A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

Data assimilation in slow-fast systems using homogenized climate models

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization model is derived for the slow dynamics. The reliability of this reduced climate model in reproducing the statistics of the slow dynamics of the full deterministic model for finite values of the time scale separation is numerically established. The statistics however is sensitive to uncertainties in the parameters of the stochastic model. It is investigated whether the stochastic climate model can be beneficial as a forecast model in an ensemble data assimilation setting, in particular in the realistic setting when observations are only available for the slow variables. The main result is that reduced stochastic models can indeed improve the analysis skill, when used as forecast models instead of the perfect full deterministic model. The stochastic climate model is far superior at detecting transitions between regimes. The observation intervals for which skill improvement can be obtained are related to the characteristic time scales involved. The reason why stochastic climate models are capable of producing superior skill in an ensemble setting is due to the finite ensemble size; ensembles obtained from the perfect deterministic forecast model lacks sufficient spread even for moderate ensemble sizes. Stochastic climate models provide a natural way to provide sufficient ensemble spread to detect transitions between regimes. This is corroborated with numerical simulations. The conclusion is that stochastic parametrizations are attractive for data assimilation despite their sensitivity to uncertainties in the parameters.Comment: Accepted for publication in Journal of the Atmospheric Science

Statistical signal processing of nonstationary tensor-valued data

Real-world signals, such as the evolution of three-dimensional vector fields over time, can exhibit highly structured probabilistic interactions across their multiple constitutive dimensions. This calls for analysis tools capable of directly capturing the inherent multi-way couplings present in such data. Yet, current analyses typically employ multivariate matrix models and their associated linear algebras which are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, this thesis uses the property of linear separability -- a notion intrinsic to multi-dimensional data structures called tensors -- as a linchpin to consider the probabilistic, statistical and spectral separability under one umbrella. This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems. We first introduce a new identifiable probability distribution which appropriately models the interactions between random tensors, whereby linear relationships are considered between tensor fibres as opposed to between individual entries as in standard matrix analysis. Unlike existing models, the proposed tensor probability distribution formulation is shown to yield a unique maximum likelihood estimator which is demonstrated to be statistically efficient. Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra. By introducing a model for the joint distribution of multiple random tensors, it is also possible to treat random tensor regression analyses and subspace methods within a unified separability framework. Practical utility of the proposed analysis is demonstrated through case studies over synthetic and real-world tensor-valued data, including the evolution over time of global atmospheric temperatures and international interest rates. Another overarching theme in this thesis is the nonstationarity inherent to real-world signals, which typically consist of both deterministic and stochastic components. This thesis aims to help bridge the gap between formal probabilistic theory of stochastic processes and empirical signal processing methods for deterministic signals by providing a spectral model for a class of nonstationary signals, whereby the deterministic and stochastic time-domain signal properties are designated respectively by the first- and second-order moments of the signal in the frequency domain. By virtue of the assumed probabilistic model, novel tests for nonstationarity detection are devised and demonstrated to be effective in low-SNR environments. The proposed spectral analysis framework, which is intrinsically complex-valued, is facilitated by augmented complex algebra in order to fully capture the joint distribution of the real and imaginary parts of complex random variables, using a compact formulation. Finally, motivated by the need for signal processing algorithms which naturally cater for the nonstationarity inherent to real-world tensors, the above contributions are employed simultaneously to derive a general statistical signal processing framework for nonstationary tensors. This is achieved by introducing a new augmented complex multilinear algebra which allows for a concise description of the multilinear interactions between the real and imaginary parts of complex tensors. These contributions are further supported by new physically meaningful empirical results on the statistical analysis of nonstationary global atmospheric temperatures.Open Acces

Impact of Spatial Filtering on Distortion from Low-Noise Amplifiers in Massive MIMO Base Stations

In massive MIMO base stations, power consumption and cost of the low-noise amplifiers (LNAs) can be substantial because of the many antennas. We investigate the feasibility of inexpensive, power efficient LNAs, which inherently are less linear. A polynomial model is used to characterize the nonlinear LNAs and to derive the second-order statistics and spatial correlation of the distortion. We show that, with spatial matched filtering (maximum-ratio combining) at the receiver, some distortion terms combine coherently, and that the SINR of the symbol estimates therefore is limited by the linearity of the LNAs. Furthermore, it is studied how the power from a blocker in the adjacent frequency band leaks into the main band and creates distortion. The distortion term that scales cubically with the power received from the blocker has a spatial correlation that can be filtered out by spatial processing and only the coherent term that scales quadratically with the power remains. When the blocker is in free-space line-of-sight and the LNAs are identical, this quadratic term has the same spatial direction as the desired signal, and hence cannot be removed by linear receiver processing

Sensitive White Space Detection with Spectral Covariance Sensing

This paper proposes a novel, highly effective spectrum sensing algorithm for cognitive radio and whitespace applications. The proposed spectral covariance sensing (SCS) algorithm exploits the different statistical correlations of the received signal and noise in the frequency domain. Test statistics are computed from the covariance matrix of a partial spectrogram and compared with a decision threshold to determine whether a primary signal or arbitrary type is present or not. This detector is analyzed theoretically and verified through realistic open-source simulations using actual digital television signals captured in the US. Compared to the state of the art in the literature, SCS improves sensitivity by 3 dB for the same dwell time, which is a very significant improvement for this application. Further, it is shown that SCS is highly robust to noise uncertainty, whereas many other spectrum sensors are not

A Linear Subspace Approach to Burst Communication Signal Processing

This dissertation focuses on the topic of burst signal communications in a high interference environment. It derives new signal processing algorithms from a mathematical linear subspace approach instead of the common stationary or cyclostationary approach. The research developed new algorithms that have well-known optimality criteria associated with them. The investigation demonstrated a unique class of multisensor filters having a lower mean square error than all other known filters, a maximum likelihood time difference of arrival estimator that outperformed previously optimal estimators, and a signal presence detector having a selectivity unparalleled in burst interference environments. It was further shown that these improvements resulted in a greater ability to communicate, to locate electronic transmitters, and to mitigate the effects of a growing interference environment

5GNOW: Challenging the LTE Design Paradigms of Orthogonality and Synchronicity

LTE and LTE-Advanced have been optimized to deliver high bandwidth pipes to wireless users. The transport mechanisms have been tailored to maximize single cell performance by enforcing strict synchronism and orthogonality within a single cell and within a single contiguous frequency band. Various emerging trends reveal major shortcomings of those design criteria: 1) The fraction of machine-type-communications (MTC) is growing fast. Transmissions of this kind are suffering from the bulky procedures necessary to ensure strict synchronism. 2) Collaborative schemes have been introduced to boost capacity and coverage (CoMP), and wireless networks are becoming more and more heterogeneous following the non-uniform distribution of users. Tremendous efforts must be spent to collect the gains and to manage such systems under the premise of strict synchronism and orthogonality. 3) The advent of the Digital Agenda and the introduction of carrier aggregation are forcing the transmission systems to deal with fragmented spectrum. 5GNOW is an European research project supported by the European Commission within FP7 ICT Call 8. It will question the design targets of LTE and LTE-Advanced having these shortcomings in mind and the obedience to strict synchronism and orthogonality will be challenged. It will develop new PHY and MAC layer concepts being better suited to meet the upcoming needs with respect to service variety and heterogeneous transmission setups. Wireless transmission networks following the outcomes of 5GNOW will be better suited to meet the manifoldness of services, device classes and transmission setups present in envisioned future scenarios like smart cities. The integration of systems relying heavily on MTC into the communication network will be eased. The per-user experience will be more uniform and satisfying. To ensure this 5GNOW will contribute to upcoming 5G standardization.Comment: Submitted to Workshop on Mobile and Wireless Communication Systems for 2020 and beyond (at IEEE VTC 2013, Spring

Noise conversion of Schottky diodes in mm-wave detectors under different nonlinear regimes: modeling and simulation versus measurement

This paper presents and discusses several methods for predicting the low-frequency (LF) noise at the output of a mm-wave detector. These methods are based on the extraction of LF noise source parameters from the single diode under a specific set of bias conditions and the transfer or conversion of these noise sources, under different operating conditions including cyclostationary regime, to the quasi-dc output of a mm-wave detector constructed with the same model of diode. The noise analysis is based on a conversion-matrix type formulation, which relates the carrier noisy sidebands of the input signal with the detector output spectrum through a pair of transfer functions obtained in commercial software. Measurements of detectors in individual and differential setups will be presented and compared with predictions.The authors would like to thank the Spanish Ministry of Science and Innovation (MICINN) for the financial support provided through projects TEC2011-29264-C03-01, CONSOLIDER-INGENIO CSD2008-00068 (TERASENSE), TEC2014-58341-C4-1-R, FEDER co-funding, CONSOLIDER-INGENIO CSD2010-00064 and the University of Cantabria Industrial Doctorate programme 2014, project: “Estudio y Desarrollo de Tecnologías para Sistemas de Telecomunicación a Frecuencias Milimétricas y de Terahercios con Aplicación a Sistemas de Imaging en la Banda 90–100 GHz”