14 research outputs found
Blind separation of complex-valued satellite-AIS data for marine surveillance: a spatial quadratic time-frequency domain approach
In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation
Canonical time-frequency, time-scale, and frequency-scale representations of time-varying channels
Mobile communication channels are often modeled as linear time-varying
filters or, equivalently, as time-frequency integral operators with finite
support in time and frequency. Such a characterization inherently assumes the
signals are narrowband and may not be appropriate for wideband signals. In this
paper time-scale characterizations are examined that are useful in wideband
time-varying channels, for which a time-scale integral operator is physically
justifiable. A review of these time-frequency and time-scale characterizations
is presented. Both the time-frequency and time-scale integral operators have a
two-dimensional discrete characterization which motivates the design of
time-frequency or time-scale rake receivers. These receivers have taps for both
time and frequency (or time and scale) shifts of the transmitted signal. A
general theory of these characterizations which generates, as specific cases,
the discrete time-frequency and time-scale models is presented here. The
interpretation of these models, namely, that they can be seen to arise from
processing assumptions on the transmit and receive waveforms is discussed. Out
of this discussion a third model arises: a frequency-scale continuous channel
model with an associated discrete frequency-scale characterization.Comment: To appear in Communications in Information and Systems - special
issue in honor of Thomas Kailath's seventieth birthda
Pseudodifferential operators and Banach algebras in mobile communications
AbstractWe study linear time-varying operators arising in mobile communication using methods from time–frequency analysis. We show that a wireless transmission channel can be modeled as pseudodifferential operator Hσ with symbol σ in FLw1 or in the modulation space Mw∞,1 (also known as weighted Sjöstrand class). It is then demonstrated that Gabor Riesz bases {φm,n} for subspaces of L2(R) approximately diagonalize such pseudodifferential operators in the sense that the associated matrix [〈Hσφm′,n′,φm,n〉]m,n,m′,n′ belongs to a Wiener-type Banach algebra with exponentially fast off-diagonal decay. We indicate how our results can be utilized to construct numerically efficient equalizers for multicarrier communication systems in a mobile environment
Eigenvalue Estimates and Mutual Information for the Linear Time-Varying Channel
We consider linear time-varying channels with additive white Gaussian noise.
For a large class of such channels we derive rigorous estimates of the
eigenvalues of the correlation matrix of the effective channel in terms of the
sampled time-varying transfer function and, thus, provide a theoretical
justification for a relationship that has been frequently observed in the
literature. We then use this eigenvalue estimate to derive an estimate of the
mutual information of the channel. Our approach is constructive and is based on
a careful balance of the trade-off between approximate operator
diagonalization, signal dimension loss, and accuracy of eigenvalue estimates.Comment: Submitted to IEEE Transactions on Information Theory This version is
a substantial revision of the earlier versio
Representation of Operators in the Time-Frequency Domain and Generalzed Gabor Multipliers
Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A haracterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier approximations are discussed and an efficient method for the calculation of an operator\u27s best approximation by a Gabor multiplier is derived. The spreading function of Gabor multipliers yields new error estimates for these approximations. Generalizations (multiple Gabor multipliers)
are introduced for better approximation of overspread operators. The Riesz property of the projection operators involved in generalized Gabor multipliers is characterized, and a method for obtaining an operator\u27s best approximation by a multiple Gabor multiplier is suggested. Finally, it is shown that in certain situations, generalized Gabor multipliers reduce to a finite sum of regular Gabor multipliers with adapted windows
On the time-frequency representation of operators and generalized Gabor multiplier approximations
28 pagesInternational audienceStarting from a general operator representation in the time-frequency do- main, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier approximations are discussed and an efficient method for the calculation of an operator's best approximation by a Gabor multiplier is derived. The spreading function of Gabor multipliers yields new error estimates for these approximations. Generalizations (multiple Gabor multipliers) are introduced for better approximation of overspread operators. The Riesz property of the projection operators involved in generalized Gabor multipliers is characterized, and a method for obtaining an operator's best approximation by a multiple Gabor multiplier is suggested. Finally, it is shown that in certain situations, generalized Gabor multipliers reduce to a finite sum of regular Gabor multipliers with adapted windows