Add differentiable modulation and demodulation methods for BPSK, QPSK…

[selimfirat]

Making Modulations Differentiable

Description

This PR introduces differentiable paths in the modulation and demodulation schemes within Kaira. This enables gradient-based training of neural networks that include modulation layers in their architectures.

Key Features

• Adds new utility functions for differentiable modulation operations in differentiable.py
• Extends base modulator and demodulator classes with forward_soft methods for differentiable processing
• Implements differentiable modulation for BPSK, QPSK, and QAM schemes
• Adds comprehensive tests for differentiable operations

Implementation Details

The implementation preserves backward compatibility while adding new capabilities:

• BaseModulator and BaseDemodulator classes are extended with forward_soft methods
• New utility functions in differentiable.py provide core operations for differentiable modulation
• The existing forward methods remain unchanged
• Each modulation scheme has been updated to properly handle soft bit probabilities

Testing

Added comprehensive test suite in tests/modulations/test_differentiable.py to verify:

• Differentiability of individual operations
• Gradient flow through modulation and demodulation operations
• End-to-end differentiability of the entire modulation/demodulation pipeline

Use Case Example

# Create modulators and demodulators
modulator = QPSKModulator()
demodulator = QPSKDemodulator()

# Create soft bits with gradients (represents probabilities from a neural network)
soft_bits = torch.tensor([0.1, 0.9, 0.2, 0.8], requires_grad=True)

# Apply differentiable modulation
symbols = modulator.forward_soft(soft_bits)

# Apply channel effects
# ...

# Apply differentiable demodulation
noise_var = 0.1
decoded_bits = demodulator.forward_soft(symbols, noise_var)

# Compute loss and backpropagate gradients
loss = some_loss_function(decoded_bits, target_bits)
loss.backward()  # Gradients will flow through the entire pipeline

Future Work

• Add differentiable implementations for other modulation schemes
• Optimize computational efficiency of differentiable operations
• Provide more examples for neural network training with differentiable modulations