The discrete Fourier transform (DFT) and its specialized case, the number theoretic transform (NTT), are two important mathematical tools having applications in several areas of science and engineering. However, despite their usefulness and utility, their adoption continues to be a challenge as computing the DFT of a signal can be a time-consuming and expensive operation. To speed things up, fast Fourier transform (FFT) algorithms, which are reduced-complexity formulations for computing the DFT of a sequence, have been proposed and implemented for traditional processors and their corresponding instruction sets. With the rise of GPUs, NVIDIA introduced its own FFT computation library called cuFFT, which leverages the power of GPUs to compute the DFT. However, as this paper demonstrates, there is a lot of room for improvement to accelerate the FFT and NTT algorithms on modern GPUs by utilizing specialized operations and architectural advancements. In particular, we present four major types of optimizations that leverage tensor cores and the warp-shuffle instruction. Through extensive evaluations, we show that our approach consistently outperforms existing GPU-based implementations with a speedup of up to 4× for NTT and a speed of up to 1.5× for FFT.

The fast Fourier Transform (FFT), a reduced-complexity formulation of the Discrete Fourier Transform (DFT), is an important tool in many areas of science and engineering. FFTW is a well-known package that follows this approach and is currently one of the fastest available implementations of the FFT. NVIDIA introduced its version of FFTW called cuFFT that achieves high performance on the GPUs. In this work we present a novel way to map the FFT algorithm on the newly introduced Tensor Cores by adapting the the Cooley-Tukey recursive FFT algorithm. We present four major types of optimizations that enhance the performance of our approach for varying FFT sizes and show that the approach consistently outperforms cuFFT with a speedup of about 15% to 250% on average.

Many vehicular applications such as navigation, collision avoidance, and location-based services envisioned under intelligent transportation system (ITS) framework require position information with certain accuracy and reliability. Global navigation satellite system (GNSS) are widely deployed for absolute and relative positioning in a wide range of ITS applications due to their global coverage but these systems have limited accuracy and availability to meet the requirement of many safety-critical applications. This limitation has led to the development of cooperative positioning (CP) methods in a vehicular ad-hoc network. CP methods are based on the assumption that the inter-vehicular ranges are available through some radio ranging method, such as received signal strength, time of arrival, or time difference of arrival. However, the feasibility and accuracy of these radio ranging methods is limited due to the constraints of communication medium and rapidly changing vehicular environment. In this paper, we propose a generalized version of a theoretical framework for the measurement and analysis of inter-vehicular ranges by exchanging GNSS observables between vehicles. More specifically, we investigate the utilization of GNSS observables in the following four categories for range measurement: 1) absolute positions of the vehicles provided by GNSS receivers; 2) raw code pseudoranges; 3) single difference of the raw code pseudoranges; and 4) double difference of the raw code pseudoranges. The developed theoretical framework compares the accuracy of inter-vehicular range measurement using these four observables. This framework is further validated by actual field trials in different mobile environments using two vehicles equipped with GNSS receivers.

In light of increasing interest in detection of concealed metallic weapons, there is a great need to have robust and non-obtrusive metal detection systems with large coverage areas. Conventional systems based on electromagnetic induction or X- rays are effective, but have small coverage areas in addition to requiring costly infrastructure. In this paper, we explore the use of ubiquitously present WiFi signals for non-obtrusive detection of concealed metal objects. For the purpose, we build a prototype system consisting of a single- antenna commodity WiFi radio as a transmitter, and two multi-antenna radios as receivers placed in an indoor environment of approximately 42 ft by 39 ft. We conduct extensive experiments with subjects walking through the setup with (or without) a sheet of metal placed around their chests. We use the channel state-information collected from the receivers to train a deep convolutional neural network, and find that the proposed system can differentiate between the metal and non-metal cases with an average accuracy of 86.44.