Performance Analysis for Multichannel Reception of OOFSK Signaling

In this paper, the error performance of on-off frequency shift keying (OOFSK) modulation over fading channels is analyzed when the receiver is equipped with multiple antennas. The analysis is conducted in two cases: the coherent scenario where the fading is perfectly known at the receiver, and the noncoherent scenario where neither the receiver nor the transmitter knows the fading coefficients. For both cases, the maximum a posteriori probability (MAP) detection rule is derived and analytical probability of error expressions are obtained. The effect of fading correlation among the receiver antennas is also studied. Simulation results indicate that for sufficiently low duty cycle values, lower probability of error values with respect to FSK signaling are achieved. Equivalently, when compared to FSK modulation, OOFSK with low duty cycle requires less energy to achieve the same probability of error, which renders this modulation a more energy efficient transmission technique.Comment: Proc. of the 2007 IEEE Wireless Communications and Networking Conferenc

Frugal Optimization for Cost-related Hyperparameters

The increasing demand for democratizing machine learning algorithms calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters which can cause a large variation in the training cost. But this effect is largely ignored in existing HPO methods, which are incapable to properly control cost during the optimization process. To address this problem, we develop a new cost-frugal HPO solution. The core of our solution is a simple but new randomized direct-search method, for which we prove a convergence rate of $O(\frac{\sqrt{d}}{\sqrt{K}})$ and an $O(d\epsilon^{-2})$-approximation guarantee on the total cost. We provide strong empirical results in comparison with state-of-the-art HPO methods on large AutoML benchmarks.Comment: 29 pages (including supplementary appendix

Tracial Rokhlin Property and Non-Commutative Dimensions

This dissertation focuses on finite group actions with the tracial Rokhlin property and the structure of the corresponding crossed products. It consists of two major parts. For the first part, we study several different aspects of finite group actions with certain versions of the Rokhlin property. We are able to give an explicit characterization of product-type actions with the tracial Rokhlin property or strict Rokhlin property. We also show that, in good circumstances, the actions with the tracial Rokhlin property are generic. In the second portion of this dissertation, we introduce the weak tracial Rokhlin property for actions on non-simple C*-algebras. The main results are as follows. Let A be a unital non-simple C*-algebra and α be an action of G on A with the weak tracial Rokhlin property. Assume that the crossed product C*: G, A, α) is simple. Suppose A has either of the following property: tracial rankk, stable rank one, real rank zero. Then C*: G, A, α) has the same property