A formal proof of the optimal frame setting for Dynamic-Frame Aloha with known population size

In Dynamic-Frame Aloha subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size ${\cal N}$ is known, numerical evaluations show that the maximum efficiency is achieved by setting the frame length equal to the backlog size at each subsequent frame; however, at best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct, we also prove that the asymptotical efficiency in the optimal case is $e^{-1}$, provide upper and lower bounds for the length of the entire transmission period and show that its asymptotical behaviour is $\sim ne-\zeta \ln (n)$, with $\zeta=0.5/\ln(1-e^{-1})$.Comment: 22 pages, submitted to IEEE Trans. on Information Theor

Wireless Localization Systems: Statistical Modeling and Algorithm Design

Wireless localization systems are essential for emerging applications that rely on context-awareness, especially in civil, logistic, and security sectors. Accurate localization in indoor environments is still a challenge and triggers a fervent research activity worldwide. The performance of such systems relies on the quality of range measurements gathered by processing wireless signals within the sensors composing the localization system. Such range estimates serve as observations for the target position inference. The quality of range estimates depends on the network intrinsic properties and signal processing techniques. Therefore, the system design and analysis call for the statistical modeling of range information and the algorithm design for ranging, localization and tracking. The main objectives of this thesis are: (i) the derivation of statistical models and (ii) the design of algorithms for different wire- less localization systems, with particular regard to passive and semi-passive systems (i.e., active radar systems, passive radar systems, and radio frequency identification systems). Statistical models for the range information are derived, low-complexity algorithms with soft-decision and hard-decision are proposed, and several wideband localization systems have been analyzed. The research activity has been conducted also within the framework of different projects in collaboration with companies and other universities, and within a one-year-long research period at Massachusetts Institute of Technology, Cambridge, MA, USA. The analysis of system performance, the derived models, and the proposed algorithms are validated considering different case studies in realistic scenarios and also using the results obtained under the aforementioned projects