A Unified Framework of State Evolution for Message-Passing Algorithms

This paper presents a unified framework to understand the dynamics of message-passing algorithms in compressed sensing. State evolution is rigorously analyzed for a general error model that contains the error model of approximate message-passing (AMP), as well as that of orthogonal AMP. As a by-product, AMP is proved to converge asymptotically if the sensing matrix is orthogonally invariant and if the moment sequence of its asymptotic singular-value distribution coincide with that of the Marchenko-Pastur distribution up to the order that is at most twice as large as the maximum number of iterations.Comment: Long version of a paper submitted to ISIT2019 including the proof of Theorem

Bayes-Optimal Convolutional AMP

This paper proposes Bayes-optimal convolutional approximate message-passing (CAMP) for signal recovery in compressed sensing. CAMP uses the same low-complexity matched filter (MF) for interference suppression as approximate message-passing (AMP). To improve the convergence property of AMP for ill-conditioned sensing matrices, the so-called Onsager correction term in AMP is replaced by a convolution of all preceding messages. The tap coefficients in the convolution are determined so as to realize asymptotic Gaussianity of estimation errors via state evolution (SE) under the assumption of orthogonally invariant sensing matrices. An SE equation is derived to optimize the sequence of denoisers in CAMP. The optimized CAMP is proved to be Bayes-optimal for all orthogonally invariant sensing matrices if the SE equation converges to a fixed-point and if the fixed-point is unique. For sensing matrices with low-to-moderate condition numbers, CAMP can achieve the same performance as high-complexity orthogonal/vector AMP that requires the linear minimum mean-square error (LMMSE) filter instead of the MF.Comment: submitted to IEEE Trans. Inf. Theor

Grant-Free Access via Bilinear Inference for Cell-Free MIMO with Low-Coherent Pilots

We propose a novel joint activity, channel, and data estimation (JACDE) scheme for cell-free multiple-input multiple-output (MIMO) systems compliant with fifth-generation (5G) new radio (NR) orthogonal frequency-division multiplexing (OFDM) signaling. The contribution aims to allow significant overhead reduction of cell-free MIMO systems by enabling grant-free access, while maintaining moderate throughput per user. To that end, we extend the conventional MIMO OFDM protocol so as to incorporate activity detection capability without resorting to spreading informative data symbols, in contrast with related work which typically relies on signal spreading. Our method leverages a Bayesian message passing scheme based on Gaussian approximation, which jointly performs active user detection (AUD), channel estimation (CE), and multi-user detection (MUD), incorporating also a well-structured low-coherent pilot design based on frame theory, which mitigates pilot contamination, and finally complemented with a detector empowered by bilinear message passing. The efficacy of the resulting JACDE-based grant-free access scheme without spreading data sequences is demonstrated by simulation results, which are shown to significantly outperform the current state-of-the-art and approach the performance of an idealized (genie-aided) scheme in which user activity and channel coefficients are perfectly known.Comment: 15 pages, 15 figures, submitted to an IEEE journa