## 1 Introduction
The compressed sampling theory points out that any sparse signal can be compressed and sampled simultaneously [21]. Preliminary work has been done to exploit CS for wideband spectrum sensing based upon signal sparsity in frequency domain. [PERSON] et al. [22] firstly carried out the work to take advantage of CS theory to acquire wideband signals using sub-Nyquist sampling rate. Recently, [PERSON] et al. [23] presented a structured compressed sensing. [PERSON] et al. [24] proposed a power spectrum blind sampling (PSBS) algorithm trying to reconstruct power spectrum. While the CS literature has intensely focused on problems in signal reconstruction or approximation typically relying on the assumption of sparsity, it is frequently necessary that signals are acquired only for the purpose of making detection in many signal processing applications without reconstructing the signal [25]. In terms of the application of SS in satellite communications due to the spectrum scarcity, only when the wideband signal of primary system is found absent can the SU utilize the spectrum for transmission. In this context, wideband spectrum sensing is equivalent to wideband signal detection. Hence, CS-based wideband signal detection approach, which places no assumptions on the signals being sparse or compressible, provides more spectrum access opportunities for SU with sufficient protection to PU. The sensing performance of a single node may degrade in wireless channels for several reasons such as the hidden node problem, shadowing, multipath fading, and interference/noise uncertainty. To address these issues, various collaborative spectrum sensing (CSS) schemes among multiple secondary users have been proposed [10; 26; 27; 28; 29; 30], in which several nodes collaborate with each other to enhance the overall sensing performance. According to the frame structure of periodic spectrum sensing (PSS) [31; 32], the sensing time has a direct impact on the sensing performance, such as the probabilities of detection and false alarm, which also affects the data transmission of SU because it determines transmission duration when frame length is fixed. Therefore, there exists a tradeoff between sensing time and transmission duration. The optimal sensing time varies with different optimization objectives. [PERSON] et al. [33] proposed joint optimization of the sensing time and the parameter of CSS scheme to maximize the throughput of the SU. [PERSON] et al. [34] considered a joint design of energy efficient sensing and transmission duration for CR system. [PERSON] et al. [35] investigated the efficient spectrum sensing time with the optimization of transmission delay. [PERSON] et al. [PERSON] et al. (2017) developed a theoretical framework to optimize the sensing parameters, in such a way as to maximize the sensing efficiency subject to interference avoidance constraints. Additionally, [PERSON] et al. [PERSON] et al. (2018) proposed a weighted bandwidth-based cooperative spectrum sensing scheme for satellite communication systems to detect PU in time throughout the whole frame at the cost of degraded spectrum utilization efficiency. To the best of our knowledge, most of the academic and industrial activities are concerning CR in terrestrial wireless communication network for the scenario of narrowband cooperative spectrum sensing. The metrics of spectral efficiency deserves further investigation and discussion, since it becomes particularly important for LEO MSSs due to the scarcity of frequency resources. This paper mainly investigates the problem of joint designing the compressed sensing time and the parameters (i.e., hard decision fusion threshold, scheduling strategy and number of cooperative SU) of CSS scheme to maximize the spectral efficiency of SU, subject to adequate protection to PU. The main contributions of this paper are as follows. Firstly, we establish the wideband spectrum sensing model based on compressed detection.