Fault-Tolerant Cooperative Signal Detection for Petahertz Short-Range Communication With Continuous Waveform Wideband Detectors

Motivated by unique scattering properties at petahertz frequencies, we present a novel statistical model of fault-tolerant cooperative signal detection for short-range optical petahertz wireless communications, where a single-scattering assumption holds valid. We characterize the received non-line-of-sight (NLOS) signal by a fault-tolerant continuous waveform wideband detector with a non-zero failure probability. To better reflect the physical properties of the petahertz communication, both signal-independent and signal-dependent noise sources are considered in characterizing the received signal. The distribution of the received signal is quantified with each scattered path following the Malaga distribution. We leverage the location flexibility of randomly distributed collaborative users, considering each user experiences an independent channel condition. Utilizing the Neyman-Pearson criterion, we develop the binary hypothesis testing problem and subsequently derive the likelihood ratio for the test statistics. Moreover, to quantify the performance, a framework is developed for the average area under the receiver operating characteristic (ROC) curve for both single user and cooperative scenarios. An optimal decision fusion with a majority rule for fault-tolerant signal detection is applied to exploit the maximum spectrum opportunity. It is found that with the optimal voting rule and for a given target error rate, the network requires fewer collaborative secondary users than the total number of users available in an optical network. However, in the limiting case, it is shown that, as the cost function approaches its minimum or maximum value within its allowable range, the optimal number of collaborative users becomes independent of the failure probabilities. With the realistic assumption of fault-tolerant users, it is found that the false alarm probability increases faster than the detection probability.