Sander Wahls

Coordinated Multipoint Trials in the Downlink

Coordinated multi-point (CoMP) is a new class of transmission schemes for interference reduction in the next generation of mobile networks. We have implemented and tested a distributed CoMP transmission approach in the downlink of an LTE-Advanced trial system operating in real time over 20 MHz bandwidth. Enabling features such as network synchronization, celland user-specific pilots, feedback of multicell channel state information and synchronous data exchange between the base stations have been implemented. Interferencelimited transmission experiments have been conducted using optimum combining with interference-aware link adaptation and cross-wise interference cancellation between the cells. The benefits of CoMP transmission have been studied over multi-cell channels recorded in an urban macro-cell scenario.

Field trials using coordinated multi-point transmission in the downlink

We report on field trials using CoMP transmission in the downlink of a mobile radio network. Two new features enable over-the-air CoMP transmission from physically separated base stations and terminals. These are distributed synchronization and a fast virtual local area network. Using VLAN tags, terminals feed back the multi-cell channel state information to their serving bases where it is multiplexed with shared data. Both are multicast to other cooperative base stations over the backhaul. In our trials, two terminals are served in two overlapping cells and placed in specific indoor, outdoor-to-indoor and outdoor scenarios. We have realized both intra-site as well as inter-site CoMP. While outage is indeed a big problem at the cell edge with full frequency reuse, with CoMP it is not observed anymore. Average throughput gains by factors 4 to 22 are observed when using CoMP compared to interference-limited transmission while between 27 and 78% of the isolated cell throughput is measured in both cells simultaneously.

Fast Numerical Nonlinear Fourier Transforms

The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schrödinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them - at least from a theoretical point of view. Although numerical algorithms are available for computing the transform, a fast nonlinear Fourier transform that is similarly effective as the fast Fourier transform is for computing the common Fourier transform has not been available so far. The goal of this paper is to address this problem. Two fast numerical methods for computing the nonlinear Fourier transform with respect to the NSE are presented. The first method achieves a runtime of O(D2) floating point operations, where D is the number of sample points. The second method applies only to the case where the NSE is defocusing, but it achieves an O(D log2 D) runtime. Extensions of the results to other evolution equations are discussed as well.

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

The nonlinear Fourier transform is a transmission and signal processing technique that makes positive use of the Kerr nonlinearity in optical fibre channels. I will overview recent advances and some of challenges in this field.

Introducing the fast nonlinear Fourier transform

The nonlinear Fourier transform (NFT; also: direct scattering transform) is discussed with respect to the focusing nonlinear Schrödinger equation on the infinite line. It is shown that many of the current algorithms for numerical computation of the NFT can be interpreted in a polynomial framework. Finding the continuous spectrum corresponds to polynomial multipoint evaluation in this framework, while finding the discrete eigenvalues corresponds to polynomial root finding. Fast polynomial arithmetic is used in order to derive algorithms that are about an order of magnitude faster than current implementations. In particular, an N sample discretization of the continuous spectrum can be computed with only O(N log2 N) flops. A finite eigenproblem for the discrete eigenvalues that can be solved in O(N2) is also presented. The feasibility of this approach is demonstrated in a numerical example.

Realtime Multi-User Multi-Antenna Downlink Measurements

In this paper, we present real-time broadband multi-user multi-antenna measurements in typical indoor and outdoor scenarios. For the first time, essential frequency-selective functions of a new medium access control (MAC) layer, namely fair resource assignment to multiple users, spatial mode selection and adaptive modulation, have been implemented in real-time on standard digital signal processing hardware. The new MAC layer is steered over wireless feedback and control channels in a closed loop manner. Our implementation uses parameters close to the forthcoming long-term evolution (LTE) of the 3G air interface, thus illustrating the feasibility of the new functions in next-generation cellular radio systems. The paper describes our real-time implementation and reports several test results. Benefits of the frequency-selective multi-user MIMO MAC are validated in realistic mobile propagation environments.

Model-based sensor-less wavefront aberration correction in optical coherence tomography

Several sensor-less wavefront aberration correction methods that correct nonlinear wavefront aberrations by maximizing the optical coherence tomography (OCT) signal are tested on an OCT setup. A conventional coordinate search method is compared to two model-based optimization methods. The first model-based method takes advantage of the well-known optimization algorithm (NEWUOA) and utilizes a quadratic model. The second model-based method (DONE) is new and utilizes a random multidimensional Fourier-basis expansion. The model-based algorithms achieve lower wavefront errors with up to ten times fewer measurements. Furthermore, the newly proposed DONE method outperforms the NEWUOA method significantly. The DONE algorithm is tested on OCT images and shows a significantly improved image quality.

Digital backpropagation in the nonlinear Fourier domain

Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schrödinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only O(D log2 D) floating point operations to backpropagate a signal given by D samples, independently of the fibers length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations.

Zero-forcing precoding for frequency selective MIMO channels with H∞ criterion and causality constraint

We consider zero-forcing equalization of frequency selective multiple-input multiple-output (MIMO) channels by causal and linear time-invariant precoders in the presence of intersymbol interference. Our motivation is twofold. First, we are concerned with the optimal performance of causal precoders from a worst case point of view. Therefore we construct an optimal causal precoder, where contrary to other works our construction is not limited to finite or rational impulse responses. Moreover, we derive a novel numerical approach to computation of the optimal performance index achievable by causal precoders. This quantity is important in the numerical determination of optimal precoders.

Measurements of multi-antenna gains using a 3GPP-LTE air interface in typical indoor and outdoor scenarios

In this paper we report the first real-time measurements of a 3GPP-LTE multiple antenna system in typical indoor and outdoor scenarios. In a single cell, single user scenario we demonstrate throughput exceeding 100 Mbit/s with a 2times2 MIMO configuration. This throughput gain is significant as compared to existing single antenna systems. We describe the basic LTE system design and prototype ingredients which were implemented to achieve these results. The highlight of our MIMO-OFDM system design is frequency dependent link adaptation. In principle, we show that this parallel link adaptation provides robust gains in a cellular broadband system. The robustness is seen in both our indoor and outdoor measurement results. The key feature of our work is implementation of multiple antenna concepts in such a broadband system.