19 research outputs found
SNR degradation in GNSS-R measurements under the effects of radio-frequency interference
©2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Radio-frequency interference (RFI) is a serious threat for systems working with low power signals such as those coming from the global navigation satellite systems (GNSS). The spectral separation coefficient (SSC) is the standard figure of merit to evaluate the signal-to-noise ratio (SNR) degradation due to the RFI. However, an in-depth assessment in the field of GNSS-Reflectometry (GNSS-R) has not been performed yet, and particularly, about which is the influence of the RFI on the so-called delay-Doppler map (DDM). This paper develops a model that evaluates the contribution of intra-/inter-GNSS and external RFI effects to the degradation of the SNR in the DDM for both conventional and interferometric GNSS-R techniques. Moreover, a generalized SSC is defined to account for the effects of nonstationary RFI signals. The results show that highly directive antennas are necessary to avoid interference from other GNSS satellites, whereas mitigation techniques are essential to keep GNSS-R instruments working under external RFI degradation.Peer ReviewedPostprint (author's final draft
Quantum theta functions and Gabor frames for modulation spaces
Representations of the celebrated Heisenberg commutation relations in quantum
mechanics and their exponentiated versions form the starting point for a number
of basic constructions, both in mathematics and mathematical physics (geometric
quantization, quantum tori, classical and quantum theta functions) and signal
analysis (Gabor analysis).
In this paper we try to bridge the two communities, represented by the two
co--authors: that of noncommutative geometry and that of signal analysis. After
providing a brief comparative dictionary of the two languages, we will show
e.g. that the Janssen representation of Gabor frames with generalized Gaussians
as Gabor atoms yields in a natural way quantum theta functions, and that the
Rieffel scalar product and associativity relations underlie both the functional
equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change
Gabor analysis over finite Abelian groups
The topic of this paper are (multi-window) Gabor frames for signals over
finite Abelian groups, generated by an arbitrary lattice within the finite
time-frequency plane. Our generic approach covers simultaneously
multi-dimensional signals as well as non-separable lattices. The main results
reduce to well-known fundamental facts about Gabor expansions of finite signals
for the case of product lattices, as they have been given by Qiu, Wexler-Raz or
Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a
central role is given to spreading function of linear operators between
finite-dimensional Hilbert spaces. Another relevant tool is a symplectic
version of Poisson's summation formula over the finite time-frequency plane. It
provides the Fundamental Identity of Gabor Analysis.In addition we highlight
projective representations of the time-frequency plane and its subgroups and
explain the natural connection to twisted group algebras. In the
finite-dimensional setting these twisted group algebras are just matrix
algebras and their structure provides the algebraic framework for the study of
the deeper properties of finite-dimensional Gabor frames.Comment: Revised version: two new sections added, many typos fixe
A New Compact Delay, Doppler Stretch and Phase Estimation CRB with a Band-Limited Signal for Generic Remote Sensing Applications
Since time-delay, Doppler effect and phase estimation are fundamental tasks in a plethora
of engineering fields, tractable lower performance bounds for this problem are key tools of broad
interest for a large variety of remote sensing applications. In the large sample regime and/or the high
signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér–Rao bound (CRB)
provides an accurate lower bound in the mean square error sense. In this contribution, we introduce
firstly a new compact CRB expression for the joint time-delay and Doppler stretch estimation,
considering a generic delayed and dilated band-limited signal. This generalizes known results
for both wideband signals and the standard narrowband signal model where the Doppler effect
on the band-limited baseband signal is not considered and amounts to a frequency shift. General
compact closed-form CRB expressions for the amplitude and phase are also provided. These compact
CRBs are expressed in terms of the baseband signal samples, making them especially easy to use
whatever the baseband signal considered, therefore being valid for a variety of remote sensors.
The new CRB expressions are validated in a positioning case study, both using synthetic and real
data. These results show that the maximum likelihood estimator converges to the CRB at high
signal-to-noise ratios, which confirms the exactness of the CRB. The CRB is further validated by
comparing the ambiguity function and its 2nd order Taylor expansion where the perfect match also
proves its exactness