In this paper, we consider the two-user multichannel rendezvous problem in a cognitive radio network (CRN) and derive tight lower bounds for maximum time-to-rendezvous (MTTR) and maximum conditional time-to-rendezvous (MCTTR) of various channel hopping (CH) schemes under a channel loading constraint. In the symmetric and synchronous setting, we propose a novel Cycle-Adjustable Channel Hopping (CACH) scheme to achieve the MTTR lower bound (when the channel loading is bounded above by 1/u with u being a prime power). Thus, the MTTR lower bound is tight and the CACH scheme is optimal in minimizing MTTR among all the symmetric and synchronous CH schemes under the same channel loading constraint. In the asymmetric setting, we show that the classical wait-for-mommy strategy can be used to achieve the MCTTR lower bound, and thus it is optimal. In the symmetric and asynchronous setting, we also show a hierarchical construction of an asynchronous CH sequence by using two smaller asynchronous CH sequences. To further understand the effect of channel loading to the other performance metrics in a CRN, we perform various computer simulations for various CH schemes. Our simulation results show that the average time-to-rendezvous of CACH is independent of the total number of channels, and it is also robust to the disturbance of primary users.

Establishing control channels in a cognitive radio network (CRN) is an important and challenging problem. To cope with the problem of control channel saturation and the problem of channel blocking by primary users, channel hopping (CH) schemes are commonly used in the literature for control channel establishment in CRNs. There are three metrics that are widely used for evaluating the performance of CH schemes: (i) degree of overlapping (the number of distinct rendezvous channels), (ii) worst case time-to-rendezvous (TTR), and (iii) system load. In this paper, we focus on the symmetric and synchronous setting and propose a novel Cycle-Adjustable Channel Hopping (CACH) scheme that outperforms several existing CH schemes, including SSCH and QCH, in terms of the three metrics. The key idea of CACH is to create an additional layer of logical channels on the top of physical channels so that the cycle of channel hopping sequences can be adjusted to optimize system performance. The mathematic tools for our scheme are based on the operations in Galois fields that are more general than the prime number modular arithmetic used in SSCH. We show that CACH is much more general than SSCH and it can achieve the maximum degree of overlapping while allowing the worst case TTR to be adjustable. It is also much better than QCH in terms of reducing system load while keeping the same degree of overlapping and the same worst case TTR. Our simulation results show that CACH outperforms several existing schemes in many other aspects, including throughput, and robustness to the disturbance of PUs.

In this paper, we study the delay minimization problem for wireless data broadcasting in cognitive radio networks (CRN). In CRN, each secondary user (SU) has a set of available channels to communicate with each other but there may not be a common available channel set among all the SUs. Therefore, a simple way to shorten the broadcasting delay among them is to select a minimal set of available channels which cover all SUs in the network. However, this scheme may incur a fairness problem in resource sharing among SUs and also lower the system resource utilization. To tackle this problem, we assign channels to SUs for data broadcasting service in downlink sub-frames by jointly considering broadcast delay minimization and fair resource sharing. We formulate this problem as a nonlinear integer programming problem, and show that it is NP-hard by applying a reduction from the 3-dimensional matching problem. We then propose an enumerative algorithm to find an optimal solution and design a greedy-based polynomial-time heuristic algorithm to reduce the computational complexity. The simulation results show that our enumerative algorithm not only effectively reduces the broadcasting delay but also ensures the fairness among SUs in resource sharing. We also show that the performance gap between our enumerative algorithm and our heuristic algorithm is small.

In this paper, we study how to improve the usage of wireless spectrum for secondary users (SUs) in cognitive radio networks (CRNs) by cooperative transmissions. There are two types of cooperation in CRNs, namely, vertical cooperation, which takes place between primary users (PUs) and SUs, and horizontal cooperation, which occurs among SUs. For vertical cooperation, PUs can lease their frequency bandwidth for a fraction of time to SUs in exchange for better transmission quality through cooperative transmission from the SUs. For horizontal cooperation, some SUs will help other SUs to increase their transmission throughput through cooperative transmissions without interfering with their neighboring PUs. In fact, both vertical cooperation and horizontal cooperation can improve the system throughput. Hence, if both types of cooperation can be supported in a CRN, the system throughput can be improved effectively. However, SUs cannot perform both types of cooperation simultaneously. Therefore, determining the kind of cooperation for an SU is an important issue on the system throughput improvement. We solve this problem via a greedy distributed solution in which the decision made by each SU depends only on the local information. We show by simulations that our proposed method outperforms traditional vertical cooperation schemes or horizontal cooperation schemes in terms of better resource utilization and higher system throughput.

In this paper, we propose a channel-hopping MAC protocol called dynamic hopping MAC (DH-MAC) to improve the utilization of spectrum in cognitive radio networks. In DH-MAC, each secondary user (SU) switches its operation channel with a channel-hopping sequence which is adaptive to the activity of primary users (PUs). Our proposed DH-MAC mechanism enjoys the following merits. 1) It needs no dedicated common control channel for operation. 2) It supports multiple rendezvous for multiple simultaneous transmission pairs of SUs within the interfering range. 3) The rendezvous channel of two SUs will not be blocked by PUs for a long time. 4) It allows SUs a higher probability to operate on available channels as compared with existing schemes. 5) One cognitive radio transceiver is sufficient. The simulation results show that DH-MAC outperforms existing schemes in terms of higher aggregate throughput and more robustness to the disturbance of PUs.