Topology Control in Multi-channel Cognitive Radio Networks with Non-uniform Node Arrangements Pin-Yu Chen† , Vasileios Karyotis‡ , Symeon Papavassiliou‡ , and Kwang-Cheng Chen† Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan ‡ School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), Zografou, Greece Emails: [email protected], [email protected], [email protected], [email protected] † Graduate

Abstract—Cognitive Radio (CR) techniques have been developed to allow ad hoc users to communicate with each other by exploiting the licensed bands of primary systems without disturbing the entrenched users. In this work, we take current approaches one step ahead and combine Topology Control (TC) techniques with CR technology, in order to improve operation and performance, even under the stringent and non-uniform arrangements of CR networks (CRNs). We propose a novel node-degree based Topology Control approach, denoted by Enhanced Cognitive Nearest Random Neighbor (e-CNRN), for multi-channel CRNs, aiming at maintaining network connectivity and adapting to environmental changes such as primary user activity and channel conditions. Compared with TC protocols in conventional ad hoc networks, e-CNRN requires only minimal local information and is specially designed to perform under nonuniform node arrangements, rendering e-CNRN a generic and robust distributed TC approach, especially suitable for multichannel CRNs as well. In addition, we leverage e-CNRN for distributively establishing a virtual common control channel for multi-channel CRNs. Through analysis and simulations we validate that e-CNRN guarantees network connectivity, while achieving efficient power control. Index Terms—Multi-channel Cognitive Radio networks, Distributed Topology Control, Non-uniform node arrangements, Virtual common control channel

I. I NTRODUCTION Cognitive Radio (CR) techniques have become a promising candidate technology for next-generation wireless broadband networks [1], due to the inefficient utilization of licensed spectrum bands [2]. Cognitive Radios enable dynamic spectrum access for secondary users (SUs), which spatially coexist with primary users (PUs). The Cognitive Radio Network (CRN) paradigm [3] requires that SUs must be robust to several environmental changes including primary system activity and channel conditions, in order to ensure that SU operation is transparent to PUs. The network formed by SUs (i.e. secondary network) should at least succeed in maintaining network connectivity, if not in addition enhance and increase its performance. The stringent and scarce transmission environment of CRNs (link quality and spectrum variability), the absence of central infrastructure and primary user activity, constitute the terminal arrangement of the secondary network highly asymmetric. In addition, mobility which is usually a requirement for SUs, in order to ensure a minimum of spectrum availability, leads

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Fig. 1. Multi-channel CRN under heterogeneous networks. Dark gray slotted blocks stand for primary system activity, orange slashed blocks stand for severe channel fading and gray empty blocks stand for available bands.

to non-homogeneous node distributions for the secondary network [4]. In order to alleviate the impairments of the secondary network, various resource allocation methods, such as power control [5], congestion avoidance [6], [7] and Topology Control [8], have been employed in wireless networks. The latter, in which each node controls its local neighborhood by varying its transmission power, seems a very promising technique for CRs as well, since it can offer dynamic adaptation and efficient trade-off between robustness and spatial reuse, as required. Topology Control techniques have been successful in addressing such considerations in a distributed and efficient manner for traditional networks [9]. However, in order to be combined with CRNs and heterogeneous network environments as shown in Fig. 1, Topology Control protocols need to become more resilient to instantaneous changes and address peculiarities of CRs, such as inhomogeneous node distributions. In this article we consider a more generic case of Topology Control compared to traditional approaches, i.e. Topology Control for multi-channel CRNs consisting of heterogeneous primary systems such as 802.11 WLAN, TV bands and cellular systems (Fig. 1). Exploiting capabilities of CRs, a SU has the opportunity to connect to other SUs by employing available

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channels (e.g., sub-carriers) of different primary systems, thus forming a multi-channel CRN. The assumed CRN may follow both the underlay or interweaved paradigm [10]. Intuitively, SUs exposed to various licensed bands suffer from the activity of heterogeneous primary systems and channel conditions. However, arising asymmetric node deployments, as well as spatial inter-system interference, render CRN more prone to become disconnected. Traditional Topology Control protocols [8] have been shown to be inefficient for such rapidly-varying environments [11] and especially for multi-channel CRN due to their lack of multi-channel topology awareness and spatial node inhomogeneity. To overcome such difficulties, we extend a randomized Topology Control approach for traditional networks, e-NRN [11], for multi-channel CRNs. Our aim is to increase robustness by employing a less demanding, with respect to overhead (convergence), approach for heterogeneous CRNs and by a randomization technique, establish power control with only the limited information obtained in the onehop neighborhood of a node. The proposed cognitive e-NRN (e-CNRN) technique preserves the advantages of distributed computation and small information exchange overhead, while achieving efficiently increasing connectivity performance. In addition, e-CNRN is exploited for dynamically establishing a Virtual Common Control Channel (VCCC) [12], in order to ensure spatial re-use among SU groups that share common communication channels. Since in a CRN such groups constantly alter, the proposed approach for establishing a VCCC can further enhance the reliability of dynamic spectrum access and CRN layering functions, due to its adaptive and distributed characteristics. The rest of this paper is organized as follows. In section II we describe the network model we considered, while in section III we present in detail the proposed e-CNRN Topology Control algorithm for Cognitive Radio Networks. Section IV presents an application of e-CNRN for efficiently establishing a VCCC, while in section V we present results regarding the operation of the proposed mechanism and analyze its performance. Finally, in section VI we conclude the paper. II. BACKGROUND AND S YSTEM M ODEL The benefits of Topology Control for stringent environments such as a CRN have been recently identified [13], [14]. Both [13], [14] approaches are based on a game-theoretic framework for jointly assigning transmission power and minimizing the number of channels required in a distributed fashion in wireless ad hoc networks. Among various Topology Control protocols, node-degree based protocols are regarded as a suitable approach for CRNs because they are fully distributed algorithms, requiring in general only local information. Furthermore, it has been shown [11] that a randomized Topology Control technique (i.e. Enhanced Nearest Random Neighbor(e-NRN), can be much more reliable than commonly adopted ones, e.g. the K-Neigh protocol [15], under non-uniform node arrangements, a setting commonly arising in wireless multi-hop networks. Despite the fact that K-Neigh achieves better power control in terms of

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physical neighbors, it essentially fails to maintain connectivity under non-uniform node arrangements, since every node is forced to connect to the K closest neighbors regardless of network topology. The e-NRN approach on the contrary increases spatial re-use, remaining close to the performance of K-Neigh, however, without negatively affecting connectivity. In this paper, we extend e-NRN, in order to make it suitable for multi-channel and heterogeneous CR networks and exploit it for establishing a virtual common control channel. Assume there are NP primary systems, co-existing with N SUs as shown in Fig. 1. We refer to disjoint licensed bands as separate bands. Note that channels can also be interpreted as sub-carriers or sub-channels of a primary system. With respect to the channel condition and primary system activity, SUs gather the spectrum status provided by CR [16], [17], i.e. the maximal transmission range that can be achieved by using each channel. Denoting by Υi the transmission range distribution of the ith SU over multiple channels, and NCj the number of channels of jth primary system, then NCj transmission radii are drawn from Υi in the normalized range [0, Rmax ], where Rmax is the physical transmission constraint, i.e. the maximum possible achievable transmission radius of a terminal. A direct observation is that the primary system activity and channel condition are inversely related to the characteristics of Υi , such as the mean transmission radius E[Υi ]. The majority of available approaches, both in the areas of CRNs and Topology Control, have considered uniform node arrangements. However, it has been shown, that even the simplest of network architectures may lead to non-uniform node distributions, due to mobility or variations in the channel environment. In this work, we aim at taking into account such discrepancy between research models and realistic environments and reduce the gap between them. An appropriate model for non-uniform node distributions, is that of the beta distribution β(Yα , Yβ ). Points distributed according to such continuous density function are confined within [0, 1], which better models finite realistic networks and allows various degrees of non-uniformity by modifying the Yα , Yβ parameters. We also assume that N SUs are deployed according to the beta distribution β(2, 2) over the normalized region [0, 1] × [0, 1]. We consider that two SUs are neighbors if they are within the transmission range of each other for at least one common channel, i.e. we exclude the scenario of asymmetric communication. In this work we assume the transmission radius of SU is generated from a truncated normal distribution Υi (r) =

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III. E NHANCED C OGNITIVE N EAREST R ANDOM N EIGHBORS ( E -CNRN) Connectivity

In this section we describe in detail the operation of the proposed enhanced Cognitive Radio based Topology Control approach.

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Algorithm 1 e-CNRN protocol for a generic node i Input: Initial node degree di , one-hop node degree dk of kth neighbor, node degree threshold dmin Output: Final node degree Xi Initial stage: Neighborhood discovery and one-hop node degree information feedback \ Randomized new node degree \ if di ≤ dmin then X i ← di else Xi ← Xi \ Neighbor selection \ if dk ≤ dmin then select k to be neighboring node else select neighbors randomly At the initial stage, each SU obtains the maximal transmission range of each channel and broadcasts HELLO messages for neighborhood discovery. Thus, a user can obtain local information on its neighborhood in each available channel. In the sequel, every SU feedbacks its node degree to its neighbors for Topology Control. This is known as the one-hop local information for every available channel. Note that every SU only feedbacks its node degree to its neighbor, therefore eCNRN has smaller processing overhead compared to other Topology Control protocols, e.g. the tree-based protocol family such as the local minimum spanning tree (LMST) protocol [18]. This can be asserted by the fact that the LMST protocol requires in addition node ID information for tree construction. Based on the node degree and one-hop information, every SU will perform the Topology Control protocol in a distributed fashion with a predefined parameter dmin . If node degree di ≥ dmin , then the SU obtains a new node degree Xi drawn from a probability mass function Xi on the interval [1, di ], otherwise di is retained. For demonstration purposes we select the new value for the node degree uniformly in the range [1, di ], however, such choice may be extended to more peculiar distributions, depending on the details of the operation environment and objectives of the system. In such randomized algorithms, where the new node degree follows a probability distribution, it may happen that nodes with fewer neighbors may become disconnected from other nodes since every node selects neighbors randomly. This is not frequent for threshold-based Topology Control approaches,

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e−CNRN with one−hop information e−CNRN without one−hop information K−Neigh

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such as K-Neigh. However, as it will be shown in the sequel, even under this regime, randomized approaches outperform their fixed threshold counterparts. Fig. 1 illustrates that SU4 may be disconnected from the CRN if SU2 prunes the link without knowing the one-hop information that SU2 is the only neighbor of SU4. Consequently, if every node knows the one-hop information ahead, it can preserve those nodes as neighbors to maintain network connectivity, and then randomly select other neighbors to meet the new node degree. The importance of one-hop local information is illustrated in Fig. 2, where it can be seen that the e-CNRN performs better than K-Neigh even without one-hop information. In addition, if e-CNRN is provided with one-hop information, it provides full connectivity at all instances, compared to e-CNRN without one-hop information, which provids better connectivity than K-Neigh, but fluctuating depending on network size. IV. V IRTUAL C OMMON C ONTROL C HANNEL S ETUP The e-CNRN approach can be readily employed to establish a Virtual Common Control Channel (VCCC) in multi-channel CRNs, in order to improve reliability of dynamic spectrum access and CRN layering functions. The concept is to enable each node dynamically choose some channel (among the available ones) for information exchange with neighboring SUs. The main challenge of a VCCC, especially for CRNs, is that the control channel needs to be determined instantaneously and dynamically and is likely to be constituted by different frequencies in different parts of the network. In Fig. 3 we demonstrate the configuration of virtual common control channel via the e-CNRN approach. If two nodes are connected, the control channel is randomly selected from the common available channels. Although the induced graph is not optimized in a global view, e-CNRN protocol provides a practical and efficient way to autonomously build up a VCCC with limited information, since centralized channel allocation would be generally infeasible. Since network connectivity is maintained by implementing e-CNRN, it is guaranteed that the VCCC will be established in any case, even under the more stringent operational conditions.

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V. P ERFORMANCE E VALUATION

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In order to demonstrate the operation and study the performance of the proposed CR-based Topology Control approach, we implemented e-CNRN and K-Neigh protocols on 10000 topologies generated according to N i.i.d Υi and investigated the network connectivity and the effectiveness of power control schemes. Network connectivity is defined as the portion of connected topologies yielded by the analyzed protocols, starting with an initially connected topology. Topology Control is validated in the view of the number of remaining physical neighbors in the induced topology. The instantaneous number of physical neighbors indicates the expected medium contention experienced by network nodes and thus can be further indicate the traffic carrying capabilities of the network. We compare the e-CNRN protocol with K-Neigh under different activity scenarios of heterogeneous primary systems because K-Neigh is the most commonly adopted node-degree based Topology Control protocol. Parameter dmin is set equal to 9 to be consistent with K-Neigh protocol. In general, parameter dmin can be smaller for e-CNRN without notable performance degradation and therefore it may further save energy consumption. However, in order to obtain a fair comparison with the K-Neigh protocol, we assume the same value for the fixed parameter of neighbors for each protocol and compare the two approaches under this regime. We separately provide results for dmin = 5 for e-CNRN, in order to depict the additional performance benefits compared to K-Neigh. We also investigate the average physical neighbors of the initial and subsequent topology, suggesting that e-CNRN protocol achieves efficient power control in multi-channel CRNs.

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1 = Fig. 5. Physical degree of low primary system activity. NP = 2, NC 2 = 50, d NC = 9, E[Υ ] = [0.6 0.7], R = 1 and σ = 0.1. max min i

A. Low Primary System Activity Although low primary system activity allows for larger transmission ranges of SUs, K-Neigh protocol actually suffers from low primary activity because it always selects the K nearest neighbors with respect to spatial proximity. Hence the network tends to break into several components, especially when the network size grows as shown in Fig. 4. On the other hand, e-CNRN protocol maintains network connectivity while reducing the average physical neighbors as shown in Fig. 5. The average physical neighbors exhibit approximately linear dependency with respect to SU population for e-CNRN protocol, suggesting linear scalability towards power control. We also notice that the average physical neighbors are constantly dmin for K-Neigh protocol, however, this does not offers significant benefit the K-Neigh protocol, since the latter fails to guarantee network connectivity. B. High Primary System Activity High primary system activity restricts the transmission range and available channels of SUs because of intensive channel occupancy and outage constraint. This creates an even more stringent environment for the operation of CRN, since in that

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bors, thus revealing its effectiveness with respect to power control. We have demonstrated the robustness of e-CNRN under heterogeneous primary systems and different primary system activity. Furthermore, we exploited the e-CNRN for distributively and efficiently providing a virtual common control channel for CRNs, an important implementation challenge for multi-channel CRNs, which is required in order to provide better synchronization and service quality. The minimal local information requirement and fast adaptiveness to environmental changes render e-CNRN a promising candidate for opportunistic networking applications, especially for users equipped with CR devices. R EFERENCES

Fig. 6. Network connectivity of high primary system activity. NP = 2, 1 = N 2 = 50, d NC min = 9, E[Υi ] = [0.2 0.3], Rmax = 1 and σ = 0.1. C High Traffic 30 initial e−CNRN, d

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case, SUs tend to have less physical neighbors. In Fig. 6, KNeigh protocol has a relatively better network connectivity performance than that in case of low primary system activity due to lower average physical neighbors (a single connected component has less chance to break down) as shown in Fig. 7, but it still fails to support robustness of network connectivity. On the contrary, the e-CNRN counterpart maintains network connectivity, while achieving efficient power control, compared to K-Neigh. Results show that overall e-CNRN protocol provides robust network connectivity under stringent environments, aiding CRNs from malfunctioning. VI. C ONCLUSION In order to alleviate the stringent environment of Cognitive Radio Networks (CRNs) and tackle their inherently nonuniform node arrangements, we proposed a Cognitive Radio based Topology Control algorithm, denoted by e-CNRN. We described in detail the operation of e-CNRN and showed that it can distributively maintain connectivity and provide efficient power control in multi-channel Cognitive Radio Networks. The proposed e-CNRN approach is able to guarantee network connectivity with only one-hop neighborhood information, and simultaneously it can reduce the average physical neigh-

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