# Distributed-Satellite-Clusters-Based Spectrum Sensing with Two-Stage Phase Alignment
###### Abstract
In addition, some existing research has focused on time-frequency synchronization between satellites, and the proposed methods can meet the requirements of spectrum sensing [14; 15; 16]. In practice, the location information of the target is difficult to obtain in spectrum sensing. Coupled with the high dynamics and perturbation of the satellite, the phase offset from each concomitant to the master satellite cannot be known in advance. However, the beamforming gain is achieved depending on the phase alignment among satellites in the DSC. Thus, the key problem is to compensate the phase deviations. To some extent, the solution to this problem can be identified from the distributed and collaborative beamforming technology widely used in wireless sensor networks [17; 18]. A one-bit feedback mechanism was proposed, wherein each transmitter adjusted its phase offset independently and iteratively to achieve carrier phase alignment at the distant receiver [19; 20]. On this basis, a beamforming algorithm with a directional disturbance factor was presented in [21], which can track the direction of signal strength increases and improve convergence speed. However, since only the positive feedback information was utilized, the convergence speed and performance stability of these algorithms were insufficient. To overcome these limitations, a hybrid algorithm using successive negative-feedback information was studied in [22]. However, that algorithm only considers reducing the step size to improve the convergence speed, but, when the surrounding environment changes suddenly, the performance will deteriorate, resulting in poor applicability in high dynamic scenarios. In this paper, we present a cooperative spectrum-sensing scheme based on the DSC system (SS_DSC) to enhance the sensing ability of weak signals with low SNR. A fast convergence algorithm that can select an appropriate perturbation size is proposed so as to improve the strength of the sensing target at the satellite receiver. In particular, the contributions of this article can be summarized as follows. 1. We conceive a general framework for cooperative spectrum sensing exploiting the DSC system. Based on this framework, a two-stage phase alignment method is conceived to improve the strength of the sensing signal. To be specific, in the first stage, the phase compensation is to eliminate the phase dynamics caused by satellite movement; the other is to eliminate the random phase deviations caused by satellite perturbation and non-ideal synchronization between satellites. 2. We propose a two-bit feedback algorithm to eliminate the random phase in a second stage. Such an algorithm can achieve a faster convergence speed and a better stability, relying on adjusting the disturbance step according to the dynamic environment. 3. We present a closed-form expression for the probability density function (PDF) of the sum of independent and identically distributed (i.i.d.) shadowed-Rician (SR) random variables. Based on the new PDF results, we derive the closed-form expression of the correct detection probability (\(P_{d}\)) for the considered DSC where the satellite link undergoes SR fading. The organization of this paper is as follows. Section 2 describes the system model, based on which we analyze how to obtain the optimized beamforming weight vectors. Section 3 details the two-stage phase alignment frame. Section 4 derives the PDF expression for the sum of multiple i.i.d. SR RVs and the expression of \(P_{d}\) for the considered SS_DSC system. The results and discussion are presented in Section 5 and this paper is concluded in Section 6.