SignalNet: A Low Resolution Sinusoid Decomposition and Estimation Network

TL;DR

SignalNet is a neural network designed for sinusoid detection and parameter estimation from low-resolution, quantized samples, outperforming traditional algorithms by incorporating signal reconstruction and a novel worst-case learning threshold.

Contribution

The paper introduces SignalNet, a neural network architecture that effectively estimates sinusoid parameters from quantized data, integrating domain knowledge and a new learning threshold for improved performance.

Findings

Outperforms traditional algorithms in mean squared error and Chamfer error.

Successfully surpasses the learning threshold with three-bit data.

Learns to minimize distributional loss in one-bit data scenarios.

Abstract

The detection and estimation of sinusoids is a fundamental signal processing task for many applications related to sensing and communications. While algorithms have been proposed for this setting, quantization is a critical, but often ignored modeling effect. In wireless communications, estimation with low resolution data converters is relevant for reduced power consumption in wideband receivers. Similarly, low resolution sampling in imaging and spectrum sensing allows for efficient data collection. In this work, we propose SignalNet, a neural network architecture that detects the number of sinusoids and estimates their parameters from quantized in-phase and quadrature samples. We incorporate signal reconstruction internally as domain knowledge within the network to enhance learning and surpass traditional algorithms in mean squared error and Chamfer error. We introduce a worst-case learning threshold for comparing the results of our network relative to the underlying data distributions. This threshold provides insight into why neural networks tend to outperform traditional methods and into the learned relationships between the input and output distributions. In simulation, we find that our algorithm is always able to surpass the threshold for three-bit data but often cannot exceed the threshold for one-bit data. We use the learning threshold to explain, in the one-bit case, how our estimators learn to minimize the distributional loss, rather than learn features from the data.