Non-Uniform Wavelet Sampling for RF Analog-to-Information Conversion

Abstract

Abstract-Feature extraction, such as spectral occupancy, interferer energy and type, or direction-of-arrival, from wideband radio-frequency (RF) signals finds use in a growing number of applications as it enhances RF transceivers with cognitive abilities and enables parameter tuning of traditional RF chains. In power and cost limited applications, e.g., for sensor nodes in the Internet of Things, wideband RF feature extraction with conventional, Nyquist-rate analog-to-digital converters is infeasible. However, the structure of many RF features (such as signal sparsity) enables the use of compressive sensing (CS) techniques that acquire such signals at sub-Nyquist rates. While such CS-based analog-to-information (A2I) converters have the potential to enable low-cost and energy-efficient wideband RF sensing, they suffer from a variety of real-world limitations, such as noise folding, low sensitivity, aliasing, and limited flexibility. This paper proposes a novel CS-based A2I architecture called non-uniform wavelet sampling (NUWS). Our solution extracts a carefully-selected subset of wavelet coefficients directly in the RF domain, which mitigates the main issues of existing A2I converter architectures. For multi-band RF signals, we propose a specialized variant called non-uniform wavelet bandpass sampling (NUWBS), which further improves sensitivity and reduces hardware complexity by leveraging the multi-band signal structure. We use simulations to demonstrate that NUWBS approaches the theoretical performance limits of 1-norm-based sparse signal recovery. We investigate hardware-design aspects and show ASIC measurement results for the wavelet generation stage, which highlight the efficacy of NUWBS for a broad range of RF feature extraction tasks in cost-and power-limited applications.

Analog-to-Feature (A2F) Conversion for Audio-Event Classification

“…In contrast to CS, A2F conversion is specifically designed for signal classification, which further reduces the sampling rates, costs, and power. Instead of acquiring a random subset of Nyquist samples, as it is the case for NUS [10], we extract a carefully-selected set of "wavelet features" directly from the analog signal using non-uniform wavelet sampling (NUWS) [11]. These features are then fed into a digital classifier (e.g., a neural network) that detects the events of interest.…”

“…where φ m denotes the mth row of Φ. Hence, RM acquires (pseudo-)random inner products of the signal vector x which can be implemented using a signal generator that produces the entries of φ m , an analog multiplier, and an integrator [8], [11].…”

“…NUS and RM, as well as other CS architectures (see [11] and the references therein), are specifically designed for signal recovery. Nevertheless, these methods can be used to directly perform signal classification [3] from the compressive measurements in y.…”

“…Nevertheless, these methods can be used to directly perform signal classification [3] from the compressive measurements in y. To avoid the practical limitations of NUS and RM while enabling further reductions in terms of the measurements to be acquired for signal classification tasks, we propose to use NUWS [11] for A2F conversion. In essence, NUWS combines the advantages of NUS and RM by acquiring inner products of the signal x as in (2) but with hardwarefriendly wavelet functions rather than Dirac delta functions (for NUS) or (pseudo-)random sequences (for RM).…”

Compressed sensing with continuous parametric reconstruction

“…The basic idea of CS was originally proposed by [16] with a number of sampling methods for CS proposed afterwards. Most often used are the earliest random demodulation (RD) [17], random modulation pre-integration (RMPI) [18] and random sampling (RS) [19], and the more recent non-uniform wavelet sampling [20] The goal is to capture as much information as possible with as few samples as possible without introducing aliasing. Reconstruction also presents a specific challenge-solving an underdetermined system of linear equations.…”