# Distributed-Satellite-Clusters-Based Spectrum Sensing with Two-Stage Phase Alignment
###### Abstract  
We investigate a distributed-satellite-clusters (DSC)-system-based spectrum sensing, to enhance the ability for sensing weak signals. However, the spectrum-sensing performance may be significantly decreased by the phase deviations among different satellite clusters, where the deviations may be caused by the movement and the perturbation of satellites. To eliminate such a decrement, we propose a cooperative spectrum-sensing scheme in the presence of phase deviations, where the deviations are alleviated by a special two-stage phase synchronization. Specifically, the phase compensation is first performed relying on broadcasting reference signals and the ephemeris, to address the challenges of the deviations caused by the movement. Then, a two-bit feedback algorithm, having a dynamic disturbance step size, is further adopted for controlling and mitigating the deviations caused by the perturbation. Additionally, we provide the closed-form expression of the correct detection probability of the proposed spectrum-sensing scheme, using the specially derived probability density function of the sum of the shadowed-Rician random variables with independently identical distribution. Simulation results show that the proposed scheme can achieve the best spectrum-sensing performance, comparing with the traditional energy detection, eigenvalue ratio test and the generalized likelihood ratio test. s 2022222222222222222222222222  
(NGEO) and noise. On this basis, ref. [6] utilized the GLRT and maximum a-posterior criterion to derive the decision threshold to detect spectrum misuse in the satellite-terrestrial spectrum-sharing system. However, the basic idea behind the algorithms is the extension of GLRT to some extent. Overall, all these cooperative spectrum-sensing methods only achieve a limited improvement for spectrum-sensing performance with a single satellite, especially for sensing targets with a low signal to noise ratio (SNR). With such an insignificant improvement, it is difficult to meet the requirements of some targets with high sensitivity requirements. Moreover, these algorithms generally migrate the cooperative sensing algorithm from a terrestrial communication system directly to a satellite, without considering the particularity of the satellite system. In contrast with terrestrial communication, satellites can cooperate with each other through exchanging their sensing data via inter-satellite links (ISL), which have a wide bandwidth and can complete almost error-free transmission in a vacuum environment. This unique characteristic provides new possibilities for satellite cooperation, so a distributed satellite cluster (DSC) at a short distance from each other is proposed. In general, a DSC is made up of several satellites in the same or adjacent orbit [7]. Compared with conventional satellite constellations, DSC has the advantages of low cost, high reliability and being a reconfigurable system. To the present, it has been widely used in three-dimensional imaging, meteorology, navigation and other fields [8; 9]. While, in the field of communications, virtual beamforming based on DSC was proposed in [10], which improves the system capacity through the cooperation of a multi-satellite. With a reasonable attitude-control mechanism and powerful laser link, a DSC can exploit the spatial degree of freedom to improve the receiving gain of the target signal while degrading that of the interference signal [11; 12]. Inspired by this, we use a DSC for spectrum sensing, in which the sensing signals are directly in-phase stacked, so as to enhance the sensing ability of weak signals by improving the received SNR. Although a DSC is very attractive for sensing low SNR signals, the signal-level soft fusion requires time, frequency, and phase synchronization among satellites [13]. However, since the distance from a DSC to the ground is much greater than the distance between satellites, the time delay and Doppler frequency shift of signals received by satellites are approximately the same in a certain degree.