  Analog-to-digital converters (ADCs) allow physical signals to be processed
using digital hardware. Their conversion consists of two stages: Sampling,
which maps a continuous-time signal into discrete-time, and quantization, i.e.,
representing the continuous-amplitude quantities using a finite number of bits.
ADCs typically implement generic uniform conversion mappings that are ignorant
of the task for which the signal is acquired, and can be costly when operating
in high rates and fine resolutions. In this work we design task-oriented ADCs
which learn from data how to map an analog signal into a digital representation
such that the system task can be efficiently carried out. We propose a model
for sampling and quantization that facilitates the learning of non-uniform
mappings from data. Based on this learnable ADC mapping, we present a mechanism
for optimizing a hybrid acquisition system comprised of analog combining,
tunable ADCs with fixed rates, and digital processing, by jointly learning its
components end-to-end. Then, we show how one can exploit the representation of
hybrid acquisition systems as deep network to optimize the sampling rate and
quantization rate given the task by utilizing Bayesian meta-learning
techniques. We evaluate the proposed deep task-based ADC in two case studies:
the first considers symbol detection in multi-antenna digital receivers, where
multiple analog signals are simultaneously acquired in order to recover a set
of discrete information symbols. The second application is the beamforming of
analog channel data acquired in ultrasound imaging. Our numerical results
demonstrate that the proposed approach achieves performance which is comparable
to operating with high sampling rates and fine resolution quantization, while
operating with reduced overall bit rate.
