265 research outputs found
MU-MIMO Communications with MIMO Radar: From Co-existence to Joint Transmission
Beamforming techniques are proposed for a joint multi-input-multi-output
(MIMO) radar-communication (RadCom) system, where a single device acts both as
a radar and a communication base station (BS) by simultaneously communicating
with downlink users and detecting radar targets. Two operational options are
considered, where we first split the antennas into two groups, one for radar
and the other for communication. Under this deployment, the radar signal is
designed to fall into the null-space of the downlink channel. The communication
beamformer is optimized such that the beampattern obtained matches the radar's
beampattern while satisfying the communication performance requirements. To
reduce the optimizations' constraints, we consider a second operational option,
where all the antennas transmit a joint waveform that is shared by both radar
and communications. In this case, we formulate an appropriate probing
beampattern, while guaranteeing the performance of the downlink communications.
By incorporating the SINR constraints into objective functions as penalty
terms, we further simplify the original beamforming designs to weighted
optimizations, and solve them by efficient manifold algorithms. Numerical
results show that the shared deployment outperforms the separated case
significantly, and the proposed weighted optimizations achieve a similar
performance to the original optimizations, despite their significantly lower
computational complexity.Comment: 15 pages, 15 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Dynamic Facial Expression Generation on Hilbert Hypersphere with Conditional Wasserstein Generative Adversarial Nets
In this work, we propose a novel approach for generating videos of the six
basic facial expressions given a neutral face image. We propose to exploit the
face geometry by modeling the facial landmarks motion as curves encoded as
points on a hypersphere. By proposing a conditional version of manifold-valued
Wasserstein generative adversarial network (GAN) for motion generation on the
hypersphere, we learn the distribution of facial expression dynamics of
different classes, from which we synthesize new facial expression motions. The
resulting motions can be transformed to sequences of landmarks and then to
images sequences by editing the texture information using another conditional
Generative Adversarial Network. To the best of our knowledge, this is the first
work that explores manifold-valued representations with GAN to address the
problem of dynamic facial expression generation. We evaluate our proposed
approach both quantitatively and qualitatively on two public datasets;
Oulu-CASIA and MUG Facial Expression. Our experimental results demonstrate the
effectiveness of our approach in generating realistic videos with continuous
motion, realistic appearance and identity preservation. We also show the
efficiency of our framework for dynamic facial expressions generation, dynamic
facial expression transfer and data augmentation for training improved emotion
recognition models
Rieoptax: Riemannian Optimization in JAX
We present Rieoptax, an open source Python library for Riemannian
optimization in JAX. We show that many differential geometric primitives, such
as Riemannian exponential and logarithm maps, are usually faster in Rieoptax
than existing frameworks in Python, both on CPU and GPU. We support various
range of basic and advanced stochastic optimization solvers like Riemannian
stochastic gradient, stochastic variance reduction, and adaptive gradient
methods. A distinguishing feature of the proposed toolbox is that we also
support differentially private optimization on Riemannian manifolds
Learning gradients on manifolds
A common belief in high-dimensional data analysis is that data are
concentrated on a low-dimensional manifold. This motivates simultaneous
dimension reduction and regression on manifolds. We provide an algorithm for
learning gradients on manifolds for dimension reduction for high-dimensional
data with few observations. We obtain generalization error bounds for the
gradient estimates and show that the convergence rate depends on the intrinsic
dimension of the manifold and not on the dimension of the ambient space. We
illustrate the efficacy of this approach empirically on simulated and real data
and compare the method to other dimension reduction procedures.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ206 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Joint Beamforming for RIS-Assisted Integrated Sensing and Communication Systems
Integrated sensing and communications (ISAC) is an emerging critical
technique for the next generation of communication systems. However, due to
multiple performance metrics used for communication and sensing, the limited
degrees-of-freedom (DoF) in optimizing ISAC systems poses a challenge.
Reconfigurable intelligent surfaces (RIS) can introduce new DoF for beamforming
in ISAC systems, thereby enhancing the performance of communication and sensing
simultaneously. In this paper, we propose two optimization techniques for
beamforming in RIS-assisted ISAC systems. The first technique is an alternating
optimization (AO) algorithm based on the semidefinite relaxation (SDR) method
and a one-dimension iterative (ODI) algorithm, which can maximize the radar
mutual information (MI) while imposing constraints on the communication rates.
The second technique is an AO algorithm based on the Riemannian gradient (RG)
method, which can maximize the weighted ISAC performance metrics. Simulation
results verify the effectiveness of the proposed schemes. The AO-SDR-ODI method
is shown to achieve better communication and sensing performance, than the
AO-RG method, at a higher complexity. It is also shown that the
mean-squared-error (MSE) of the estimates of the sensing parameters decreases
as the radar MI increases.Comment: 30 pages, 8 figures. This paper has been submitted to IEEE
Transactions on Communication
A Geometric Variational Approach to Bayesian Inference
We propose a novel Riemannian geometric framework for variational inference
in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold
of probability density functions. Under the square-root density representation,
the manifold can be identified with the positive orthant of the unit
hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric.
Exploiting such a Riemannian structure, we formulate the task of approximating
the posterior distribution as a variational problem on the hypersphere based on
the alpha-divergence. This provides a tighter lower bound on the marginal
distribution when compared to, and a corresponding upper bound unavailable
with, approaches based on the Kullback-Leibler divergence. We propose a novel
gradient-based algorithm for the variational problem based on Frechet
derivative operators motivated by the geometry of the Hilbert sphere, and
examine its properties. Through simulations and real-data applications, we
demonstrate the utility of the proposed geometric framework and algorithm on
several Bayesian models
- …