Karlheinz Ochs

The degrees of freedom of the MIMO Y-channel

The degrees of freedom (DoF) of the MIMO Y-channel, a multi-way communication network consisting of 3 users and a relay, are characterized for arbitrary number of antennas. The converse is provided by cut-set bounds and novel genie-aided bounds. The achievability is shown by a scheme that uses beamforming to establish network coding on-the-fly at the relay in the uplink, and zero-forcing pre-coding in the downlink. It is shown that the network has min{2M2+2M3, M1+ M2 + M3,2N} DoF, where Mj and N represent the number of antennas at user j and the relay, respectively. Thus, in the extreme case where M1+M2+M3 dominates the DoF expression and is smaller than N, the network has the same DoF as the MAC between the 3 users and the relay. In this case, a decode and forward strategy is optimal. In the other extreme where 2N dominates, the DoF of the network is twice that of the aforementioned MAC, and hence network coding is necessary. As a byproduct of this work, it is shown that channel output feedback from the relay to the users has no impact on the DoF of this channel.

Generation of wave digital structures for networks containing multiport elements

Most standard wave digital filters are derived from passive reference circuits, where only parallel and serial connections between one-port elements occur. In this paper, a framework for the automated generation of the wave digital structures is presented, where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its so-called SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with networks containing certain multiport elements. We propose two different novel approaches to finding a valid tree representation from a given reference circuit. The first approach relies on the usage of apt replacement graphs for the multiport elements. The second one is based on searches for circles on suitably constructed graph representations and generates wave digital structures with minimum implementation effort even in presence of nonreciprocal elements. In both approaches, standard separation algorithms with known efficient implementations can be applied.

A comprehensive analytical solution of the nonlinear pendulum

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.

A systematic approach for interference alignment in CSIT-less relay-aided X-networks

The degrees of freedom (DoF) of an X-network with M transmit and N receive nodes utilizing interference alignment with the support of J relays each equipped with Lj antennas operating in a half-duplex non-regenerative mode is investigated. Conditions on the feasibility of interference alignment are derived using a proper transmit strategy and a structured approach based on a Kronecker-product representation. The advantages of this approach are twofold: First, it extends existing results on the achievable DoF to generalized antenna configurations. Second, it unifies the analysis for time-varying and constant channels and provides valuable insights and interconnections between the two channel models. It turns out that a DoF of NM/M+N-1 is feasible whenever the sum of the L2j ≥ [N - 1][M - 1].

Numerical stability properties of passive Runge-Kutta methods

Recently, network-theoretical considerations of numerical integration methods have led to so-called passive Runge-Kutta methods. In this paper, it is shown that these numerical integration methods exhibit a variety of numerical stability properties. For an intuitive understanding, the methods as well as the stability properties and criteria are formulated by means of Kirchhoff networks and the corresponding transfer matrices.

An enhanced lumped element electrical model of a double barrier memristive device

The massive parallel approach of neuromorphic circuits leads to effective methods for solving complex problems. It has turned out that resistive switching devices with a continuous resistance range are potential candidates for such applications. These devices are memristive systems - nonlinear resistors with memory. They are fabricated in nanotechnology and hence parameter spread during fabrication may aggravate reproducible analyses. This issue makes simulation models of memristive devices worthwhile. Kinetic Monte-Carlo simulations based on a distributed model of the device can be used to understand the underlying physical and chemical phenomena. However, such simulations are very time-consuming and neither convenient for investigations of whole circuits nor for real-time applications, e.g. emulation purposes. Instead, a concentrated model of the device can be used for both fast simulations and real-time applications, respectively. We introduce an enhanced electrical model of a valence change mechanism (VCM) based double barrier memristive device (DBMD) with a continuous resistance range. This device consists of an ultra-thin memristive layer sandwiched between a tunnel barrier and a Schottky-contact. The introduced model leads to very fast simulations by using usual circuit simulation tools while maintaining physically meaningful parameters. Kinetic Monte-Carlo simulations based on a distributed model and experimental data have been utilized as references to verify the concentrated model.

Wave digital emulation of charge-or flux-controlled memristors

Memristors are passive elementary circuit elements, which essentially are resistors with memory. This property makes the memristor well suited for applications in neuromorphic computation circuits. In such circuits the functionality mainly depends on the memristor. Hence, different desired functionalities for the resulting circuit need appropriate devices. Normally, memristors are not commercially available. This makes the use of emulators, which mimic the memristive behavior, expedient. For this purpose, we introduce a method based on wave digital virtualization for emulating real memristors after identifying them from i-u-measurements. The so virtualized memristor can be directly integrated in a real circuit.

Sensitivity analysis of memristors based on emulation techniques

Memristors are novel elementary passive circuit elements, which behaves like a resistor with memory. Because of their similar functionalities with synapses in human brain, they are well suited for neuromorphic computation circuits. Noisy signals and parameter spreading are common in biological systems. Electronic circuits, including memristors for modeling biological systems, are equivalently exposed with these distortions. Both, noisy signals and parameter spreading can harm the functionality of such memristive circuits. A careful investigation needs reproducible sensitivity analysis with memristors. For this purpose, we use memristor emulators, based on the wave digital method, for sensitivity analysis. With this, we get a reproducible investigation method, which can be used in real circuits, before fabricating the real device.

Wave digital emulation of a double barrier memristive device

A memristor is a novel elementary passive device which is essentially a resistor with memory. This new device is capable of different technical applications like non-volatile memory, reconfigurable logic, and neuromorphic computation. Unfortunately, the commercial use of memristors is not common, which complicates the fabrication of devices with an arbitrarily desired functionality. This makes an investigation and development of real memristive circuits dedicated to a specific utilization very cumbersome. In order to circumvent these problems, we propose a wave digital memristor emulator, which is inherently passive like its analog counterpart. Due to its passivity even stable neuromorphic computation circuits with unpredictable interconnection structure can reliably be emulated.

Systematic derivation of reference circuits for wave digital modeling of passive linear partial differential equations

Finding an appropriate reference circuit, is an integral part of numerical integration using wave digital (WD) concepts. We show an approach for the systematic derivation of a canonical internally passive electrical circuit from a class of linear partial differential equations (PDEs). We present two methods to transform this circuit into a reference circuit, having a one-to-one corresponding wave digital structure. As an example, we deduce a reference circuit for a wave digital algorithm from Maxwells equations and depict simulation results.