Dynamic access approach to multiple channels in pervasive wireless multimedia communications for technology enhanced learning

Abstract

With the development of multimedia and Internet of things technologies, technology enhanced learning applications such as smart class and smart learning at home have received more attentions from industrial and academic communities. However, pervasive wireless communications, which builds new collaborative and personalized learning patterns, have an important impact on learning and teaching. For current pervasive wireless networks, spectrum resources become increasing lack due to the introduction of a large number of new wireless technologies and thus the access of many new devices to wireless networks for all kinds of applications such as online smart learning. How to exploit effectively spectrum resources in current pervasive wireless networks is a larger challenge. To this end, we study dynamic access problem for spectrum resources. In this paper, we analyze more complex multiple channel model with multiple primary and secondary users. We exploit the lognormal distribution to characterize primary user behaviors and use opportunistic spectrum access to obtain the sensing status of channels. To raise the channel utility, we control transmission radiuses of secondary users to make primary and secondary users simultaneously utilize the channel. Finally, we propose the dynamic access algorithm to multiple channels. Simulation results show that our approach is feasible and promising.

Keywords

Cognitive networks dynamic access channel allocation technology enhanced learning multi-hop wireless communications

1 Introduction

With the development of multimedia and Internet of things technologies, technology enhanced learning applications such as smart class, smart school, and smart learning at home have received more attentions from industrial and academic communities [1, 2]. However, pervasive wireless communications, which builds new collaborative and personalized learning patterns, have an important impact on learning and teaching, due to their extensive applications than other networking technologies. Moreover, based on pervasive wireless communications, efficient management and analysis for technology enhanced learning are significantly important for developing smart school or individual learning application at home [3 –5]. Current wireless networks have encountered spectrum resource lack because many novel technologies appears and much more devices require to access to wireless networks [6 –10]. Due to the fixed allocation strategies of traditional wireless radio spectrum resources, the utility of current spectrum resources is very low [11 –13]. How to effectively exploit the existing spectrum resources is a larger challenge. Dynamic access has received extensive attention and becomes a import way to overcome this problem [14 –17]. However, To perform the effective and feasible dynamic access to wireless networks, specially with multiple primary and secondary users, is still to face a large number of unknowndifficulties.

To raise spectrum resource utility [2], load-balancing [14] and self learning [18] were used to improve dynamic access capability of secondary users. The contention-based broadcast forwarding protocol was proposed to dynamically select forwarding paths in vehicular ad-hoc networks [13, 19]. Some new methods such as event-oriented dictionary learning, graph model, smart learning, low power modeling, and compressive sensing [20 –24] are used to improve the performance of multi-hop wireless networks. Additionally, to attain the better network performance, some researchers taken into account the maximum network throughput as a optimal objective when performing channel allocation in cognitive networks [25, 26]. With the Internet of Things and peer-to-peer network applications increasing [27, 28], some new approaches are considered to raise the performance of wireless networks. Moreover, the collaborations among secondary users were also exploited to improve the network performance of dynamic access to cognitive networks [29, 30]. The distributed method was proposed to enforce dynamic access capability of secondary users [31]. Although these methods can obtain the better dynamic access performance, they still face many challenges to achieve the feasible and effective dynamic access, specially for cognitive network with multiple primary and secondary users. Specially, for technology enhanced learning in pervasive wireless multimedia communications, it is necessary to find more effective and efficient dynamic access approaches.

In this paper, for pervasive wireless multimedia communications in technology enhanced learning applications, we propose a new dynamic access algorithm to multiple channels in cognitive network with multiple primary and secondary users, combining opportunistic spectrum access and dynamic spectrum allocation. Firstly, we describe our system model with multiple primary and secondary users. Then we state our problem to overcome in this paper. Secondly, We utilize the lognormal distribution to characterize primary user behaviors based on the heavy-tailed nature of network traffic found in current studies. By such a way, we can build our sensing method for the channel status. After analyzing the sensing process of primary and secondary users’ status, we can make full use of opportunistic spectrum access to obtain the idle status of channels. Thirdly, different from general dynamic access, we control transmission radiuses of secondary user to make primary and secondary users simultaneously utilize the channel. As a result, we can effectively raise the channel utility. After discussing the dynamic access to multiple channels, we propose our dynamic access algorithm to cognitive networks with multiple primary and secondary users. Finally, we conduct a series of numerical experiments to validate our approach. Simulation results show that our approach is promising and effective.

The remainder is organized as follows. Section 2 introduces related work. In Section 3 we describe the system model. Section 4 formulate the transmission sensing of secondary users. In Section 5, we discuss the dynamic access to multiple channels. Section 6 conducts the numerical experiments and analysis. We conclude our work in Section 7.

2 Related work

We study in this paper how to perform dynamic access to multiple channels in cognitive networks. This has some studies about this problem. Li et al. proposed a new channel allocation based on the social relationship and the channel condition, using semi-definite programming to seek the optimal solution of their allocation method [32]. Han et al. presented the Repeated spectrum auctions with Bayesian nonparametric learning [33]. Wang et al. studied the spectrum decision taking into account load-balancing [6]. Unnikrishnan et al. proposed dynamic spectrum access algorithm with learning [18]. Lee et al. studied the multichannel selection algorithm and scheme using spectrum hole prediction and channel characteristics to improve network performance [26]. Our method takes in consideration the more complex dynamic access with multiple primary and secondary users. The proposed method can sense channel status according to network traffic.

In addition, Liang et al. studied the selection and the prioritization problem of the cooperative opportunistic routing in multi-hop wireless mesh networks and proposed a throughput improvement scheme [25]. Toka et al. studied distributed dynamic spectrum allocation problem [31]. Zhang et al. studied the performance for multi-hop relay networks by considering contention overhead of relay nodes in IEEE 802.11 Distributed Coordination Function (DCF) protocols [34]. We exploit the collaboration to improve the network performance. Different from these methods, our approach considers the idle status of channels and combines the transmission radius of secondary users in the collaboration process. Ding et al. proposed a cross-layer opportunistic spectrum access and dynamic routing algorithm for cognitive networks to maximize network throughput [29]. Additionally, random allocation of channels in a cognitive radio network based on maximum throughput analysis was also studied [35]. Elkourdi et al. used the information theory and secondary cooperation to make spectrum leasing [30]. Tang et al. studied the routing and channel assignment problem in multi-hop and multi-flow mobile ad hoc cognitive networks and presented a cross-layer distributed approach based on joint design to maximize the network throughput [37]. Lai et al. proposed an symmetric strategy to maximize the total throughput of cognitive users and presented a game-theoretic model to avoid their possible selfish behaviors [36]. Hao et al. built a joint channel allocation and power control optimal game model and algorithm to reach the lower network interference and balance the network energy consumption [38]. Lin studied multi-hop cooperative routing in cognitive networks [39]. We make opportunistic spectrum access and dynamic spectrum allocation. By controlling transmission radiuses of secondary user, we can to make primary and secondary users simultaneously utilize the channel and thus improve the channel utility.

3 System model

In this paper, we study the dynamic spectrum access problem in the cognitive network with multiple primary users and multiple secondary users, which is used for pervasive wireless multimedia communications in technology enhanced learning applications. Our system model is shown in Fig. 1, where primary users are {p₁₁, p₁₂, p₂₁, p₂₂}, secondary users are {s₁, s₂, …, s₁₁}, primary user pair {p₁₁, p₁₂} uses channel 1, primary user pair {p₂₁, p₂₂} exploits channel 2. To build the path from source node s₁ to destination node s₈, we are be able to attain the possible forwarding path s₁ → s₃ → s₄ → s₆ → s₁₀ → s₁₁ → s₈. To guarantee the reliable communication of primary users and secondary users, we study how to perform the dynamic spectrum access of secondary users in such the multiple users namely multiple primary and secondary users. Different previous methods, we investigate the hybrid situation with multiple cognitive channel to be selected for secondary users. In our studies, different primary user pairs use different channels to communicate each other and they are distributed randomly in the observed field. Without loss of generality, assume that there are n pairs of primary users p = {{p₁₁, p₁₂} , {p₂₁, p₂₂} , …, {p_n1, p_n2}} and z secondary users s = {s₁, s₂, …, s_z}. In a result, there are n channels available to secondary users. For such system model, we study how to perform the effectively dynamic access of hybrid model to raise the channel utility as possible.

Next, we discuss the dynamic spectrum access to multiple channels combining the opportunistic spectrum access and dynamic spectrum allocation. Our method makes full use of the advantages of the two approaches, which considers the channel usage situation by primary user and the location information of primary users and secondary users for system model in Fig. 1. Thereby, we can use the channel as possible and improve the coverage of transmitting nodes of secondary users.

4 Transmission sensing of secondary users

In this section, we discuss how secondary users perform the transmission sensing process, i.e., opportunistic spectrum access. To add the channel availability in the cognitive network with multiple primary and secondary users, we exploit the threshold to sense the available channel. By the threshold that the secondary user use to access the channel at different points of time, our method can exploit the idle time slots of primary users’ channel as possible while protect the performance of primary users. In multi-channel system model, one need to learn the idle probability threshold for each channel. Since the heavy-tailed distribution nature of network traffic, we use Pareto distribution to describe idle status of primary users in this paper.

During the sensing of secondary users, there exist two sensing results: the time slot is busy and the time slot is idle. Ideally, each time secondary users can correctly sense the channel status. However, in practice, the sensing results of secondary users can have some detection errors. We use two parameters P_f and P_d to characterize the sensing result. P_f represents the probability of false positives of secondary users while P_d denotes their detection probability.

When detecting that the channel is idle at a certain timeslot, the secondary user can use the channel to transmit data. In such a case, there exist tow results for data transmission of the secondary user, namely successful and unsuccessful. After the secondary user transmits data successfully each time, its receiving end are to feed back an ACK signal to it. If the transmission is unsuccessful, NACK signal is returned. However, due to time-varying nature of wireless channels, feedback signals of ACK and NACK may be lost during the transmission in the channel. Therefore, one can use γ₀ and γ₁ to represents the conditional probability of receiving NACK when the secondary user does not collide with primary users and denotes the conditional probability of receiving NACK when secondary user collide with primary users, respectively. For the transmission sensing process, our method includes four parts: primary user status, secondary user status, utility function, and time limitation. Next, we will discuss them in detail.

4.1 Primary user status

Because network traffic meets the heavy-tailed nature, we use the lognormal distribution to characterize the idle status of primary users, namely: $p (t) = {\begin{matrix} \frac{1}{\sqrt{2 π} δ t} exp (- \frac{(ln t - μ)^{2}}{2 δ^{2}}), & t > 0 \\ 0, & t \leq 0 \end{matrix}$ (1) where μ and δ, respectively, denote the mean value and the variance of the logarithm of the variable t, ln(.) denotes the natural logarithm function. Equation (1) represents the lognormal distribution.

One can define t to represent the time that the primary user changes from the BUSY status to IDLE status. If channel i is idle at time t, the probability that channel i is still idle after the sensing or transmitting data of the secondary user: ${\begin{matrix} g_{i}^{S} (t) = \frac{\sqrt{2 π} δ - \int_{0}^{t} \frac{1}{t} exp (- \frac{(ln x + T_{S} - μ)^{2}}{2 δ^{2}}) dx}{\sqrt{2 π} δ - \int_{0}^{t} \frac{1}{t} exp (- \frac{(ln x - μ)^{2}}{2 δ^{2}}) dx} \\ g_{i}^{T} (t) = \frac{\sqrt{2 π} δ - \int_{0}^{t} \frac{1}{t} exp (- \frac{(ln x + T_{K} - μ)^{2}}{2 δ^{2}}) dx}{\sqrt{2 π} δ - \int_{0}^{t} \frac{1}{t} exp (- \frac{(ln x - μ)^{2}}{2 δ^{2}}) dx} \end{matrix}$ (2) where i = 1, 2 … , n, T and S, respectively, represent the sensing and the transmission behavior of secondary user, T_S is the sensing duration of secondary users, and T_K represents the transmission duration of secondary users.

4.2 Secondary user status

Define p_t as idle probability of primary users. When secondary users detect the channel, we can obtain two results: the channel is idle and the channel is busy, respectively. One can use Pr (d^S = I) and Pr (δ^S = B) represent the probability of both observing results above. Equation (2) indicates that according to different sensing results of secondary users, $g_{t}^{S}$ is to be obtained. Then we can calculate the probability of Pr (δ^S = I) and Pr (δ^S = B). According to Bayesian theory, After performing the sensing for T_S, one can obtain the probability that channel i is idle and busy is, respectively, $g_{I}^{s} (t + T_{S})$ and $g_{B}^{s} (t + T_{S})$ : ${\begin{matrix} g_{i, I}^{s} (t + T_{S}) \\ = \frac{(1 - P_{d}) * \Pr (δ^{S} = I)}{p_{t} [1 - P_{f} - \Pr (δ^{S} = I) * (P_{d} - P_{f})]} \\ g_{i, B}^{s} (t + T_{S}) \\ = \frac{\Pr (δ^{S} = B) P_{d}}{p_{t} [1 - \Pr (δ^{S} = B) * (P_{d} - P_{f})]} \end{matrix}$ (3) where Pr denotes the probability function.

When secondary users transmit data, there also exist two different results, i.e. secondary users successfully transmit data and unsuccessfully transmit data. One can use Pr (δ^T = A) and Pr (δ^T = N) represent the probability of both the results above, namely using “A” to denote the ACK signal for secondary users successfully transmit data, while using “N” to denote the NACK signal for unsuccessfully transmit data. Equation (2) shows that according to the results of secondary users’ transmitting data, $g_{t}^{T}$ can also be successfully calculated. Then we can attain the probability of Pr (δ^T = A) and Pr (δ^T = N). Likewise, after performing the transmitting for T_K, one can obtain the probability that channel i is idle and busy is, respectively, $g_{i, A}^{T} (t + T_{K})$ and $g_{i, N}^{T} (t + T_{K})$ : ${\begin{matrix} g_{i, A}^{T} (t + T_{K}) \\ = \frac{(1 - g_{1}) * \Pr (d^{T} = A)}{p_{t} [1 - g_{0} - \Pr (d^{T} = A) * (g_{1} - g_{0})]} \\ g_{i, N}^{T} (t + T_{K}) \\ = \frac{\Pr (d^{T} = N) g_{1}}{p_{t} [1 - \Pr (d^{T} = N) * (g_{1} - g_{0})]} \end{matrix}$ (4) where Pr denotes the probability function.

4.3 Utility function

If the idle probability of the channel is p_t, the probability that primary user is still idle is $p_{t} g_{t}^{T}$ after data transmission last T_K. Therefore, the probability that secondary user successfully transmit data and receives ACK signal feeding back from the receiving end is $b_{t} (p_{t}) = p_{t} g_{t}^{T} (1 - γ_{0}) + (1 - p_{t} g_{t}^{T}) (1 - γ_{1})$ . The reward utility function can be expressed as: $r_{t} (p_{t}, a) = {\begin{matrix} [b_{t} (p_{t}) R - c_{t} (p_{t}) C] T_{K} & a = δ^{T} \\ 0 & a = δ^{S} \end{matrix}$ (5) where R and C, respectively, denotes the reward factor and the penalty factor.

When successfully transmitted data, secondary user will be given incentives; when conflicted with primary users, secondary user will be given punishment. When the secondary user does not transmit data, the utility value is 0.

Define E (t, p) as the maximum ideal utility function of the secondary user at time t: $E (t, p) = max {L (t, p^{t}, M (t, p^{t}))}$ (6) where p denotes the value of p_t meeting the maximum utility value at time t, and L (t, p^t) and M (t, p^t) are satisfied with ${\begin{matrix} L (t, p^{t}) = [\Pr (δ^{s} = I) + \Pr (δ^{s} = B)] \\ E (t + T_{S}, p_{t}) + r_{t} (p_{t}, δ^{S}) \\ M (t, p^{t}) = [\Pr (δ^{T} = A) + \Pr (δ^{T} = N)] \\ E (t + T_{K}, p_{t}) + r_{t} (p_{t}, δ^{T}) \end{matrix}$ (7) where Pr denotes the probability function.

4.4 Time limitation

Since the performance of primary users need to be protected as possible, the channel cannot be can be used by secondary users all the time. It can be proved $g_{t}^{T}$ is a decreasing function. Because $g_{t}^{T}$ is calculated according to the historical record of primary users, the error is also increasing with the increment of time. In a result, then $g_{t}^{T}$ is to decrease. Therefore, for $g_{t}^{T}$ , we expect that there exists a minimum value g_t,min. When $g_{t}^{T} < g_{t, min}$ , the time t is the stop time T^*.

4.5 Algorithm

Next we describe the sensing transmission algorithm in detail as shown in Algorithm 1.

Algorithm 1.

1. Initialize Pareto parameters k and b, and

2. initialize γ₀, γ₁, P_d, P_f, T_K, T_S, I_max,

3. Calculate $g_{t}^{S}, g_{t}^{T}$

4. Let t = 1

6. while t < T^* do

7. for p^t = 0.0001 : 0.0001 : 1 do

8. Calculate Pr (δ^S = I) and Pr (δ^S = B)

9. Calculate $g_{I}^{s} (t + T_{S})$ and $g_{B}^{s} (t + T_{S})$

10. Calculate Pr (δ^S = A) and Pr (δ^T = N)

11. Calculate $g_{i, A}^{T} (t + T_{K})$ and $g_{i, N}^{T} (t + T_{K})$

12. Calculate L (t, p) and M (t, p)

13. if L (t, p) ≤ M (t, p)

14. Calculate E (t, p)

15. Save p

16. t = t + 1

17. end if

18. end for

19. end while

20. Return p and E (t, p)

In algorithm 1, lines 1 to 2 are to initialize the parameters. Line 3 is to calculate idle probability of primary users according to Equations (1) and (2) after secondary users sense the channel or transmit data. Line 8 is compute the idle and busy probability of the channel that secondary users sense by Equation (3). Lines 9 and 10 obtains the probability of secondary user receiving ACK and NACK when transmitting data by Equation (4). Lines 11 and 12 calculates the utility value when secondary users sense or transmit data in terms of Equations (6) and (7). Lines 13 to 17 is to increase the idle probability if the sensed utility value is less than the transmitted utility value. Algorithm 1 shows the better performance in the usage of spectrum holes. However, due to primary users’ frequent usage of these spectrum holes, secondary users need to exit the channel, consequently causing secondary users to frequently switch the channel or terminate communication. To overcome this problem, this paper further proposes to let secondary users use the channel according to some strategies at the time when primary users are using the channel.

5 Dynamic access to multiple channels

Next, we study how to perform the effective dynamic access for the cognitive network with multiple secondary users and multiple available channels, i.e. dynamic spectrum allocation. For a single channel available, the transmission radius of different secondary users is different when they use the same channel at the same moment and the transmission radius of the same secondary user is different when it utilizes the same channel at different moments. This is mainly caused by the interference among different locations of primary and secondary users when they use the same channel. In the cognitive network with multiple secondary users and multiple available channels (namely multiple primary users), the relative locations relationships between primary users, secondary user, and primary and secondary users are much more complex. To effectively improve the channel utility is more difficult. In our method, dynamic access to multiple channels includes two parts: attaining available channel information and determining transmission radius. In the following, we will discuss them in detail.

5.1 Available channels

According to Algorithm 1, we can calculate the idle probability threshold for different channels at different moments. To allocate multiple channels to different secondary users at different, we need to attain the information that each channel is available at different moments. To this end, we are to use the probability distribution attained in Algorithm 1 to determine which channels are available at which moments. our detailed method deciding whether the channel is available is as follows:

If $p < \bar{p}$ at moment t, the corresponding channel is available at this moment, where $\bar{p}$ denotes the average idle probability of the channel.

If cp < cp^* at moment t, the corresponding channel is available at this moment, where cp denotes the theoretical collision probability when the secondary user sends data and cp^* represents the threshold of collision probability. cp is satisfied with the following equation: $cp = \Pr (δ^{s} = I) \times \Pr (δ^{T} = N)$ (8) where Pr denotes the probability function.

To determine which secondary users can use the detected available channel at the corresponding moment, one needs to recognize whether their transmission radiuses can cover other secondary users and further ensure whether they are used to build the path from source node to destination node. In the following section, we discuss the transmission radius of secondary users using the available channels.

5.2 Transmission radius

According to Algorithm 1 and the available information of channels, we can obtain the situation of channels used by primary user p_n at moment t, which is denoted as U_n,t. When primary user p_n uses channel n at moment t and a certain secondary user also uses channel n, data must be sent with the limited transmission radius, which is denoted as U_n,t = 1. When primary user p_n does not use the channel n at moment t and a certain secondary user uses channel n, data can be sent with the maximum coverage radius, which is denoted as U_n,t = 0.

Generally, the reception power of secondary users can be denoted as $P_{R}^{t} = P_{T}^{t} \times L_{T, R}^{- δ}$ , where $P_{T}^{t}$ and $P_{R}^{t}$ denote the transmission power and reception power of nodes at moment t, and δ is the attenuation factor of the link. When the SNIR received by the node exceeds the given threshold, one can believe that node is able to receive the transmitted data successfully. The probability of the node receiving the data successfully is denoted as: $μ = \Pr {SINR \geq Θ} = μ_{SNR} \times μ_{SIR}$ (9) where Pr is the probability function, Θ represents the threshold of SINR, μ_SNR and μ_SIR represent the SNR and SIR received by the node, respectively, μ_SNR denotes the probability that nodes can receive the data successfully with only the influence of noise, μ_SIR is the probability that nodes can receive the data successfully only with the influence of interference, and μ ≤ 1, μ_SNR ≤ 1, and μ_SIR ≤ 1. For moment t and influence factor ζ, Equation (9) can be converted as: $μ_{ζ}^{t} = {\begin{cases} e^{^{(- \frac{Θ \times N_{0}}{P_{S}^{t} \times L_{T, R}^{- δ}})}} ζ = S N R \\ \frac{1}{1 + Θ \times \frac{P_{I}^{t}}{P_{S}^{t}} {(\frac{L_{T, R}}{L_{I, R}})}^{- δ}} ζ = S I R \end{cases}$ (10) where $P_{S}^{t}$ denotes the transmission power of source node at moment t, $P_{I}^{t}$ represents the transmission power of interference node at moment t, N₀ denotes the noise power, L_I,R stands for the physical distance from interference node to destination node. When μ is larger than its threshold ɛ, the receiving ends of primary users and secondary uses can receive the information correctly.

When U_n,t = 0, the secondary user send data with the maximum transmission radius. At this moment, the primary user has not sent data, and thus the transmission power of the secondary user is mainly to overcome the effect of noise. If the maximum transmission power of the primary user is max _ P_c, namely, μ_C = μ_SNR ≥ ɛ_C when there is no interference, we can obtain the maximum transmission power of the secondary user as follows: $P_{C}^{t} = - \frac{Θ_{C} N_{0}}{log ɛ_{C}} L$ (11) where L denotes the maximum transmission radius of the secondary user, namely $L = d_{i, j}^{C, C}$ .

When U_n,t = 1, the secondary user sends data with the limited transmission radius. To simultaneously send data, primary user’s and secondary user’s SNIRs need to satisfy the corresponding threshold, respectively. To this end, two constraints are proposed to constrain the transmission power of the secondary user when the simultaneous communication of primary user and secondary user. In addition, the primary user meets the constraint Pr {μ_{P
_S
INR} ≥ Θ_P} ≥ ɛ_P. The secondary user is satisfied with the constraint Pr {μ_{C
_S
INR} ≥ Θ_C} ≥ ɛ_c. According to two constraints above, the maximum and minimum transmission power of the secondary user can be determined.

According to the primary user’s constraint, when secondary user s_i and primary user p_n use the channel n simultaneously, the maximum transmission power of secondary user s_i can be denoted as: ${\begin{matrix} P_{c_{i}, c_{j}, max}^{n, t} = τ_{P_{n}}^{n, t} \times {(\frac{d_{i, d}^{C, P}}{d_{n, d}^{P, P}})}^{δ_{n}} \times P_{P_{n}} \\ i, j \in {1, 2, \dots, K}, i \neq j \end{matrix}$ (12)

Likewise, in terms of the secondary user’s constraint, the minimum transmission power of secondary user s_i is: ${\begin{matrix} P_{c_{i}, c_{j}, min}^{n} = τ_{c_{j}}^{n, t} \times (N_{0} + \frac{P_{p_{n}} \times N_{0}}{N_{0} \times {(d_{i, j}^{C, C})}^{δ}}) \\ \times {(d_{i, j}^{C, C})}^{δ_{n}} \\ i, j \in {1, 2, \dots, K}, i \neq j \end{matrix}$ (13)

Due to $P_{c_{i}, c_{j}, min}^{n} < P_{c_{i}, c_{j}, max}^{n}$ , we can get the following Equation: ${\begin{matrix} D_{c_{i}, c_{j}}^{n, t} = d_{n, j}^{P, C} \times \frac{d_{i, d}^{C, P}}{d_{n, d}^{P, P}} \times {(\frac{τ_{p_{n}}^{n, t}}{| τ_{c_{j}}^{n, t} |})}^{\frac{1}{δ_{n}}} \\ = d_{n, j}^{P, C} \times r_{p_{n}, c_{i}}^{n, t} \\ n \in {1, 2, \dots, N}, i, j \in {1, 2 \dots, K}, i \neq j \end{matrix}$ (14)

Equation (14) can further be converted as:

$\begin{matrix} D_{c_{i}, c_{j}}^{n, t} \\ = \frac{r_{p_{n}, c_{i}}^{n, t} \times d_{n, j}^{P, C} (\sqrt{1 - [r_{p_{n}, c_{i}}^{n, t}]^{2} \times sin (α_{n, i, j})^{2}}}{1 - [r_{p_{n}, c_{i}}^{n, t}]^{2}} \\ - \frac{r_{p_{n}, c_{i}}^{n, t} \times cos (α_{n, i, j}))}{1 - [r_{p_{n}, c_{i}}^{n, t}]^{2}} \end{matrix}$ (15) where α_n,i,j represents the angle formed by primary user’s sending end, secondary user’s sending end, and secondary user’s receiving end, namely ∠ (p_n - c_i - c_j), sin ² stands for the square of function sin(.), and $D_{c_{i}, c_{j}}^{n, t}$ denotes the maximum transmission distance at moment t from secondary user c_i sending data to secondary user c_j using the channel n. In order to avoid the interference on primary user, we define the maximum transmission distance of secondary user c_i as follows: ${\begin{matrix} {Tr}_{c_{i}}^{n, t} = min (D_{c_{i}, c_{1}}^{n, t}, D_{c_{i}, c_{2}}^{n, t}, \dots, D_{c_{i}, c_{j}}^{n, t}) \\ j \in {1, 2, \dots, i - 1, i + 1, \dots, K} \end{matrix}$ (16)

When U_n,t = 0, primary user p_n does not utilize the channel n at moment t. As a result, the transmission radius of secondary user c_i at moment t is independent from primary user and it holds the maximum transmission radius R.

According to the discussion above, we can obtain: ${Tr}_{c_{i}}^{n, t} = {\begin{matrix} min (D_{c_{i}, c_{1}}^{n, t}, D_{c_{i}, c_{2}}^{n, t}, \dots, D_{c_{i}, c_{j}}^{n, t}), & U_{n, t} = 1 \\ R_{c_{i}}^{n}, & U_{n, t} = 0 \end{matrix}$ (17) where j ∈ {1, 2, …, i - 1, i + 1, …, K}.

According to Equation (17), we can obtain the maximum transmission radius of secondary user c_i about all the channels at moment t as follows: ${Tr}_{c_{i}}^{t} = [{Tr}_{c_{i}}^{1, t}, {Tr}_{c_{i}}^{2, t}, \dots {Tr}_{c_{i}}^{N - 1, t}, {Tr}_{c}^{N, t}]$ (18)

According to Equation (18), we can obtain the maximum transmission radius matrix Tr^t of all the secondary users using different channels at moment t:

$\begin{matrix} {Tr}^{t} & = & (\begin{matrix} {Tr}_{c_{1}}^{1, t} & {Tr}_{c_{1}}^{2, t} & \dots & {Tr}_{c_{1}}^{N - 1, t} & {Tr}_{c_{1}}^{N, t} \\ {Tr}_{c_{2}}^{1, t} & {Tr}_{c_{2}}^{2, t} & \dots & {Tr}_{c_{2}}^{N - 1, t} & {Tr}_{c_{2}}^{N, t} \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ \\ {Tr}_{c_{K - 1}}^{1, t} & {Tr}_{c_{K - 1}}^{2, t} & \dots & {Tr}_{c_{K - 1}}^{N - 1, t} & {Tr}_{c_{K - 1}}^{N, t} \\ {Tr}_{c_{K}}^{1, t} & {Tr}_{c_{K}}^{2, t} & \dots & {Tr}_{c_{K}}^{N - 1, t} & {Tr}_{c_{K}}^{N, t} \end{matrix}) \\ = & ({Tr}_{c_{1}}^{t}, {Tr}_{c_{2}}^{t}, \dots {Tr}_{c_{K - 1}}^{t}, {Tr}_{c_{K}}^{t}) \end{matrix}$ (19)

According to Equation (19), we can obtain the maximum transmission radius Tr of secondary users using the same channel at all the moments as follows: $Tr = [{Tr}^{1}, {Tr}^{2}, \dots, {Tr}^{I}]$ (20)

5.3 Algorithm

So far we have discussed our algorithm. Next, we give the detailed algorithm steps as follows:

Step 1: Select initial channel n and sending node s_i of secondary user.

Step 2: Carry out Algorithm 1 and generate the idle probability threshold of secondary user s_i using channel n.

Step 3: Judge whether primary user p_n uses channel n at moment t and generate the corresponding value of U_n,t. If U_n,t = 1, go to Step r, or otherwise go to Step 7.

Step 4: According to Equation (12), calculate the maximum transmission power of secondary user s_i using channel n.

Step 5: According to Equation (13), calculate the minimum transmission power from secondary user s_i to secondary user c_i using channel n.

Step 6: According to Equation (14) and (15), calculate the maximum transmission radius from secondary user s_i to secondary user c_i using channel n.

Step 7: According to Equation (17), calculate the maximum transmission radius of secondary user s_i using channel n.

Step 8: According to Equation (18), calculate the maximum transmission radius of secondary user s_i for all channels;

Step 9: According to Equation (19), calculate the maximum transmission radius of all the secondary users for all the channels at moment t;

Step 10: According to Equation (20), calculate the maximum transmission radius of all the secondary users for all the channels at all the moments.

6 Numerical experiments and analysis

Next, we conduct a series of tests to validate our algorithm. Our simulation scenarios include 20 pairs of primary users in the network (namely 20 channels able to be used by secondary users), different sizes of secondary users, and exploit multi-hop communications from source node to destination node. The parameters include penalty factor C = 20, award factor R = 1, sensing time T_s = 30, transmission time T_K = 5, total duration I_max = 1000, and let γ₀ = 0, γ₁ = 1, P_f = 0, and P_d = 1. Current studies have reported one method to exploit ACK and NACK to obtain the better performance, while it only used a single primary and a single secondary user. Different from it, our algorithm studies more complex cognitive networks with multiple primary and secondary users. To fairly compare our algorithm with it, this method also exploits the lognormal distribution to characterize the behaviors of primary users in this paper, and we call it as Single channel-based Extended Dynamic Access algorithm (SEDA). Our algorithm is for short as Multiple Channel Dynamic Access algorithm (MCDA). In the following section, we are to analyze our algorithm in detail by simulations.

6.1 Sensing probability threshold

We firstly discuss the sensing probability threshold about our algorithm. For different variance parameters, we can use the lognormal distribution to obtain the reasonable idle probability after secondary users perform the sensing or transmitting process shown in Fig. 2 where δ denotes the variance of the lognormal distribution. Figure 2(a) shows that after secondary users make the channel sensing for the duration Ts, the probability that the channel is idle decreases with the time elapsing. Moreover, from Fig. 2(a), we can also see that when the variance of lognormal distribution increases, the idle probability also reduces. Similarly, Fig. 2(b) shows that after secondary users perform the data transmitting process for the duration Tk, the probability that the channel is idle decreases with the time passing. Figure 2(b) also indicates that when the variance of lognormal distribution increases, the idle probability also decreases. This is reasonable because the longer the time becomes, the lower the channel that is still idle is. Furthermore, according to the distribution characteristics of lognormal distribution, The larger its variance is, the lower the corresponding probability is. This is consistent to the heavy-tailed nature of network traffic.

Next, we analyze the impact of different variances of lognormal distribution on the transmission probability threshold. Figure 3 plots shows that the transmission probability threshold increases with the time going away. We can also see that it grows with the addition of the variances of lognormal distribution. To analyze further our algorithm performance, we discuss the impact of different sensing durations Ts on the transmission probability threshold distribution shown in Fig. 4. It is interesting that for different sensing durations, the transmission probability threshold distribution is not nearly affected by the time change while it reduces with the grown of different sensing durations Ts. This shows that we should select the appropriate parameters to obtain better algorithm performance. It is clear that our algorithm MCDA holds much larger transmission probability thresholds than SEDA. This further indicate that our algorithm exhibits the better sensing performance.

6.2 Impact of the number of secondary users

Now we analyze the impact of the number of secondary users on network performance. Figure 5 plots the ratio of available time to total time of secondary users for channels, where ‘cp’ denotes the collision threshold. We can clearly see that when adding secondary users, we can obtain the bigger ratio. At the same time, when the collision threshold changes from 0.18 to 0.22, one can obtain the larger ratio of available time to total time of secondary users using the channel. This indicates that the number of secondary users and the collision threshold have an impact on the available time of secondary users using the channel. Thereby, we need to select the suited parameters to the better performance. It is interesting that our algorithm MCDA holds the larger ratio of available time than SEDA.

Figure 6 shows the average transmission radius of each node when there exist different collision thresholds and different scales of secondary users. From Fig. 6, one can find that the larger collision threshold is corresponding to the lower average transmission radius. This is because the lower the collision threshold is, the lower the chance that secondary users make the collision with primary users. Thereby, they can use the longer transmission radius to carry out communications with each other. However, Fig. 6 illustrates that the larger scales of secondary users produce the much lower average transmission radius. This is reasonable because the more secondary users are, the larger the interference between network users (including between primary users, secondary users, and primary and secondary users) is. To achieve the reliable communication, secondary users have to shorten the transmission radius. As a result, the average transmission radius is to become lower. In contrast to SEDA, MCDA exhibits the larger coverage.

Figure 7 shows the ratio of transmission radius to maximum transmission radius of each secondary user for different scales of secondary users, where R denotes the maximum transmission radius of each secondary user. Then the number of secondary users become small, the ratio also gets lower. It is interesting that the larger maximum transmission radius is corresponding to the smaller ratio of transmission radius. This indicates that the number of secondary users and the maximum transmission radius of each secondary user have an import impact on its real transmission radius. This is because the larger maximum transmission radius and more secondary users are to lead to larger interference among primary and secondary users. As a result, this further creates the much lower real transmission radius than the maximum transmission radius of each secondary user. Despite of this, our algorithm still obtains the better performance. In contrast to SEDA, MCDA holds much larger ratio. This shows that MCDA can transmit data packets via the transmission radius as close to the maximum transmission radius of each secondary user as possible.

6.3 Impact of transmission radius

Next, we demonstrate the impact of the maximum transmission radius of each secondary user on network performance. Figure 8 plots the impact of different maximum transmission radius on network energy consumption of MCDA, where SUs represents the number of secondary users. Figure 8(a) shows that the bigger maximum transmission radius leads to much larger total transmission power. It is clear that larger sizes of secondary users result in a bit larger total transmission power. Similarly, Fig. 8(b) indicates the impact of different maximum transmission radius on network energy consumption of SEDA. It can also clear that the more secondary users and the larger maximum transmission lead to the higher total transmission power. In contrast to SEDA, MCDA holds much lower total transmission power. This indicates that MCDA exhibits the better network performance as the whole.

Figure 9 shows the channel utility of both algorithms under different sizes of secondary users and different maximum transmission radiuses. We can see that when the maximum transmission radius increases, the channel utility of both algorithms decreases. However, when adding the number of secondary users, we can obtain the larger channel utility. This is because the larger maximum transmission radius is to lead to the larger interference among primary and secondary users. Moreover, although the more secondary users can lead to the larger interference, they can transmit data packets via the shorter radius in such a case. Thereby, secondary users far from each other can use the same channel at the same moment. As a result, this raises the channel utility. In contrast to SEDA, MCDA holds much channel utility. This indicates that MCDA holds the better performance.

Figure 10 plots the available channels of both algorithms under different maximum transmission radiuses. It is clear that the larger maximum transmission radius obtains the smaller available channels. When adding the scales of secondary users, we can attain the larger available channels. Comparing to SEDA, the number of available channels of MCDA is much larger. This further illustrates that MCDA can make fuller use of channels.

Figure 11 shows the network connectivity of both algorithms under different maximum transmission radiuses. For different sizes of secondary users, the larger maximum transmission radius of both algorithms exhibits the higher network connectivity. Moreover, the larger scales of secondary users holds the higher network connectivity for both algorithms. In contrast to SEDA, MCDA exhibits much higher network connectivity. This further shows that MCDA holds the better performance.

7 Conclusions

This paper proposes a new dynamic access algorithm to cognitive networks with multiple primary and secondary users, arming at pervasive wireless multimedia communication in technology enhanced learning applications. We exploit the lognormal distribution to characterize primary user behaviors and use opportunistic spectrum access to obtain the sensing status of channels. By controlling transmission radiuses of secondary users to make primary and secondary users simultaneously utilize the channel and thereby raise the channel utility. Finally, we propose the dynamic access algorithm to multiple channels. Simulation results show that our approach is promising. In our future work, we will consider the impact of network traffic changes and users’ behaviors, and implement our approach in the large-scale real wireless network.

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Nos. 61571104, 61071124), the General Project of Scientific Research of the Education Department of Liaoning Province (No. L20150174), the Program for New Century Excellent Talents in University (No. NCET-11-0075), the Fundamental Research Funds for the Central Universities (Nos. N150402003, N120804004, N130504003), and the State Scholarship Fund (201208210013). The authors wish to thank the reviewers for their helpful comments.

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