Diffuse Reflection Diameter in Simple Polygons

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with $n$ walls from any interior point light source is $\lfloor n/2 \rfloor - 1$. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.Comment: To appear in Discrete Applied Mathematic

Localization and cooperative communication methods for cognitive radio

We study localization of nearby nodes and cooperative communication for cognitive radios. Cognitive radios sensing their environment to estimate the channel gain between nodes can cooperate and adapt their transmission power to maximize the capacity of the communication between two nodes. We study the end-to-end capacity of a cooperative relaying scheme using orthogonal frequency-division modulation (OFDM) modulation, under power constraints for both the base station and the relay station. The relay uses amplify-and-forward and decodeand-forward cooperative relaying techniques to retransmit messages on a subset of the available subcarriers. The power used in the base station and the relay station transmitters is allocated to maximize the overall system capacity. The subcarrier selection and power allocation are obtained based on convex optimization formulations and an iterative algorithm. Additionally, decode-and-forward relaying schemes are allowed to pair source and relayed subcarriers to increase further the capacity of the system. The proposed techniques outperforms non-selective relaying schemes over a range of relay power budgets. Cognitive radios can be used for opportunistic access of the radio spectrum by detecting spectrum holes left unused by licensed primary users. We introduce a spectrum holes detection approach, which combines blind modulation classification, angle of arrival estimation and number of sources detection. We perform eigenspace analysis to determine the number of sources, and estimate their angles of arrival (AOA). In addition, we classify detected sources as primary or secondary users with their distinct second-orde one-conjugate cyclostationarity features. Extensive simulations carried out indicate that the proposed system identifies and locates individual sources correctly, even at -4 dB signal-to-noise ratios (SNR). In environments with a high density of scatterers, several wireless channels experience non-line-of-sight (NLOS) condition, increasing the localization error, even when the AOA estimate is accurate. We present a real-time localization solver (RTLS) for time-of-arrival (TOA) estimates using ray-tracing methods on the map of the geometry of walls and compare its performance with classical TOA trilateration localization methods. Extensive simulations and field trials for indoor environments show that our method increases the coverage area from 1.9% of the floor to 82.3 % and the accuracy by a 10-fold factor when compared with trilateration. We implemented our ray tracing model in C++ using the CGAL computational geometry algorithm library. We illustrate the real-time property of our RTLS that performs most ray tracing tasks in a preprocessing phase with time and space complexity analyses and profiling of our software

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop