4,764 research outputs found
Adaptive Interference Removal for Un-coordinated Radar/Communication Co-existence
Most existing approaches to co-existing communication/radar systems assume
that the radar and communication systems are coordinated, i.e., they share
information, such as relative position, transmitted waveforms and channel
state. In this paper, we consider an un-coordinated scenario where a
communication receiver is to operate in the presence of a number of radars, of
which only a sub-set may be active, which poses the problem of estimating the
active waveforms and the relevant parameters thereof, so as to cancel them
prior to demodulation. Two algorithms are proposed for such a joint waveform
estimation/data demodulation problem, both exploiting sparsity of a proper
representation of the interference and of the vector containing the errors of
the data block, so as to implement an iterative joint interference removal/data
demodulation process. The former algorithm is based on classical on-grid
compressed sensing (CS), while the latter forces an atomic norm (AN)
constraint: in both cases the radar parameters and the communication
demodulation errors can be estimated by solving a convex problem. We also
propose a way to improve the efficiency of the AN-based algorithm. The
performance of these algorithms are demonstrated through extensive simulations,
taking into account a variety of conditions concerning both the interferers and
the respective channel states
OptShrink: An algorithm for improved low-rank signal matrix denoising by optimal, data-driven singular value shrinkage
The truncated singular value decomposition (SVD) of the measurement matrix is
the optimal solution to the_representation_ problem of how to best approximate
a noisy measurement matrix using a low-rank matrix. Here, we consider the
(unobservable)_denoising_ problem of how to best approximate a low-rank signal
matrix buried in noise by optimal (re)weighting of the singular vectors of the
measurement matrix. We exploit recent results from random matrix theory to
exactly characterize the large matrix limit of the optimal weighting
coefficients and show that they can be computed directly from data for a large
class of noise models that includes the i.i.d. Gaussian noise case.
Our analysis brings into sharp focus the shrinkage-and-thresholding form of
the optimal weights, the non-convex nature of the associated shrinkage function
(on the singular values) and explains why matrix regularization via singular
value thresholding with convex penalty functions (such as the nuclear norm)
will always be suboptimal. We validate our theoretical predictions with
numerical simulations, develop an implementable algorithm (OptShrink) that
realizes the predicted performance gains and show how our methods can be used
to improve estimation in the setting where the measured matrix has missing
entries.Comment: Published version. The algorithm can be downloaded from
http://www.eecs.umich.edu/~rajnrao/optshrin
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
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