References & Further Reading

References

1. C. Trabelsi et al., Deep Complex Networks, ICLR, 2018

   Comprehensive framework for complex-valued deep learning with complex BN and residual networks.

2. A. Hirose, Complex-Valued Neural Networks, Springer, 2012

   Monograph on complex-valued neural networks, covering theory and applications.

3. T. O'Shea and J. Hoydis, An Introduction to Deep Learning for the Physical Layer, IEEE Trans. CSIT, 2017

   End-to-end learning of communication systems through differentiable channel models.

4. D. H. Brandwood, A Complex Gradient Operator and Its Application in Adaptive Array Theory, IEE Proceedings, 1983

   Foundational work on Wirtinger calculus for signal processing optimisation.

5. PyTorch Team, Complex Numbers in PyTorch, 2024

   Documentation for PyTorch's native complex tensor support and autograd.

Further Reading

• Wirtinger calculus for signal processing

  Kreutz-Delgado, The Complex Gradient Operator, arXiv:0906.4835

  Rigorous treatment of complex derivatives for optimisation.

• Deep unfolding for MIMO detection

  He et al., TCOM 2020

  Applies complex-valued networks to iterative MIMO detection.

• PyTorch complex autograd internals

  https://pytorch.org/docs/stable/notes/autograd.html#complex-autograd-doc

  Official documentation on how PyTorch handles complex gradients.