A Useful Metaheuristic for Dynamic Channel Assignment in Mobile Cellular Systems

The prime objective of a Channel Assignment Problem (CAP) is to assign appropriate number of required channels to each cell in a way to achieve both efficient frequency spectrum utilization and minimization of interference effects (by satisfying a number of channel reuse constraints). Dynamic Channel Assignment (DCA) assigns the channels to the cells dynamically according to traffic demand, and hence, can provide higher capacity (or lower call blocking probability), fidelity and quality of service than the fixed assignment schemes. Channel assignment algorithms are formulated as combinatorial optimization problems and are NP-hard. Devising a DCA, that is practical, efficient, and which can generate high quality assignments, is challenging. Though Metaheuristic Search techniques like Evolutionary Algorithms, Differential Evolution, Particle Swarm Optimization prove effective in the solution of Fixed Channel Assignment (FCA) problems but they still require high computational time and therefore may be inefficient for DCA. A number of approaches have been proposed for the solution of DCA problem but the high complexity of these proposed approaches makes them unsuitable/less efficient for practical use. Therefore, this paper presents an effective and efficient Hybrid Discrete Binary Differential Evolution Algorithm (HDB-DE) for the solution of DCA Problem.


I. INTRODUCTION
It is important to efficiently utilize the scarce radio spectrum using a proper channel assignment scheme [1]. The aim of a channel assignment algorithm is to determine a spectrum efficient assignment of channels to the cells such that the traffic demand can be met as far as possible while satisfying the channel reuse constraints: co-channel constraints, channels separation constraints, and co-site constraints. A channel can be reused is that the same channel can be assigned to multiple cells simultaneously due to the radio propagation path loss. Channel assignment algorithms can be classified as static or dynamic. In a static approach, which is commonly called Fixed Channel Assignment (FCA) the channels are allocated and prefixed to each cell during the setup according to the traffic intensity estimated by the designer in the cell. FCA is still in use because it requires a moderate amount of BS radio installer and equipment and a simple monitoring procedure/algorithm. However, high efficiency of total channel usage over the whole service area if the traffic varies dynamically from cell to cell cannot be attained by FCA. To solve this problem, DCA [2] has been in trend since last twenty years. In DCA, channels are assigned dynamically over the cells in accordance with traffic load. FCA being a static technique can afford to spend more time to generate a better solution and is also easier to implement FCA in practice. However, from a resource utilization point of view, DCA is more preferable over FCA as DCA is designed to adjust resource assignment according to traffic demand, and hence, can support a higher capacity (or lower call blocking probability). The advantages of DCA are that it has a lower blocking rate than FCA at low traffic intensity and a lower forced call termination rate than FCA when blocking rates are equal [3]. DCA Problem is NP-hard and its effectiveness depends on its algorithm's efficiency in determining fast solution, good quality solution and its ease of implementation. Thus, devising a DCA, that is practical, efficient, and which can generate high quality assignments, is a challenging problem [4]. Metaheuristic Search techniques prove effective in the solution of DCA problem. A number of approaches [5][6][7][8][9][10][11][12][13]17,19,20,21,22] have been proposed for the solution of Channel Assignment Problem. The initial efforts for the solution of FCA were based on deterministic methods but as the problem is NP-hard these methods proved ineffective and inefficient for practical implementation for the next generation of mobile systems in which higher traffic demand was expected. To overcome the difficulties associated with the deterministic methods other heuristic methods such as Simulated Annealing [5], Tabu Search [6], Neural Networks [7,8] and Genetic Algorithms [9,11,12] were used for the solution of FCA problem. Later, Feedforward Neural Networks [19], Hopfield Neural Networks [20,21], Genetic Algorithms [10,13], Combinatorial Evolution Strategy [22], and Particle Swarm Optimization [17] have been used for the solution of DCA problem. However, the ever increasing number of mobile cellular users and the increasing demand for bandwidth call for more and more efficient Dynamic Channel Assignment strategies. Therefore, this paper presents an effective and efficient Hybrid Discrete Binary Differential Evolution (HDB-DE) for the solution of DCA Problem. HDB-DE is a discrete binary version of Differential Evolution [23] which is an effective stochastic parallel search evolutionary algorithm for global optimization. The problem formulation and the implementation of HDB-DE take care of the soft constraints as well as hard constraints and hence focuses search only in the feasible regions of the search space

II. PROBLEM FORMULATION FOR DCA
A. Constraints in Channel Assignment Problem In any cellular network, whenever two cells use the same channel or when two cells use channels adjacent to each other on the spectrum or when two channels are assigned to the same cell, interference occurs; these types of interference are called Co-channel Interference, Adjacent Channel Interference and Co-site Interference respectively [14]. They lower the signal-to-noise ratio at the receiving end, leading to the deterioration of system performance. Though the computation of the actual level of interference is tough, primarily owing to its dependence on the topology of the real environment, experiments show that the effect of interference is reasonably low if the following three constraints are satisfied: Co-Channel Constraint (CCC): The same channel cannot be simultaneously allocated to a pair of cells unless there is a minimum geographical separation between them. Adjacent Channel Constraint (ACC): Adjacent channels cannot be assigned to a pair of cells unless there is a minimum distance between them. Co-Site Constraint (CSC): A pair of channels can be employed in the same cell only if there is a minimum separation in frequency between them. These constraints are called Electromagnetic Compatibility Constraints, which together with the traffic demand constraint, are known as hard constraints. Apart from the hard constraints, another set of constraints called soft constraints is also considered, which may be described as follows: The packing condition requires that a channel, in use in one cell, should be reused in another cell as close as possible (but obviously not interfering with the former) so that the number of channels used by the network is minimal, thereby lowering the probability of future call blocking in other cells. The resonance condition tries to ensure that same channels are assigned to cells belonging to the same reuse scheme [4], as far as possible. Another soft constraint is that, when a call arrives, minimum number of channel reassignment operations should be performed because excessive reassignment in a cell may lead to increase in blocking probability.
A solution to the CAP must satisfy the hard constraints whereas a soft constraint may be violated; the latter only helps maximize the utilization of resources and/or improve the quality of service. Apart from the traffic demand constraint, the only other hard constraint that we have taken into account is Co-channel Constraint; other sources of interference are assumed to be absent, as reported in literature Vidyarthi et al [15], Battiti et al [16], and Chakraborty et al [17].

B.
Assumption Pertaining to Cellular Model and Call Arrival 1) The topological model is a group of hexagonal cells that form a parallelogram shape (equal number of cells along x-axis and y-axis) as shown in figure 1(adapted from [15], figure 1]).  We set a minimum "reuse distance", which represents the minimum allowable normalized distance between two cells which may use the same channel at the same time as shown in figure 3. 8) A call is blocked if the entire set of channels in the network is in use in the cell involved in call arrival and its neighborhood that is there is no channel that satisfies the co-channel interference. 9) Existing calls in a cell involved in a new call arrival may be rearranged.

C. Formulation of Fitness Function
The equations 1, 2, 3 & 4 given below correspond to the different conditions i.e. co-channel interference, packing conditions, resonance conditions, and discouraging excessive rearrangement condition. These equations are combined to constitute a quadratic energy function (equation 5) whose minimization leads to an optimal solution for DCA [13].
Equation (1) expresses the hard condition. Where V k is output vector for cell k, with dimension channel (CH). V k,j =1 if channel j is assigned to cell k, otherwise V k,j =0. Here k signifies in which cell, call arrives. The energy function increases in case a channel j which is assigned in cell i is selected by cell k that interferes with i. It thus ensures that solutions with no interference give better (smaller) fitness values. A i,j is the ij th element of the assignment table A, which is 1 if channel j is assigned to cell i, and 0 otherwise.
This term expresses the packing condition. The energy decreases if channel j assigned to cell k is also selected by cell and interf (i, k) =0. Energy reduction depends on the distance between i and k. The packing condition requires that a channel, in use in one cell, should be reused in another cell as close as possible (but obviously not interfering with the former) so that the number of channels used by the network is minimal, thereby lowering the probability of future call blocking in other cells.
Where res(i, k) is function whose value is 1 if cells i and k belongs to the same reuse scheme, otherwise 0. Equation (3) symbolize the resonance condition. The resonance condition tries to ensure that same channels are assigned to cells belonging to the same reuse scheme, as far as possible.
Which subtracts 1 whenever a channel already being used by cell k, before the arrival of the new call, is considered in the candidate solution (i.e. in the new configuration) so that a mobile terminal being served need not change its channel too often. Finally, the fitness function F(X) is given by,

III. HDB-DE
HDB-DE is a discrete binary version of Differential Evolution which is an effective stochastic parallel search evolutionary algorithm for global optimization. Unlike DE here the individuals are initialized as binary strings. HDB-DE algorithm consists of three major operationsmutation, crossover and selection, which are carried out for each member of the population (called as target vector). Mutation on each target vector of the population generates a new mutant vector uniquely associated with it. The resultant mutant vector is no longer binary because of the difference operator and the control parameter. Therefore, the discretization process from a real continuous space to a binary space is done. Then the crossover operation generates a new trial vector using the mutant vector and the target vector itself. In selection phase the fitness of the trial vector is compared with the target vector and the vector with higher fitness replaces the target vector in the population for the next iteration.

A.
Pseudo-Code of HDB-DE 1) Initialize parameters t=0, NP (NP is number of individuals in population), CR and F. Where 2) Initialize target population t X . 3) Evaluate each individual i in the population using the objective function. 4) Obtain the mutant population (a mutant individual, 12 [ , ,..., ] bi ci X X and X are three randomly chosen individuals from the population such that ai bi ci . 5) Discretization process from a real continuous space to binary space is done according to the following equation I refers to a randomly chosen dimension (j=1,2,..,n)) 7) Evaluate trial population 8) Selection (The selection is based on the survival of the fittest among the trial population and target population such that: Repeat steps 2 to 8 While Termination condition not reached. 10) Output best solution.

IV. IMPLEMENTATION DETAILS OF HDB-DE FOR DCA
The Dynamic Channel Assignment problem is specified in the literature in terms of the number of cells in the network (N ce ), the number of channels in the pool (N ch ) and a demand vector D which is a vector whose i th element denotes the traffic demand in cell i, i= 1,2,…, N ce . We assume that the new call demand is placed at cell k which is already serving demand (k) calls where demand (k) denotes the total traffic load (ongoing) in cell k at time t; and no ongoing call is terminated in the entire network. Our problem is to assign an available channel to the incoming call with possible reassignment of channels to the calls in progress in cell k.

A. Solution Representation
The candidate solution to the problem is represented as a binary string X which is the representation of V k mentioned earlier where k signifies the cell in which call arrives. The size of the vector X is equal to the number of available channels (N ch ) and X k,j =1 if channel j is assigned to cell k, otherwise X k,j =0. The number of 1s in each solution vector is equal to demand(k)+1 i.e. the total ongoing calls plus the call that arrives at the concerned time instant.

B.
Mutation A new mutation operator has been designed for HDB-DE which is more effective than the one which has been used earlier [17] for mutation of solutions with binary representation in DE. The new mutation operator is as given below: () The effectiveness of the operator can be seen from the fact that if both t bi X and t ci X assume a value 1 then in the earlier mutation operation the difference becomes 0 and therefore does not result in any change in the value of t ai X whereas in the newly designed mutation operation it does not happen so and leads to the generation of better mutants and thereby faster convergence.
V. COMPUTATIONALRESULTS HDB-DE algorithm was implemented in Matlab and the following benchmark problems were used for its evaluation: 1) The first benchmark problem CSys 49 [13] consists of 49 hexagonal cells that are arranged to form a parallelogram structure with 70 channels available to the system. 2) The second and third benchmark problems i.e. HEX 1 and HEX 3 [18] are based on a 21-cell system. 3) The last four benchmark problems i.e. EX 1, EX 2, KUNZ 1 and KUNZ 2 [18] are based on a 4, 5, 10 and 15-cell system respectively. The details of the benchmark problems and the used demand vectors are summarized in Table I.  11,9,5,9,4,4,7,4,8 KUNZ 2 15 44 10,11,9,5,9,4,4,7,4,8,8,9,10,7,7 For each of the considered problems it has been assumed that all cells are arranged in the form of a parallelogram, the given N ce of each problem is expressed in the form r × c, where r, c are integers, and hence determine the configuration of the cellular network by setting the number of rows to r and the number of all columns to c [17]. A cell is arbitrarily selected and then it is assumed that, just before a call demand arrives in this cell at time t, demand(i) calls were already in progress in the i th cell, i =1 ,2,…, N ce , and demand(k) calls are ongoing in the k th cell. Accordingly, N ce X N ch assignment matrix, avoiding co-channel interference has been manually determined which describes the status of ongoing calls in each cell before the new call arrival and thus represents the initial condition. The assignment table used for HEX3 problem is given in Table II.
Whenever a simulation results in a solution, which violates Co-Channel Constraint (CCC) the call is rejected. Call Rejection Probability (CRP) as given in [17] is used as a parameter for determining the effectiveness of the proposed method. CRP= N rejected / N total Where N rejected = number of simulations in which the incoming call is rejected in the host cell considered; N total = total number of simulations.  Thus, CRP is the cumulative proportion of simulations, for which the call is rejected, in the long run. This parameter CRP is based on but different from the call blocking probability used in the [13,14]. The former characterizes a particular cell under a given initial condition while the latter characterizes the cellular network as a whole. The simulation results obtained by HDB-DE and those obtained by Simple Genetic Algorithm (SGA), Modified Genetic Algorithm (MGA) [24] and PSO [17] for the different benchmark problems are shown in Table III.
The results shown in table III indicate that the performance of HDB-DE and MGA is good compared to PSO. The comparison of the convergence curves and the average number of Evaluation expended to yield the best solution over a good number of runs of the algorithms will further throw light on the efficiency, efficacy and consistency of the algorithms.    He is an active researcher, guiding research, published papers in journals of national and international repute, and is also involved in R&D projects. He is a member of IEEE and a life member of Systems Society of India (SSI). He is also the Publication Manager of Literary Paritantra (Systems)-An International Journal on Literature and Theory.