realistic setup)

Each script runs independently and automatically generates plots, CSV files, and training logs.

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📡 Main Functionality

1. Dataset Generation

The scripts generate synthetic datasets consisting of:

• Modulations: BPSK & QPSK
• Channels:
  • AWGN
  • Rayleigh fading (optional)
• Channel State Information (CSI):
  • Perfect CSI (AWGN)
  • Imperfect CSI for Rayleigh fading scenarios

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2. Neural Detector Architecture

Both scripts implement MLP-based receivers with:

• Input: Received complex samples (mapped to real-valued features)
• Hidden layers: ReLU activations
• Output: Bit-wise predictions via sigmoid activations
• Loss function: Binary Cross-Entropy (BCE)

Optimization:

• ψηφιακατηλεπ.py: Gradient Descent
• adam.py: Adam optimizer

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3. Performance Evaluation

The scripts compute and compare Bit Error Rate (BER) as a function of Eb/N₀.

They include comparisons against:

• Optimal detector in AWGN
• Mismatched classical detector in Rayleigh fading with imperfect CSI
• Theoretical BER curves based on the Q-function (for AWGN)

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4. Visualizations & Outputs

Each script automatically saves:

AWGN Results

• ber_awgn_results*.csv
• ber_awgn_curves*.png
• qpsk_mlp_decisions_awgn_6dB*.png

Rayleigh Fading Results

• ber_fading_results*.csv
• ber_fading_curves*.png
• qpsk_mlp_decisions_fading_6dB*.png

Training Diagnostics

• training_losses_all*.png (training & validation loss curves)

Example visualizations include:

• BER vs. Eb/N₀ curves (AWGN & Rayleigh fading)
• Training/validation loss vs. epoch curves
• QPSK decision scatter plots at 6 dB (AWGN and fading)

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🚀 How to Run

Make sure you have Python and NumPy installed.

From the terminal:

# Version 1: Simple MLP + Gradient Descent
python ψηφιακατηλεπ.py

# Version 2: Deeper MLP + Adam optimizer
python adam.py

Each script will automatically:

• Generate datasets
• Train the neural detectors
• Evaluate BER over a predefined Eb/N₀ range
• Save all results (plots, CSVs, training logs) in the current directory

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📊 Example Training Logs

BPSK (AWGN)

=== Training BPSK MLP (AWGN) ===
Epoch 1/10: loss=0.2976 val_loss=0.2989
...
Epoch 10/10: loss=0.1022 val_loss=0.1026

QPSK (AWGN)

=== Training QPSK MLP (AWGN) ===
Epoch 1/12: loss=0.1556 val_loss=0.1538
...
Epoch 12/12: loss=0.0549 val_loss=0.0543

QPSK (Rayleigh Fading, Imperfect CSI)

=== Training QPSK MLP (Rayleigh fading, imperfect CSI) ===
Epoch 1/15: loss=0.6250 val_loss=0.6283
...
Epoch 15/15: loss=0.5763 val_loss=0.5814

Adam Version (Faster Convergence)

=== Training BPSK MLP (AWGN) with Adam ===
loss ≈ 0 from epoch 2 onward

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🧠 Key Insights

• AWGN channel
  The MLP successfully learns the optimal maximum-likelihood detector.
  → The simulated BER curves closely match the theoretical ones.

• Rayleigh fading with imperfect CSI
  The neural detector learns a robust nonlinear decision rule.
  → It often outperforms the mismatched classical detector.

• Adam vs. Gradient Descent

  • Adam converges significantly faster.
  • It provides more stable training, especially in fading scenarios.

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🔮 Possible Extensions

This project can serve as a starting point for more advanced research directions, such as:

• CNN- or RNN-based sequence detectors
• Joint equalization + detection using deep learning
• Training over OFDM channel models
• Adversarial robustness experiments against structured noise
• Exporting models for on-device / TinyML inference

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📜 License

This project is released under the MIT License.