Title: Wirtinger Flow for Nonconvex Blind Demixing with Optimal Step Size
The prospect of massive deployment of devices for Internet-of-Things (IoT) motivates grant-free access for simultaneously uplink transmission by multiple nodes. Blind demixing represents a promising technique for recovering multiple such source signals over unknown channels. Recent studies show Wirtinger Flow (WF) algorithm can be effective in blind demixing. However, existing theoretical results on WF step size selection tend to be conservative and slow down convergence rates. To overcome this limitation, we propose an improved WF (WF-OPT) by optimizing its step size in each iteration and expediting the convergence. We provide a theoretical guarantee on the strict contraction of WF-OPT and present the upper bounds of the contraction ratio. Simulation results demonstrate the expected convergence gains. more »« less
Feres, Carlos; Ding, Zhi(
, IEEE transactions on signal processing)
null
(Ed.)
In this work, we analyze the convergence of constant
modulus algorithm (CMA) in blindly recovering multiple signals
to facilitate grant-free wireless access. The CMA typically solves a
non-convex problem by utilizing stochastic gradient descent. The
iterative convergence of CMA can be affected by additive channel
noise and finite number of samples, which is a problem not fully
investigated previously. We point out the strong similarity
between CMA and the Wirtinger Flow (WF) algorithm originally
proposed for Phase retrieval. In light of the convergence proof of
WF under limited data samples, we adopt the WF algorithm to
implement CMA-based blind signal recovery. We generalize the
convergence analysis of WF in the context of CMA-based blind
signal recovery. Numerical simulation results also corroborate the
analysis.
Jalali, Amin; Shi, Yuanming; Ding, Zhi(
, IEEE International Conference on Communications)
As applications of Internet-of-things (IoT) rapidly
expand, unscheduled multiple user access with low latency and
low cost communication is attracting growing more interests. To
recover the multiple uplink signals without strict access control
under dynamic co-channel interference environment, the problem
of blind demixing emerges as an important obstacle for us to
overcome. Without channel state information, successful blind
demixing can recover multiple user signals more effectively by
leveraging prior information on signal characteristics such as
constellations and distribution. This work studies how forward
error correction (FEC) codes in Galois Field can generate more
effective blind demixing algorithms. We propose a constrained
Wirtinger flow algorithm by defining a valid signal set based on
FEC codewords. Specifically, targeting the popular polar codes
for FEC of short IoT packets, we introduce signal projections
within iterations of Wirtinger Flow based on FEC code information.
Simulation results demonstrate stronger robustness of
the proposed algorithm against noise and practical obstacles and
also faster convergence rate compared to regular Wirtinger flow
algorithm.
Sharma, Gaurav; Majdalani, Joseph(
, 2020 AIAA Propulsion and Energy Forum)
null
(Ed.)
This work focuses on the use of a finite-volume solver to describe the wall-bounded cyclonic flowfield that evolves in a swirl-driven thrust chamber. More specifically, a non-reactive, cold-flow simulation is carried out using an idealized chamber configuration of a square-shaped, right-cylindrical enclosure with eight tangential injectors and a variable nozzle size. For simplicity, we opt for air as the working fluid and perform our simulations under steady, incompressible, and inviscid flow conditions. First, a meticulously developed mesh that consists of tetrahedral elements is generated in a manner to minimize the overall skewness, especially near injectors; second, this mesh is converted into a polyhedral grid to improve convergence characteristics and accuracy. After achieving convergence in all variables, our three velocity components are examined and compared to an existing analytical solution obtained by Vyas and Majdalani (Vyas, A. B., and Majdalani, J., “Exact Solution of the Bidirectional Vortex,” AIAA Journal, Vol. 44, No. 10, 2006, pp. 2208-2216). We find that the numerical model is capable of predicting the expected forced vortex behavior in the inner core region as well as the free vortex tail in the inviscid region. Moreover, the results appear to be in fair agreement with the Vyas–Majdalani solution derived under similarly inviscid conditions, and thus resulting in a quasi complex-lamellar profile. In this work, we are able to ascertain the axial independence of the swirl velocity no matter the value of the outlet radius, which confirms the key assumption made in most analytical models of wall-bounded cyclonic motions. Moreover, the pressure distribution predicted numerically is found to be in fair agreement with both theoretical formulations and experimental measurements of cyclone separators. The bidirectional character of the flowfield is also corroborated by the axial and radial velocity distributions, which are found to be concurrent with theory. Then using parametric trade studies, the sensitivity of the numerical simulations to the outlet diameter of the chamber is explored to determine the influence of outlet nozzle variations on the mantle location and the number of mantles. Since none of the cases considered here promote the onset of multiple mantles, we are led to believe that more factors are involved in producing more mantles than one. Besides the exit diameter, the formation of a multiple mantle structure may be influenced by the physical boundary conditions, nozzle radius, inlet curvature, and length. In closing, we show that the latter plays a significant role in controlling the development of backflow regions inside the chamber.
Feres, Carlos J.; Ding, Zhi(
, IEEE transactions on signal processing)
We propose a new nonconvex framework for blind multiple signal demixing and recovery. The proposed Riemann geometric approach extends the well known constant modulus
algorithm to facilitate grant-free wireless access. For multiple signal demixing and recovery, we formulate the problem as non-convex problem optimization problem with signal orthogonality constraint in the form of Riemannian Orthogonal CMA(ROCMA). Unlike traditional stochastic gradient solutions that require large data samples, parameter tuning, and careful initialization, we leverage Riemannian geometry and transform the orthogonality requirement of recovered signals into a Riemannian manifold optimization. Our solution demonstrates full recovery of multiple access signals without large data sample size or special initialization with high probability of success.
Ma, Philip Y.; Tait, Alexander N.; Zhang, Weipeng; Karahan, Emir Ali; Ferreira de Lima, Thomas; Huang, Chaoran; Shastri, Bhavin J.; Prucnal, Paul R.(
, Optics Letters)
Microwave communications have witnessed an incipient proliferation of multi-antenna and opportunistic technologies in the wake of an ever-growing demand for spectrum resources, while facing increasingly difficult network management over widespread channel interference and heterogeneous wireless broadcasting. Radio frequency (RF) blind source separation (BSS) is a powerful technique for demixing mixtures of unknown signals with minimal assumptions, but relies on frequency dependent RF electronics and prior knowledge of the target frequency band. We propose photonic BSS with unparalleled frequency agility supported by the tremendous bandwidths of photonic channels and devices. Specifically, our approach adopts an RF photonic front-end to process RF signals at various frequency bands within the same array of integrated microring resonators, and implements a novel two-step photonic BSS pipeline to reconstruct source identities from the reduced dimensional statistics of front-end output. We verify the feasibility and robustness of our approach by performing the first proof-of-concept photonic BSS experiments on mixed-over-the-air RF signals across multiple frequency bands. The proposed technique lays the groundwork for further research in interference cancellation, radio communications, and photonic information processing.
@article{osti_10351732,
place = {Country unknown/Code not available},
title = {Wirtinger Flow for Nonconvex Blind Demixing with Optimal Step Size},
url = {https://par.nsf.gov/biblio/10351732},
DOI = {10.1109/LWC.2022.3203313},
abstractNote = {The prospect of massive deployment of devices for Internet-of-Things (IoT) motivates grant-free access for simultaneously uplink transmission by multiple nodes. Blind demixing represents a promising technique for recovering multiple such source signals over unknown channels. Recent studies show Wirtinger Flow (WF) algorithm can be effective in blind demixing. However, existing theoretical results on WF step size selection tend to be conservative and slow down convergence rates. To overcome this limitation, we propose an improved WF (WF-OPT) by optimizing its step size in each iteration and expediting the convergence. We provide a theoretical guarantee on the strict contraction of WF-OPT and present the upper bounds of the contraction ratio. Simulation results demonstrate the expected convergence gains.},
journal = {IEEE wireless communications letters},
author = {Hsu, Chih-Ho and Feres, Carlos and Ding, Zhi},
}
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