Paolo Banelli

Giuseppe Baruffa, Luca Rugini, Francesco Binucci et al.

Fleets of autonomous vehicles (AV) often are at the core of intelligent transportation scenarios for smart cities, and may require a wireless Internet connection to offload computer vision tasks to data centers located either in the edge or the cloud section of the network. Cooperation among AVs is successful when the environment is unknown, or changes dynamically, so as to improve coverage and trip time, and minimize the traveled distance. The AVs, while mapping the environment with range-based sensors, move across the wireless coverage areas, with consequences on the experienced access bit rate, latency, and handover rate. In this paper, we propose to modify the cost of common path planning algorithms such as Dijkstra and A*, so that the best path solution takes into account not only the traveled distance, but also the radio coverage experience. To this aim, several radio-related cost-weighting functions are introduced and tested, to assess the performance of the proposed approaches with extensive simulations. The proposed mapping algorithm can achieve a mapping error probability below $2\%$, while the proposed path-planning algorithms extend the radio coverage of the AVs, with only a limited increase in traveled distance with respect to shortest-path existing methods, such as conventional Dijkstra and A* algorithms.

Paolo Di Lorenzo, Paolo Banelli, Elvin Isufi et al.

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.

Elvin Isufi, Geert Leus, Paolo Banelli

Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the input signal. In this work, we propose an extension of FIR graph filters to capture also the signal variations over time. By considering also the past values of the graph signal, the proposed FIR graph filter extends naturally to a 2-dimensional filter, capturing jointly the signal variations over the graph and time. As a particular case of interest we focus on 2-dimensional separable graph-temporal filters, which can be implemented in a distributed fashion at the price of higher communication costs. This allows us to give filter specifications and perform the design independently in the graph and temporal domain. The work is concluded by analyzing the proposed approach for stochastic graph signals, where the first and second order moments of the output signal are characterized.

Paolo Di Lorenzo, Sergio Barbarossa, Paolo Banelli et al.

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.