On the Performance of Spectrum Sensing Algorithms using Multiple Antennas

In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorithms using sample covariance matrices are considered: maximum eigenvalue detection (MED) and condition number detection (CND). The earlier studies usually assume that the number of antennas (K) and the number of samples (N) are both large, thus random matrix theory (RMT) can be used to derive the asymptotic distributions of the maximum and minimum eigenvalues of the sample covariance matrices. While assuming the number of antennas being large simplifies the derivations, in practice, the number of antennas equipped at a single secondary user is usually small, say 2 or 3, and once designed, this antenna number is fixed. Thus in this paper, our objective is to derive the asymptotic distributions of the eigenvalues and condition numbers of the sample covariance matrices for any fixed K but large N, from which the probability of detection and probability of false alarm can be obtained. The proposed methodology can also be used to analyze the performance of other EBD algorithms. Finally, computer simulations are presented to validate the accuracy of the derived results.Comment: IEEE GlobeCom 201

Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.Comment: 15 pages, 5 figure

Are Fruit and Vegetable Prices Non-linear Stationary? Evidence from Smooth Transition Autoregressive Models

Over the last decade, there has been a growing interest in investigating agricultural commodity prices. We apply two more powerful smooth transition autoregressive models of the non-linear unit-root test - namely, the ESTAR model of Kapetanios et al. [Journal of Econometrics (2003)] and the LSTAR model of Leybourne, et a . [Journal of Time Series Analysis (1998)] - with a view to investigating non-linear stationarity for the retail prices of 8 major kinds of fruit and 18 major kinds of vegetable in Taiwan. The empirical evidence clearly finds that the Kapetanios et al. model provides solid, substantive evidence in favor of a non-linear mean-reverting adjustment for the individual price of 4 kinds of fruit and 5 kinds of vegetable. However, when we employ the Leybourne et al. model, we find that any such similar evidence of non-linear stationarity is considerably weaker. Finally, compared with the traditional linear unit root tests, it is important to note here that, all in all, the non-linear unit root tests do indeed provide much more evidence of the stationarity, albeit to varying degrees. This paper offers some policy implications.Smooth transition autoregressive model; Non-linear stationary; Fruit price; Vegetable price; Taiwan

Im2Pano3D: Extrapolating 360 Structure and Semantics Beyond the Field of View

We present Im2Pano3D, a convolutional neural network that generates a dense prediction of 3D structure and a probability distribution of semantic labels for a full 360 panoramic view of an indoor scene when given only a partial observation (<= 50%) in the form of an RGB-D image. To make this possible, Im2Pano3D leverages strong contextual priors learned from large-scale synthetic and real-world indoor scenes. To ease the prediction of 3D structure, we propose to parameterize 3D surfaces with their plane equations and train the model to predict these parameters directly. To provide meaningful training supervision, we use multiple loss functions that consider both pixel level accuracy and global context consistency. Experiments demon- strate that Im2Pano3D is able to predict the semantics and 3D structure of the unobserved scene with more than 56% pixel accuracy and less than 0.52m average distance error, which is significantly better than alternative approaches.Comment: Video summary: https://youtu.be/Au3GmktK-S