arXiv subjects

Difan Zou

Publications and source records attributed to Difan Zou.

114 records · Page 7Linked to original sources

arXiv2019

Two Dimension Intensity Distribution of Ultraviolet Scattering Communication

Consider a ultraviolet (UV) scattering communication system where the position of the transmitter is fixed and the receiver can move around on the ground. To obtain the link gain effectively and economically, we propose an algorithm based on one-dimensional (1D) numerical integration and an off-line data library. Moreover, we analyze the 2D scattering intensity distributions for both LED and laser, and observe that the contours can be well fitted by elliptic models. The relationships between the characteristics of fitting ellipses and the source parameters are provided by numerical results.

eess.SP↗

arXiv2018

Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for a broad family of loss functions, with proper random weight initialization, both gradient descent and stochastic gradient descent can find the global minima of the training loss for an over-parameterized deep ReLU network, under mild assumption on the training data. The key idea of our proof is that Gaussian random initialization followed by (stochastic) gradient descent produces a sequence of iterates that stay inside a small perturbation region centering around the initial weights, in which the empirical loss function of deep ReLU networks enjoys nice local curvature properties that ensure the global convergence of (stochastic) gradient descent. Our theoretical results shed light on understanding the optimization for deep learning, and pave the way for studying the optimization dynamics of training modern deep neural networks.

cs.LG↗

arXiv2018

A 1Mbps Real-time NLOS UV Scattering Communication System with Receiver Diversity over 1km

In the non-line of sight (NLOS) ultraviolet (UV) scattering communication, the received signals exhibit the characteristics of discrete photoelectrons due to the extremely large path loss. We design and demonstrate an NLOS UV scattering communication system in this work, where the receiver-side signal detection is designed based on a discrete-time Poisson channel model. In our system, a laser and multiple photomultiplier tubes are employed as the optical transmitter and detector, respectively. Furthermore, we design algorithms for pulse-counting, synchronization, channel estimation and $LLR$ computation for hardware realization in FPGA board. Simulation results are provided to evaluate the proposed system design and specify the system key parameters. We perform field tests for real-time communication with the transmission range over $1$km, where the system throughput reaches $1$Mbps.

eess.SP↗

arXiv2017

Saving Gradient and Negative Curvature Computations: Finding Local Minima More Efficiently

We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the core of our algorithms is the division of the entire domain of the objective function into small and large gradient regions: our algorithms only perform gradient descent based procedure in the large gradient region, and only perform negative curvature descent in the small gradient region. Our novel analysis shows that the proposed algorithms can escape the small gradient region in only one negative curvature descent step whenever they enter it, and thus they only need to perform at most $N_ε$ negative curvature direction computations, where $N_ε$ is the number of times the algorithms enter small gradient regions. For both deterministic and stochastic settings, we show that the proposed algorithms can potentially beat the state-of-the-art local minima finding algorithms. For the finite-sum setting, our algorithm can also outperform the best algorithm in a certain regime.

cs.LG↗

arXiv2017

Characterization on Practical Photon Counting Receiver in Optical Scattering Communication

We characterize the practical photon-counting receiver in optical scattering communication with finite sampling rate and electrical noise. In the receiver side, the detected signal can be characterized as a series of pulses generated by photon-multiplier (PMT) detector and held by the pulse-holding circuits, which are then sampled by the analog-to-digit convertor (ADC) with finite sampling rate and counted by a rising-edge pulse detector. However, the finite small pulse width incurs the dead time effect that may lead to sub-Poisson distribution on the recorded pulses. We analyze first-order and second-order moments on the number of recorded pulses with finite sampling rate at the receiver side under two cases where the sampling period is shorter than or equal to the pulse width as well as longer than the pulse width. Moreover, we adopt the maximum likelihood (ML) detection. In order to simplify the analysis, we adopt binomial distribution approximation on the number of recorded pulses in each slot. A tractable holding time and decision threshold selection rule is provided aiming to maximize the minimal Kullback-Leibler (KL) distance between the two distributions. The performance of proposed sub-Poisson distribution and the binomial approximation are verified by the experimental results. The equivalent arrival rate and holding time predicted by the of sub-Poisson model and the associated proposed binomial distribution on finite sampling rate and the electrical noise are validated by the simulation results. The proposed the holding time and decision threshold selection rule performs close to the optimal one.

cs.IT↗

arXiv2016

Signal Detection under Short-Interval Sampling of Continuous Waveforms for Optical Wireless Scattering Communication

In optical wireless scattering communication, received signal in each symbol interval is captured by a photomultiplier tube (PMT) and then sampled through very short but finite interval sampling. The resulting samples form a signal vector for symbol detection. The upper and lower bounds on transmission rate of such a processing system are studied. It is shown that the gap between two bounds approaches zero as the thermal noise and shot noise variances approach zero. The maximum a posteriori (MAP) signal detection is performed and a low computational complexity receiver is derived under piecewise polynomial approximation. Meanwhile, the threshold based signal detection is also studied, where two threshold selection rules are proposed based on the detection error probability and the Kullback-Leibler (KL) distance. For the latter, it is shown that the KL distance is not sensitive to the threshold selection for small shot and thermal noise variances, and thus the threshold can be selected among a wide range without significant loss from the optimal KL distance. The performances of the transmission rate bounds, the signal detection, and the threshold selection approaches are evaluated by the numerical results.

cs.IT↗