Christian A. Hofmann

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23ranked-venue papers
9as first author
10since 2021 · last 2025
0000-0001-8421-4433ORCID · verified

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Computer networks · 17 · 7 first-author · 8 since 2021
YearPublicationVenuePosition
2025 Propagation Measurements and Models for 14 GHz FR3 and Starlink Coexistence
abstract
Under the evolution of 6G, the spectrum crunch for new frequencies has introduced the discussion of the 7-24 GHz spectrum, referred to as FR3, for mobile network usage. This spectrum is traditionally known as the dedicated operating frequency for satellite communication, particularly in the Ku-Band (12-18 GHz). To date, little is known about the coexistence of these two entities within the FR3 spectrum and the propagation environment in this frequency range. This paper presents measurements in the 14-14.5GHz spectrum for an outdoor channel scenario, conducted using both a reference communication chain with a low-gain isotropic antenna and a commercially available, highly directive, electronically steerable Starlink user terminal. Evaluations were performed for the received power from the reference antenna, alongside parallel measurements of spurious emissions from the Starlink terminal. In conclusion, this work provides measurements and path loss models to support future investigations of the 14 GHz spectrum for FR3 usage.
Kevin T. Li, Christian A. Hofmann, Andreas Knopp
ICC2
2025 Time, Frequency, and Phase Synchronization in Satellite Swarms
abstract
This paper presents a master-slave architecture for time, frequency and phase synchronization, implemented in a closed-loop system with an RF inter-satellite link. This addresses the emerging need for accurate and cost-effective synchronization in swarm satellite networks. The design relies on a single reference clock, eliminating the need for unsynchronized local oscillators at secondary nodes. Moreover, it proposes an inherently relative range measurement method between the satellites based on phase unwrapping. Performance analysis, focused on phase accuracy, confirms the system's suitability for satellite swarms in applications like communications and remote sensing. A comprehensive analysis offers additional guidelines for implementation and future research.
Daniel Weinzierl, Christian A. Hofmann, Andreas Knopp
ICC2
2024 Evaluation and Analysis of Interference in NGSO Mega-Constellations in a Multi-Beam Satellite Scenario
abstract
The growing interest in space-based broadband internet, propelled by the rapid expansion of mega-constellations, amplifies the mounting concerns about interference and spectral coexistence for both operators and users. Given the complexity of these systems, deriving reliable estimates for data rates and interference typically requires labor-intensive simulations. However, recent advancements have introduced analytical methods rooted in stochastic geometry to assess system performances. Building on these insights, our work aims to precisely evaluate interference in these systems, focusing on adjacent satellite interference and multi-beam inter-cell interference. Significantly, we introduce a more refined estimation of these effects based on the nature of highly directive antennas, an aspect missing in current literature. We, therefore, propose numerical approximations for these key values detrimental to high-speed telecommunication systems. We present simulation results to validate our analytical approach and share numerical findings from our proposal to offer deeper insight into mega-constellation systems and designs.
Kevin T. Li, Christian A. Hofmann, Andreas Knopp
VTC Fall2
2022 Machine Learning-based Flexible Payload Power Resource Allocation for Non-orthogonal SATCOM
abstract
To meet the actual traffic demand, this work applies machine learning-based flexible payload power resource-allocation for non-orthogonal SATCOM. Specifically, a tailored deep neural network (DNN) architecture with a customized loss function is trained to intelligently allocate payload power resources among both the beams and users, by learning the undercover structure of its input (i.e., unsupervised learning). Since the DNN-based scheme doesn't need signaling and real-time information exchange between the gateways and the users, it can significantly decrease the implementation complexity by employing the channel statistics of users in multibeam SATCOM. Moreover, the DNN-based scheme can be trained as a universal approximator of the payload power resource-allocation agent for any unseen satellite channel and has the potential for a real-time operation with reduced implementation complexity, compared to the mathematical optimization-based scheme. Numerical results show the DNN-based scheme achieves comparable performance.
Christian A. Hofmann, Andreas Knopp
GLOBECOM2
2022 Ka-Band LEO Satellite Internet of Things Channel Characterization: Survey and Measurement
abstract
In this work, the LEO Land Mobile Satellite (LMS) channel at Ka-band is studied. This work firstly reviews existing Ka-band LMS channel models and measurements, which are mostly related to model the dynamic characteristics for LEO satellite communications, specifically in a restrictive small satellite platform. Moreover, as pervasive satellite Internet of Things (IoT) networks involve on-ground users with low-gain and non-directional antennas, multipath effects cause a frequency selective fading of the received signal. Although extensive propagation experiments are carried out for Ka-band LMS systems, experimental characterizations and studies on multipath effects are lacking. Therefore, this work aims to address this limitation by considering the critical issue of the multipath effects on the Ka-band LEO propagation channel. Hence, we present the results of recent propagation experiments and investigate the multipath effects on Ka-band LEO SATCOM links. The results show comparably large values for the delay spread especially in mountainous scenarios. It is further revealed that results on the multipath propagation that are derived from terrestrial measurements may not be transformed to the LEO satellite channel without the need for adaption.
Christian A. Hofmann, Andreas Knopp
ICC2
2022 Phase Noise Limits in Low-Rate Communication via Satellite
abstract
In the Internet of Remote Things (IoRT), when satellite communication (SATCOM) is the preferred or the only available connection for Internet of Things (IoT)-devices, massive machine type communication (mMTC) is enabled by upcoming and established systems using sophisticated multiple access (MA) techniques. To close the radio link between compact and battery-powered devices, very low symbol rates must be chosen in many cases, due to the constraints of the link budget. If at the same time MA interference must be tolerated, orthogonal signaling with successive interference cancellation (SIC) receivers is usually the physical layer technology of choice in many IoT solutions. While SIC has been investigated for medium and high data rates, phase noise (PN) poses additional challenges for very low data rate transmission. We derive a general performance estimation applicable to SIC-based transmission schemes under PN with different levels of orthogonality between the user signals. Realistic values for the PN are derived from a PN model that includes all relevant PN processes and is parametrized by measurements of the Allan variance of real hardware. It is shown that PN strongly limits the performance of systems with high orthogonality at symbol rates below 1 kHz, while systems with less orthogonal transmit signals and lower spreading gain are more robust.
Christian A. Hofmann, Andreas Knopp
IEEE Internet Things J.1
2022 Distributed Resource Optimization for NOMA Transmission in Beamforming SATCOM
abstract
This work studies the application of nonorthogonal transmission in beamforming (BF) based forward links for next-generation satellite communication (SATCOM) with multiple gateways. With the aim of enhancing the throughput of BF SATCOM systems, the state-of-the-art nonorthogonal multiple access (NOMA) technique is exploited by serving multiple users per beam in the same time slot. In this regard, the feeder link limitations and multibeam satellite payload constraints must be considered for BF design and power allocation (PA) optimization in nonorthogonal SATCOM. To address these challenges, distributed resource optimization strategies are investigated for BF and flexible payload power resource allocation in multigateway (multi-GW) nonorthogonal SATCOM systems. Specifically, a per-feed available power-constrained BF strategy via maximization of the worst-user signal-to-leakage-and-noise ratio (SLNR) is explored with local channel state information (CSI) for a distributed operation of GWs. As an upper-bound performance limit, a centralized multilayer BF strategy is processed in a central unit with full global CSI and data sharing. After the BF direction optimization, a weighted sum-rate maximization-based (WSRM-based) power resource optimization strategy is locally applied at each GW to efficiently use the power resources for higher performance increment. The nonconvex WSRM problem, under the constraints of the practical satellite payload power budget, successful successive interference cancellation (SIC) decoding, and minimum data rate, is recast into an equivalent weighted sum-MSE minimization (WMMSE) counterpart for a tractable solution. Finally, an efficient user scheduling is designed to enable the operator to capture a substantial system-throughput gain. Accurate simulations are conducted with the near-to-real coverage area (footprints), the random distributions of users, and interference, relying on geographical locations of users. The results over a realistic simulation environment show the efficiency of our strategies.
Christian A. Hofmann, Andreas Knopp
IEEE J. Sel. Areas Commun.2
2021 Impact of Phase Noise and Oscillator Stability on Ultra-Narrow-Band-IoT Waveforms for Satellite
abstract
It has been shown that ultra-narrow-band (uNB) massive machine type communication using very compact devices with direct access to satellites is possible at ultra low rate. This enables global ubiquitous coverage for terminals without terrestrial service in the Internet of Remote Things and provides access to any satellite up to the the geostationary earth orbit. The lower data rate for waveforms providing uNB communication is set by the stability and the phase noise of the applied oscillators. In this paper we analyze the physical layer of two candidate waveforms, which are LoRa and Unipolar Coded Chirp-Spread Spectrum (UCSS) with respect to phase noise and oscillator frequency drifts. It is figured out that UCSS is more robust against linear frequency drifts, which is the main source of error for uNB transmissions.
Christian A. Hofmann, Kai-Uwe Storek, Andreas Knopp
ICC1
2021 Performance Optimization for Multi-Gateway NOMA-Beamforming in Multi-Beam SATCOM
abstract
To provide high throughput of beamforming (BF) based forward links in multi-beam satellite communication (SATCOM), the state-of-the-art non-orthogonal multiple access (NOMA) technique has been explored, by serving multiple users per beam in the same time slot. Nevertheless, the feeder link limitations and satellite payload constraints need to be considered for BF design and power allocation (PA) optimization in NOMA based transmission. To tackle these challenges, performance optimization algorithms are investigated for applying NOMABF in the upcoming multiple gateway (multi-GW) architectures. Specifically, centralized multi-layer BF is first processed in a central unit with full global channel state information (CSI) and data sharing, which is considered as an upper-bound performance. Next, per-feed available power-constrained BF via maximization of the worst-user signal-to-leakage-and-noise ratio (SLNR) is explored with local CSI for a distributed operation of GWs. Then, weighted sum-rate maximization (WSRM) based PA is applied to optimally use the power resources for more performance increment, where the non-convex WSRM problem is recast into an equivalent weighted sum mean square error minimization (WMMSE) problem for a tractable solution. Simulation results reveal the efficiency of our proposal.
Christian A. Hofmann, Andreas Knopp
ICC2
2021 Techno-Economic Design Aspects of Satellite Mega-Constellations for 6G Services
abstract
6th Generation (6G) Non- Terrestrial Networks (NTN) prove to be the next step for integrating satellites into existing communication network infrastructure. Moreover, mega-constellations will play a predominant role in this integration. With the success of disruptive and innovative constellations, such as Starlink and OneWeb, a highly competitive field of commercial broadband satellite internet is currently established. In this paper, we introduce a novel technological framework demonstrating the economic performance indicators of mega-constellations to compete with the existing terrestrial broadband internet market. Furthermore, we implement a comprehensive economic model to measure the influence of technology on decreasing the costs in mega-constellations and compare the technological parameters in their cost reduction efficiency. Our analysis enables the identification of main cost drivers in the technical design of mega-constellations, independently of the applied waveform or transmission standard. By optimizing these cost drivers, mega-constellations can achieve a cost regime comparable to terrestrial competitors to secure their participation in future integrated 6G networks.
Kevin T. Li, Christian A. Hofmann, Florian Völk, Andreas Knopp
VTC Fall2
2020 Tracking of Remote IoT Devices by Satellite Assisted Geolocation
abstract
In previous work, it has been shown that massive machine type communication (mMTC) is possible with direct access to satellites in the geostationary earth orbit (GEO) using very compact Internet of Things (IoT) devices. The non-directive antenna of preferably small terminals restricts the transmit power to limit the interference for other satellites. The ultra narrow-band (uNB)-IoT signals received by adjacent satellites are used in this paper for the geolocation of the transmitter. By this, the amount of data is reduced if the position of the sender shall be transmitted. We investigate the accuracy of remote geolocation of IoT devices transmitting short bursts at low power directly to GEO satellites. We further derive the geolocation error in latitudinal and longitudinal directions and calculate the required amount of information to be transmitted to achieve a desired resolution for the position information of the tracked object. For a typical scenario, we find that 35% to 63% of the transmitted bits could be saved, which results in a huge saving of transmit energy of battery powered small devices in the Internet of Remote Things (IoRT).
Christian A. Hofmann, Andreas Knopp
ICC1
2019 Ultranarrowband Waveform for IoT Direct Random Multiple Access to GEO Satellites
abstract
Direct access of small terminals in the Internet of Things (IoT) to geostationary satellites may provide wide coverage and almost 100% availability for remote locations without access to terrestrial networks. However, existing waveforms and IoT solutions do not close the link to the geostationary earth orbit (GEO) for massively deployed small devices. We present a novel modulation and signaling scheme based on chirp-spread spectrum (CSS) that enables reliable transmission at ultra low bit-rate. The proposed structure for the transmit signal applies unipolar codes in a novel manner, which allows random multiple access to a common channel for a large number of devices. Further, the transmit signal is designed to allow robust signal detection with low effort even at high carrier frequency offsets. We propose a system concept for the receiver including synchronization, and provide the results of extensive simulations carried out on system and link levels. As a result, we demonstrate that the proposed scheme, referred to as unipolar-coded CSS (UCSS), enables true random multiple access for a very large number of devices, closing the challenging link between IoT devices and satellites in the GEO even at high carrier frequencies from C-band to Ka-Band.
Christian A. Hofmann, Andreas Knopp
IEEE Internet Things J.1
2017 Joint MMSE precoder and equalizer for massive MIMO using 1-bit quantization
abstract
We present a novel linear minimum-mean-squared-error (MMSE) joint precoding and equalization technique for a downlink (DL) massive multiple-input-multiple-output (MIMO) scenario. To lower the power consumption, the computational and the design complexity, 1-bit digital to analog converters (DACs) and analog to digital converters (ADCs) are used at the transmitter and at the receiver antennas. These economical and computational gains come at the cost of a performance loss which can be recovered by the large number of antennas deployed at the base station and by implementing appropriate precoders and equalizers which can mitigate the coarse quantization effects. The proposed technique implements a two-stage digital and an analog precoder with a digital equalizer, both of which take into account the effects of the 1-bit quantizers. The simulation results indicate the superiority of the novel joint precoder and equalizer design to the previously proposed linear precoders and equalizers not only in terms of the uncoded bit error rate (BER) performance but also in terms of the robustness to errors in the estimation of channel state information at the transmitter (CSIT).
Ovais Bin Usman, Josef A. Nossek, Christian A. Hofmann, Andreas Knopp
ICC3
2016 Spatial MIMO over satellite: A proof of concept
abstract
If multiple-input multiple-output (MIMO) satellite communications (SATCOM) systems use spatial multiplexing instead of polarization multiplexing, the channel capacity depends on the geometrical conditions of the antenna setup. This theoretical result is proven and confirmed for the first time by a true-MIMO measurement campaign. We utilize two Ku-band satellites and a ground station with two antennas as a 2 × 2 MIMO SATCOM probing system. The channel capacity is estimated and compared to its theoretical prediction. Moreover, an error analysis is provided for the capacity estimation.
Christian A. Hofmann, Kai-Uwe Storek, Robert T. Schwarz, Andreas Knopp
ICC1
2015 Impact of the Atmosphere on the Signal Phase and the Channel Capacity in EHF MIMO Satellite Links
abstract
Multiple-input multiple-output (MIMO) satellite systems are currently under intensive research due to their enormous potential to improve the link capacity. The key to achieve high multiplexing gains are the fine tuned phase relations inside the MIMO channel matrix. These relations are realized by a smart placement of the ground station antennas. However, the signal phase of a space- earth link is influenced by atmospheric distortions. Therefore measurements of the signal phase from related field campaigns are analyzed and examined regarding their relevance for the capacity prediction of real MIMO satellite links. Further, the impact of these phase distortions with respect to the resulting ergodic capacity and to the complementary cumulative distribution function of the channel capacity is investigated. Simulations point out only minor performance losses under the expectable conditions. Nevertheless, for a reliable forecast of MIMO satellite communication systems, additional measurements are needed.
Kai-Uwe Storek, Christian A. Hofmann, Andreas Knopp
GLOBECOM2
2015 Measurement and modeling of the UHF satellite channel for animal tracking systems
abstract
In contrast to present space communication systems in the Ultra-High-Frequency (UHF) band, like military communications or communication to space crafts, present and upcoming animal tracking systems introduce a novel UHF propagation channel with a larger bandwidth, low-gain antennas and new challenging propagation scenarios like for example the forest. The ground reflection, as a phenomenon of wave propagation, is relevant in this scenario. Unlike other multipath components with larger excess delays or lower power, the ground reflection cannot be equalized; even not at large system bandwidths. In this paper, the relevance of the ground reflection for animal tracking systems is proven by measurement and simulation. Further results from a measurement campaign are presented, where the forest as a novel scenario is included. A statistical model is provided to predict the received signal power, and to estimate the required additional fading margin to close the link of UHF animal tracking systems in the presence of a reflected signal from the ground.
Christian A. Hofmann, Robert T. Schwarz, Andreas Knopp
ICC1
2015 Interferometer for Measurements of the MIMO Satellite Channel at Ku-Band
abstract
We present a novel interferometer for the accurate measurement of the channel transfer matrix of future multiple-input multiple-output (MIMO) satellite communication (SATCOM) systems. The capacity of such a SATCOM system heavily depends on the phase relations inside the channel matrix. Above 10 GHz, these phase relations are affected and determined by tropospheric perturbations when the signal passes through the atmosphere. To measure the transfer matrix of the signal phase with sufficient accuracy, the interferometer must provide a fine temporal resolution. The paper shows a low-cost measurement approach at Ku-band with remarkable precision as well as the first results of the measurement campaign.
Kai-Uwe Storek, Christian A. Hofmann, Andreas Knopp
VTC Fall2
2010 Indoor LOS MIMO Channel Measurements with a Focus on Antenna Array Design
abstract
The bandwidth efficiency of Multiple Input - Multiple Output (MIMO) channels with different antenna arrays is analyzed. MIMO channels with a strong and unobstructed line-of-sight (LOS) signal component are considered, as it is the case in indoor in-room scenarios. The bandwidth efficiency of such channels is strongly dependent upon the applied antenna array and its orientation. Simulations of the pure LOS channel without multipath components are carried out to demonstrate this effect. So called polyhedron antenna arrays with antenna elements mounted on the faces of a regular polyhedron as well as the MIMO Cube deliver a bandwidth efficiency that is almost invariant from rotations of the antenna arrays. The measurement results verify this result. Polyhedron arrays appear to be a good alternative for MIMO systems, as the measured bandwidth efficiency of a polyhedron array is comparable to this of an uniform linear array (ULA), while the standard deviation is reduced to a large extend.
Christian A. Hofmann, Andreas Knopp, Berthold Lankl
GLOBECOM1
2009 Amplify-and-forward relay stations in correlated line-of-sight indoor MIMO channels
abstract
The bandwidth efficiency of Multiple Input - Multiple Output (MIMO) channels is analyzed for point-to-point (P2P) and relay channels. The focus lies on channels with a strong and unobstructed line-of-sight (LOS) signal component between transmitter (Tx) and receiver (Rx), as it is the case in indoor in-room scenarios. The bandwidth efficiency of the resulting correlated P2P MIMO channel is strongly dependent upon the geometrical antenna setup. Especially the angle of arrival (AOA) and the inter-array antenna spacing of uniform linear arrays (ULAs) influence the bandwidth efficiency. Both influences are minimized by the use of distributed simple amplify-and-forward relay stations, while the resulting relay MIMO channel is correlated. In the relay case, the total transmit power spent at the Tx and the relay is limited to the transmit power of the Tx in the P2P case for a fair comparison. Relay stations are capable to enhance the bandwidth efficiency of the pure LOS MIMO channels, while the high bandwidth efficiency of channels with LOS and non line-of-sight (NLOS) signal components is not further increased in the considered scenario.
Christian A. Hofmann, Andreas Knopp, Dirk Ogermann, Berthold Lankl
PIMRC1
2008 Satellite System Design Examples for Maximum MIMO Spectral Efficiency in LOS Channels
abstract
MIMO satellite links have recently attracted a high interest with respect to possible link capacity enhancements. In it has been shown that especially in Line-of-Sight (LOS) satellite channels maximum multiplexing gain can be achieved via the construction of orthogonal channels by means of the geometrical arrangement of the ground terminal antennae in relation to the antennae in orbit. Based on these theoretical results, we present practically relevant design and configuration examples for satellite communication systems, involving transparent pay loads for the first time. Thus, we significantly extend the results, that have been limited to regenerative payloads. The examples cover multiple-satellite and single-satellite MIMO scenarios. The assets and drawbacks of the applications are investigated, especially highlighting system-inherent design uncertainties.
Andreas Knopp, Robert T. Schwarz, Dirk Ogermann, Christian A. Hofmann, Berthold Lankl
GLOBECOM4
2008 Deficiencies of common MIMO channel models with regard to indoor Line-of-Sight channels
abstract
Different multiple input - multiple output (MIMO) channel models are analyzed with regard to the indoor line-of-sight (LOS) MIMO channel. In the literature this channel is proven to achieve high capacities while being highly correlated. The modeling results from physical as well as analytical models are compared with measured channels, showing that none of the established models is exactly suitable for the considered indoor LOS MIMO channel. However, there is a promising approach that applies an extended Saleh model in conjunction with the physically correct spherical wave propagation. Although in its current state this basic approach cannot be regarded as a complete MIMO channel model, at least it provides an adequate origin for the correct prediction of MIMO capacities in different types of LOS channels. This is due to the fact, that the crucial prerequisites for an appropriate LOS MIMO channel model, which are by name the application of the physically correct spherical wave propagation, the correct modeling of the high correlation in LOS channels and the inclusion of the geometrical antenna setup, are regarded correctly. Contrarily, these prerequisites are included in none of the current models that are widely accepted in MIMO radio communications nowadays. The proof of this statement using measured data is a major objective of this paper.
Christian A. Hofmann, Andreas Knopp, Dirk Ogermann, Robert T. Schwarz, Berthold Lankl
PIMRC1
2007 Exploiting Single SISO Impulse Responses to Predict the Capacity of Correlated MIMO Channels
abstract
A novel strategy of precalculating potential MIMO spectral efficiencies of correlated channels based on both, measured as well as appropriately modeled SISO channel impulse responses is presented. Besides capacity prediction, the model is capable of comprising the physical nature of the channel in form of its frequency response. The method is applied to indoor MIMO channels where the correlation is introduced mainly by a strong LOS signal component coinciding with low mobility. A spherical wave model is applied and the distributions of angle of arrival and angle of departure turn out to be important modeling parameters. The modeled MIMO capacities are compared to measured capacity records for verification, proving high accuracy.
Andreas Knopp, Christian A. Hofmann, Mohamed Chouayakh, Berthold Lankl
GLOBECOM2
2007 Extension of Indoor SISO Propagation Models for Correlated MIMO Channels - An Exemplification Applying Saleh's Model
abstract
A novel strategy for the modeling of indoor MIMO channels based on a spatial extension of appropriate SISO channel models is presented. The approach enables a precalculation of potential MIMO spectral efficiencies within a particular environment from the SISO channel information while taking into account the correlation of the MIMO channel. The objective measure is given by the spatial probability distribution of the MIMO capacity which is to be predicted correctly. The method is exemplified by Saleh's popular SISO indoor channel model. However, the approach is not limited to this SISO model. In order to practically verify the method, firstly, the key parameters for the SISO model are derived from measured data, before the extension to the MIMO channel model is performed. Finally, the spatial cumulative distribution function, which is predicted by the model is compared to its counterpart which was derived using a fast MIMO radio channel sounder. In the measurements a strong line-of-sight (LOS) signal component was always present resulting in correlated entries within the MIMO channel matrix. For the accurate capacity modeling in such correlated channels, the characterization of the LOS signal part by a spherical wave model is a crucial prerequisite.
Andreas Knopp, Christian A. Hofmann, Mohamed Chouayakh, Berthold Lankl
PIMRC2