# Stable Throughput Analysis of Heterogeneous Hybrid FSO/RF Networks with Cognitive Radio Capability
###### Abstract  
This study explores the potential of heterogeneous hybrid Free Space Optical (FSO) and Radio Frequency (RF) cognitive networks, which feature both cooperative and economic systems. The cooperative system is defined as a heterogeneous network where the hybrid FSO/RF node possesses dedicated RF resources and shares these resources to create additional transmission opportunities. In contrast, the low-cost economic system consists of a heterogeneous network where only an RF node has RF resources, and the hybrid node shares these resources. We provide a comprehensive analysis for each system, employing stay-and-switch (SAS) and simultaneous multipacket transmission (SMT) methods to ensure a thorough understanding of its performance. As a performance measure, we investigate the stability region of the proposed cognitive and economic systems and devise a reference system without cognitive capability for comparison. Numerical evaluations indicate that the cooperative system using SMT typically outperforms the reference system, increasing stability throughput by up to 52%. However, this advantage diminishes when SAS is used or in rainy conditions. The economic model shows performance levels comparable to the reference model, particularly when incoming traffic is low and when SAS is implemented in clear or hazy environments. a _sub_supp  
FSO/RF pairs each with dedicated RF frequencies (\(f_{1}\) and \(f_{2}\)) that are shared based on threshold signal-to-noise ratios (SNRs). In this configuration, each pair transmits over the FSO link if the SNR is above a specific threshold and switches to the RF link when the FSO SNR falls below the threshold, optimizing resource utilization while enhancing overall system performance. The existing literature presents a range of strategies aimed at improving the reliability of hybrid FSO/RF systems, broadly classified into three categories: hard switching, soft switching, and multiplexing. Hard switching schemes involve selecting either the FSO or RF link based on channel conditions, typically with feedback signals sent from the destination to the source to optimize the link selection [6; 7; 8; 9; 10; 11; 12; 13]. In soft switching schemes, which are more complex, the system utilizes joint coding or the maximum ratio combining (MRC) of FSO and RF signals to enhance performance under variable channel conditions [14; 15; 16; 17; 18; 19; 20]. Multiplexing schemes, in contrast, allow multiple signals to be transmitted over FSO and RF links simultaneously, leveraging the distinct strengths of both channels [21; 22]. Each of these switching schemes offers specific benefits, from maximizing link availability to optimizing the efficient use of resources. For hard-switching schemes, various hybrid FSO/RF systems have been developed to select the FSO or RF channel with the highest SNR, thus reducing the outage probability and error rates under different environmental conditions [6; 7; 8; 9; 10; 11; 12; 13]. Systems that incorporate decode-and-forward relays or multi-input-multi-output (MIMO) configurations have shown enhanced resilience by dynamically selecting FSO or RF channels according to channel state information [9; 10]. In contrast, soft-switching schemes rely on MRC to combine FSO and RF signals, thus minimizing the impact of atmospheric interference on signal quality [16; 19]. This study extends these approaches by analyzing configurations that focus on spectral efficiency, aiming to maximize data throughput by optimizing channel selection within hybrid FSO/RF frameworks. Multiplexing-based approaches also play a significant role, especially in systems with finite buffer sizes. These systems are designed to support simultaneous signal transmissions across FSO and RF links, storing data packets in buffers for optimized relay to the appropriate channel based on SNR thresholds [21; 22; 23]. By employing relay selection mechanisms, these systems seek to optimize buffer size to reduce data loss, improve throughput, and manage latency.