Leonard Schulz

Leonard Schulz, Jürgen Vollmer, Miguel D. Mahecha et al.

Understanding the dynamics of the land-atmosphere exchange of CO$_2$ is key to advance our predictive capacities of the coupled climate-carbon feedback system. In essence, the net vegetation flux is the difference of the uptake of CO$_2$ via photosynthesis and the release of CO$_2$ via respiration, while the system is driven by periodic processes at different time-scales. The complexity of the underlying dynamics poses challenges to classical decomposition methods focused on maximizing data variance, such as singular spectrum analysis. Here, we explore whether nonlinear data-driven methods can better separate periodic patterns and their harmonics from noise and stochastic variability. We find that Nonlinear Laplacian Spectral Analysis (NLSA) outperforms the linear method and detects multiple relevant harmonics. However, these harmonics are not detected in the presence of substantial measurement irregularities. In summary, the NLSA approach can be used to both extract the seasonal cycle more accurately than linear methods, but likewise detect irregular signals resulting from irregular land-atmosphere interactions or measurement failures. Improving the detection capabilities of time-series decomposition is essential for improving land-atmosphere interactions models that should operate accurately on any time scale.

Leonard Paul Schulz, Stefan Schwarz, Gerhard Bauch

Cooperative massive multiple-input multiple-output (MIMO) promises large gains over cellular deployments, but existing comparisons of different architectures often mix antenna distribution, inter-site coordination, and processing assumptions. This paper introduces a graph-based framework for fair comparison of cellular, coordinated, and cell-free massive-MIMO systems. We differentiate between two key properties, namely antenna distribution and inter-site cooperation, which yields seven representative system types. We derive compatible uplink and downlink spectral efficiency (SE) expressions, including an uplink bound for detectors with mixed instantaneous and statistical effective channel state information (CSI), and adapt scalable user association and processing rules to all considered architectures. We evaluate these systems using extensive numerical simulations and show that for a fair comparison much larger simulation areas (at least 2.5 $\times$ 2.5 km2) than commonly used are required. We introduce the relative capacity, which measures how closely each architecture approaches centralized cell-free processing. The results show that coordinated, phase-aligned beamforming across spatially distributed antennas is the main source of cooperation gains. In dense deployments with few antennas per access point (AP), coordinated Distributed Antenna System (DAS) and hybrid cell-free architectures achieve much of the centralized cell-free performance while requiring substantially weaker midhaul assumptions.