Spectral estimation on a sphere in geophysics and cosmology

We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the one-dimensional (1-D) periodogram, (ii) the maximum likelihood method, and (iii) a spherical analogue of the 1-D multitaper method. The periodogram exhibits strong spectral leakage, especially for small regions of area $A\ll 4\pi$, and is generally unsuitable for spherical spectral analysis applications, just as it is in 1-D. The maximum likelihood method is particularly useful in the case of nearly-whole-sphere coverage, $A\approx 4\pi$, and has been widely used in cosmology to estimate the spectrum of the cosmic microwave background radiation from spacecraft observations. The spherical multitaper method affords easy control over the fundamental trade-off between spectral resolution and variance, and is easily implemented regardless of the region size, requiring neither non-linear iteration nor large-scale matrix inversion. As a result, the method is ideally suited for most applications in geophysics, geodesy or planetary science, where the objective is to obtain a spatially localized estimate of the spectrum of a signal from noisy data within a pre-selected and typically small region.Comment: Submitted to the Geophysical Journal Internationa

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Galaxy clustering and redshift-space distortions at z=0.8 in the first data release

We present in this paper the general real- and redshift-space clustering properties of galaxies as measured in the first data release of the VIPERS survey. VIPERS is a large redshift survey designed to probe the distant Universe and its large-scale structure at 0.5 < z < 1.2. We describe in this analysis the global properties of the sample and discuss the survey completeness and associated corrections. This sample allows us to measure the galaxy clustering with an unprecedented accuracy at these redshifts. From the redshift-space distortions observed in the galaxy clustering pattern we provide a first measurement of the growth rate of structure at z = 0.8: f\sigma_8 = 0.47 +/- 0.08. This is completely consistent with the predictions of standard cosmological models based on Einstein gravity, although this measurement alone does not discriminate between different gravity models.Comment: 19 pages, 19 figures, accepted for publication in A&

Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays

Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies - once viewed prohibitively complicated and costly - is well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin

Direct exoplanet detection and characterization using the ANDROMEDA method: Performance on VLT/NaCo data

Context. The direct detection of exoplanets with high-contrast imaging requires advanced data processing methods to disentangle potential planetary signals from bright quasi-static speckles. Among them, angular differential imaging (ADI) permits potential planetary signals with a known rotation rate to be separated from instrumental speckles that are either statics or slowly variable. The method presented in this paper, called ANDROMEDA for ANgular Differential OptiMal Exoplanet Detection Algorithm is based on a maximum likelihood approach to ADI and is used to estimate the position and the flux of any point source present in the field of view. Aims. In order to optimize and experimentally validate this previously proposed method, we applied ANDROMEDA to real VLT/NaCo data. In addition to its pure detection capability, we investigated the possibility of defining simple and efficient criteria for automatic point source extraction able to support the processing of large surveys. Methods. To assess the performance of the method, we applied ANDROMEDA on VLT/NaCo data of TYC-8979-1683-1 which is surrounded by numerous bright stars and on which we added synthetic planets of known position and flux in the field. In order to accommodate the real data properties, it was necessary to develop additional pre-processing and post-processing steps to the initially proposed algorithm. We then investigated its skill in the challenging case of a well-known target, $\beta$ Pictoris, whose companion is close to the detection limit and we compared our results to those obtained by another method based on principal component analysis (PCA). Results. Application on VLT/NaCo data demonstrates the ability of ANDROMEDA to automatically detect and characterize point sources present in the image field. We end up with a robust method bringing consistent results with a sensitivity similar to the recently published algorithms, with only two parameters to be fine tuned. Moreover, the companion flux estimates are not biased by the algorithm parameters and do not require a posteriori corrections. Conclusions. ANDROMEDA is an attractive alternative to current standard image processing methods that can be readily applied to on-sky data