Multichannel Sampling of Pulse Streams at the Rate of Innovation

TL;DR

This paper introduces a multichannel sampling scheme for pulse streams with arbitrary shapes that operates at the minimal rate of innovation, enabling stable recovery and practical implementation improvements.

Contribution

It presents a novel multichannel architecture for sampling pulse streams at the rate of innovation, applicable to arbitrary pulse shapes, with enhanced robustness and practical considerations.

Findings

Achieves minimal-rate sampling for arbitrary pulse shapes.

Enables stable recovery using spectral estimation techniques.

Improves noise robustness and reduces hardware complexity.

Abstract

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches.