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In this letter, we consider a novel problem of blind source separation from observed magnitude-only measurements of their convolutive mixture in different communication systems. The problem setups correspond to a blind receiver architecture that either does not have phase information in the measurements or has excessive phase noise that cannot be easily recovered. We have formulated the problem as a matrix recovery problem by using the lifting technique and proposed a convex programming-based solution for joint recovery of the unknown channel and source signals. We have implemented the proposed solution using the alternating direction method of multipliers (ADMM). We have plotted a phase transition diagram for random Gaussian subspaces that shows, for s source signals each of length n and channel of length k, the minimum measurements required for exact recovery are m ≥ 1.19 (s n + k) log 2 m that is in accord with our theoretical result. We have also plotted a phase transition diagram for the case where the channel delays matrix is deterministic (consisting of the first k columns of the identity matrix) that shows the minimum measurements required for exact recovery are m ≥ 2.86 (s n + k) log 2 m which are higher than random subspaces. [ABSTRACT FROM AUTHOR]

Blind deconvolution and demixing is the problem of reconstructing convolved signals and kernels from the sum of their convolutions. This problem arises in many applications, such as blind MIMO. This work presents a separable approach to blind deconvolution and demixing via convex optimization. Unlike previous works, our formulation allows separation into smaller optimization problems, which significantly improves complexity. We develop recovery guarantees, which comply with those of the original non-separable problem, and demonstrate the method performance under several normalization constraints. [ABSTRACT FROM AUTHOR]

Assume we are given a sum of linear measurements of s different rank-r matrices of the form y=∑k=1sAk(Xk). When and under which conditions is it possible to extract (demix) the individual matrices Xk from the single measurement vector y? And can we do the demixing numerically efficiently? We present two computationally efficient algorithms based on hard thresholding to solve this low rank demixing problem. We introduce an Amalgam-Restricted Isometry Property which is especially suitable for demixing problems and prove that under appropriate conditions these algorithms are guaranteed to converge to the correct solution at a linear rate. We discuss applications in connection with quantum tomography and the Internet-of-Things. Numerical simulations demonstrate the empirical performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We consider simultaneous blind deconvolution of $r$ source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding using i.i.d. complex Gaussian matrices is used at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in $r$ our result significantly improves over recent works. [ABSTRACT FROM AUTHOR]

Suppose that we have r sensors and each one intends to send a function {g}_{i} (e.g., a signal or an image) to a receiver common to all r sensors. During transmission, each gi gets convolved with a function {f}i . The receiver records the function y , given by the sum of all these convolved signals. When and under which conditions is it possible to recover the individual signals gi and the blurring functions fi from just one received signal y ? This challenging problem, which intertwines blind deconvolution with blind demixing, appears in a variety of applications, such as audio processing, image processing, neuroscience, spectroscopy, and astronomy. It is also expected to play a central role in connection with the future Internet-of-Things. We will prove that under reasonable and practical assumptions, it is possible to solve this, otherwise, highly ill-posed problem and recover the $r$ transmitted functions gi and the impulse responses fi in a robust, reliable, and efficient manner, from just one single received function y by solving a semidefinite program. We derive explicit bounds on the number of measurements needed for successful recovery and prove that our method is robust in the presence of noise. Our theory is actually suboptimal, since numerical experiments demonstrate that, quite remarkably, recovery is still possible if the number of measurements is close to the number of degrees of freedom. [ABSTRACT FROM PUBLISHER]