  Channel modelling is essential to designing modern wireless communication
systems. The increasing complexity of channel modelling and the cost of
collecting high-quality wireless channel data have become major challenges. In
this paper, we propose a diffusion model based channel sampling approach for
rapidly synthesizing channel realizations from limited data. We use a diffusion
model with a U Net based architecture operating in the frequency space domain.
To evaluate how well the proposed model reproduces the true distribution of
channels in the training dataset, two evaluation metrics are used: $i)$ the
approximate $2$-Wasserstein distance between real and generated distributions
of the normalized power spectrum in the antenna and frequency domains and $ii)$
precision and recall metric for distributions. We show that, compared to
existing GAN based approaches which suffer from mode collapse and unstable
training, our diffusion based approach trains stably and generates diverse and
high-fidelity samples from the true channel distribution. We also show that we
can pretrain the model on a simulated urban macro-cellular channel dataset and
fine-tune it on a smaller, out-of-distribution urban micro-cellular dataset,
therefore showing that it is feasible to model real world channels using
limited data with this approach.
