@article{16479,
  author = {Leila Ben Saad and Baltasar Beferull-Lozano and Elvin Isufi},
  title = {Quantization Analysis and Robust Design in Distributed Graph Filters},
  abstract = {Distributed graph filters have recently found applications in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and reconstruction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities.Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the twomost common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive analysis, we devise theoretical performance guarantees on the filter performancewhen the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more reduction of the quantization noise than in the fixed-stepsize quantization. For ARMAgraph filters,we showthat decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both time-invariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.},
  year = {2021},
  journal = {IEEE Transactions on Signal Processing},
  volume = {70},
  pages = {643 - 658},
  month = {12/2021},
  publisher = {IEEE},
  address = {IEEE Transactions on Signal Processing},
  issn = {1053-587X},
  url = {https://ieeexplore.ieee.org/document/9665348},
  doi = {10.1109/TSP.2021.3139208},
  note = {This work is a joint collaboration between SimulaMet  and University of Agder. This work was supported in part by the TOPPFORSK WISECART under Grant 250910/F20 and in part by the IKTPLUSS INDURB under Grant 270730/O70 from the Research Council of Norway.},
}