5 research outputs found
Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order
Gridless methods show great superiority in line spectral estimation. These
methods need to solve an atomic norm (i.e., the continuous analog of
norm) minimization problem to estimate frequencies and model order. Since
this problem is NP-hard to compute, relaxations of atomic norm, such as
nuclear norm and reweighted atomic norm, have been employed for promoting
sparsity. However, the relaxations give rise to a resolution limit,
subsequently leading to biased model order and convergence error. To overcome
the above shortcomings of relaxation, we propose a novel idea of simultaneously
estimating the frequencies and model order by means of the atomic norm.
To accomplish this idea, we build a multiobjective optimization model. The
measurment error and the atomic norm are taken as the two optimization
objectives. The proposed model directly exploits the model order via the atomic
norm, thus breaking the resolution limit. We further design a
variable-length evolutionary algorithm to solve the proposed model, which
includes two innovations. One is a variable-length coding and search strategy.
It flexibly codes and interactively searches diverse solutions with different
model orders. These solutions act as steppingstones that help fully exploring
the variable and open-ended frequency search space and provide extensive
potentials towards the optima. Another innovation is a model order pruning
mechanism, which heuristically prunes less contributive frequencies within the
solutions, thus significantly enhancing convergence and diversity. Simulation
results confirm the superiority of our approach in both frequency estimation
and model order selection.Comment: This work has been submitted to the IEEE for possible publication.
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Multi-Antenna Dual-Blind Deconvolution for Joint Radar-Communications via SoMAN Minimization
Joint radar-communications (JRC) has emerged as a promising technology for
efficiently using the limited electromagnetic spectrum. In JRC applications
such as secure military receivers, often the radar and communications signals
are overlaid in the received signal. In these passive listening outposts, the
signals and channels of both radar and communications are unknown to the
receiver. The ill-posed problem of recovering all signal and channel parameters
from the overlaid signal is terms as dual-blind deconvolution (DBD). In this
work, we investigate a more challenging version of DBD with a multi-antenna
receiver. We model the radar and communications channels with a few (sparse)
continuous-valued parameters such as time delays, Doppler velocities, and
directions-of-arrival (DoAs). To solve this highly ill-posed DBD, we propose to
minimize the sum of multivariate atomic norms (SoMAN) that depends on the
unknown parameters. To this end, we devise an exact semidefinite program using
theories of positive hyperoctant trigonometric polynomials (PhTP). Our
theoretical analyses show that the minimum number of samples and antennas
required for perfect recovery is logarithmically dependent on the maximum of
the number of radar targets and communications paths rather than their sum. We
show that our approach is easily generalized to include several practical
issues such as gain/phase errors and additive noise. Numerical experiments show
the exact parameter recovery for different JRCComment: 40 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2208.0438