A Survey on the Channel Assignment Problem in ... - Semantic Scholar

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A Survey on the Channel Assignment Problem in Wireless Networks Goutam K. Audhya] , Koushik Sinha† , Sasthi C. Ghosh§ and Bhabani P. Sinha‡

Abstract Efficient allocation of channels for wireless communication in different network scenarios has become an extremely important topic of recent research. The main challenge lies in the fact that the channel allocation problem is NP-complete [30], [86], [87]. Because of a maximum allowable time limit imposed in practical situations for allocation of channels, sometimes we may need to be satisfied with a near-optimal solution. In this correspondence, we present a discussion on the various challenges and approaches that have been used by different researchers to solve the problem of channel allocation taking into account different interference issues and efficient utilization of available communication channels for cellular mobile (including multimedia communication) environment and cognitive radio based networks.

I. I NTRODUCTION Wireless communication constitutes one of the fastest growing industry segments in recent years, encompassing a number of application domains such as the cellular networks, ad hoc networks, ubiquitous and pervasive computing, sensor networks and so on. One of the major concerns in most of these applications involves the availability of communication channels to satisfy the channel requirements for all users of a specific network or application type. In this survey paper, we attempt to address the channel assignment problem (CAP) in the context of two important classes of wireless networks - cellular mobile networks and cognitive radio networks. Mobile computing, particularly over cellular networks, has emerged as an important topic of research because of the need for computing abilities even when people are on the move. Over the last decade, the number of such cellular network dependent mobile users has been increasing nearly exponentially. With the advances in technology, there has been an increasing demand from the mobile users for providing multimedia services like voice, text, still image and video over wireless networks. On the other hand, the available bandwidth required for such multimedia data communication for a large number of mobile users is very much limited. Such a limited availability of the radio spectrum, signal distortion and the interference caused by the environment and other mobile users impose an inherent bound on the capacity of such wireless networks. Therefore, developing methods to utilize the scarce radio spectrum efficiently is more critical than ever before. Based on the application scenario, the common ways to design wireless networks are: i) infrastructure based network design such as the cellular structure approach, ii) infrastructure-less networks such as ad hoc networks and, iii) hybrid networks which uses a mix of infrastructure with ad hoc network architecture and can typically be found in many sensor network applications. In an infrastructure based network design - such as the cellular networks, the geographical region under consideration is spatially divided into a number of cells - which can be either overlapping or non-overlapping. A base station is established in each cell, and each mobile station in the cell communicates through this base station via a channel assigned by the base station. Several techniques such as Frequency Division Multiplexing (FDM), Time Division Multiplexing (TDM) or Code Division ] Goutam

K. Audhya is with BSNL, Calcutta-700001, India. Email: [email protected] Sinha is with Honeywell Technology Solutions, Bangalore, India. Email: sinha [email protected]. § Sasthi C. Ghosh is with DRTC, Indian Statistical Institute, Bangalore Center, Bangalore-560059, India. Email: [email protected] ‡ Bhabani P. Sinha is with the ACM Unit, Indian Statistical Institute, Kolkata, India. Email: [email protected]. † Koushik

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Multiplexing (CDM) can be used to divide the available radio spectrum into such channels. Further efficient techniques based on combining the above can also be designed to divide the radio spectrum into channels. A channel can simultaneously be used by multiple base stations, if their mutual separation is sufficient to satisfy the interference constraints. As an alternative to either the cellular or the ad hoc network architecture, there has been a great deal of interest in recent times on wireless mesh networks (WMNs). WMNs may be considered to be somewhere in between infrastructure-based networks such as wireless local area networks (WLANs) and ad hoc networks with no pre-installed infrastructure support. In WMNs, the network consists of a set of fixed gateway nodes and a set of non-gateway nodes (either stationary or mobile). The nongateway nodes must access a gateway node (similar to WLANs) in order to establish communication to the outside world. These non-gateway nodes can act as either hosts or as wireless routers - forwarding packets from other users (similar to ad hoc networks), enabling other non-gateway nodes to establish link with the gateway nodes in a multi-hop fashion, if required. This fusion of ad hoc network and infrastructure-based network properties not only allows significant extension of the coverage area of the network, but also enables nodes in areas with poor signal propagation properties to contact the outside world with higher probability of success. The overall effect of such a deployment is thus a substantial reduction in the number of deployed gateway nodes in order to cover a zone and consequently, the overhead in installation, operational and maintenance expenses. Furthermore, such a network structure also allows for scalable operations - simply by adding new gateway nodes when/where required. The reliability also improves as multiple paths to gateway nodes are more common and re-routing of packets in case of node failures are handled as in ad hoc networks. Because of the above mentioned advantages, even traditional infrastructure-based networks such as cellular networks are beginning to look at possibilities of migrating to either WMN based or WMN like topologies [111], [112], [113], [114]. The promises are several: reducing infrastructure setup and maintenance cost, improving fault tolerance and robustness in the face of unnatural events such as disasters and natural calamities and enhancing network coverage, among others. However, with the use of a mesh architecture, the importance of the channel assignment problem becomes even more accentuated due to the increased probability of interference between the links of a WMN, as most applications of WMNs (e.g., dense sensor networks) tend to contain more links than either traditional cellular or ad hoc networks in an attempt to improve reliability through path diversity [114], [116], [117], [118]. As an example, Lan and Trang [125] have proposed a technique for channel assignment in WMNs with multiple channels and multiple radios at each node of the network for increasing the network throughput. Interference is a function primarily of transmitter power, receiver sensitivity, antenna gains, and channel loss. Channel loss is a function of distance, frequency and weather, and is quantified by the minimum acceptable signal to noise ratio. Assuming that most of these factors are already determined or beyond the ability to influence, the interference can be defined directly as a function of frequency and distance. Based on that, three types of interference are generally taken into consideration in the form of constraints: i) co-channel constraint, due to which the same channel is not allowed to be assigned to certain pairs of cells simultaneously, ii) adjacent channel constraint, for which adjacent channels are not allowed to be assigned to certain pairs of cells simultaneously, and iii) co-site constraint, which implies that any pair of channels assigned to the same cell must be separated by a certain number of channels [46].

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The task of assigning frequency channels to the cells satisfying the interference constraints and using as small bandwidth as possible is known as the Channel Assignment Problem (CAP). In its most general form, the CAP is equivalent to the generalized graph-coloring which is a well-known NP-complete problem [30], [86], [87]. Quite similar to the mobile computing environment - which typically operates in licensed spectrum bands, with the explosive growth in the number of wireless devices operating in the unlicensed radio spectrum bands, a severe shortage of available, unlicensed radio spectrum has arisen in recent times. The multitude of wireless networks and protocols (e.g., Wi-Fi, Bluetooth, Zigbee, etc.) operating in the unlicensed bands and vying for their share of the spectrum to enable their respective operational parameters leads to interference and performance degradation for all. Interestingly though, while the unlicensed bands are heavily loaded, in contrast, there exists portions of the spectrum - particularly the licensed bands, that are relatively under utilized. As an example, recent studies by the Federal Communication Commission (FCC) [75] in US have shown that at any given time and in any given geographic locality, less than 10% of the available spectrum in the TV band (from 470MHz to 698MHz) is utilized. Similar spectrum utilization statistics were observed in the UK by the regulatory body OFCOM and in other parts of Europe, as well as in other parts the world [109]. To exploit these under utilized parts of the spectrum (also referred to as white spaces or spectrum holes), the FCC thus advocates the development of a new generation of programmable, smart radios that can dynamically access various parts of the spectrum, including the licensed bands. Such radios would operate as secondary users in the licensed bands and are required to possess the capabilities of spectrum usage sensing, environment learning and interference avoidance with the primary users of the licensed spectrum bands while simultaneously ensuring the quality of service (QoS) requirements of both the primary and secondary users. Radios with such capabilities are referred to as cognitive radios (CRs). Cognitive radios are today widely accepted as the wireless technology of the future and it is envisioned that by 2015, most radios on portable devices (e.g., cellphones, Wi-Fi enabled notebook PCs, etc.) will possess some amount of cognitive capability [119]. In the context of networks operating in licensed bands, the ability to exploit unused parts of the spectrum can provide a multitude of additional benefits. Taking the case of cellular networks as an example, such frequency agility can dramatically reduce operational and deployment/licensing costs, increase the number of users that can be supported under a single base station and improve the operator’s ability to provide guaranteed service through the intelligent exploitation of such large additional unused spectrum pool. Moreover, such cognitive radio based cellular networks can offer benefit in the event of attacks or natural disasters. While a conventional cellular system is centralized in nature and can only operate in licensed bands, a cognitive system is capable of establishing communications even if some network elements are out of order or the total requested bandwidth by the users exceeds the operator’s licensed bandwidth. It is thus apparent that cognitive radios would play a pivotal role in the coming generations of wireless networks [89], [90], [94], [95], [102], [109], [119], [121], [122], [129]. We describe below the channel assignment problem in these two types of networks. We begin with a discussion on the channel assignment problem under the framework of a cellular mobile network, followed by describing the motivations and challenges in channel assignment for cognitive radio networks.

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II. C HANNEL A SSIGNMENT P ROBLEM IN C ELLULAR M OBILE N ETWORKS The available radio frequency spectrum is assumed to lie on a straight line which is divided in equal intervals, with each such interval being termed as a channel and numbered as 0, 1, 2, ..., in the increasing order of their center frequencies. Thus, the frequency separation between two channels i and j can be abstracted as |i − j|. The channel assignment problem (CAP) in a cellular mobile network is then represented by means of a Channel Assignment Problem graph (CAP graph) [43] as follows. Each call to a cell is represented by a node of the CAP graph and two nodes i and j are connected by an edge with weight cij , (cij > 0), where cij represents the minimum frequency separation requirement between a call in cell i and a call in cell j to avoid interference. Let us now consider the following example of CAP graph as presented in [26]. Example 1. Fig. 1(a) shows a CAP graph with 3 cells where channel demands on cells 0, 1 and 2 are 1, 2, and 2 respectively. Each node in Fig. 1 is labeled as (rs) where r is the cell number at which a call is generated and s is the call number to this cell r. That is, the node (10) represents call 0 in cell 1. The frequency separation requirements for this example is given by the following matrix: cell

no. →

0 1

2

0

7

3

2

1

3

7

4

2

2

4

7

↓ C=

The edges of the CAP graph are labeled with weights according to this matrix C. Let us now assume a simple channel assignment scheme where the channels are assigned to the nodes of the CAP graph in a specific order and a node will be assigned the channel corresponding to the smallest integer that will satisfy the frequency separation constraints with all the previously assigned nodes. Following this strategy, if the channels are assigned to the nodes of CAP graph in the order ((21), (00), (10), (11), (20)), as shown in Fig. 1(b), the minimum bandwidth required will be 16. But, if the channels are assigned to nodes in the order ((20), (00), (10), (21), (11)), as shown in Fig. 1(c), the minimum bandwidth required will be just 13. The label [α] associated with each node of the CAP graph of Figs. 1(b) and (c) indicates that the frequency channel α is assigned to that node. It is clear from the above example that the ordering of the nodes has a strong impact on the required channel bandwidth. Suppose there are m nodes in the CAP graph. Therefore, the nodes can be ordered in m! ways and hence for sufficiently large m, it is impractical to find the best ordering by an exhaustive search. Channel assignment schemes can be classified into several categories. In the fixed (or static) channel assignment problem (FCA), the number of calls to each cell is known a priori and a number of nominal channels is permanently allocated to each cell for its exclusive use. In the simple uniform FCA, the same number of nominal channels is allocated to each cell. Since the traffic in cellular systems is mostly nonuniform, uniform allocation may result in poor channel utilization [48]. To achieve a relatively better channel utilization, the number of channels allocated to each cell should depend on the expected traffic

5

(10)

3

7

(00)

3 4

(11)

4

2

2

4 (20)

7

4 (21)

(a) [5] [2]

[2]

(10)

3

7

(00)

4

2

7

4

(11)

(21)

4

2 4 (20)

7

[13] (11) 4

(21) [9]

[0]

(b)

Fig. 1.

7 3

4

[0]

[16]

(10)

3

(00)

2

4 (20)

[12]

3 4

2

[5]

(c)

(a) A typical CAP graph and (b)-(c) two different frequency assignments on it.

load in that cell. This technique is called non-uniform channel allocation [23], [24]. Although simple, FCA schemes are not adaptive to temporal and spatial fluctuations of user demands and to overcome this drawback, dynamic channel assignment (DCA) schemes have been developed which may also tackle the problem of handoff requirements [120]. In DCA, all channels are available to every cell and they are assigned to newly generated calls as and when required, provided they satisfy the interference constraints. Though DCA schemes provide flexibility and traffic adaptability at the cost of higher complexity, they are less efficient than FCA under high load situations [48], [14], [15], [124]. To address this drawback under high load situation, many hybrid schemes by combining the benefits of both FCA and DCA have been developed. Both the FCA and DCA schemes can be implemented in centralized or distributed fashion. In centralized schemes, a channel is assigned by the central controller whereas in the distributed schemes, a channel is selected either by the base station at which the call is initiated or by the mobile itself [48]. For the case where the base stations select the channel, each base station keeps the information about the currently available channels in its vicinity and also these information are updated by exchanging status information among these stations. In the other situation where the mobile terminals are allowed to select the channel, the mobile terminals choose the channels based on the local signal to signal interference measurements [48]. Because of the NP-completeness of the CAP, researchers attempted to develop more and more time-efficient heuristic or approximation algorithms for its solution which, however, cannot guarantee optimal solutions. A number of techniques based on neural networks [25], [34], [36], [45], [65], [123], simulated annealing [22], [39], [55], tabu search [54], [52], [56], [59], [61], [63], [60] and genetic algorithms [2], [38], [41], [5], [10], [26], have been proposed to tackle this problem. The cellular network is often modeled as a graph and the CAP has been formulated as a graph coloring problem by several authors [32], [44], [49], [6], [42], [43], [26], [4], [27], [31], [37], [40]. To judge the quality of the results obtained from these approximation algorithms and heuristics, it is extremely necessary to know the lower bounds on the minimum number of frequencies needed for a solution.

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A. The General Model and Different Formulations of CAP In general, CAP can be modeled by the following components [32], [43], [44]: 1) A set X = (xi ) (0 ≤ i ≤ n − 1) of n distinct cells in a cellular network. 2) A demand vector W = (wi )(0 ≤ i ≤ n − 1) where wi represents the number of channels required for cell i (may or may not be known a priory). 3) A frequency separation matrix C = (cij ) where cij represents the minimum frequency separation requirement between a call in cell i and a call in cell j (0 ≤ i, j ≤ n − 1) to avoid interference. 4) A frequency assignment matrix Φ = (φij ), where φij represents the frequency assigned to call j in cell i (0 ≤ i ≤ n − 1, 0 ≤ j ≤ wi − 1). 5) A set of frequency separation constraints specified by the frequency separation matrix: |φik − φjl | ≥ cij for all i, j, k, l (except when both i = j and k = l). Based on this model a channel assignment problem P can be characterized by the triplet (X,W,C). A frequency assignment Φ for P is said to be admissible if φij ’s satisfy the component 5 above for all i, j, where 0 ≤ i ≤ n − 1 and 0 ≤ j ≤ wi − 1. The span S(Φ) of a frequency assignment Φ is the maximum frequency assigned to the system. That is, S(Φ) = max φij . i,j

Thus, one possible formulation of CAP is to find an admissible frequency assignment with the minimum span S0 (P ), where S0 (P ) = min{S(Φ)| Φ is admissible for P }. The objective of this formulation is to assign frequencies to the cells satisfying the frequency separation constraints in such a way that the required span becomes optimal. This formulation is commonly known as the minimum span frequency assignment problem. The advantage of this category of algorithms is that the derived channel assignment always fulfills all the interference constraints for a given demand. However, it may be hard to find an optimal solution in case of large and difficult problems, even with quite powerful optimization tools [26]. In an alternative formulation of CAP we look for the channel assignment where the span B of the system is given, which may even be smaller than the required lower bound on minimum span for the given problem. Depending on B, it may or may not be possible to satisfy all the channel demands of each cell unless B is sufficiently large. Given B, the approach is typically to formulate a cost function, such as the number of interference constraints violated, the number of calls blocked by a given channel assignment, and then tries to minimize this cost function. This formulation is commonly known as the fixed spectrum frequency assignment problem. The principal disadvantage of this formulation is that, in case of very hard problems, it is almost impossible to minimize the cost function to the desired value of zero with the minimum number of channels, [26]. There is, however, another class of problems of real-life importance known as the Perturbation-Minimizing Frequency Assignment Problem (PMFAP) [47] which is described as follows. Assume that initially an assignment has been obtained for a given network to satisfy the required channel demands. After some time, demands of some of the cells may be changed due to either, i) newly generated calls or, ii) a handoff situation or, iii) completion of some ongoing calls. The objective of this variant of CAP is to accommodate these small changes in demands; but while doing so, the number of changes in the existing

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assignment should be minimized, while meeting the desired Quality of Service. This variant is particularly useful to address the short-term demand fluctuations that often arise in real-life scenarios.

B. Lower Bounds As mentioned in the earlier subsection, because of the complexity of the channel assignment problem, researchers attempted to solve the problem based on heuristic approaches or approximation algorithms. Many of these algorithms do not assess how far their results are away from the optimality, whereas some of them over-estimate the number of frequencies by more than 100% [19], [17]. As a result, even if by some lucky coincidence, an optimal assignment is found, it may not be recognized as an optimal one unless one has the clear idea about the lower bound on the required bandwidth. In heuristic approaches like genetic algorithm, the process usually terminates after a certain number of iterations. Hence, a prior idea about the lower bound on the required bandwidth will be very much useful in deciding the termination condition of these algorithms. Furthermore, in the approaches based on neural net, simulated annealing and tabu search, the techniques typically start from some known lower bounds and then gradually improve the results through each iteration. The problem of determining the lower bounds on bandwidth has been extensively studied by several authors [16], [17], [18], [46], [43], [26], [27], [20], [64]. In [16], a lower bound on bandwidth has been developed for CAP which considered exclusively the co-channel interference constraints. In [17], Gamst presented some lower bounds on bandwidth for CAP taking the additional constraints for adjacent channel interferences and co-site interferences into account. Improving these results, Gamst et. al. [18] presented some results on the lower bound which, however, did not explicitly include the co-site constraints. In [46], the authors derived a lower bound which, in some cases, is tighter than those presented in [17] considering all the co-channel, adjacent channel and co-site constraints. In [29], new lower bounds have been developed which are generalization of the bounds presented in [46], [17]. All these lower bounds are defined on a general network of arbitrary cell structure. For the special case of hexagonal cellular networks, the problem of determining the lower bounds has been studied by several authors [26], [27]. In this special type of hexagonal cellular networks, we say that a k-band buffering exists in the network if the channels assigned to any two calls in two cells which are more than distance k apart, do not interefere with each other. In other words, for a k-band buffering network, we need to define k + 1 constants s0 , s1 , s2 , · · · , sk to specify the constraints for avoiding channel interefernces, where si , 1 ≤ i ≤ k denotes the minimum gap between two channels assigned to two calls in two cells which are distance i apart. Clearly, s0 ≤ s1 ≤ s2 ≤ · · · ≤ sk . Authors in [26], [27] have studied the problem of determining the lower bounds for a 2-band buffering situation in hexagonal cellular networks using only the three parameters s0 , s1 and s2 , where s0 , s1 and s2 are the minimum frequency separations required to avoid interference for calls in the same cell, cells at distances one and two, respectively. They have derived expressions for the lower bound on bandwidth for different relative values of s0 , s1 and s2 for both uniform and non-uniform demand situations. These lower bounds have been computed based on the minimum bandwidth requirement for assigning frequencies to a seven-node subgraph as shown in Fig. 2. Note that every node in this subgraph is within distance two from each other. Therefore, under the 2-band buffering scenario, the channels assigned to these nodes may interfere with each other if they are not sufficiently far apart. Most importantly, no frequency reuse is possible within this subgraph. Hence, the bandwidth requirement of this subgraph will give a lower bound

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Fig. 2.

A seven-node subgraph of a hexagonal cellular graph.

on the bandwidth requirement for the whole cellular network which is not necessarily a tight one. For the uniform demand of only one channel per cell, the lower bound as derived in [26] is (s1 + 5s2 ) when s2 ≤ s1 ≤ 2s2 , and (2s1 + 3s2 ) when s1 ≥ 2s2 . The corresponding assignments are shown in Figs. 3(a) and 3(b) respectively, where the label (α, β) associated with a node indicates that a frequency (αs1 + βs2 ) is assigned to that node. For the uniform demands of w (w ≥ 2) channels per cell, the corresponding lower bounds for s2 ≤ s1 ≤ 2s2 , are

1) (2s1 + 5s2 ) + (w − 2)(s0 + 6s2 ) + 6s2 , when s1 ≤ s0 ≤ (2s1 − s2 ), 2) (w − 1)(2s1 + 5s2 ) + 6s2 , when (2s1 − s2 ) ≤ s0 ≤ 6s2 , 3) (w − 1)(2s1 + 5s2 ) + s0 , when 6s2 ≤ s0 ≤ (s1 + 5s2 ), 4) (w − 1)(2s1 + 5s2 ) + (s1 + 5s2 ), when (s1 + 5s2 ) ≤ s0 ≤ (2s1 + 5s2 ), and 5) (w − 1)s0 + (s1 + 5s2 ), when s0 ≥ (2s1 + 5s2 ). For the case of s1 ≥ 2s2 , the corresponding lower bounds are: 1)

a) (3s1 + 3s2 ) + (w − 2)(s0 + 6s2 ) + 6s2 , when s1 ≤ s0 ≤ 3s2 , b) (3s1 + 3s2 ) + (w − 2)(3s0 ) + 2s0 , when 3s2 ≤ s0 ≤ (s1 + s2 ),

2) (w − 1)(3s1 + 3s2 ) + (2s1 + 2s2 ), when (s1 + s2 ) ≤ s0 ≤ (2s1 + 2s2 ), 3) (w − 1)(3s1 + 3s2 ) + s0 , when (2s1 + 2s2 ) ≤ s0 ≤ (2s1 + 3s2 ), 4) (w − 1)(3s1 + 3s2 ) + (2s1 + 3s2 ), when (2s1 + 3s2 ) ≤ s0 ≤ (3s1 + 3s2 ), and 5) (w − 1)s0 + (2s1 + 3s2 ), when s0 ≥ (3s1 + 3s2 ). The lower bounds for the non-uniform demands have been derived in [27]. These lower bounds are also based on the minimum bandwidth requirement for assigning frequencies to the seven node subgraph as shown in Fig. 2. Let wi represent

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the demand of node i and w = max(wi ), i = 1, 2, · · · , 7. Then, the lower bound as derived in [27] is given by the following expressions. P7 1) max((w − 1)s0 , ( i=1 wi − 1)s2 + (s0 − s2 )(w4 − 2) + 2(s1 − s2 )) for s1 ≤ s0 ≤ (2s1 − s2 ), and P7 2) max((w − 1)s0 , ( i=1 wi − 1)s2 + 2(s1 − s2 )(w4 − 2) + 2(s1 − s2 )) for s0 ≥ (2s1 − s2 ). 1(1,0)

3(1,3)

1(1,0)

2(1,4)

4(0,0)

5(1,2)

(a)

Fig. 3.

4(0,0)

3(2,1)

7(1,5)

6(1,1)

2(2,2)

6(1,1)

5(1,2)

7(2,3)

(b)

Different frequency assignments to Fig. 2 for (a) s2 ≤ s1 ≤ 2s2 (b) s1 ≥ 2s2

It has also been shown that these lower bounds are either equal to or tighter than those in [46], [17], [18] when applied to the special cases of hexagonal cellular network with 2-band buffering.

C. Channel Assignment Schemes Several algorithms using neural networks [25], [34], [36], [45], [65], simulated annealing [22], [39], [55], tabu search [54], [52], [56], [59], [61], [63], [60] and genetic algorithms [2], [38], [41], [5], [10], [26], have been proposed to solve this problem. In the following subsections, we briefly discuss about each of these commonly used approaches. 1) Genetic Algorithm Based Approach: For solving an optimization problem using genetic algorithm (GA), the parameter set of the optimization problem is required to be coded as a finite-length string or chromosome over some finite alphabet Q. A fitness function is used to evaluate the fitness of different strings. A collection of M such strings or chromosomes is called a population. A simple genetic algorithm is composed of three basic operators: 1) reproduction or selection, 2) crossover, and 3) mutation [58]. GA starts with a randomly generated initial population and in each iteration, a new population is generated from the current population applying the above mentioned three operators on the strings of the current population. The newly generated population is then used to generate the next population and so on. All the algorithms reported in [2], [38], [41], [5], [10], [26] are broadly based on this approach. The differences in these approaches lie only in the representation of different steps mentioned above and its implementations. For example, in [2], the call list is represented by a string and the quality of the generated call list is evaluated following the Frequency Exhaustive Assignment (FEA) strategy, which assigns calls to the minimum available frequencies, while satisfying the interference constraints. The authors started the procedure by estimating the lower bound B on bandwidth. If the algorithm does not find a solution with B, the value of B is incremented by one and the algorithm is repeated until a valid solution is derived. Thus, in this approach the computation time will be highly dependent on the proximity of the prior estimation of the lower bound on bandwidth to its optimal value. In [26], the elitist model (EGA) [58] is utilized to solve the general CAP. After representing the CAP by means of a CAP graph, a random order of the nodes of the CAP graph is considered as a string S. Channels are assigned to the nodes of the CAP graph in a specific order and a node is assigned the channel corresponding to the smallest integer that satisfies the frequency separation constraints with all the

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previously assigned nodes. The maximum frequency required for a given ordering is then regarded as the fitness of that string, represented by the ordering. Let Sb be the best string (with respect to the fitness value) of the population generated up to iteration t. In this elitist model, if Sb or any string better than Sb is not present in the population generated in iteration (t + 1), Sb is included in the (t + 1)-th population. This ensures that the population gets improved in successive iterations. 2) Simulated Annealing Based Approach: For solving an optimization problem using simulated annealing (SA), the solution space of the problem must be represented as a state space. A suitable cost function has to be designed to evaluate the cost of a state. In each iteration, the SA considers some neighborhood s0 of the current state s, and probabilistically decides between moving to the new state s0 or staying in current state s. The definition of the neighborhood of a state is normally application-specific. The probability function which is a function of new state s0 , current state s and a global time varying parameter called temperature T , is chosen so that the system tends to move to the states of lower cost. However, in order to avoid getting stuck at a local minimum, higher cost states are sometimes accepted with some nonzero probability, meaning that the system may move to the new state even when it is worse than the current state. Temperature T is set high initially and it is gradually reduced according to some annealing schedule as the simulation proceeds, and becomes 0 when the process terminates. Typically the process terminates when a state that is good enough for the application is found or after a certain number of iterations has been completed. All the algorithms presented in [22], [39], [55] are broadly based on this approach. The differences in these approaches lie in the representation of the state space, definition of the neighborhood of a state, and choice of the probability function. In general, the simulated annealing approach guarantees global optimal solution asymptotically, but the rate of convergence is rather slow. For example, in [55], simulated annealing is used to solve the fixed spectrum frequency assignment problem, where the number of constraint violations is regarded as the cost function. Neighborhood states are determined through selecting a random frequency at a randomly selected transmitter. The number of constraint violations is then calculated for the new state Enew as well as the current state Eold . The probability function is chosen in the standard way, resembling the exponential form of Metropolis’s approach, prob = e−

(Enew −Eold ) T

.

Hurley et al. [55] compared the performance of simulated annealing with the approaches based on tabu search and genetic algorithms for solving a set of fixed spectrum scenarios in military applications and found that the simulated annealing approach with smaller number of constraint violations compared favorably with the other two approaches. A simulated annealing based algorithm was developed in [22] for the channel assignment problem with the objective of minimizing interference while simultaneously assigning a certain prescribed number of channels to each cell. Mathar et al. [39] investigated several algorithms based on the simulated annealing approach and through simulation the authors showed that all variants gave good quality solutions when compared to the optimal results. 3) Tabu Search Based Approach: Tabu search is a local or neighborhood search procedure to iteratively move from a solution x to a solution x0 in the neighborhood of x, until some stopping criterion has been satisfied [57]. To escape from a local optimal solution and to prevent cycling, it modifies the neighborhood structure of each solution, as the search progresses. The solution admitted to a new neighborhood is then determined through an appropriate data structure,

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which is the tabu list containing the solutions that have already been obtained in the recent past. Tabu search then excludes solutions in the tabu list from the new neighborhood. Sometimes when it is deemed favorable, a tabu move can be overridden. Such aspiration criterion is used when a tabu leads to a solution better than the currently known best solutions. Most common stopping criterion is to stop the process when some threshold on acceptable solutions has been reached or a certain number of iterations has been completed. Tabu search is a relatively simple technique which can provide considerably improved results by defining proper rules tailored to specific problems. The disadvantage is that the performance is highly dependent on the fine-tuning of several parameters [53]. All the algorithms presented in [54], [52], [56], [59], [61], [63], [60] are broadly based on this approach. The differences in these approaches lie in the representation of the move, in the definition of neighborhood of a move, and in the way of defining a tabu move. As an example, let us consider the tabu search used in [59] for solving the fixed spectrum frequency assignment problem with the objective of minimizing the total interference. Let N be the number of calls to be assigned and a1 , a2 , · · · , aF be the F available frequencies. A frequency assignment f = (f1 , f2 , · · · , fN ) is represented using an array of indexes [x1 , x2 , · · · , xN ] where fj = axj for 1 ≤ j ≤ N . The neighbors of f are those assignments where the array of indexes differs in precisely one component. Let f 0 be another frequency assignment represented by [x01 , x02 , · · · , x0N ]. Then, 0 ) is a neighbor of f if there exists a j, 1 ≤ j ≤ N , such that xj 6= x0j , and for all i = 1, 2, · · · N f 0 = (f10 , f20 , · · · , fN

with i 6= j we have x0i = xi . Each neighbor corresponds to a pair (j, x0j ) with 1 ≤ j ≤ N , 1 ≤ x0j ≤ F , (x0j 6= xj ). To illustrate this, let there be 2 frequencies and assume that 4 calls need to be assigned. Then f = (1, 2, 2, 1) is a frequency assignment where frequency 1 is assigned to calls 1 and 4, whereas frequency 2 is assigned to calls 2 and 3. Similarly, f 0 = (1, 2, 2, 2) is a neighbor of f = (1, 2, 2, 1). A move to a neighbor (i, x0i ) is said to be a tabu if it does not satisfy the recency and frequency conditions. The recency condition specifies that i does not appear in any of the previous r moves, where r is some positive integer. The frequency condition specifies that the proportion of the number of times i has been changed over all iterations, does not exceed some given s, 0 < s < 1. Lanfear [54] investigated a tabu search algorithm by formulating the radio relay network channel assignment problem as a generalized graph coloring problem. Their model involves coloring several graphs represented by the co-channel, adjacent-channel and co-cite constraints. [52] implemented a tabu thresholding method and reported that it outperformed simulated annealing and genetic algorithm on fixed spectrum channel assignment using simulated data sets. For the fixedspectrum frequency assignment problem, in [56], a robust tabu search algorithm with a dynamic tabu list is presented. The algorithm is tested on several test problems and the results show its effectiveness when solution quality is a more important criterion than solution speed. In [61], a reactive tabu search method [62] is applied and the performance of the algorithm is compared with the classical tabu search based method [63]. 4) Neural Network Based Approach: Neural network based approaches use an energy function which contains the objective function as well as an individual term for each of the constraints of the problem. Therefore, defining an appropriate energy function is crucial for using neural networks. Moreover, the terms of the energy function compete among themselves for minimization. As a result, a trade-off between the constraints and objective may be required in most cases. The Hopfield neural network has been used for solving CAP by many authors [123]. Several algorithms using neural networks [25],

12

[34], [36], [45], [65], [66], [123] have been proposed to solve the problem. In [65], discrete competitive Hopfield neural network (DCHNN) is used for solving the CAP. The objective is to minimize the total interference in the entire cellular network. The DCHNN can always satisfy the problem constraint and therefore guarantee the feasibility of the solutions for the CAP. Furthermore, the DCHNN permits temporary energy increases to escape from local minima by introducing stochastic dynamics. In [66], a multistage self-organizing channel assignment algorithm is proposed based on the Transiently Chaotic Neural Network (TCNN) for the CAP. An inherent disadvantage of neural network based approaches is that they tend to converge to local optima, and hence optimal solutions cannot always be guaranteed. The neural network based approaches thus typically perform well only on unrealistic small test problems [53]. 5) Graph Based Algorithms: The cellular network is often modeled as a graph and the channel assignment problem has been formulated as a graph coloring problem by several authors [32], [44], [49], [6], [42], [43], [26], [4], [27], [31], [37], [40]. In all these studies the graph used to model the cellular network ignores the geometry of the network. Some authors [31], [37], [40], [42], [43], [27] have, however, considered the geometry of the network and solved the channel assignment problem optimally in some cases. In [42], Sen, Roxborough and Medidi presented three channel assignment algorithms taking the hexagonal cell structure into account. The first algorithm considered only co-channel constraints while the remaining two considered both the co-channel and adjacent channel constraints. Another channel assignment scheme based on hexagonal cellular network with a 2-band buffering restriction has been presented in [43] which assumes a uniform demand of only one channel per cell. In [26], three different frequency assignment schemes were proposed, resulting in improvement of nearly 25% in the required bandwidth of the assigned channels over that reported in [43] under the same set of assumptions. A survey on several algorithms based on graph multicoloring have been reported in [4]. 6) Other Approaches: In [7], the authors have used a hyper-heuristic technique based on the great deluge algorithm to solve the problem. In [8], [9], a different approach has been taken where the presented algorithms solve the channel assignment problem in a scenario where the coverage area is divided into a number of circular cells with different sizes. A two-phase meta-heuristic called the GRASP or Greedy Randomized Adaptive Search Procedure is presented in [13] for solving the CAP. In the first phase, a set of initial solutions is constructed and in the second phase, a local search is carried out in the neighborhood of each constructed solution. A common local search technique is FEA (Frequency Exhaustive Assignment) which assigns calls to the minimum available frequencies, while respecting the interference constraints. In [3], a hybrid GRASP-FEA is proposed which achieves optimal solution for all benchmark instances considered. In [11], [12], the authors have also used the GRASP approach to solve the CAP, both using a graph coloring model. In [26], the authors considered the CAP for a hexagonal cellular network and by exploiting the symmetry of the network, proposed several channel assignment schemes for the case of uniform demands on each node. According to these schemes, channels are assigned to the nodes in a very regular and systematic manner so that, application of GA using these schemes led to near-optimal assignments in a very small number of iterations. For solving the CAP with non-uniform demands on hexagonal cellular network, a novel idea of critical block, a clique whose minimum bandwidth

13

requirement is maximum among all other such cliques, is introduced in [27]. The non-uniform demands on the critical block is then partitioned (through a linear integer programming formulation) into uniform demands on several smaller sub-networks which provides an elegant way of assigning frequencies to the critical block using the schemes in [26]. This idea of partitioning is then extended for assigning frequencies to the rest of the network. In [28], an algorithm is presented which is applicable to the general non-hexagonal network too. In this approach, the original problem is transformed to an equivalent smaller problem requiring much smaller search space. The smaller problem is then solved using appropriate approximation algorithm quickly. Finally, the solution to the original problem is obtained from the solution of the transferred problem using a modified Forced Assignment with Rearrangement (FAR) operation reported in [47]. Moreover, as a bye-product of this approach, there will be, in general, some unused or redundant channels in some cells. These redundant channels may effectively be utilized to address the short-term demand fluctuations that arise in real-life scenarios. D. Performance Comparisons of Different Approaches In this section, we first present different benchmark instances widely used in the literature and then compare the performances of different approaches based on the results obtained from applying these benchmarks. 1) Benchmark Instances: To compare the performances of different channel assignment algorithms, eight well-known benchmark problems have been used widely in the literature [44], [49], [2], [47], [34], [1], [21]. These benchmark problems (Philadelphia benchmarks) have been defined on a hexagonal cellular network of 21 cells as shown in Fig. 4, with either of the two non-homogeneous demand vectors D1 and D2 , as shown in Table I. The columns of Table I indicate the channel demands for the respective cells corresponding to D1 or D2 . These benchmarks have been defined on a 2-band buffering system, where channel interference does not extend beyond two cells away from the call originating cell. In order to account for a 2-band buffering, let s0 , s1 and s2 be the minimum frequency separations required to avoid interference for calls in the same cell, or cells at distances one and two, respectively. Table II shows the specifications of these eight problems (problems 1 through 8) in terms of the specific values of s0 , s1 and s2 for a 2-band buffering system, and the corresponding demand vector used for each of them. Apart from these Philadelphia benchmarks, a practical assignment problem (Problem 9) from Helsinki, Finland is also used by some authors [36], [21], [1], [50], [25], [28]. This problem has been formulated on a 25-cell system, whose frequency separation matrix C and demand vector W are shown in Tables III and IV respectively. The entry corresponding 1

0

5

12

7

6

13

14

Fig. 4.

The benchmark cellular network.

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16

15

19

20

4

10

9

8

18

3

2

11

14

TABLE I T WO DIFFERENT DEMAND VECTORS FOR BENCHMARK PROBLEMS

Cell nos. D1 D2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 8 25 8 8 8 15 18 52 77 28 13 15 31 15 36 57 28 8 10 13 8 5 5 5 8 12 25 30 25 30 40 40 45 20 30 25 15 15 30 20 20 25 TABLE II T HE SPECIFICATION OF BENCHMARK PROBLEMS

Problems Frequency s0 separation s1 constraints s2 Demand vector

1 5 1 1 D1

2 5 2 1 D1

3 7 1 1 D1

4 7 2 1 D1

5 5 1 1 D2

6 5 2 1 D2

7 7 1 1 D2

8 7 2 1 D2

to the ith row and the j th column of Table III, i.e., cij , represents the minimum frequency separation requirement between a call in cell i and a call in cell j (0 ≤ i, j ≤ 24). The ith corresponding to D3 of Table IV indicates the channel demand wi from cell i. Two other benchmarks defined on the 55-cell system are also used by some authors [21], [28]. The cellular graph corresponding to this 55-cell cellular network has been shown in Fig. 5. The demand vectors of these two problems are given by D4 and D5 as shown in Table V. These two benchmarks (problems 10 and 11) also have been defined on a 2-band buffering system where s0 , s1 and s2 are given to be 7, 1 and 1 respectively. 0 6

7

14 21 29

15

9

48

33

49

11

25

50

19

34

13 20

27

28 36

35

52

37 45

44

43 51

5

12

26

42

41

4

18

17

32 40

3

10

24

23

39

2

16

31

30

47

Fig. 5.

8

22

38

1

53

46 54

The cellular graph corresponding to the 55-cell cellular network.

2) Comparison of Results: Most of the authors [2], [25], [33], [34], [35], [41], [44], [46], [47], [49] have used their assignment algorithms on eight well-known benchmark instances for the given channel demands on hexagonal cells. Among the eight benchmarks, other than problems 2 and 6, for the remaining six, it is easy to derive the optimal solution because in all these six cases the required bandwidth is primarily limited by the co-channel interference constraint only. Most difficult is, however, to get the optimal solution for the other two benchmark instances - problems 2 and 6 [1], [2]. For instance, the optimal assignment for problem 6 needs 253 channels, whereas the assignment algorithm given in [41] requires 165 hours to solve this problem on an unloaded HP Apollo 9000/700 workstation, but giving only a non-optimal solution with 268 channels. Frequency Exhaustive Strategy with Rearrangement (FESR) in [47] and the

15

TABLE III F REQUENCY SEPARATION MATRIX FOR 25- CELL BENCHMARK P ROBLEM

                       C=                      

2110101111011110000000000 1210101101011110000000000 1121111111111100000000000 0012001111111000000000111 1110200001111111000000000 0010021111000000000000000 1111012111111000000000000 1111011211111000000000010 1011011121110000000000011 1111111112111111000001010 0011101111201111011111111 1111101111021100000000000 1111101101112111111100000 1110100001111211111100000 1100100001101121111111000 0000100001101112111100000 0000000000001111211000000 0000000000101111121100000 0000000000101111112111100 0000000000101111011211100 0000000000100010001121100 0000000001100010001112111 0001000000100000001111211 0001000111100000000001121 0001000010100000000001112

                                             

TABLE IV T HE DEMAND VECTORS FOR 25- CELL BENCHMARK PROBLEM

Cell nos. D3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 10 11 9 5 9 4 5 7 4 8 8 9 10 7 7 6 4 5 5 7 6 4 5 7 5

TABLE V T WO DIFFERENT DEMAND VECTORS FOR 55- NODE BENCHMARK PROBLEMS

Cell nos. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 D4 5 5 5 8 12 25 30 25 30 40 40 45 20 30 25 15 15 30 20 20 25 8 D5 10 11 9 5 9 4 5 7 4 8 8 9 10 7 7 6 4 5 5 7 6 4 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 5 5 5 5 5 5 8 12 25 30 25 30 40 40 45 20 30 25 15 15 30 20 20 25 5 7 5 10 11 9 5 9 4 5 7 4 8 8 9 10 7 7 6 4 5 5 7 6 46 47 48 49 50 51 52 53 54 8 5 5 5 25 8 5 5 5 4 5 7 5 6 4 5 7 5

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heuristic algorithm in [21] also produces non-optimal solutions to problems 2 and 6 both. A Randomized Saturation Degree (RSD) heuristic reported in [1] also produces non-optimal solutions for both the problems 2 and 6. However, combining the RSD heuristic with a Local Search (LS) algorithm, the authors in [1] were able to find an optimal solution for problem 2 but not for problem 6. Later, however, the authors in [2], [26], [27], [3], [28] proposed algorithms all of which provided optimal solutions to both the problems 2 and 6. Authors of [27] reported execution time between 30-60 seconds for the problems 2 and 6. The coalesced CAP approach given later in [28] improved these execution times to 10-20 seconds for problems 2 and 6. However, in practice, the allowable time limit to set up a call request is still much smaller than these figures. Hence, more efficient heuristics are still called for. The required bandwidths with different approaches have been shown in Table VI for the purpose of comparison. The row Lower Bound in Table VI corresponds to the lower bound for each of the problems as reported in [26]. As a final remark, we would like to mention that the algorithm proposed in [28] may be used for long-term channel allocation where the channel allocation algorithm may be called say, once an hour for optimal assignment of channels. Thus, depending on a priori statistical knowledge of the call demands during every hour of the day, this algorithm may be called for optimally assigning the channels to calls in different cells. For short-term allocation of channels arising due to handoff situations or sudden change (increase or decrease) in cell demands, some efficient near-optimal fast algorithms need to be developed. The solutions provided by such algorithms may be expected to deviate from optimality by a small percentage (say, 5% to 10%), but the algorithms need to be executed very fast (say, within tens of milliseconds). A mix of such optimal and near-optimal fast algorithms would be the best possible solution. TABLE VI C OMPARISONS OF REQUIRED BANDWIDTH

P roblems Lower Bounds (2008)[3] (2006)[10] (2006)[28] (2004)[7] (2003)[26] (2002)[51] (2001)[21] (2001)[1] (2000)[47] (1998)[2] (1998)[41] (1997)[34] (1997)[46] (1997)[50] (1996)[33] (1994)[35] (1992)[25] (1991)[36] (1989)[44]

1 381 381 381 381 381 381 381 381 381 381 381 − 381 381 381 381 381 381 − 381

2 427 427 432 427 457 427 438 463 427 433 427 − − 436 433 − 464 − − 447

3 533 533 533 533 533 533 533 533 533 533 533 − 533 533 533 533 533 533 − 533

4 533 533 533 533 533 533 533 533 533 533 533 − 533 533 533 533 536 533 − 533

5 221 221 − 221 − 221 − 221 221 − 221 221 221 − 221 − − 221 − −

6 253 253 253 253 265 253 266 273 254 260 253 268 − 268 263 − 293 − − 270

7 309 309 − 309 − 309 − 309 309 − 309 − 309 − 309 − − 309 − −

8 309 309 309 309 309 309 309 309 309 309 309 309 309 309 309 − 310 309 − 310

9 73 − − 73 − − − 73 73 − − − − − 73 − − 73 73 −

10 309 − − 309 − − − 309 − − − − − − − − − − − −

11 71 − − 71 − − − 79 − − − − − − − − − − − −

III. C HANNEL A SSIGNMENT FOR M ULTIMEDIA C ELLULAR N ETWORKS As mentioned in the earlier section, a lot of research has been done on the optimal assignment of channels for only one type of signal in cellular mobile networks. However, the next generation (4G and beyond) wireless networks aim at supporting

17

multimedia to meet the demands for a variety of services, e.g., voice, video and data at any time at any place [126], [127], [128]. Multimedia clients require larger bandwidth to meet the QoS guarantee for video applications whereas services like voice or e-mail requires smaller bandwidth. Thus a mobile cellular network, supporting multimedia services, must assign frequency channels of different bandwidths to support different types of service calls in a particular cell. Recent works in [67], [68], [69], [70] have focused on the channel assignment problem in a hexagonal cellular network with two-band buffering, supporting multimedia services. Authors here, considered hexagonal cellular networks, dealing with two types of multimedia signals of different bandwidths, where each cell has a single demand for each type of signal. In [67], the authors derived the lower bound on minimum bandwidth requirement for a hexagonal cellular network supporting multimedia, with the objective of using it for comparing the performance of any multimedia channel assignment algorithm with regard to the optimality of the bandwidth used. To do this, they defined a general model for channel assignment in a cellular network, supporting multimedia signal communication. As already mentioned, different types of multimedia signals may require different bandwidths. Authors in [67] assumed that the total frequency band is divided into a number of smallest size channels numbered as 0, 1, 2, · · · . Then a signal of a specific type may need to be assigned one or more such adjacent channels, depending upon the bandwidth requirement, to maintain the QoS. For instance, a call request for voice communication may be assigned only one channel, while a call request for video communication may possibly need a number of adjacent channels to be assigned for maintaining the required quality of service. The difference between the center frequencies of the bands (a set of adjacent channels) assigned to different calls will, however, be appropriately chosen to avoid channel interference. Based on these ideas, the general model for representing the multimedia channel assignment problem in a cellular mobile network has been described [67] by the following components: 1) A set X of n distinct cells, with labels 0, 1, · · · n − 1. 2) A set of distinct channels numbered as 0, 1, · · · . 3) t different types of multimedia signals denoted by T1 , T2 , · · · , Tt , where a signal of type Tj requires a bandwidth of BWTj . That is, BWTj number of adjacent channels need to be assigned to a signal of type Tj . 4) A demand vector W = (wi1 , wi2 , · · · , wit ) for cell i, where wik represents the channel demand of cell i for the multimedia signal of type Tk . 5) A channel assignment matrix Φ = (φijk ), where φijk represents the set of channels assigned to call j of type k in cell i (0 ≤ i ≤ n − 1, 1 ≤ j ≤ wik , 1 ≤ k ≤ t) with the required bandwidth, i.e., |φijk | = BWTk . 6) A frequency separation matrix C = (cij,kl ) where cij,kl represents the minimum frequency separation requirement between the center frequencies assigned to a call of type Tj in cell i, and a call of type Tl in cell k, 0 ≤ i, k ≤ n − 1 and 1 ≤ j, l ≤ t. 7) A set of frequency separation constraints specified by the frequency separation matrix as follows : midpoint{φi1 j1 k1 } − midpoint{φi2 j2 k2 } ≥ ci1 k1 ,i2 k2 , ∀i1 , i2 , j1 , j2 , k1 , k2 (except when both i1 = i2 and j1 = j2 ), where midpoint(φijk ) refers to the center frequency of the channel φijk . The frequency separation requirements in a 2-band buffering system using only two types of signal for avoiding interference are defined in [67]. For simplicity of notations, the two types of multimedia signals are denoted as type A, having bandwidth

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A

B

BW A Fig. 6.

BW A > BW B

BW B

Typical frequency response curves for type A and type B signals.

BWA and type B, having bandwidth BWB , respectively, with BWA ≥ BWB . Thus, type A signal may represent video, while type B may represent voice data. s0 , s1 and s2 are used to denote the required frequency separations between two type A calls in the same cell, in two cells at distance 1 apart and two cells at distance 2 apart, respectively. Similarly, the corresponding frequency separations between one of type A and one type B are denoted as s00 , s01 and s02 , respectively and those between two type B calls are denoted as s000 , s001 and s002 , respectively. Because BWA ≥ BWB , it is assumed that s0 ≥ s00 ≥ s000 , s1 ≥ s01 ≥ s001 and s2 ≥ s02 ≥ s002 . Further, it is assumed that s0 ≥ s1 ≥ s2 , s00 ≥ s01 ≥ s02 and s000 ≥ s001 ≥ s002 . The lower bound on minimum bandwidth in a two band buffering system with these two types of signal has been derived in [67] by considering a seven-node subgraph of a hexagonal cellular graph, as in Fig. 2, where node 4 is the central node and every other node of the subgraph is at distance one from node 4. Then, every node in the subgraph is within distance two from each other, and hence, no frequency reuse is possible within this subgraph. Under such situation, the bandwidth required for assigning channels in this subgraph gives a lower bound on the bandwidth requirement for the whole cellular network. It has been shown in [67] that the minimum bandwidth assignment for two different multimedia signals corresponds to the situation where the type A call at the central node 4 must be assigned a band containing either the lowest or the highest channel number. They presented the lower bounds on the required bandwidth for the multimedia cellular network in terms of different relative values of the frequency separation requirements, represented by the nine parameters s0 , s1 , s2 , s00 , s01 , s02 , s000 , s001 , s002 . However, these s-parameters are not entirely independent and in real-life situations, the relative values of the frequency separation constraints are somewhat restricted [67]. For most practical scenarios, the frequency response curves for the bands assigned to type A and type B signals are typically assumed to be trapezoidal shaped, as shown in Fig. 6, where BWA ≥ BWB . Considering the above ideas, it can be shown that the following relationship among the different frequency separation requirements holds:

s1 − s01 = s2 − s02 = s01 − s001 = s02 − s002 . Using the above stated results, they obtained a general expression for the lower bounds on the minimum bandwidth requirement of the seven-node subgraph in terms of the nine s-parameters as:

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min[(s00 + s01 + 4s2 + 2s02 + 5s002 ), (s1 + 2s01 + 3s2 + 2s02 + 5s002 ), (s1 + s01 + s001 + 4s2 + s02 + 5s002 ), (s1 + s01 + 4s2 + 2s02 + 5s002 )] (1) In [68], the authors proposed an algorithm for solving the multimedia channel assignment problem in its most general form using genetic algorithm (GA) and for a 2-band buffering system with two types of multimedia signals, having single demand for each type. They applied this general approach to their network model by exploiting the symmetric nature of the hexagonal cellular structure, and assigned the frequency channels optimally with a very small execution time. To achieve this, a subset of only nine nodes of the hexagonal cellular network, forming a 9-node block is first selected. A clever technique for re-using the frequency channels is then utilized, wherein the required assignment for the whole network can be completed by repeatedly using only eighteen bands (two bands for each node for assigning both the types of multimedia signals). For this purpose, the required frequency separation constraints among the channels to be assigned to the different nodes of the network are derived and then, by using the proposed GA-based algorithm, the multimedia channels are assigned optimally for the whole network. Experiments with different values of the frequency separation constraints show that the proposed assignment algorithm converges very rapidly and generates optimal results, which are pretty close to the derived lower bounds on the minimum bandwidth requirement given in [67], within a reasonable computing time. In [69], the authors address the limitations of the results on the lower bounds on bandwidth derived in [67]. In particular, the derivations of the lower bounds on bandwidth in [67] were based on the formulation of certain specific assignment orders of a seven node subgraph (Fig. 2) to assign channels successively. These assignments were done considering the minimum possible bandgaps with only the immediately previous node assigned by their proposed technique, disregarding the presence of any other neighboring node(s) which might have been assigned before the immediate previous assignment. As a result, it may so happen that an assignment, although satisfying the minimum frequency separation constraints with the immediately previous assignment to a node in the chosen assignment order, may fail to avoid interference with some earlier assigned nodes. The actual assignment, where successive nodes are assigned considering the feasibility with respect to all perviously assigned neighbors, may require larger bandwidth. To justify this, they cited an example in [69]: Example 2. Let s1 and s2 be the minimum frequency separations between the calls in cells at distance one and two respectively, with each cell having a demand of only one type of signal in a 2-band buffering system where the interference does not extend beyond two cell distance. Then, for s1 ≥ 2s2 , the lower bound for assignment of the nodes in Fig.2, would be s1 + 5s2 [26], considering only the absolute minimum bandgap requirements between the consecutively assigned nodes. But, if the presence of other perviously assigned neighboring nodes are also considered, the lower bound on minimum bandwidth would be 2s1 + 3s2 [26], which is larger than s1 + 5s2 . Thus, for s1 ≥ 2s2 , although s1 + 5s2 is a lower bound on bandwidth, the feasible assignment raises this lower bound to a tighter value of 2s1 + 3s2 . Following a similar argument in case of multimedia signals, it is stated that the results on lower bound given in [67] may be rather loose under typical situations and hence, may not provide a clear idea about the performance of any multimedia channel assignment algorithm in regard to the optimality

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of the bandwidth used. Based on the above observation, the authors in [69] then provide improved lower bounds on the minimum bandwidth for multimedia channel allocation in a cellular network by considering the feasibility of assignments based on all the previously assigned nodes. Using only two types of multimedia signals, they proposed three possible assignment schemes based on the assignment orders of the peripheral nodes of the seven-node subgraph, for different relative values of the frequency separation p constraints. For ease of notation, Bqrs has been used to denote the minimum feasible bandwidth BWmin for scheme p

(p = 1, 2, 3), under case q (q = 1, 2, 3), for different subcases and conditions as indicated by the suffixes r and s, respectively. The consolidation of their results on the minimum required bandwidth BWmin , under different conditions is summarized below: •

For the case where 2s002 < s001 and 2s2 < s1 : 1) When s00 ≤ s02 + 2s002 , BWmin = B1111 for s00 < s1 and B1112 for s00 ≥ s1 . 2) When s02 + 2s002 < s00 ≤ 2s01 + s02 , we have BWmin = min[B1121 , B121 ] for s00 < s1 and min[B1122 , B121 ] for s00 ≥ s1 . 3) When s00 > 2s01 + s02 , BWmin = B122 .

•

For the case where 2s002 < s001 and 2s2 ≥ s1 as well as for the case of 2s002 ≥ s001 : 1) When s00 ≤ s02 + 2s002 , we have BWmin = B2111 for s00 < s1 and B2112 for s00 ≥ s1 . 2) When s02 + 2s002 < s00 ≤ 3s02 + 2s2 , we get BWmin = min[B2121 , B221 ] for s00 < s1 and min[B2122 , B221 ] for s00 ≥ s1 . 3) When s00 > 3s02 + 2s2 , BWmin = B222 .

Where,

B1111 = s00 + s1 + s01 + s2 + 4s02 + 4s002 , B1112 = 2s1 + s01 + s2 + 4s02 + 4s002 , B1121 = 3s00 + s1 + s01 + s2 + 2s02 , B1122 = 2s00 + 2s1 + s01 + s2 + 2s02 , B2111 = s00 + s01 + 3s2 + 4s02 + 4s002 , B2112 = s1 + s01 + 3s2 + 4s02 + 4s002 , B2121 = 3s00 + s01 + 3s2 + 2s02 , B2122 = 2s00 + s1 + s01 + 3s2 + 2s02 , B121 = 4s01 + s001 + 3s02 + 2s002 , B122 = s00 + 2s01 + s001 + 2s02 + 2s002 , B221 = s01 + s001 + 3s2 + 6s02 + 2s002 , B222 = s00 + s01 + s001 + s2 + 3s02 + 2s002 ,

¤

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Coexistence with Other Wireless Networks Learn Patterns

Dynamic Adaptibility

Cognitive Capabilities SDR

Environment Awareness

Sense Spectrum

Efficient Spectrum Utilization

Fig. 7.

Functionalities of a typical cognitive radio

These derived lower bounds are tighter than those given in [67] under typical situations. The new lower bounds can be verified by assuming typical values of s0 , s00 , s000 , s1 , s01 , s001 , s2 , s02 and s002 as to 11, 10, 9, 8, 7, 6, 3, 2 and 1, respectively, which correspond to the case 2s002 < s001 , 2s2 < s1 and s00 < 2s01 + s02 . The BWmin comes to be 42 for this situation, compared to 36 based on the results in [67], [68]. Thus, the lower bounds derived in [69] lead to a tighter lower bound by nearly 20% in this case. The authors concluded that these lower bounds can be very useful in comparing the performances of various multimedia channel assignment algorithms with regard to the optimality of the required bandwidth and can thus design more efficient channel allocation algorithms for multimedia based applications over cellular networks. IV. C HANNEL A LLOCATION IN C OGNITIVE R ADIO BASED N ETWORKS The term cognitive radios was first coined by Joseph Mitola III in 2000 [71], [72], [73]. Cognitive radios represent the evolution of software defined radios (SDRs) into intelligent, operating environment aware and adaptive radios that promise reliable wireless communication as well as provide efficient sharing of the radio spectrum [122]. Fig. 7 depicts the basic functionalities of a cognitive radio. Central to the operation of every CR in a licensed band is the tacit understanding that such radios would minimally degrade the performance of the primary users - which includes both transmitters and receivers. Furthermore, the primary users are neither required to be aware of the presence of secondary users, nor are they required to change their transmission parameters to mitigate the interference to and from secondary users. The IEEE 802.22 working group [74] is currently exploring solutions for cognitive radio standards that would enable them to operate in the white spaces of the TV spectrum band from 470MHz to 698MHz through the formation of wireless regional area networks (WRANs). The holy grail of research on cognitive radios is the creation of reconfigurable wireless networks [82]. The objective of reconfigurable wireless networks is to use SDRs so as to enable encapsulation of i) dynamic spectrum access and, ii) protocols for end-to-end control and management of applications, services and content. Reconfigurable networks imply reconfigurability

22

at all layers (terminal, network and services) [88], [119]. Such a terminal can move across different radio networks and be able to adapt at every instant to an optimum mode of operation. However, implementing such capabilities require coordinated reconfiguration management support from both the terminal and the network. Thus, a reconfigurable radio of the future may possess the capability to seamlessly switch between different protocols such as 3GPP, 802.11b/g, WiMax, Bluetooth, Zigbee, etc [82]. While reconfiguration can be done explicitly, the ultimate goal is to utilize an underlying cognitive radio in order to reconfigure the entire protocol stack transparent to the user. Thus, in a nutshell, while SDRs would provide the flexibility to switch across spectrum bands, cognitive radios would allow reconfigurability of protocol stacks and dynamic spectrum management for improving the spectrum utilization and network throughput, and therefore, in the process make it possible to enable seamless interoperability between various network protocols/architectures. In the context of wireless mesh networks where interference between neighboring users play a big role in adversely affecting the link qualities and network throughput because of all nodes operating in the same spectrum band, it is thus clear that cognitive radios can offer a direct advantage in terms of improving the overall network utilization and link reliability through their dynamic spectrum management capabilities. Indeed, as observed in the literature [117], [115], the capacity of WMNs can be substantially increased by overlaying a WMN with a cognitive radio model. Simulation results in [117] shows a capacity gain of 36% for arbitrary topologies. We present below a discussion on some of the key challenges faced in designing a cognitive radio based network that can operate across a wide range of the RF frequency spectrum through efficient allocation of channels to users in order to meet their individual requested service quality parameters. While the ability to modify operating parameters on-the-fly offers a great deal of flexibility, it also introduces many challenges hitherto unseen in conventional wireless networks. These range from the choice and design of the hardware architecture to the method of spectrum sensing and sharing/allocation.

A. Cognitive Radio Hardware Design Challenges The key challenge in the design of the physical architecture of a cognitive radio is the accurate and fast detection of weak signals over a wide frequency range of primary users when operating in licensed spectrum bands. In a typical cognitive radio device architecture, a wideband signal is received through a RF front-end and then sampled by a high speed analog-to-digital (A/D) converter. The sampled digital output is then measured for the detection of primary user’s signal. The RF front-end needs to be able to receive signals from various transmitters operating with different power levels, source coding techniques, bandwidths, etc. Thus, it must have the ability to quickly modify it’s parameters and detect even weak signals over a large and dynamic frequency range. Unfortunately, this requirement translates into using multi-GHz speed A/D converters, which may not always be feasible due to cost and other design limitations. Thus, various techniques are being explored by the research community to reduce the dynamic range of the signal to be sampled [90], [94], [95], [121], [135] such as: i) filtering of strong signals using tunable notch filters and, ii) use of multiple antennae in conjunction with beam forming techniques to perform signal filtering in spatial domain rather than in the frequency domain. The principal reconfigurable parameters that are incorporated in cognitive radios are:

23

•

Operating Frequency: Based on available radio spectrum information, the cognitive radio needs to be able to quickly change its operating frequency.

•

Modulation Techniques: A cognitive radio also may require to modify its source coding technique in order to be able to receive as well as transmit data to and from different radios operating on different protocols.

•

Transmission Power: Transmission power control provides an effective way of reducing interference to other users of a shared spectrum band and allows more users to share a spectrum.

•

Communication Stack: Based upon the need, it may be necessary for a cognitive radio to change its protocol stack for optimal data communication performance as well as for interoperability between various networks.

Reconfigurability of operating parameters being an essential criterion in designing cognitive radios, most existing cognitive radios utilize an FPGA-based design rather than DSPs due to ease of programming. Most modern FPGAs usually come with highly optimized features implemented as non-standard configurable blocks (CLBs) like phase-locked loops, low voltage differential signal, clock data recovery, internal routing resources, hardware multipliers, memory, programmable I/O and microprocessor cores, among others [90]. B. Spectrum Sensing in Cognitive Radio Networks Central to the ability to reconfigure operational parameters of cognitive radios is the ability to do spectrum sensing in order to identify spectrum holes that match the data transmission QoS requirements [130], [131]. Identification of spectrum holes suffers from the well known problems of exposed and hidden (primary user) nodes. To avoid interference and performance degradation of primary users in the TV band, the 802.22 working group has set −116dBm as the sensitivity level for detecting whether a particular channel is free or not. While this might prevent interference to television receivers from unfortunately faded cognitive radios, the -116dBm rule leaves little spectrum in the TV-band open to detection and utilization by cognitive radios [133]. Various studies have shown that the spectrum utilization in time and space is far lower than what would actually be possible because of the −116dBm restriction. For example, it was observed in [84] that while on an average 56% of the TV-band channels are free in Midwest US, only 22% can be recovered on an average by the -116dBm rule. Typically, in most locations, channels with signal strength above the -116dBm limit will still be safe to use for a large majority of the cognitive radios not experiencing any unfortunate fading. In a single radio based sensing approach, even weak TV signals must be detected to avoid causing interference to TV receivers within its transmission zone that are not faded, even if the CR is actually experiencing only an unfortunate fading. The traditional signal processing approach is to treat this as a hypothesis testing problem [76], [84], [81]. The basic hypothesis problem for transmitter detection is usually formulated as:

x(t) =

   n(t)

H0 ,

  h · s(t) + n(t)

H1 ,

(2)

where x(t) is the signal received by the cognitive radio, s(t) is the transmitted signal of the primary user, n(t) is the additive white gaussian noise (AWGN) and h is the amplitude gain of the channel. H0 is the null hypothesis for the scenario that there

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is no primary user on the channel. H1 is the alternative hypothesis that there exists a primary user currently transmitting on the channel. In general, by increasing the amount of time (up to a certain extent) for which the test statistics is averaged, the hypothesis can be tested arbitrarily well. However, there exists an SNR wall [83], below which a detector will fail to be robust, no matter how long it can observe the channel. A survey of the literature [76], [84], [81], [83] reveals that three schemes are generally utilized for transmitter detection using the above hypothesis model in (2). They are: matched filter based, energy based and feature based detection. Besides these three techniques, people have also looked at cooperative and interference temperature based spectrum sharing schemes. We provide below a brief description of these various schemes. 1) Matched Filter based Detection: When the nature of the primary user’s signal is known a priori, the matched filter is the optimal detector for stationary AWGN as it maximizes the received signal-to-noise ratio (SNR) [81]. The cognitive radio requires to know the modulation type, pulse shape and the packet format (in case of digital transmission) of the primary user [81], [76]. Considering the fact that most primary users have a fixed transmission scheme with well defined pilot, preamble, synchronization word or spreading codes, coherent detection using matched filter thus offers a useful way of spectrum hole detection in real-life scenarios. 2) Energy based Detection: In scenarios where not enough information about the primary’s signal is known, the optimal detector can be the energy detector which requires knowledge of only the AWGN power. In this scheme, the received signal at the CR is passed through a bandpass filter, squared and then integrated over the observation interval. The output of the integrator is then compared to a threshold value to detect the presence of a licensed user. Because of the ease of implementation and ability to adjust to varying primary user transmission types, most recent works on primary transmitter detection have adopted the energy detector [84], [81], [96], [98], [99]. Several recent works attempt to build more sophisticated energy based detectors that incorporates shadowing and multi-path fading factors. The main drawbacks of the energy based detection method are: •

Susceptibility to the uncertainties - both spatial and temporal, in noise power and,

•

Inability to differentiate between various signal types and identify specific features in the received signal. Thus, often times it is difficult to ascertain whether the received signal at the CR is from a primary user or from another secondary user.

3) Cyclostationary based Feature Detection: Cyclostationary based feature detection techniques attempt to take advantage of the fact that most modulated signals are in general coupled with sine wave carriers, pulse trains, repeated spreading, hopping sequences or cyclic prefixes, which lead to inherent periodicity in the received signal. Such modulated signals are characterized as cyclostationary since their mean and autocorrelation exhibit periodicity [76]. The features are detected by analyzing a spectral correlation function. The main advantage of using a spectral correlation function is that it provides a far superior detection quality due to its robustness against uncertainty in noise power. However, the price to be paid for this improved signal detection capability are higher computational complexity and significantly longer observation time. Even better efficient, reliable and enhanced feature detection are possible by combining cyclic spectral analysis with pattern recognition techniques

25

(e.g., using neural networks, Hidden Markov Models, etc.) [97], [105], [140]. Furthermore, the ability to detect features in the transmitted primary signal may provide scope to the secondary CR to adapt its transmission strategy. As an example, if the secondary CR can detect that the primary’s transmitted signal does not require real-time QoS, then it may be possible to accordingly adjust the secondary’s transmitted signal (e.g., communication protocol, modulation, transmitted power, etc.) so as to transmit simultaneously on the same channel along with the primary user, without hampering the primary’s signal quality beyond some threshold value. 4) Cooperation based Detection: In light of the -116dBm rule, the spectrum utilization factor can be improved by using multiple cognitive radios in a neighborhood to sense and detect spectrum holes as such an approach provides for a statistically better decision on whether a channel is actually being used currently by a primary user or not [131], [138]. While it is possible that an individual secondary radio may be experiencing deep fading, the probability of all cognitive radios in a region suffering the same simultaneously is quite low. It is to be noted that while wireless multi-path fading is largely independent for physical reasons [84], [81], [83], shadowing on the other hand, may be correlated. For example, the chances that everybody is indoor during bad weather conditions is quite high. In fact, shadowing may be correlated not only across radios, but also across frequencies for a single radio [84]. As an example, a cognitive radio in indoor environment would experience shadowing for both TV stations, as well as GPS. By exploiting such information, multiband, multi-user sensing has the potential to detect more accurately the channels that are currently available for use by secondary users in a particular location. Cooperation based sensing can also help in alleviating the hidden node problem to a large extent. As such, most current work in the literature focus on coordination based spectrum sensing techniques. This technique also has the additional advantage that a single radio does not have to scan the entire spectrum for holes - thereby saving both valuable scan time as well as limited node battery energy. Cooperative sensing can be implemented as either a centralized or a distribute solution. While cooperative sensing provides more accurate sensing information, it comes with the overhead in terms of higher complexity due to exchange of spectrum information through messages (e.g., local broadcast) between nodes and decision making [130]. Furthermore, the problem of detecting a primary receiver’s location still remains. Some other issues that need to be addressed in the context of cooperation based sensing are: •

The trade-off between time overhead for sensing (sensing time + message exchange time) and the spatial coverage overhead (area covered under sensing + sensing MAC effects) need to be understood for application specific cognitive radio networks. Various signal processing approaches need to be evaluated for identifying the most suitable ones for specific application scenarios [94], [90], [84], [81], [76], [77], [79], [80].

•

Under the single radio based sensing, an SNR wall [83] for a sensing algorithm sets the bound on how sensitive a detector can be, given the noise model. The role of SNR walls need to be understood for cooperation based sensing too.

•

Considering that cooperative spectrum sensing requires expenditure of energy, time and computational resources, there is a need for some standards or regulations to be followed by all secondary users in order to make cooperation

26

based detection a reality. In this connection, various economic pricing models such as those based on cooperative games [85], [103], [121] are actively being explored by researchers which would provide sufficient incentive to cognitive radios in a neighborhood to take part in a cooperation based spectrum sensing scheme. 5) Interference based Detection: As stated above, the problem of determining a primary receiver’s location remains whether using a single radio based detection or cooperation based detection. However, the most compelling reason behind spectrum sensing is to avoid causing interference at a primary receiver. Interference is traditionally regulated in a transmitter-centric way - through various techniques such as transmit power control, out-of-band emissions, etc. Unfortunately, as interference actually takes place at the receiver, it is difficult for the transmitter to dynamically vary its transmission parameters so as to minimize at any instance of time the interference at the receiver. Therefore, FCC recently rolled out a new model for measuring interference, called the interference temperature [139]. This model describes the signal of a radio station designed to operate in a range at which the received power approaches the noise power. As additional interfering signals appear at the receiver, the noise floor increases at various points within the service area of the primary transmitter. Unlike the traditional transmitter centric approach, the interference temperature model manages interference at the receiver through the interference temperature limit which is defined as the amount of new interference the receiver can tolerate [96], [136], [139]. That is, the interference temperature model accounts for the cumulative RF energy from multiple sources at a point and sets a maximum permissible level on that energy. Thus, as long as the secondary users do not exceed this limit at a particular location, they may continue to use the same spectrum band. There are of course certain drawbacks that are yet to be addressed in developing a practical spectrum hole detection method using the interference temperature model: •

Modeling multiple users: The interference temperature model describes the interference caused by a single secondary user and does not consider multiple such users.

•

Location awareness: If secondary users are unaware of the location of nearby primary users, then naturally the actual interference at a primary receiver can not be measured.

•

Computational complexity: Finally, the use of interference temperature based detection also adds to the hardware complexity and consequently the cost of the secondary user’s system.

C. Spectrum Allocation and Sharing in Cognitive Radio Networks Once spectrum holes have been identified - either using a single cognitive radio or coordination based sensing, the next step is to allocate spectrum bands from the white spaces to the CRs so as to meet their QoS requirements as well as maximize spectrum utilization. The typical goal of a dynamic spectrum allocation algorithm can be stated as follows: given the dynamic demands of each CR node in a network, the spectrum allocation algorithm computes a feasible allocation scheme that attempts a best-efforts satisfaction of the individual node demands while, i) maximizing spectrum utilization and, ii) avoiding interference to other spectrum blocks assigned to other links, including those assigned to primary users of the spectrum block.

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The spectrum allocation problem in cognitive radio networks throws up challenges that are not present in conventional wireless technologies (e.g., Wi-Fi, cellular networks, etc.). Two primary reasons can be cited for this: 1) The spectrum holes are typically fragmented and of varying size. Moreover, the availability of the spectrum holes, both in terms of geographical location and size varies temporally as well as spatially. 2) Cognitive radios can dynamically alter their center frequency and the bandwidth for each transmission. Due to lack of predefined channel widths for cognitive radios, this leads to the problem of determining which node should use which center frequency and of what bandwidth, in order to meet their respective QoS requirements while avoiding/minimizing interference to active primary users as well as other secondary users in the neighborhood. The above stated reasons make the spectrum allocation problem harder than the channel allocation problem (CAP) encountered in wireless networks such as cellular networks, which is already an NP-complete problem. The authors in [86], [87] show that the spectrum allocation problem for cognitive radios is also NP-hard. Most existing allocation schemes utilize techniques such as graph coloring, genetic algorithm (GA), simulated annealing, matching, etc. for solving this allocation problem [91], [92], [100], [86], [93]. As with CAP, the dynamic spectrum allocation issue can be tackled as either a centralized or a distributed computational problem. In [86], [87], a centralized approximation algorithm is presented for solving the dynamic allocation problem with regard to maximizing the proportionally-fair throughput of a cognitive network. They also present a distributed algorithm for achieving high throughput and fairness in allocation under various scenarios. For both the approaches, [86] show that their algorithms are close to optimal in most scenarios. IEEE 802.22 [74], DSAP [100] and DIMSUMNet [102] are some other centralized schemes. Most distributed schemes [91] are based on channels of fixed bandwidth [87], such as the multichannel MAC protocols for 802.11 like SSCH [106], MMAC [104], DCA [107], among others. A survey of various spectrum sharing and management techniques can be found in [77], [78], [79], [80], [132], [134]. Besides classifying spectrum allocation schemes as centralized vs. distributed, it is also possible to categorize them based on the allocation behavior and the access technique employed [76]. Under the allocation behavior based classification we have: Cooperative spectrum sharing: Cooperative solutions for spectrum sharing/allocation consider the effect of a node’s communication requirements and parameters on other nodes [76], [98], [99], [100], [84], [85], [86], i.e., the interference measurements of each node is shared with others. Non-cooperative spectrum sharing: As the name suggests, under the non-cooperative schemes each node considers only its own requirements, oblivious to the requirements of other nodes. In general, non-cooperative solutions are easier to implement than cooperative ones - both in terms of message and computation complexity, but as expected, produce inferior solutions and higher interference between various links. In cognitive radio networks, the issue of handling selfish users is of particular importance as they may prevent other users from being able to communicate with their required QoS constraints, even though such solution(s) may exist. Selfish or rogue users may provide false information about themselves or collude with other such rogue nodes to get a larger share of the spectrum at the expense of others. In this context, various economic pricing models are being investigated by the research community that attempt to provide incentive/penalty based on behavior of nodes. For example, [85] presents two game theoretical mechanisms

28

to prevent cheating and collusion between rogue nodes. Similarly, several works [103], [137] have tried to explore the spectrum sharing problem using human behavior inspired models. The competition and cooperation between various nodes in a cognitive radio network can be well modeled as spectrum sharing games [121]. The strategy space of the individual players (i.e., the CR nodes) may include the various transmission parameters they want to adopt (e.g., transmit power, bit rate, transmission duration, etc.). The utility functions are often defined as non-decreasing function of the QoS the individual nodes receive. With such a definition of the game, in a non-cooperative game, each user attempts to maximize his/her own utility by choosing an optimal strategy. As an example, the optimal strategy such a selfish node may determine is to transmit at its maximum possible power, with no regard to the other active links within its transmission zone. From the access methodology point of view, spectrum sharing schemes can be classified as either overlay based or underlay based schemes: Overlay spectrum sharing schemes: Overlay based schemes include techniques that attempt to utilize spectrum holes within a licensed spectrum band for spectrum allocation so as to cause minimum interference to the primary users. Underlay spectrum sharing schemes: Underlay spectrum sharing schemes exploit spread spectrum techniques to simultaneously access a spectrum band currently being used by a licensed user [141]. The spectrum utilization factor is in general higher than in overlay based schemes but comes at an increased device cost/complexity. In [101], the effects of underlay and overlay approaches on cooperative spectrum sharing was investigated. Non-cooperative sharing was investigated using game theoretical framework. Another comparative study can be found in [108] where they considered underlay schemes such as CDMA and UWB. Some other works have tried to utilize hybrid techniques such as spreading based underlay with interference avoidance for better performance. We now present a mathematical formulation of the dynamic spectrum allocation problem using the notations and ideas from [86]. 1) System Model, Notations and Basic Idea: We consider a cognitive radio equipped with a reconfigurable transceiver. The reconfiguration of operating parameters of the transceiver such as the center frequency and bandwidth typically require around 10s of microseconds and can only tune to a contiguous segment of spectrum. Due to hardware limitations, in most transceivers the possible bandwidth values are a discrete set. Let this operating frequency range be denoted by [bmin , bmax ], where bmin and bmax denote the lower and upper bounds of the supported bandwidth, respectively. Typically, the largest usable bandwidth is typically below 40MHz [86]. We consider a cognitive radio network modeled as a set of n nodes V = {v1 , . . . , vn } placed on a two-dimensional Euclidean plane. Let d(vi , vj ) denote the Euclidean distance between nodes vi and vj . Let fbot and ftop denote the lower and upper end of the accessible target spectrum band. We further assume that each node vi ² V is equipped with a radio transceiver that is capable of dynamically accessing any contiguous frequency band [f, f + ∆f ] such that, fbot ≤ f ≤ f + ∆f ≤ ftop , and bmin ≤ ∆f ≤ bmax . For each pair of nodes (vi , vj ) ² V within mutual communication range, let Dij (t, ∆t) denotes the demand in bit/s that vi would like to transmit to vj during time interval [t, t + ∆t]. As in [86] we assume that this link-based demand subsumes

29

the traffic of all flows that are routed over this particular link. The advantage of the above definition of Dij (t, ∆t) is that it captures all the scenarios corresponding to i) demands varying between different links and, ii) demand variation for a single link over time. The primary difference between the dynamic spectrum allocation in cognitive radio networks and spectrum allocation using predefined channels of fixed channel-width (e.g., dynamic channel allocation in Wi-Fi and other radio networks) are: i) the bandwidth of the spectrum allocated to different links becomes an additional variable and, (ii) the radio parameters can be k adjusted in a fine timescale. Using the notation from [86], we say that a time-spectrum block Bij = (tk , ∆tk , fk , ∆fk ) is

assigned to link (vi , vj ) if sender vi is assigned a contiguous frequency band [fk , fk + ∆fk ] of bandwidth ∆fk during time interval [tk , tk + ∆tk ]. In any channel assignment problem, a feasible solution needs to account for interference between users. There can be three different types of channel interferences: i) co-site interference, for channels not separated enough in frequency assigned to two nodes at the same location, ii) adjacent channel interference, for using two channels not separated enough in frequency in two nodes that are neighbors of each other and, iii) co-channel interference, for using two channels not separated enough in frequency in nodes not sufficiently distant from each other (distance-2 neighbors and beyond). Hence, as stated earlier, the channel assignment problem in its general form usually considers multiple minimum frequency separation constraints, based on the distance between a pair of nodes. Depending on the distance between the nodes, the appropriate minimum frequency separation value is chosen. For example, the channel assignment problem in cellular networks with a demand for only one type of signal from each cell is typically modeled with three frequency separation constraints - s0 , s1 and s2 . s0 defines the minimum band-gap required for two channel assignments in the same cell, s1 represents the minimum band-gap required for frequencies assigned to two adjacent cells while s2 captures the minimum frequency separation required for two channels assigned to two cells at distance 2 from each other. Due to such restrictions on channel assignment, spatial frequency reuse is extremely critical to support a large number of users with a limited available spectrum band. In cognitive radio networks, we also have an additional feature of temporal frequency reusability due to dynamic variation in the available white spaces. For our problem, we assume a simplistic model where every node vi has a transmission range Ri and an (usually larger) interference range Riint . A message sent by vi to vj is received successfully, only if there is no simultaneous transmitter vk in the vicinity of vj such that vj is within the interference range of vk . k l Thus, two time-spectrum blocks Bij (tk , ∆tk , fk , ∆fk ) and Bmn (tj , ∆tl , fl , ∆fl ) are mutually non-interfering if one or more

of the following three conditions is satisfied: 1) Spatial separation: d(vj , vm ) > Rjint and d(vi , vn ) > Riint 2) Frequency separation: max (fk , fl ) ≥ min (fk + ∆fk , fl + ∆fl ) 3) Temporal separation: max (tk , tl ) ≥ min(tk + ∆tk , tl + ∆tl ) To avoid causing harmful interference to primary and other secondary users, we therefore define a set of prohibited bands P = {P1 , . . . , Pn }, where every Pi ² P denotes a band-gap, (e.g., a spectrum band currently being used by a primary user

30

and hence not accessible to the cognitive radio). Thus, for any two given links link (vi , vj ) and (vm , vn ), a spectrum allocation schedule, S, thus needs to generate an k l k l k l assignment of two time-spectrum blocks Bij and Bmn respectively, such that: Bij ∩Bmn = ∅, Bij ∩Pr = ∅ and Bmn ∩Pr = ∅,

∀Pr ² P. We can thus view the dynamic spectrum allocation problem in cognitive radio networks as dynamic allocation of spectrum blocks in a three-dimensional resource space, composed of frequency, space and time [86]. 2) Problem Formulation: Given a set of dynamic demands Dij (tk , ∆tk ), the objective of a dynamic channel allocation scheme is to compute a feasible spectrum allocation schedule S that assigns non-interfering time spectrum blocks to each of the links such that i) the individual link demands are satisfied as best as possible and, ii) spectrum utilization is maximized through minimization of the fragmentation of the spectrum white space. From this objective, we can formulate various measures and combinatorial optimization problems. Two important examples of such optimization problems are: •

Maximizing the network throughput and,

•

Maintaining a proportionally-fair throughput among all the demands.

While the throughput maximization problem does not include any notion of fairness among the various demands, a high minimum proportionally-fair throughput guarantees that in every time-interval of a pre-defined duration, every demand gets its fair share of throughput. The shorter the interval chosen, the more short-term and fine-grained this notion of fairness becomes. A protocol that guarantees good minimum proportionally-fair throughput over very small values of such a time interval leads to lower latencies and jitter [86]. Lower latencies and jitter in turn are especially useful for real-time communication requirements as found in many streaming data applications and control over wireless networks. In our problem formulation, we have assumed that spectrum block assignments are mutually non-interfering. However, in certain scenarios, it may be possible that it is sufficient to have an assignment where the interference is below a certain threshold as in the previously stated underlay based allocation schemes. This introduces an additional variable in the problem and makes the dynamic spectrum allocation problem computationally even harder. V. C ONCLUSION We have described the importance and challenges involved in assigning communication channels to an ever increasing number of users for the cellular mobile networks as well as for the cognitive radio networks operating in both licensed and unlicensed bands. The major challenge is that the number of users is very large, but the number of available channels is very small. Yet we have to assign channels to all users - possibly in an optimal way for maximum utilization of the available channels and with minimum interference - within a very small amount of time as demanded by the practical situations. For cellular mobile networks, benchmark problems for comparing the performances of various approaches exist in the literature. The performances are measured in terms of the optimality of assignments and also the execution time of the assignment algorithms. Assignment algorithms which provide optimal assignment, but take long execution time may be used for long-term allocation of channels (e.g., once an hour, if the execution time is of the order of 1 minute), while for short-term channel allocation, algorithms providing near-optimal solutions, but requiring very small execution time (of the order of tens of milliseconds) may

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