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Signal & System Theory Group

Professor Peter Schreier
Universität Paderborn, Germany

Selected research projects

Our current research focuses on statistical signal processing with applications ranging from mobile communications to (bio-) medicine. Some of our current and past projects include the following.

Improper Gaussian signaling schemes for interference-limited communications

This project aims at developing novel signaling schemes for interference-limited mobile communication networks. Already today, multiuser interference presents the major limiting factor of the end-toend performance in wireless communications. In pursuit of efficient interference management schemes, current research focuses on interference coordination by means of a joint precoder design that exploits the channel state information. The vast majority of these works assumes that the transmitted signals are distributed as proper Gaussian random signals, which are known to be optimal when the system is not interference-limited. Recently, alternative signaling schemes that deviate from these standard assumptions have been proposed in the literature. It has been shown that the transmission of improper Gaussian signals, whose real and imaginary parts are correlated and/or have unequal power, outperform proper Gaussian signals in various interference-limited networks. This project studies improper signaling schemes for different interference-limited networks. It has the following objectives:
  • To provide insights on when improper signaling enables better performance than its proper counterpart. To this end, we will focus on single-antenna and partially connected interference channels, where the analysis is tractable and permits insights that can be extended to more general scenarios.
  • To design algorithms that optimize the transmission parameters for general interference channels. An improper signaling scheme contains not only the parameters associated with a proper scheme, but also additional ones that describe the impropriety of the signal, which makes the optimization more challenging.
  • To apply improper signaling to underlay cognitive radio scenarios, which can be regarded as a paradigm for low-cooperative multiuser networks. In these scenarios, the interference is managed by setting interference constraints, so that its effect can be upper-bounded and thereby require less cooperation. We will explore new interference constraints taking impropriety into account, as well as the optimization of the transmission parameters subject to these constraints.
Interference management in wireless communications with realistic assumptions on the knowledge of channel state information at the transmitters

This project aims at developing efficient transmission and reception schemes for interference-limited multi-user communication networks with realistic assumptions on the availability of channel state information (CSI) at the transmitter side. Extensive research on the capacity limits of interference-limited networks in the last several years has proved that knowledge of CSI at the transmitters (CSIT) can provide considerable performance improvements. Indeed, for many networks it has been shown that at high SNR the optimal performance can be achieved by exploiting the CSIT using a method called interference alignment (IA). However, the global CSI of the network must be available at each transmitter to perform IA in a multiuser network. In this proposal, we consider more realistic IA scenarios where the transmitters only have access to a limited amount of CSI. The goal is to develop schemes that optimally exploit whatever CSI is available to improve spectral efficiency.

In our first scenario, we assume that the transmitters have access to delayed CSI, which means that the available information is completely outdated with respect to the current channel. It has been previously shown that using only delayed CSI it is still possible to achieve multiplexing gains over the case where no CSI is available. However, many of the solutions in the delayed-CSI problem are based on heuristic methods. We are looking for unified and compact solutions that can be applied to general settings.

The second scenario is the case where some transmitters do not create interference for some receivers. This situation is common in the real world where some devices are at distant locations. In partially connected networks, it has been previously shown that IA can be effective even without CSI at the transmitter. Our objective here is to improve the IA-based schemes by exploiting network properties. For example, multi-antenna nodes at the transceivers can receive or transmit in reduced-dimensional subspaces while creating a virtual partially connected network.

Finally, we investigate several realistic scenarios and adapt our solutions to account for practical impairments. We study joint application of different IA methods as multiple conditions coexist in reality.
A unifying framework for detecting cyclostationarity with applications to cognitive radio

Cyclostationary (CS) signals can model periodic phenomena occurring in a wide range of areas in science and technology. The detection of CS signals is a particularly important problem. For instance, detection of CS signals is a key ingredient in the dynamic spectrum management of cognitive radio (CR), where cognitive users are allowed to access unused licensed bands. This requires testing for the presence of licensed users, which transmit CS signals. Because detection of cyclostationarity is such an important problem, many detectors have been proposed for it. However, a close analysis of these detectors reveals that most of the proposed techniques are not based on sound statistical theory. While they may be sensible ad-hoc detectors, they do not offer any kind of optimality. Moreover, most of these detectors make unrealistic assumptions such as known cycle period or not accounting for the fact that sampled CS signals are generally only almost CS. Thus, the main objective of this project is the development of detectors for cyclostationarity based on solid statistical arguments, without the need for unrealistic simplifying assumptions. These detectors will be based on well-established statistical techniques, such as the generalized likelihood ratio test, the locally most powerful invariant test, and - if it exists - the uniformly most powerful invariant test. We also consider the case of unknown cycle period. Since the sampling of a cyclostationary signal generally results in an almost cyclostationary signal this will involve the development of tests for almost cyclostationarity.
Signal processing for identifying coupled effects in high-dimensional data

This project is concerned with identifying coupled effects in high-dimensional data. The goal is to extract only a few modes that explain much of the joint variability between two or more sets of data. This is a common objective, with numerous applications in many areas of the natural and social sciences and engineering. In this project, we deal with high-dimensional problems with extremely low sample support, where the coupling must be identified from very few measurements. In such a small sample scenario, only very few, dominant, modes are trustworthy, as the remaining modes are due to the spurious effects of noise or sample variability. This requires the right trade-off between bias and variance. Too simple a model is a poor representation of the data, causing large bias. Too complicated a model overfits the data, causing large variance. We need to strike the right balance between underfitting and overfitting. Getting this balance right is the problem of model-order selection. Model-order selection for single data sets, where a single model order needs to be determined and sample support is sufficient, is a well-studied problem. There are also techniques that work for small sample support and techniques that work for two or more datasets. However, the combination - two or more datasets with small sample support - is still a very challenging open problem.
Medical image processing of X-ray images

We are assisting one of the world's leading medical technology companies in their development of a revolutionary product in computer assisted surgery (CAS). CAS has been successfully used in brain and spine surgeries for many years. However, classical CAS systems have some disadvantages (changed operating room workflow and increased complexity) so that they are rarely used in trauma surgery, where efficiency and simplicity are critical. This is what we address here. The product to be developed is completely adaptive and requires little to no interaction between surgeon and system. In order to achieve this, the system automatically processes X-ray images, using sophisticated image processing algorithms, which we develop.
Nonparametric techniques for analyzing directional structure in space-time random fields (completed)

The analysis of directional structure in images and space-time data is crucial to many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Estimating the orientation of such patterns is particularly important. For example, Synthetic Aperture Radar (SAR) images are frequently analyzed for structures such as oceanic waves, hurricane rain bands, tsunamis, etc., which all exhibit locally unidirectional structure. Other examples include the analysis of texture and optical flow by estimating multidimensional orientation, the efficient coding of local differential structures in images, and the analysis of superimposed directional patterns, which may occur in X-ray projection imaging. Much of the existing work on orientation estimation treats deterministic data, which means that it may fail for very noisy data. On the other hand, much of the work on random fields has focused on the isotropic case. In this project, we develop statistical techniques for analyzing directional (i.e., highly non-isotropic) structure in random images and space-time random fields.
Iterative subspace expansions for space-time adaptive wireless communications, radar and sonar (completed)

This project addresses the fundamental challenge of high computational complexity in receivers for bandwidth-efficient, high data-rate wireless communications, radar and sonar. We study conjugate gradient Wiener filters that enable effective low complexity approximation if the signal correlation matrix has a small number of distinct or clustered eigenvalues. In this case, these filters converge with warp speed. Hence, by properly designing signal transmissions in multi-access communications, we can build receivers that rapidly adapt. A critical question is the sensitivity of repeated/clustered eigenvalues to perturbations, e.g., in time-varying communication channels. We analyse this question from the point of view of feedback control.