- freely available
- re-usable

*Algorithms*
**2014**,
*7*(3),
418-428;
doi:10.3390/a7030418

^{1}

^{2}

^{3}

^{4}

## Abstract

**:**In a dynamic spectrum access network, when a primary user (licensed user) reappears on the current channel, cognitive radios (CRs) need to vacate the channel and reestablish a communications link on some other channel to avoid interference to primary users, resulting in spectrum handoff. This paper studies the problem of designing target channel visiting order for spectrum handoff to minimize expected spectrum handoff delay. A particle swarm optimization (PSO) based algorithm is proposed to solve the problem. Simulation results show that the proposed algorithm performs far better than random target channel visiting scheme. The solutions obtained by PSO are very close to the optimal solution which further validates the effectiveness of the proposed method.

## 1. Introduction

Spectrum is generally regulated by governments via a command and control approach. However, this approach has led to underutilization of a spectrum in vast temporal and geographic dimensions as shown in the survey made by the Federal Communications Commission (FCC) [1]. Motivated by this observation, cognitive radio (CR) has been proposed to improve spectrum utilization by dynamically accessing spectrum “white spaces” (i.e., spectrum holes) without causing harmful interference to primary users [2]. In this dynamic spectrum access framework, CRs are considered as secondary users (SUs) of the spectrum. When a primary user (licensed user) reappears on the current channel, the CRs need to vacate the channel and reestablish a communications link on some other channel to avoid interference to primary users. This process is referred to as spectrum handoff [3]. Target channels play an important role in spectrum handoff design because target channels are the hopes that SUs can resume their unfinished transmissions.

Based on the decision timing for selecting target channels for spectrum handoff, the target channel selection approaches can be categorized into two kinds: on-demand channel selection for reactive-decision spectrum handoff and predetermined channel selection for proactive-decision spectrum handoff [4]. On-demand channel selection searches target channels after spectrum handoff [5,6,7]. This may result in long spectrum handoff delay because an available channel needs to be searched in a wide frequency range. Predetermined channel selection determines target channels before spectrum handoff based on the long-term history information on channel status. It can save spectrum sensing time. This paper focuses on predetermined channel selection. Most prior work on predetermined channel selection selected a single target channel based on some objective, for instance, maximum spectrum lifetime [8], maximum residual idle time [9], maximum idle probability [10], and minimum waiting time [11]. However, in a dynamic spectrum environment, as the pre-selected channel may no longer be available, relying on a single target channel may result in low probability of link maintenance. A better mechanism is to select multiple target channels and try each target channel sequentially. The visiting order of these target channels is crucial to spectrum handoff. In our prior work [12], we designed a target channel visiting order which can realize the minimum probability of spectrum handoff failure. In this paper, we consider spectrum handoff delay as the objective for target channel visiting order design. We propose to use particle swarm optimization (PSO) to solve this combinatorial problem. PSO is an intelligent bio-inspired optimization algorithm that has shown its effectiveness for spectrum sensing, spectrum allocation and link adaptation in cognitive radio in our prior work [13,14,15]. To the best of our knowledge, this paper applies PSO for target channel visiting order design for spectrum handoff for the first time. Simulations are conducted to validate the effectiveness of the proposed PSO based algorithm in determining the target channel visiting order in this paper.

The rest of the paper is organized as follows. In Section 2, we formulate the target channel visiting order design problem for spectrum handoff as a combinatorial optimization problem which aims to minimize spectrum handoff delay. In Section 3, we propose PSO for solving the problem. In Section 4, simulation results are provided and finally in Section 5, conclusions are made.

## 2. Problem Formulation

We consider a similar system model as we formulated in [12]. Specifically, we consider two cognitive radios in a cognitive radio network communicating with each other. They operate on the same frequency range which consists of N channels. During communications, the two radios exchange the channel state information so common vacant channels are known to both radios. We denote M current vacant channels (except the current operating channel) as ${\{{c}_{k}\in \{1,2,\mathrm{...},N\left\}\right\}}_{k=1}^{M}$, M ≤ N − 1. If a primary user appears on the current channel, the two cognitive radios would initiate spectrum handoff and switch to another vacant channel for data transmission. A proactive-sensing spectrum handoff is assumed where the target channels for spectrum handoff are ready before initiating the spectrum handoff process [16]. In this paper, ${\{{c}_{k}\in \{1,2,\mathrm{...},N\left\}\right\}}_{k=1}^{M}$ are used as target channels for spectrum handoff. Before spectrum handoff, the visiting order of these target channels needs to be determined to optimize some objective. Denote the vector corresponding to the visiting order as $\mathit{v}=[{v}_{1},{v}_{2},\mathrm{...},{v}_{M}]$, then the process of spectrum handoff can be illustrated as in Figure 1. When handshake on a particular channel is successful, spectrum handoff is completed successfully and a new link is maintained on this channel. However, in a dynamic spectrum environment, as primary users may reoccupy the visiting target channel during spectrum handoff, handshake may still fail. When CRs try out all the channels and all handshakes fail, then spectrum handoff is failed.

Denote ρ_{i} as the probability that the handshake on v_{i} is successful, then the probability of spectrum handoff failure is

An important metric for evaluating spectrum handoff is spectrum handoff delay. If spectrum handoff is successful, then the handoff delay is $T\ell $, where $\ell $ is the number of handshakes till success. If spectrum handoff is failed, then some other rendezvous scheme needs to be performed to maintain communications. We assume the rendezvous time is τ. So the handoff delay when spectrum handoff is failed is MT + τ. The expected handoff delay is

Denote the set of vectors corresponding to all permutations of all elements in ${\left\{{c}_{k}\right\}}_{k=1}^{M}$ as Ω, then in order to minimize spectrum handoff delay, the problem of target channel visiting order design for spectrum handoff can be represented as

Note that ρ_{i} depends on the specific distribution of channel v_{i} remaining vacant. In this paper, we consider five distributions: Uniform, Exponential [17], Generalized Pareto [18], Rayleigh [19], and Weibull [19]. As in [17], we do not consider the case where the channel state changes twice or more because the probability is too low within the relatively short duration. The probability density functions (PDFs) and the corresponding expressions of ρ_{i} are shown in Table 1. For uniform distribution, the probability that the handshake on v_{i} is failed equals to the probability that the state of channel v_{i} changes to occupied before the end of this handshake, which is

_{i}can be obtained similarly.

Distribution | ρ_{i} | |
---|---|---|

Uniform ( ${b}_{{v}_{i}}>0$) | $f(x)=\{\begin{array}{l}1/{b}_{{v}_{i}},\begin{array}{c}\end{array}0<x<{b}_{{v}_{i}}\\ \text{0,}\begin{array}{c}\end{array}\text{else.}\end{array}$ | $1-\mathrm{min}\left\{\frac{(i-1)T+{T}_{h}}{{b}_{{v}_{i}}},1\right\}$ |

Exponential ( ${\lambda}_{{v}_{i}}>0$) | $f(x)=\{\begin{array}{l}{\lambda}_{{v}_{i}}{e}^{-{\lambda}_{{v}_{i}}x},\begin{array}{c}\end{array}x>0\\ \text{0,}\begin{array}{c}\end{array}\text{else.}\end{array}$ | $\mathrm{exp}\left(-{\lambda}_{{v}_{i}}((i-1)T+{T}_{h})\right)$ |

Generalized Pareto ( ${\sigma}_{{v}_{i}}>0$, $k\ne 0$) | $f(x)=\{\begin{array}{l}\frac{1}{{\sigma}_{{v}_{i}}}{\left(1+k\frac{x}{{\sigma}_{{v}_{i}}}\right)}^{-1-1/k},\begin{array}{c}\end{array}x>0\\ \text{0,}\begin{array}{c}\end{array}\text{else}\end{array}$ | ${\left(1+k\frac{(i-1)T+{T}_{h}}{{\sigma}_{{v}_{i}}}\right)}^{-1/k}$ |

Rayleigh ( ${\sigma}_{{v}_{i}}>0$) | $f(x)=\{\begin{array}{l}\frac{x}{{\sigma}_{{v}_{i}}^{2}}{e}^{-{x}^{2}/2{\sigma}_{{v}_{i}}^{2}},\begin{array}{c}\end{array}x>0\\ \text{0,}\begin{array}{c}\end{array}\text{else}\end{array}$ | $\mathrm{exp}\left(-\frac{{((i-1)T+{T}_{h})}^{2}}{2{\sigma}_{{v}_{i}}^{2}}\right)$ |

Weibull ( ${\lambda}_{{v}_{i}}>0$, $\alpha >0$) | $f(x)=\{\begin{array}{l}\alpha {\lambda}_{{v}_{i}}{x}^{\alpha -1}{e}^{-{\lambda}_{{v}_{i}}{x}^{\alpha}},\begin{array}{c}\end{array}x>0\\ \text{0,}\begin{array}{c}\end{array}\text{else}\end{array}$ | $\mathrm{exp}\left(-{\lambda}_{{v}_{i}}{((i-1)T+{T}_{h})}^{\alpha}\right)$ |

## 3. Proposed Target Channel Visiting Order Design Algorithm

The optimal solution for combinatorial optimization problem (3) is hard to deduct. In this paper, we propose to use PSO for solving this problem.

#### 3.1. Introduction of PSO

PSO is a bio-inspired optimization method which is inspired by observing the bird flock [20]. In PSO, each solution is a bird in the swarm and is referred to as a “particle”. In order to solve optimization problems in a discrete number space, Kennedy and Eberhart [21] developed a discrete binary version of PSO, which is the focus of this paper.

To begin with the iteration, a swarm with S particles is initialized. Let ${\mathit{x}}_{i}^{k}=[{x}_{i1}^{k},{x}_{i2}^{k},\mathrm{...},{x}_{iD}^{k}]$ denote the position of particle i (1 ≤ i ≤ S) at iteration k, where D is the number of dimensions to represent a particle. ${x}_{id}^{k}$ takes binary values from {0,1}. The velocity of particle i at iteration k is denoted as ${\mathit{y}}_{i}^{k}=[{y}_{i1}^{k},{y}_{i2}^{k},\mathrm{...},{y}_{iD}^{k}]$, ${\mathit{y}}_{id}^{k}\in R$. Each particle in the swarm is assigned a fitness value indicating how good it is for an optimization objective. We use ${\mathit{p}}_{i}^{k}=[{p}_{i1}^{k},{p}_{i2}^{k},\mathrm{...}{p}_{iD}^{k}]$ and ${\mathit{p}}_{g}^{k}=[{p}_{g1}^{k},{p}_{g2}^{k},\mathrm{...},{p}_{gD}^{k}]$ to denote the best solution that particle i and the whole swarm have obtained until iteration k, respectively. At each iteration, each particle adjusts its velocity according to its last velocity, its distance to the best solution it has obtained and its distance to the best solution of the swarm. The velocity of the particle is updated as follows:

_{1}and ξ

_{2}are two positive constants, r

_{1}and r

_{2}are random numbers uniformly chosen from the range [0,1]. Furthermore, the velocity is transformed to a value in the range [0,1] by using the following sigmoid function:

_{max}is used to avoid $\text{sig}({y}_{id}^{k})$ approaching 0 or 1, i.e., ${y}_{id}^{k}\in [-{V}_{\mathrm{max}},+{V}_{\mathrm{max}}]$.

#### 3.2. Proposed PSO Based Algorithm for Target Channel Visiting Order Design

The first step to use PSO for solving problem (3) is to map the particle to a possible solution. As the position of a particle contains binary bits while the visiting order takes decimal values, we need to convert these binary bits to decimal integers or the way around. Figure 2a shows the mapping process. We need $B=\lceil {\mathrm{log}}_{2}M\rceil $ bits to represent a value in [1,M], where $\lceil a\rceil $ denotes the closest integer which is greater than a. In consequence, the number of bits in a particle position is $MB=M\lceil {\mathrm{log}}_{2}M\rceil $. Consecutive B bits in the position represent a channel index. For instance, 000 represents channel c_{1}, 001 represents channel c_{2}, and so on. Figure 2b illustrates an example.

**Figure 2.**Mapping the position to the solution. (

**a**) General representation. (

**b**) An example where M = 6 and $B=\lceil {\mathrm{log}}_{2}M\rceil =3$.

The initial swarm is generated randomly to maintain a uniform distribution of these particles on the search space. Mapping a randomly generated position to a specific **v** may result in a solution which contains repeated channels. As a same target channel will not be visited twice or more in spectrum handoff, we propose the following procedure to ensure that a solution is valid. For position ${\mathit{x}}_{i}^{k}=[{x}_{i1}^{k},{x}_{i2}^{k},\mathrm{...},{x}_{iD}^{k}]$, we convert it to decimal integers and denote the resulting vector as ${\mathit{z}}_{i}^{k}=[{z}_{i1}^{k},{z}_{i2}^{k},\mathrm{...},{z}_{iM}^{k}]$. Update ${\mathit{z}}_{i}^{k}$ by computing ${\mathit{z}}_{i}^{k}=[{z}_{i1}^{k}\mathrm{mod}M,{z}_{i2}^{k}\mathrm{mod}M,\mathrm{...},{z}_{iM}^{k}\mathrm{mod}M]$, where amod M computes the reminder obtained after a is divided by M. Store all distinct values in ${\mathit{z}}_{i}^{k}$on a set Ω. Denote ℧ = [0,1,2,…,M − 1]. If the number of elements in Ω is smaller than M, we repeat the following two steps to make ${\mathit{z}}_{i}^{k}$ valid: (a) For any two elements in ${\mathit{z}}_{i}^{k}$ which are identical, randomly choose one of them and replace it with a value (denoted by λ) randomly chosen from the set $\Theta =\mho -\Omega $; (b) update Ω by adding λ into the set. The above procedure is repeated when all elements in ${\mathit{z}}_{i}^{k}$ are distinct. After the above procedure, ${\mathit{z}}_{i}^{k}$ is converted back to binary string and ${\mathit{x}}_{i}^{k}=[{x}_{i1}^{k},{x}_{i2}^{k},\mathrm{...},{x}_{iD}^{k}]$ is replaced by this string. For simplicity, we refer to this procedure as “position correction” in the rest of the paper. Fig.3 shows an example of “position correction”.

After initialization, the fitness of each particle is evaluated. We use the opposite of handoff delay (2) for fitness function. After fitness evaluation, the velocity and the position are updated by (6) and (8) and a new swarm of particle is obtained. Note that we also need to use the procedure of “position correction” discussed previously to make all positions valid. The iteration continues until the maximum number of iterations is reached. The proposed algorithm is shown in Table 2.

Steps | Procedures |
---|---|

1 | Swarm initialization. Set k = 0, and randomly generate ${x}_{id}^{k}$ and ${y}_{id}^{k}$, where ${x}_{id}^{k}\in \{0,1\}$, ${y}_{id}^{k}\in [-{V}_{\mathrm{max}},+{V}_{\mathrm{max}}]$, and 1 ≤ i ≤ S. Apply “position correction” procedure to all particles in the swarm. |

2 | Fitness evaluation. Compute the fitness value of each particle according to (2). Set ${\mathit{p}}_{i}^{k}=[{p}_{i1}^{k},{p}_{i2}^{k},\mathrm{...}{p}_{iD}^{k}]$ and ${\mathit{p}}_{g}^{k}=[{p}_{g1}^{k},{p}_{g2}^{k},\mathrm{...},{p}_{gD}^{k}]$, where g is the index of the particle which has the highest fitness value. |

3 | Velocity updating. Set k = k + 1, and update the velocity of the particle according to (6). If ${y}_{id}^{k}>{V}_{\mathrm{max}}$, set ${y}_{id}^{k}={V}_{\mathrm{max}}$; if ${y}_{id}^{k}<-{V}_{\mathrm{max}}$, set ${y}_{id}^{k}=-{V}_{\mathrm{max}}$. |

4 | Position updating. Update the position of the particle according to (7). Apply “position correction” procedure to all particles in the swarm. |

5 | Fitness evaluation. Compute the fitness value of each particle according to (2). For particle i, if it’s fitness value is greater than the fitness value of ${\mathit{p}}_{i}^{k-1}$, then set ${\mathit{p}}_{i}^{k}={x}_{i}^{k}$; if it’s fitness value is greater than the fitness value of ${\mathit{p}}_{g}^{k-1}$, then set ${\mathit{p}}_{g}^{k}={x}_{i}^{k}$. |

6 | Stop criteria evaluation. If k equals to the predefined maximum iteration, the algorithm is terminated; otherwise, go to step 3. |

## 4. Simulation Results

In the simulations, we assume T = 40 ms, T_{h} = 4 ms and T_{r} = 400 ms. Eight target channels are considered with the mean vacant time durations of 10 ms, 60 ms, 25 ms, 170 ms, 83 ms, 5 ms, 54 ms, and 155 ms, respectively. The parameters for PSO are as follows. Thirty habitats in a swarm are used. ξ_{1} = ξ_{2} = 2. V_{max} = 4. Figure 4 illustrates the convergence property of the algorithm. It can be observed that as the number of iterations increases, better solutions are obtained. Note that we only plot results when time duration during which a channel remains vacant follows Uniform and Exponential distributions. Similar trends have been observed with the other three distributions. For simplicity, we omitted these results.

Table 3 and Table 4 show the performance of the proposed algorithm compared with the other two target channel visiting methods: the random target channel visiting and the optimal target channel visiting. Two cases are considered respectively: (Case A) Nine target channels with the mean vacant time durations of 170 ms, 30 ms, 210 ms, 300 ms, 52 ms, 5 ms, 130 ms, 59 ms, 111 ms, respectively, and (Case B) Eight target channels with the mean vacant time durations of 10 ms, 60 ms, 25 ms, 170 ms, 83 ms, 5 ms, 54 ms, and 155 ms, respectively. The optimal target channel visiting order is obtained by exhaustive search. It can be seen that the proposed method performs far better than the random channel visiting scheme. The solutions obtained by the proposed algorithm are very close to the optimal solutions. The small standard deviation values also indicate that the proposed scheme is quite stable.

**Figure 4.**Convergence property of the algorithm averaged over 100 independent experiments. (

**a**) Performance of the best particle of the swarm (time duration during which a channel remains vacant follows Uniform distribution). (

**b**) Average performance of the whole swarm (time duration during which a channel remains vacant follows Uniform distribution). (

**c**) Performance of the best particle of the swarm (time duration during which a channel remains vacant follows Exponential distribution). (

**d**) Average performance of the whole swarm (time duration during which a channel remains vacant follows Exponential distribution).

**Table 3.**Performance comparison (Case A). Note that “Proposed10” and “Proposed50” stands for “Proposed algorithm with 10 iterations” and “Proposed algorithm with 50 iterations”, respectively.

Distribution | Uniform | Exponential | Pareto | Rayleigh | Weibull | |
---|---|---|---|---|---|---|

Mean | Random | 47.1070 | 50.5568 | 43.1053 | 42.9436 | 44.4931 |

Optimal | 40.4067 | 40.9428 | 40.3052 | 40.0660 | 40.0651 | |

Proposed10 | 40.4411 | 41.0199 | 40.3109 | 40.0062 | 40.0694 | |

Proposed50 | 40.4159 | 40.9638 | 40.3063 | 40.0060 | 40.0660 | |

Standard Deviation | Random | 13.6106 | 16.2251 | 4.8572 | 8.5445 | 11.0222 |

Proposed10 | 0.0269 | 0.0483 | 0.0048 | 1.2614 × 10^{−4} | 0.0035 | |

Proposed50 | 0.0119 | 0.0255 | 0.0011 | 3.0954 × 10^{−5} | 0.0012 |

**Table 4.**Performance comparison (Case B). Note that “Proposed10” and “Proposed50” stands for “Proposed algorithm with 10 iterations” and “Proposed algorithm with 50 iterations”, respectively.

Distribution | Uniform | Exponential | Pareto | Rayleigh | Weibull | |
---|---|---|---|---|---|---|

Mean | Random | 60.8031 | 70.3932 | 46.3667 | 49.4641 | 54.7102 |

Optimal | 41.2141 | 43.0155 | 40.6554 | 40.0270 | 40.2594 | |

Proposed10 | 41.2141 | 43.0481 | 40.6614 | 40.0270 | 40.2604 | |

Proposed50 | 41.2141 | 43.0222 | 40.6568 | 40.0270 | 40.2595 | |

Standard Deviation | Random | 31.9083 | 35.4822 | 7.3149 | 22.8160 | 27.3215 |

Proposed10 | 7.1776 × 10^{−15} | 0.0449 | 0.0061 | 1.9842 × 10^{−5} | 0.0021 | |

Proposed50 | 7.1776 × 10^{−15} | 0.0125 | 0.0022 | 1.8236 × 10^{−6} | 3.6255 × 10^{−4} |

Table 3 and Table 4 show the performance of the proposed algorithm compared with the other two target channel visiting methods: the random target channel visiting and the optimal target channel visiting. Two cases are considered respectively: (Case A) Nine target channels with the mean vacant time durations of 170 ms, 30 ms, 210 ms, 300 ms, 52 ms, 5 ms, 130 ms, 59 ms, 111 ms, respectively, and (Case B) Eight target channels with the mean vacant time durations of 10 ms, 60 ms, 25 ms, 170 ms, 83 ms, 5 ms, 54 ms, and 155 ms, respectively. The optimal target channel visiting order is obtained by exhaustive search. It can be seen that the proposed method performs far better than the random channel visiting scheme. The solutions obtained by the proposed algorithm are very close to the optimal solutions. The small standard deviation values also indicate that the proposed scheme is quite stable.

## 5. Conclusions

In this paper, we have investigated the problem of designing target channel visiting order for spectrum handoff to minimize the expected spectrum handoff delay. We proposed discrete PSO for solving this combinatorial problem. Our results show that the proposed algorithm performs far better than random target channel visiting scheme in terms of the obtained mean handoff delay and the standard deviation of obtained solutions. Another attractive result is that the solutions obtained by our PSO based algorithm are very close to the optimal solutions which are obtained by exhaustive search. An interesting future work is to use some other bio-inspired optimization method such as cuckoo search [22] and bat algorithm [23] to solve the problem.

## Acknowledgments

The authors thank the anonymous reviewers for their insightful comments.

## Author Contributions

Xiaoniu Yang initiated the idea of this research. Shilian Zheng formulated the optimization problem, proposed the procedure of the algorithm, and wrote the initial manuscript, which is critically reviewed by Zhijin Zhao and Xiaoniu Yang. Zhijin Zhao also helped with the PSO design. Changlin Luo helped with the Matlab coding and did the simulations.

## Conflicts of Interest

The authors declare no conflict of interest.

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