You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We formulate throughput maximizing, max-min fair, weighted max-min fair, and proportionally fair scheduling problems for cognitive radio networks managed by a centralized cognitive base station. We propose a very general scheduling model accomplishing goals such as making frequency, time slot, and data rate allocation to secondary users with possibly multiple antennas, in a heterogenous multi-channel and multi-user scenario. Moreover, our schedulers ensure that reliable communication between the cognitive base station and secondary users are maintained, no collisions occur among secondary users, and primary users in the service area of the cognitive base station are not disturbed. Two distinctive features of our fair schedulers are that they provide joint temporal and throughput fairness, and take throughput values experienced by secondary users in the recent past, referred to as window size, into account and use this information in the current scheduling decision. We also propose a heuristic algorithm for our fair schedulers and demonstrate through simulations that our proposed heuristic yields very close solutions to the values obtained from the optimization softwares. Furthermore, we make extensive simulations to evaluate our schedulers' performance in terms of both total throughput and fairness for varying number of secondary users, frequencies, antennas, and window size.

Cited Abstract(s):
[1]: In this paper, we investigate a joint scheduling and power control for an infrastructure-based cognitive radio network (CRN) in coexistence with a cellular primary radio network (PRN). The PRN uses a set of licensed nonoverlapping orthogonal frequency channels for transmission. This set of channels is also accessed in an opportunistic manner by a set of cognitive radio base stations (CR-BSs) to support secondary users (SUs). The problem is formulated to maximize the spectrum utilization of SUs without causing excessive interference to active primary users (PUs) of the PRN. In addition, all the serviced SUs must meet a certain Quality of Service (QoS), such as satisfying a predefined signal to interference noise ratio (SINR). A centralized solution for joint scheduling and power control is derived to make the global accessing decision for all unserved SUs. With the assumption that the knowledge of all subscribers is available, a coordinator of the CRN can use the joint scheduling and power control algorithm to maximize the spectrum utilization of serviced SUs by solving a mixed-integer linear programming (MILP) with an NP-hard complexity. To avoid the NP-hard complexity, we propose a suboptimal heuristic greedy algorithm that can be obtained at a much lower complexity based on the coloring interference graph among unserved SUs effected by serviced SUs and active PUs. Its superior performance over the existing algorithms is demonstrated through simulations.

[2]: 

[3]: Cognitive radio networks (CRNs) have the potential to utilize spectrum efficiently and are positioned to be the core technology for the next-generation multihop wireless networks. An important problem for such networks is its capacity. We study this problem for CRNs in the SINR (signal-to-interference-and-noise-ratio) model, which is considered to be a better characterization of interference (but also more difficult to analyze) than disk graph model. The main difficulties of this problem are two-fold. First, SINR is a nonconvex function of transmission powers; an optimization problem in the SINR model is usually a nonconvex program and NP-hard in general. Second, in the SINR model, scheduling feasibility and the maximum allowed flow rate on each link are determined by SINR at the physical layer. To maximize capacity, it is essential to follow a cross-layer approach, but joint optimization at physical (power control), link (scheduling), and network (flow routing) layers with the SINR function is inherently difficult. In this paper, we give a mathematical characterization of the joint relationship among these layers. We devise a solution procedure that provides a (1- ) optimal solution to this complex problem, where is the required accuracy. Our theoretical result offers a performance benchmark for any other algorithms developed for practical implementation. Using numerical results, we demonstrate the efficacy of the solution procedure and offer quantitative understanding on the interaction of power control, scheduling, and flow routing in a CRN.
Most of the scheduling works about underlay spectrum sharing in the literature focused on rate and power allocation without emphasizing other criteria such as frequency allocation, possibly having multiple antennas, ensuring reliable communication, and joint temporal throughput fairness. The work in [1] proposed a joint scheduling and power control scheme for centralized CRNs. Authors in [3] focused on capacity maximization in multi-hop CRNs. None of the works in [1] [2] focused on issues such as fairness or multiple antennas.