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:
In this paper, a cross-layer framework to jointly optimize spectrum sensing and scheduling in resource constrained agile wireless networks is presented. A network of secondary users (SUs) accesses portions of the spectrum left unused by a network of licensed primary users (PUs). A central controller (CC) schedules the traffic of the SUs, based on distributed compressed measurements collected by the SUs. Sensing and scheduling are jointly controlled to maximize the SU throughput, with constraints on PU throughput degradation and SU cost. The sparsity in the spectrum dynamics is exploited: leveraging a prior spectrum occupancy estimate, the CC needs to estimate only a residual uncertainty vector via sparse recovery techniques. The high complexity entailed by the POMDP formulation is reduced by a low-dimensional belief representation via minimization of the Kullback-Leibler divergence. It is proved that the optimization of sensing and scheduling can be decoupled. A partially myopic scheduling strategy is proposed for which structural properties can be proved showing that the myopic scheme allocates SU traffic to likely idle spectral bands. Simulation results show that this framework balances optimally the resources between spectrum sensing and data transmission. This framework defines sensing-scheduling schemes most informative for network control, yielding energy efficient resource utilization.

Cited Abstract(s):
[1]: In this paper, a cross-layer framework for joint distributed spectrum sensing, estimation and scheduling in agile wireless networks is presented. A network of secondary users (SUs) opportunistically accesses portions of the spectrum left unused by a network of licensed primary users (PUs). A central controller (CC) schedules the spectrum bands detected as idle for access by the SUs, based on compressed measurements acquired by the SUs and local feedback information from the PUs. The sparsity in the spectrum occupancy dynamics is exploited: leveraging the spectrum occupancy estimate in the previous slot, the CC needs to estimate only a residual uncertainty vector via sparse recovery techniques, thus few measurements suffice. The sensing probability of the SUs and the spectrum scheduling are adapted over time by the CC, based on the current spectrum occupancy estimate, and jointly optimized so as to maximize the SU throughput, under constraints on the PU throughput degradation and the sensing-transmission cost incurred by the SUs. The high dimensionality of the POMDP formulation is reduced by resorting to a compact state space representation via minimization of the Kullback-Leibler divergence. Simulation results demonstrate improvements up to 70 in the SU throughput over a scheme where sensing is done only locally at the CC, at a fraction of the sensing cost with respect to a scheme where sensing is done in each slot by the SUs.

[2]: Cognitive radio methodologies have the potential to dramatically increase the throughput of wireless systems. Herein, control strategies which enable the superposition in time and frequency of primary and secondary user transmissions are explored in contrast to more traditional sensing approaches which only allow the secondary user to transmit when the primary user is idle. In this paper, the optimal transmission policy for the secondary user when the primary user adopts a retransmission-based error control scheme is investigated. The policy aims to maximize the secondary users' throughput, with a constraint on the throughput loss and failure probability of the primary user. Due to the constraint, the optimal policy is randomized, and determines how often the secondary user transmits according to the retransmission state of the packet being served by the primary user. The resulting optimal strategy of the secondary user is proven to have a unique structure. In particular, the optimal throughput is achieved by the secondary user by concentrating its transmission, and thus its interference to the primary user, in the first transmissions of a primary user packet. The rather simple framework considered in this paper highlights two fundamental aspects of cognitive networks that have not been covered so far: 1) the networking mechanisms implemented by the primary users (error control by means of retransmissions in the considered model) react to secondary users' activity; 2) if networking mechanisms are considered, then their state must be taken into account when optimizing secondary users' strategy, i.e., a strategy based on a binary active idle perception of the primary users' state is suboptimal.

[3]: This paper introduces a novel technique for access by a cognitive Secondary User (SU) to a spectrum with an incumbent Primary User (PU), which uses Type-I Hybrid ARQ. The technique allows the SU to perform selective retransmissions of previously corrupted SU data packets. The temporal redundancy introduced by the primary ARQ protocol and by the selective SU retransmission process can be exploited by the SU receiver to perform Interference Cancellation (IC) over the entire interference pattern, thus creating a "clean" channel for the decoding of the concurrent message. The chain decoding technique, initiated by a successful decoding operation of a SU or PU message, consists in the iterative application of IC, as previously corrupted messages become decodable. Based on this scheme, we design an optimal policy that maximizes the SU throughput under a constraint on the average long-term PU throughput degradation. We show that the optimal policy can be found by first optimizing the SU access policy using a Markov Decision Process formulation, and then applying a chain decoding protocol defined by five basic rules. Such an approach enables a compact state representation of the protocol, and its efficient numerical optimization. Finally, we show by numerical results the throughput benefit of the proposed technique.
In this work, we assume that the PUs employ a retransmission process, which induces structure in the PU signal. This structure has been exploited in [2] to design adaptive SU access techniques, and in [3] to design smart interference cancellation techniques that exploit redundancy introduced by retransmission. In this work, instead, we exploit the structure in the signal as a result of sparse network dynamics, to design compressive spectrum sensing techniques and sparse recovery schemes. We extend the model studied in [1] to include a more general traffic model for the SU network, and propose a low-complexity solution based on the aforementioned partially myopic scheduling scheme.