###### Abstract  
In this paper, we investigate users' performance under the hybrid spectrum access model in the massive cognitive radio network (CRN), where multiple primary users (PUs) and secondary users (SUs) transmit on the same channel simultaneously. SUs first detect the state of the channel via channel sensing and select an appropriate channel access scheme (either underlay or overlay) for their transmissions based on the outcome of the channel sensing. When at least one PU is active, SUs transmit under the underlay channel access scheme by employing the power control technique to ensure that the interference generated in the primary network is below the pre-defined interference threshold. In the absence of PU, SUs transmit with full transmit power under the overlay channel access scheme, thereby maximizing their throughput. Using the tool of stochastic geometry, we obtained tractable analyses for important metrics such as success probability, throughput, and the average age of information (AoI) in both primary and secondary networks, while capturing the interference between the two networks. The obtained analyses offer an efficient way to understand the metrics of AoI, throughput and success probability in the hybrid spectrum access-based CRN. We further compared users' performance under the hybrid spectrum access scheme with performances under overlay and underlay spectrum access schemes. The outcome of the numerical simulations shows that the hybrid spectrum access scheme can significantly improve the performance of users in the network, while also capturing more key features of real-life systems. a 2021 17 January 2021 23 February 2021 232 232 232 232 232 232 232 232 2  
In the overlay channel access scheme, SUs are not allowed to transmit in the presence of PUs and must regularly perform channel sensing to determine the state of the channel [2]. If the outcome of the channel sensing indicates the presence of at least one PU on any typical channel, no SU is allowed to access such a channel for transmissions. SUs must, therefore, wait until such a channel is idle or can switch to any other idle channel via the channel switching process. Hence, interference resulting from the activities of SUs at the PUs in the overlay channel access scheme depends on the sensing accuracy level of SUs. Although interference in the overlay channel access scheme can be significantly controlled and reduced, it may be difficult to satisfy SUs' spectrum access requirements, especially on channels with the dominant presence of PUs, since SUs must always vacate the band before the arrival of PUs on such channels. The underlay spectrum access scheme, on the other hand, allows SUs to transmit on channels belonging to PUs at any time, provided that the interference received at any tagged PU is below the pre-defined maximum allowable interference level-known as interference temperature. Hence, SUs are expected to adopt appropriate power control techniques during transmissions. The need to adopt adequate power control techniques in the underlay model, however, means that the underlay spectrum access CRN is a more aggressive spectrum access technique [1]. The last paradigm is the hybrid model which combines the uniqueness of both the underlay and overlay models. The hybrid spectrum access model has, however, received less attention because of the difficulty in obtaining various analyses of interest for such a model. The hybrid spectrum access mechanism permits SUs' transmissions in both the overlay and underlay schemes depending on the state of the channel [1; 3] and has been receiving attention recently owing to the need to compare its performance and demonstrate its advantages over the conventional underlay and overlay spectrum access models. In the hybrid model, SUs must carry out regular channel sensing for effective detection of PUs' channel information. Each SU must then select an appropriate channel access scheme based on the sensing outcome.