Deriving Bounds on the Size of Spatial Areas

Many application domains such as surveillance, environmental monitoring or sensor-data processing need upper and lower bounds on areas that are covered by a certain feature. For example, a smart-city infrastructure might need bounds on the size of an area polluted with fine-dust, to re-route combustion-engine traffic. Obtaining such bounds is challenging, because in almost any real-world application, information about the region of interest is incomplete, e.g., the database of sensor data contains only a limited number of samples. Existing approaches cannot provide upper and lower bounds or depend on restrictive assumptions, e.g., the area must be convex. Our approach in turn is based on the natural assumption that it is possible to specify a minimal diameter for the feature in question. Given this assumption, we formally derive bounds on the area size, and we provide algorithms that compute these bounds from a database of sensor data, based on geometrical considerations. We evaluate our algorithms both with a real-world case study and with synthetic data

Deriving Bounds on the Size of Spatial Areas

Many application domains such as surveillance, environmental monitoring or sensor-data processing need upper and lower bounds on areas that are covered by a certain feature. For example, a smart-city infrastructure might need bounds on the size of an area polluted with fine-dust, to re-route combustion-engine traffic. Obtaining such bounds is challenging, because in almost any real-world application, information about the region of interest is incomplete, e.g., the database of sensor data contains only a limited number of samples. Existing approaches cannot provide upper and lower bounds or depend on restrictive assumptions, e.g., the area must be convex. Our approach in turn is based on the natural assumption that it is possible to specify a minimal diameter for the feature in question. Given this assumption, we formally derive bounds on the area size, and we provide algorithms that compute these bounds from a database of sensor data, based on geometrical considerations. We evaluate our algorithms both with a real-world case study and with synthetic data

Spatial Interference Cancelation for Mobile Ad Hoc Networks: Perfect CSI

Interference between nodes directly limits the capacity of mobile ad hoc networks. This paper focuses on spatial interference cancelation with perfect channel state information (CSI), and analyzes the corresponding network capacity. Specifically, by using multiple antennas, zero-forcing beamforming is applied at each receiver for canceling the strongest interferers. Given spatial interference cancelation, the network transmission capacity is analyzed in this paper, which is defined as the maximum transmitting node density under constraints on outage and the signal-to-interference-noise ratio. Assuming the Poisson distribution for the locations of network nodes and spatially i.i.d. Rayleigh fading channels, mathematical tools from stochastic geometry are applied for deriving scaling laws for transmission capacity. Specifically, for small target outage probability, transmission capacity is proved to increase following a power law, where the exponent is the inverse of the size of antenna array or larger depending on the pass loss exponent. As shown by simulations, spatial interference cancelation increases transmission capacity by an order of magnitude or more even if only one extra antenna is added to each node.Comment: 6 pages; submitted to IEEE Globecom 200

Active Markov Information-Theoretic Path Planning for Robotic Environmental Sensing

Recent research in multi-robot exploration and mapping has focused on sampling environmental fields, which are typically modeled using the Gaussian process (GP). Existing information-theoretic exploration strategies for learning GP-based environmental field maps adopt the non-Markovian problem structure and consequently scale poorly with the length of history of observations. Hence, it becomes computationally impractical to use these strategies for in situ, real-time active sampling. To ease this computational burden, this paper presents a Markov-based approach to efficient information-theoretic path planning for active sampling of GP-based fields. We analyze the time complexity of solving the Markov-based path planning problem, and demonstrate analytically that it scales better than that of deriving the non-Markovian strategies with increasing length of planning horizon. For a class of exploration tasks called the transect sampling task, we provide theoretical guarantees on the active sampling performance of our Markov-based policy, from which ideal environmental field conditions and sampling task settings can be established to limit its performance degradation due to violation of the Markov assumption. Empirical evaluation on real-world temperature and plankton density field data shows that our Markov-based policy can generally achieve active sampling performance comparable to that of the widely-used non-Markovian greedy policies under less favorable realistic field conditions and task settings while enjoying significant computational gain over them.Comment: 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), Extended version with proofs, 11 page

Mitigating Interference in Content Delivery Networks by Spatial Signal Alignment: The Approach of Shot-Noise Ratio

Multimedia content especially videos is expected to dominate data traffic in next-generation mobile networks. Caching popular content at the network edge has emerged to be a solution for low-latency content delivery. Compared with the traditional wireless communication, content delivery has a key characteristic that many signals coexisting in the air carry identical popular content. They, however, can interfere with each other at a receiver if their modulation-and-coding (MAC) schemes are adapted to individual channels following the classic approach. To address this issue, we present a novel idea of content adaptive MAC (CAMAC) where adapting MAC schemes to content ensures that all signals carry identical content are encoded using an identical MAC scheme, achieving spatial MAC alignment. Consequently, interference can be harnessed as signals, to improve the reliability of wireless delivery. In the remaining part of the paper, we focus on quantifying the gain CAMAC can bring to a content-delivery network using a stochastic-geometry model. Specifically, content helpers are distributed as a Poisson point process, each of which transmits a file from a content database based on a given popularity distribution. It is discovered that the successful content-delivery probability is closely related to the distribution of the ratio of two independent shot noise processes, named a shot-noise ratio. The distribution itself is an open mathematical problem that we tackle in this work. Using stable-distribution theory and tools from stochastic geometry, the distribution function is derived in closed form. Extending the result in the context of content-delivery networks with CAMAC yields the content-delivery probability in different closed forms. In addition, the gain in the probability due to CAMAC is shown to grow with the level of skewness in the content popularity distribution.Comment: 32 pages, to appear in IEEE Trans. on Wireless Communicatio

A HEURISTIC FIXED-CHARGE QUADRATIC ALGORITHM

Research Methods/ Statistical Methods,