Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

Non-Linear Digital Self-Interference Cancellation for In-Band Full-Duplex Radios Using Neural Networks

Full-duplex systems require very strong self-interference cancellation in order to operate correctly and a significant part of the self-interference signal is due to non-linear effects created by various transceiver impairments. As such, linear cancellation alone is usually not sufficient and sophisticated non-linear cancellation algorithms have been proposed in the literature. In this work, we investigate the use of a neural network as an alternative to the traditional non-linear cancellation method that is based on polynomial basis functions. Measurement results from a full-duplex testbed demonstrate that a small and simple feed-forward neural network canceler works exceptionally well, as it can match the performance of the polynomial non-linear canceler with significantly lower computational complexity.Comment: Presented at the IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 201

Reliable and Repeatable Power Measurements in DVB-T Systems

Non

The Multistep Beveridge-Nelson Decomposition

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper introduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge-Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge-Nelson trend is more efficient than the standard one in the presence of model misspecification and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.Trend and Cycle; Forecasting; Filtering.