766 research outputs found
On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling
This paper investigates the information rate loss in analog channels when the
sampler is designed to operate independent of the instantaneous channel
occupancy. Specifically, a multiband linear time-invariant Gaussian channel
under universal sub-Nyquist sampling is considered. The entire channel
bandwidth is divided into subbands of equal bandwidth. At each time only
constant-gain subbands are active, where the instantaneous subband
occupancy is not known at the receiver and the sampler. We study the
information loss through a capacity loss metric, that is, the capacity gap
caused by the lack of instantaneous subband occupancy information. We
characterize the minimax capacity loss for the entire sub-Nyquist rate regime,
provided that the number of subbands and the SNR are both large. The
minimax limits depend almost solely on the band sparsity factor and the
undersampling factor, modulo some residual terms that vanish as and SNR
grow. Our results highlight the power of randomized sampling methods (i.e. the
samplers that consist of random periodic modulation and low-pass filters),
which are able to approach the minimax capacity loss with exponentially high
probability.Comment: accepted to IEEE Transactions on Information Theory. It has been
presented in part at the IEEE International Symposium on Information Theory
(ISIT) 201
Structured Compressed Sensing: From Theory to Applications
Compressed sensing (CS) is an emerging field that has attracted considerable
research interest over the past few years. Previous review articles in CS limit
their scope to standard discrete-to-discrete measurement architectures using
matrices of randomized nature and signal models based on standard sparsity. In
recent years, CS has worked its way into several new application areas. This,
in turn, necessitates a fresh look on many of the basics of CS. The random
matrix measurement operator must be replaced by more structured sensing
architectures that correspond to the characteristics of feasible acquisition
hardware. The standard sparsity prior has to be extended to include a much
richer class of signals and to encode broader data models, including
continuous-time signals. In our overview, the theme is exploiting signal and
measurement structure in compressive sensing. The prime focus is bridging
theory and practice; that is, to pinpoint the potential of structured CS
strategies to emerge from the math to the hardware. Our summary highlights new
directions as well as relations to more traditional CS, with the hope of
serving both as a review to practitioners wanting to join this emerging field,
and as a reference for researchers that attempts to put some of the existing
ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal
Processin
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
Wideband analog signals push contemporary analog-to-digital conversion
systems to their performance limits. In many applications, however, sampling at
the Nyquist rate is inefficient because the signals of interest contain only a
small number of significant frequencies relative to the bandlimit, although the
locations of the frequencies may not be known a priori. For this type of sparse
signal, other sampling strategies are possible. This paper describes a new type
of data acquisition system, called a random demodulator, that is constructed
from robust, readily available components. Let K denote the total number of
frequencies in the signal, and let W denote its bandlimit in Hz. Simulations
suggest that the random demodulator requires just O(K log(W/K)) samples per
second to stably reconstruct the signal. This sampling rate is exponentially
lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one
must use nonlinear methods, such as convex programming, to recover the signal
from the samples taken by the random demodulator. This paper provides a
detailed theoretical analysis of the system's performance that supports the
empirical observations.Comment: 24 pages, 8 figure
D11.2 Consolidated results on the performance limits of wireless communications
Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin
Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells
Adherent cells exert traction forces on to their environment, which allows
them to migrate, to maintain tissue integrity, and to form complex
multicellular structures. This traction can be measured in a perturbation-free
manner with traction force microscopy (TFM). In TFM, traction is usually
calculated via the solution of a linear system, which is complicated by
undersampled input data, acquisition noise, and large condition numbers for
some methods. Therefore, standard TFM algorithms either employ data filtering
or regularization. However, these approaches require a manual selection of
filter- or regularization parameters and consequently exhibit a substantial
degree of subjectiveness. This shortcoming is particularly serious when cells
in different conditions are to be compared because optimal noise suppression
needs to be adapted for every situation, which invariably results in systematic
errors. Here, we systematically test the performance of new methods from
computer vision and Bayesian inference for solving the inverse problem in TFM.
We compare two classical schemes, L1- and L2-regularization, with three
previously untested schemes, namely Elastic Net regularization, Proximal
Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that
Elastic Net regularization, which combines L1 and L2 regularization,
outperforms all other methods with regard to accuracy of traction
reconstruction. Next, we develop two methods, Bayesian L2 regularization and
Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.
Using artificial data and experimental data, we show that these methods enable
robust reconstruction of traction without requiring a difficult selection of
regularization parameters specifically for each data set. Thus, Bayesian
methods can mitigate the considerable uncertainty inherent in comparing
cellular traction forces
Signal Processing for Compressed Sensing Multiuser Detection
The era of human based communication was longly believed to be the main driver for the development of communication systems. Already nowadays we observe that other types of communication impact the discussions of how future communication system will look like. One emerging technology in this direction is machine to machine (M2M) communication. M2M addresses the communication between autonomous entities without human interaction in mind. A very challenging aspect is the fact that M2M strongly differ from what communication system were designed for. Compared to human based communication, M2M is often characterized by small and sporadic uplink transmissions with limited data-rate constraints. While current communication systems can cope with several 100 transmissions, M2M envisions a massive number of devices that simultaneously communicate to a central base-station. Therefore, future communication systems need to be equipped with novel technologies facilitating the aggregation of massive M2M. The key design challenge lies in the efficient design of medium access technologies that allows for efficient communication with small data packets. Further, novel physical layer aspects have to be considered in order to reliable detect the massive uplink communication. Within this thesis physical layer concepts are introduced for a novel medium access technology tailored to the demands of sporadic M2M. This concept combines advances from the field of sporadic signal processing and communications. The main idea is to exploit the sporadic structure of the M2M traffic to design physical layer algorithms utilizing this side information. This concept considers that the base-station has to jointly detect the activity and the data of the M2M nodes. The whole framework of joint activity and data detection in sporadic M2M is known as Compressed Sensing Multiuser Detection (CS-MUD). This thesis introduces new physical layer concepts for CS-MUD. One important aspect is the question of how the activity detection impacts the data detection. It is shown that activity errors have a fundamentally different impact on the underlying communication system than data errors have. To address this impact, this thesis introduces new algorithms that aim at controlling or even avoiding the activity errors in a system. It is shown that a separate activity and data detection is a possible approach to control activity errors in M2M. This becomes possible by considering the activity detection task in a Bayesian framework based on soft activity information. This concept allows maintaining a constant and predictable activity error rate in a system. Beyond separate activity and data detection, the joint activity and data detection problem is addressed. Here a novel detector based on message passing is introduced. The main driver for this concept is the extrinsic information exchange between different entities being part of a graphical representation of the whole estimation problem. It can be shown that this detector is superior to state-of-the-art concepts for CS-MUD. Besides analyzing the concepts introduced simulatively, this thesis also shows an implementation of CS-MUD on a hardware demonstrator platform using the algorithms developed within this thesis. This implementation validates that the advantages of CS-MUD via over-the-air transmissions and measurements under practical constraints
- …