# Open Topics for Master Theses

This is only a selection of the possible topics. You may also contact Professor Utschick or one of the group members to talk about your interests and what fascinates you.

If you are interested in perfoming a smaller research project at MSV (Bachelor Thesis, Research Internship, etc.), please contact Professor Utschick or one of the group members. It will either be possible to work on a limited aspect of one of the following topics, or we will look for another current research question whose complexity fits to the intended type of research project.

## Open Topics for Master Theses

## Convex Relaxation and Distributed Solution of the Security-Constrained Optimal Power Flow Problem for Hybrid Transmission Grids

#### Description

In power systems, the operational task of determining the optimal allocation of generation resources and the corresponding system state is known as optimal power flow (OPF). However, for a reliable operation of the system, the resource allocation shall also be resilient to potential outages, e.g., line or generator faults. To this end, the OPF problem is augmented with additional constraints that ensure operability under a postulated set of contingencies, which is then called the security-constrained optimal power flow (SCOPF) problem [1].

The OPF is a nonconvex and large-scale optimization problem that is challenging to solve, while the SCOPF exaggerates these issues by a multiplication of the problem size. Recently, we proposed a hybrid transmission grid architecture and showed that it permits an exact convex relaxation of the OPF problem [2], i.e., it renders the OPF amenable to the powerful theory and methods of convex optimization. In this thesis, these results are utilized to formulate a convex relaxation of the SCOPF problem. On this basis, decomposition methods [3] are applied to facilitate a distributed solution of this large-scale optimization problem. The solution method is implemented in Python on the basis of an OPF framework developed at MSV and some case studies are conducted.

#### Related Literature

[1] F. Capitanescu, J.L. Martinez Ramos, P. Panciatici, D. Kirschen, A. Marano Marcolini, L. Platbrood, and L. Wehenkel, “State-of-the-art, challenges, and future trends in security constrained optimal power flow,” in Electric Power Systems Research, vol. 81, no. 8, 2011.

[2] M. Hotz and W. Utschick, "A Hybrid Transmission Grid Architecture Enabling Efficient Optimal Power Flow," in IEEE Transactions on Power Systems, vol. 31, no. 6, pp. 4504-4516, Nov. 2016.

[3] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” in Foundations and Trends in Machine Learning, vol. 3, no. 1, 2011.

#### Prerequisites

- profound knowledge of convex optimization
- basic knowledge of circuit theory and graph theory
- programming experience in Python is beneficial, but not necessary

#### Supervisor

#### Start date

anytime

## Optimizing the Data Rate in the MIMO Relay Channel using Partial Decode-and-Forward and Convex Programming

#### Description

In a MIMO relay channel, a source node transmits information to a destination with the help of a relay, and all nodes are equipped with multiple antennas. For this scenario, the capacity-achieving coding scheme is still unknown, but the so-called partial decode-and-forward protocol has been shown to perform close to the (unknown) capacity [1] if the statistical properties of the transmit signals are chosen optimally. To choose these parameters, an algorithm based on convex programming techniques was derived in [2]. However, this method requires that the so-called innovation covariance matrix, which is one of the optimization variables, has full rank. Unfortunately, this is not necessarily fulfilled in the optimal solution, and it is not even clear how well the approach can approximate the global optimum in cases where a rank-deficient innovation covariance is needed.

The aim of this thesis is to study how close the proposed algorithm can come to the optimal solution in these cases, and/or whether the algorithm can be generalized in a way that it allows for a singular innovation covariance matrix. The challenge is that the constraint qualifications of one of the arising subproblems are no longer fulfilled in case of such a singularity, i.e., it might be necessary to study other optimality criteria instead of the conventional Karush-Kuhn-Tucker (KKT) conditions.

#### Related Literature

[1] X. Jin and Y.-H. Kim, “The approximate capacity of the MIMO relay channel,” IEEE Trans. Inf. Theory, vol. 63, no. 2, pp. 1167–1176, Feb. 2017.

[2] T. Wiegart, C. Hellings, and W. Utschick, “Close-to-optimal partial decode-and-forward rate in the MIMO relay channel via convex programming,” in Proc. 20th Int. ITG Workshop on Smart Antennas (WSA), Mar. 2016, pp. 581–588.

#### Prerequisites

- profound knowledge of convex optimization
- basic knowledge of stochastics and linear algebra
- knowledge of (multiuser) information theory and/or MIMO systems is helpful, but can also be acquired while working on the topic

#### Supervisor

#### Start date

anytime

## Transmit Signal Processing with Quantized Constant Envelope Signals

#### Description

In massive multiple-input multiple-output (MIMO) wireless systems, where the number of power amplifiers (PAs) scales up with the number of transmit antennas, constant envelope (CE) signaling is beneficial in terms of power efficiency. With CE input signals, the PAs can be operated at their saturation regions and hence use the available power efficiently. Moreover, the input signals of the PAs are the radio-frequency signals that are at an early stage converted from the digital to the analog domain by the digital-to-analog converters (DACs). The power consumption of the DACs grows exponentially with their resolution To further enhance the hardware power efficiency it is desirable to decrease the DACs' resolution. Thus, we combine the idea of CE signaling at the PA input and the coarse quantization of the DACs to end up with coarsely quantized CE signals.

In the context of Multi-User (MU) MIMO systems, transmit signal processing techniques have to be designed to mitigate the MU interference as well as the quantization distortions.

#### Related Literature

[1] S. Jacobsson, G. Durisi, M. Coldrey, T. Goldstein, and C. Studer, “Quantized Precoding for Massive MU-MIMO,” IEEE Transactions on Communications, vol. 65, no. 11, pp. 4670–4684, 2017

[2] H. Jedda, A. Mezghani, J. A. Nossek, and A. L. Swindlehurst, “Massive MIMO Downlink 1-Bit Precoding with Linear Programming for PSK Signaling,” in Proc. 18th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2017

#### Prerequisites

- MATLAB programming skills
- profound knowledge of linear algebra
- knowledge of (multiuser) information theory and/or MIMO systems is helpful, but can also be acquired while working on the topic

#### Supervisor

#### Start date

anytime

## Tensor Decompositions for Parameter Estimation in MIMO Radar

#### Description

Multiple-input multiple-output (MIMO) radars are a natural generalization of phased array radars, where each transmit antenna is able to transmit a different waveform. In so-called pulse-Doppler radars, each transmit antenna transmits a train of pulses in order to estimate the target velocities using the Doppler effect. The discrete-time receive signal of all pulses can be conveniently arranged in a multi-way tensor with, e.g., three dimensions which correspond to azimuth, delay, and Doppler, respectively. The formulation of the receive data as a tensor leverages the use of tensor decompositions for joint parameter estimation in the azimuth-delay-Doppler domain and provides a framework for identifiability considerations. Tensor decompositions for parameter estimation in MIMO radar have been proposed in, e.g., [1], for the case of a single delay bin of interest, only.

The aim of this thesis is to study, extend, and develop tensor decomposition algorithms for joint azimuth, delay, and Doppler estimation in MIMO radar. Of particular interest is the development of algorithms which take the specific structure of the MIMO radar receive data tensor into account. Numerical simulations can be, e.g., implemented in MATLAB.

#### Related Literature

[1] D. Nion and N. D. Sidiropoulos, "Tensor Algebra and Multidimensional Harmonic Retrieval in Signal Processing for MIMO Radar," in IEEE Transactions on Signal Processing, vol. 58, pp. 5693-5705, Nov. 2010.

#### Prerequisites

- profound knowledge of linear algebra
- knowledge of array processing, radar, and MIMO radar is helpful, but can also be acquired while working on the topic

#### Supervisor

#### Start date

anytime

## Robust Design of an Automatic Emergency Braking System for Increasing the Vehicular Safety in the Presence of Multiple Sensor Measurement Errors

#### Description

Vehicular safety functions that intervene in dangerous situations the driver is not able to control like automatic emergency braking (AEB) help to reduce the number as well as the severity of collisions and thus increase vehicular safety. A variety of sensors are used for the perception of the environment of a car. Based on the measurements of the sensors, vehicular safety functions have to interpret the driving situation and trigger appropriate actions in order to defuse critical driving situations. Unavoidable measurement errors made by the sensors can have a severe impact on the interpretation of the driving situation and thus on the performance of the whole system [1]. Therefore, designing functions and sensors such that the performance is robust to measurement errors is crucial. Probabilistic modelling of the uncertainty caused by measurement errors allows to determine the parameters of vehicular safety functions and to derive sensor accuracy requirements such that the desired performance is achieved [2].

The goal of this thesis is to study the robust design of an AEB system in the presence of multiple sensor measurement errors. This design problem of determining the function and sensor parameters should be formulated as an optimization problem, and investigated both analytically and numerically. If it turns out that an analytical solution of the optimization problem in closed form is impossible, it can be solved numerically using MATLAB.

#### Related Literature

[1] T. Dirndorfer, M. Botsch and A. Knoll, "Model-based analysis of sensor-noise in predictive passive safety algorithms," Proceedings of the 22nd Enhanced Safety of Vehicles Conference, Washington, D.C., June 13-16, 2011

[2] J. E. Stellet, J. Schumacher, W. Branz and J. M. Zöllner, "Uncertainty propagation in criticality measures for driver assistance," 2015 IEEE Intelligent Vehicles Symposium (IV), Seoul, June 28 - July 1, 2015, pp. 1187-1194.

#### Prerequisites

- profound knowledge in stochastics
- basic knowledge in (convex) optimization
- knowledge in vehicular safety is helpful, but can also be acquired while working on the topic

#### Supervisor

#### Start date

anytime

## Optimization of Interference Shapes for Cellular Full-Duplex Networks Based on Channel Statistics

#### Description

Full-duplex communication in cellular networks promises a significant performance gain due to a simultaneous up- and downlink operation on a single resource block. Finding optimal transmit strategies in these systems, however, is highly non-trivial as the resulting system resembles a MIMO interference channel, the solution of which is still unknown. We will use interference shaping to find sub-optimal solutions to this problem at a reasonable complexity. With this approach, sets of admissible transmit covariance matrices are defined that allow to decouple the difficult sum rate problem into multiple simpler sub-problems.

Yet, finding these sets reamins a difficult problem and current approaches rely on the availability of channel state information of the entire network. To get towards a more practical implementation, the aim of this thesis is to explore to what extent the availability of channel statistics only is sufficient to allow for a good performance. This will include an analysis of available channel models, a theoretical derivation of shaping sets as well as a numerical evaluation of the proposed scheme. The simulations can be implemented in MATLAB or Python.

#### Related Literature

[1] C. Lameiro, W. Utschick, I. Santamaría, "Spatial interference shaping for underlay MIMO cognitive networks," in Signal Processing, Volume 134, 2017, pp. 174-184.

[2] M. Newinger and W. Utschick, "Covariance shaping for interference coordination in cellular wireless communication systems," Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2015, pp. 648-652.

#### Prerequisites

- knowledge of basic information theory and MIMO systems
- knowledge of convex optimization

#### Supervisor

#### Start date

by arrangement

## Deep Learning for Bayesian Channel Estimation in Millimeter Wave Communication Systems

#### Description

Channel estimation based on structural prior information is a crucial topic in future millimeter wave communication systems. This is in contrast to current systems where channel estimation is model-free because of rich scattering. Of particular interest are conditionally normal channel models. In these models, the channel vector is assumed to be Gaussian distributed with a covariance matrix that depends on a hidden variable, which cannot be observed. The channel matrix is assumed to be approximately low rank. Thus, the coefficients of the channel vector have a very strong correlation structure and this can be exploited to improve channel estimation.

Recently, we proposed a neural network based approach that approximates the minimum mean squared error (MMSE) estimator of the channel vector [1]. This estimator was designed as a proof-of-concept for a very simple flat-fading uplink scenario. In more realistic scenarios, not all receive antennas are equipped with their own analog-digital converters. Instead, an analog network of phase shifters and combiners is employed to reduce power consumption. The goal of this thesis is to derive the MMSE estimator for this particular model and design an appropriate neural network that can be used as an efficient alternative to the MMSE estimator.

#### Related Literature

[1] D. Neumann, T. Wiese, and W. Utschick, “Learning the MMSE channel estimator,” 2017, arXiv:1707.05674v2.

#### Prerequisites

- familiarity with numerical linear algebra, statistical signal processing, and Bayesian estimation
- some programming experience

#### Supervisors

Michael Koller and Christoph Hellings

#### Start date

anytime