Optimal quantization for compressive sensing under message passing reconstruction

Abstract—We consider the optimal quantization of compressive sensing measurements along with estimation from quantized samples using generalized approximate message passing (GAMP). GAMP is an iterative reconstruction scheme inspired by the belief propagation algorithm on bipartite graphs which generalizes approximate message passing (AMP) for arbitrary measurement channels. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers. I

Random Access in C-RAN for User Activity Detection with Limited-Capacity Fronthaul

Cloud-Radio Access Network (C-RAN) is characterized by a hierarchical structure in which the baseband processing functionalities of remote radio heads (RRHs) are implemented by means of cloud computing at a Central Unit (CU). A key limitation of C-RANs is given by the capacity constraints of the fronthaul links connecting RRHs to the CU. In this letter, the impact of this architectural constraint is investigated for the fundamental functions of random access and active User Equipment (UE) identification in the presence of a potentially massive number of UEs. In particular, the standard C-RAN approach based on quantize-and-forward and centralized detection is compared to a scheme based on an alternative CU-RRH functional split that enables local detection. Both techniques leverage Bayesian sparse detection. Numerical results illustrate the relative merits of the two schemes as a function of the system parameters.Comment: 6 pages, 3 figures, under revision in IEEE Signal Processing Letter

Message-Passing Estimation from Quantized Samples

Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowing the linear expansion to be overcomplete or undercomplete and the scalar quantization to be regular or non-regular. GAMP is a recently-developed class of algorithms that uses Gaussian approximations in belief propagation and allows arbitrary separable input and output channels. Scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization. Non-regular quantization is empirically demonstrated to greatly improve rate-distortion performance in some problems with oversampling or with undersampling combined with a sparsity-inducing prior. Under the assumption of a Gaussian measurement matrix with i.i.d. entries, the asymptotic error performance of GAMP can be accurately predicted and tracked through the state evolution formalism. We additionally use state evolution to design MSE-optimal scalar quantizers for GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.Comment: 12 pages, 8 figure