Exercises

Create a complex-valued tensor in PyTorch and compute its magnitude, phase, real, and imaginary parts. Verify z = |z| * exp(j*angle(z)).

Implement CReLU and verify it on a grid of complex numbers. Plot input and output in the complex plane.

Convert a complex signal $z \in \mathbb{C}^{64}$ to a real tensor of shape $(128,)$ by stacking real and imaginary parts. Convert back.

Compute the MSE loss between two complex tensors using abs().pow(2).mean(). Verify it matches computing on real/imag parts separately.

Create a complex parameter with nn.Parameter(torch.randn(..., dtype=torch.cfloat)) and compute gradients through it. Print the gradient dtype.

Implement a ComplexLinear layer using the structured weight matrix approach. Compare output with native complex multiplication.

Implement modReLU with a learnable bias parameter and train it on a simple complex regression task.

Build a complex-valued CNN with 3 ComplexConv2d layers and CReLU activations. Apply it to a complex-valued 2D signal.

Implement a differentiable AWGN channel and verify that gradients flow through it correctly (the gradient of the noise should be zero).

Compare a real-split MLP (2 channels) vs a complex-structured MLP on learning the mapping $\hat{h} = f(y_p)$ for channel estimation. Report MSE and parameter count.

Implement a differentiable OFDM forward model including IFFT, cyclic prefix addition, channel convolution, and FFT at receiver.

Train an autoencoder end-to-end through a Rayleigh fading channel. The encoder maps bits to complex symbols and the decoder recovers bits.

Implement complex BatchNorm with 2x2 covariance whitening and compare performance to independent real/imag BatchNorm.

Verify phase equivariance empirically: apply a complex linear layer to inputs rotated by various phases and check outputs rotate equally.

Implement a complex-valued U-Net for OFDM channel estimation on the resource grid. Compare with real-split U-Net.