We propose a joint channel estimation and data detection algorithm for massive multilple-input multiple-output systems based on diffusion models. Our proposed method solves the blind inverse problem by sampling from the joint posterior distribution of the symbols and channels and computing an approximate maximum a posteriori estimation. To achieve this, we construct a diffusion process that models the joint distribution of the channels and symbols given noisy observations, and then run the reverse process to generate the samples. A unique contribution of the algorithm is to include the discrete prior distribution of the symbols and a learned prior for the channels. Indeed, this is key as it allows a more efficient exploration of the joint search space and, therefore, enhances the sampling process. Through numerical experiments, we demonstrate that our method yields a lower normalized mean squared error than competing approaches and reduces the pilot overhead.

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of our unknown variables of interest while being computationally more efficient than their first-order counterpart and the nonconditioned versions of both dynamics. Moreover, we prove that both pre-conditioned dynamics are well-defined and have the same unique invariant distributions as the non-conditioned cases. We also incorporate an annealing procedure that has the double benefit of further accelerating the convergence of the algorithm and allowing us to accommodate the case where the unknown variables are discrete. Numerical experiments in two different tasks (MIMO symbol detection and channel estimation) showcase the generality of our method and illustrate the high performance achieved relative to competing approaches (including learningbased ones) while having comparable or lower computational complexity.

Optimal symbol detection in multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Recently, there has been a growing interest to get reasonably close to the optimal solution using neural networks while keeping the computational complexity in check. However, existing work based on deep learning shows that it is difficult to design a generic network that works well for a variety of channels. In this work, we propose a method that tries to strike a balance between symbol error rate (SER) performance and generality of channels. Our method is based on hypernetworks that generate the parameters of a neural network-based detector that works well on a specific channel. We propose a general framework by regularizing the training of the hypernetwork with some pre-trained instances of the channel-specific method. Through numerical experiments, we show that our proposed method yields high performance for a set of prespecified channel realizations while generalizing well to all channels drawn from a specific distribution.

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An approach based on the Green function and the Born approximation is used for impulsive radio ultra‐wideband microwave imaging, in which a permittivity map of the illuminated scenario is estimated using the scattered fields measured at several positions. Two algorithms are applied to this model and compared: the first one solves the inversion problem using a linear operator. The second one is based on the Bayesian compressive sensing technique, where the sparseness of the contrast function is introduced as a priori knowledge in order to improve the inverse mapping. In order to compare both methods, measurements in real scenarios are taken using an ultra‐wideband radar prototype. The results with real measurements illustrate that, for the considered scenarios, the Bayesian compressive sensing imaging algorithm has a better performance in terms of range and cross‐range resolution allowing object detection and shape reconstruction, with a reduced computational burden, and fewer space and frequency measurements, as compared to the linear operator.