2,898 research outputs found
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
Xampling: Signal Acquisition and Processing in Union of Subspaces
We introduce Xampling, a unified framework for signal acquisition and
processing of signals in a union of subspaces. The main functions of this
framework are two. Analog compression that narrows down the input bandwidth
prior to sampling with commercial devices. A nonlinear algorithm then detects
the input subspace prior to conventional signal processing. A representative
union model of spectrally-sparse signals serves as a test-case to study these
Xampling functions. We adopt three metrics for the choice of analog
compression: robustness to model mismatch, required hardware accuracy and
software complexities. We conduct a comprehensive comparison between two
sub-Nyquist acquisition strategies for spectrally-sparse signals, the random
demodulator and the modulated wideband converter (MWC), in terms of these
metrics and draw operative conclusions regarding the choice of analog
compression. We then address lowrate signal processing and develop an algorithm
for that purpose that enables convenient signal processing at sub-Nyquist rates
from samples obtained by the MWC. We conclude by showing that a variety of
other sampling approaches for different union classes fit nicely into our
framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio
Compressive Identification of Active OFDM Subcarriers in Presence of Timing Offset
In this paper we study the problem of identifying active subcarriers in an
OFDM signal from compressive measurements sampled at sub-Nyquist rate. The
problem is of importance in Cognitive Radio systems when secondary users (SUs)
are looking for available spectrum opportunities to communicate over them while
sensing at Nyquist rate sampling can be costly or even impractical in case of
very wide bandwidth. We first study the effect of timing offset and derive the
necessary and sufficient conditions for signal recovery in the oracle-assisted
case when the true active sub-carriers are assumed known. Then we propose an
Orthogonal Matching Pursuit (OMP)-based joint sparse recovery method for
identifying active subcarriers when the timing offset is known. Finally we
extend the problem to the case of unknown timing offset and develop a joint
dictionary learning and sparse approximation algorithm, where in the dictionary
learning phase the timing offset is estimated and in the sparse approximation
phase active subcarriers are identified. The obtained results demonstrate that
active subcarrier identification can be carried out reliably, by using the
developed framework.Comment: To appear in the proceedings of the IEEE Global Communications
Conference (GLOBECOM) 201
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