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Emerging cognitive radio networking technology potentially provides a promising solution to the spectrum underutilization problem in wireless access. In this paper, a cross-layer routing for secondary multihop is studied in cognitive radio network operating in television white spaces. The framework considers a joint channel, power, and routing assignment under signal to interference noise ratio (SINR) constraints. The problem is formulated as a maximum concurrent multicommodity flow problem. The goal of conducting this research is to develop a new routing protocol for the secondary multihop cognitive radio network. Therefore, the objective of this paper focuses on maximizing a flow rate scaling factor. Moreover, the paper focuses on achieving multipath routing when it is possible under SINR constraints to utilize all possible unused channels efficiently. The numerical results proved the strength of the proposed algorithm in its routing ability under the physical model of SINR, in addition to the ability of using multipath routing if there are available free channels to be used in the cognitive communication paradigm.

The radio spectrum is a finite natural resource that is the primary resource for wireless communication. The growing need for high data rate wireless communications has prompted an excellent development of telecommunication technologies. As a result, a nontraditional paradigm [

Classical fixed spectrum allocation is the root cause of ineffective spectrum utilization [

Television white space (TVWS) is a good example of underutilized spectrum. It consists of Ultrahigh Frequency/Very High Frequency (UHF/VHF) that are either freed via the digital switch over process or unused due to local regulations [

The main problem of routing in multihop cognitive radio networks aims at the creation and the maintenance of wireless multihop paths among SUs by deciding which relay nodes will be involved in the transmission and the spectrum to be used on each link of the path. Moreover, for interference and power control model it is necessary to assign the appropriate transmission power level for each active link and avoid weak channels. The main objective of this work is to achieve a joint channel assignment and power allocation based on maximum concurrent multicommodity flow problem to ensure fairness among all commodities. Moreover, taking into consideration the physical model of signal to interference noise ratio (SINR) model which is a model of key importance for interference characterization is targeted.

This paper examines the impact of SU node transmission power division to a different finite number of levels on the channel capacity scaling factor. It formulates the model as a joint channel assignment and power allocation based on maximum concurrent multicommodity flow (MCMCF) problem to ensure fairness among all commodities. The obtained mathematical model is a nonconvex mixed integer nonlinear program (MINLP), which requires an appropriate solution technique. This problem is mathematically treated with Branch-and-Bound algorithm. The problem is solved under SINR constraints since it is of key importance for interference characterization.

The remainder of this paper is organized as follows: Section

In the last years, joint channel assignment routing in wireless networks has been the subject of many of research works. In [

Channel allocation is considered with improving the routing process in [

In [

Joint opportunistic routing and channel assignment in multichannel multiradio cognitive radio networks is examined in [

In [

An approach that maximizes the aggregated flow rate of the SUs under the interference power constraint was presented in [

In [

In [

In [

Per-node joint power control, scheduling, and routing in the network were proposed in [

As presented, there are some efforts in the literature addressing the problem of routing in cognitive radio networks. The most critical issue in the routing in cognitive radio networks is capturing the physical layer characteristics precisely. Most work in literature ignores the precise representation of the interference noise level to avoid complexity associated with this kind of constraints. Adding this constraint converts the problem to nonconvex mixed integer nonlinear problem which requires a nontraditional customized solution approach. In this paper, a tailored solution is presented to solve this problem.

In this section, the cognitive radio network is described to formulate the mathematical model for the configuration and assumptions. All variables used are defined in Table

Nomenclature.

| |
---|---|

| CR-aware nodes indices |

| Path loss index |

| Session index |

| Set of the total available channels |

| Common available channels between nodes |

| Maximum number of power control levels |

| Maximum transmit power |

| Binary variables represent the channel |

| Signal to interference ratio on channel |

| SINR threshold value to avoid weak channels |

| Quantization variable for power control on channel |

| Path losses between nodes |

| Channel capacity between nodes |

| Bandwidth of channel |

| Flow rate on session |

| Minimum flow rate demand during session |

Session flow rate scaling factor | |

| Source node and destination node respectively |

| Thermal Gaussian noise |

| Number of CR-aware nodes |

| Number of primary users |

| Set of available sessions for the entire network |

A cross-layer routing for secondary multihop cognitive radio network operating in TVWS that complied with the FFC regulations design is presented. The proposed framework considers a joint channel, power, and routing assignment under SINR physical model. The problem is mathematically formulated as MCMCF problem. The objective of maximizing a flow rate scaling factor is considered. Furthermore, the impact of power levels digitization on that flow rate scaling factor is studied and presented. The obtained mathematical model is a nonconvex mixed integer nonlinear program, which requires an appropriate solution technique. Therefore, a tailored Branch-and-Bound algorithm is used in the proposed solution.

The considered secondary cognitive radio multihop network consists of a set of cognitive radio aware nodes

The power control at the transmitting node affects the SINR level at the receiving node. Moreover, SINR level affects the channel scheduling. For instance, if the node is scheduled to receive, then its SINR must exceed threshold value

Channel allocation status of a communication link between nodes

A node

Regarding power control representation, a power ranging variable is assumed as

In case of concurrent transmission, a node

Interfering CR-nodes path loss gain.

It is supposed that the entire network has a set of active sessions

Therefore, it is guaranteed that the amount of traffic flowing between node

The flow conservation law states that the input flow to a certain node equals the output of this node. This constraint is applied for all intermediate nodes between source and destination. Therefore, the flow conservation constraints can be expressed as follows.

For intermediate node,

For the source node,

For the destination node,

The previous section obtained the mathematical model that describes the system, but this program needs some reformulation progress to be suitable for the mathematical treatment. Constraints in (

Therefore, it is better to combine these variables into one nonlinear variable. Assume that

This optimization problem is classified as nonconvex MINLP. From the perspective of the theory of computational complexity [

The nonlinearity of the problem is due to the product term

Regarding the product term

Then, the product term

On the other hand, the second term

Formulating the convex envelope.

The intersection between tangents

Therefore, the convex zone can be mathematically described by

Thus, the original program is relaxed to a linear program as shown in The Relaxed Linear Program. Formulation shown is compact form that is amenable to mathematical operation. These formulation constraints in summary are as follows: Equation (16a) ensures that the assigned flow on an active link does not exceed the channel capacity. Equation (16b) guarantees that the same frequency channel is not scheduled for transmission and reception simultaneously. Equations (16c) and (16d) are implemented to keep the flow conservation from the source node to the destination node. Equation (16e) is used to set the reception threshold to avoid weak channels. Equations (16h) to (16q) are used as implemented via the linear relation to remove the nonlinear terms.

Branch-and-Bound [

Figure

Branch-and-Bound main algorithm.

On the other hand, if that condition is not satisfied, the original problem is portioned into two problems

By comparing the new obtained upper bounds with the original upper bound, a tighter upper bound can be achieved. The algorithm obtains optimal solution if the lower and upper bounds are close enough to achieve the conditional formula LB≥ (

The nonlinear logarithmic term is relaxed into a set of linear constraints. After relaxing all nonlinear terms for a problem, a relaxed problem can be solved by a linear program in polynomial time. Solving the relaxed linear program provides the upper bound.

Lower bound can be determined by local search algorithm. Thus, it starts with any initial feasible solution. That solution may be distant from the optimum one. Consequently, it is improved by iterative algorithm as shown in Figure

Lower bound local search algorithm.

Thus, the obtained SINR is compared to the threshold value. If that SINR value is greater than the threshold value, the transmission is successful. Channel capacity can be calculated by (

In case of

On the other hand, having _{min} among all links which is the minimum ratio of all links. Increasing_{min} improves the current solution. Subsequently, in the next iteration, improving the current solution is targeted.

Branching variable selection approach is considered a key factor of Branch-and-Bound algorithm efficiency. As well, selecting the right variables to branch results in a spectacular reduction number of problems is required to solve an instance. Traditional branching strategy exhaustively examines variables at every problem node and selects the best variable in terms of tight gap between the best feasible solution and the recent bound [

This strategy does not take the advantage of network flow routing problem characteristics. The nature of flow routing problem necessitates making the decision of which channels will be active firstly. Then, the power level for each active link is assigned. Based on this nature, a priority of the variables is assumed by the channel status variable

In this section, configuration parameters and results are presented. The results are portioned into two parts. First, finding the impact of the number of power levels (

Second, studying the performance of the proposed routing scheme in terms of the available frequency channels and connectivity graph is required. In this study, three network configurations are assumed. For each network configuration, there are two cases: the number of available frequency bands (

In this section, the configuration setup is presented. For all cases, nodes are arbitrarily positioned in a square area of 70m×70m. Each channel has a bandwidth of ^{6}

Based on the performance benchmarking for the two network configurations, the best number of transmission power levels

20-node position and 10-channel availability.

Node | Position | Available frequency bands | |
---|---|---|---|

| | ||

N1 | 2.84 | 11.77 | 3,7,10 |

N2 | 31.94 | 33.57 | 1,2,3,4 |

N3 | 1.10 | 1.07 | 1,4,5,6 |

N4 | 27.74 | 6.87 | 5,8 |

N5 | 18.54 | 11.57 | 5,7,8,10 |

N6 | 19.04 | 21.37 | 3,5,6,8,9 |

N7 | 7.34 | 5.27 | 1,4,8 |

N8 | 25.34 | 42.77 | 1,2,3,5,7,9,10 |

N9 | 38.04 | 12.17 | 2,9,5 |

N10 | 34.64 | 21.47 | 3,4,5,6,7,8,9 |

N11 | 30.84 | 27.47 | 4,5,6,7,8,9 |

N12 | 34.94 | 39.87 | 1,8,9,10 |

N13 | 49.94 | 4.47 | 3,5,10 |

N14 | 47.44 | 16.87 | 2,3,6,7,8 |

N15 | 47.44 | 25.87 | 5,6,7 |

N16 | 50.64 | 45.67 | 1,3 |

N17 | 49.14 | 18.67 | 1,7,9 |

N18 | 14.24 | 14.07 | 2,5,6,10 |

N19 | 30.94 | 16.67 | 6,7,8,9 |

N20 | 5.24 | 16.37 | 1,7 |

Source-destination minimum flow rate.

Session | Source | Destination | Minimum flow rate (Mbps) |
---|---|---|---|

1 | N16 | N10 | 8 |

2 | N18 | N3 | 5 |

3 | N5 | N9 | 1 |

4 | N13 | N17 | 7 |

5 | N15 | N6 | 6 |

Relation between flow rate scaling factor and number of power levels in 20- and 30-node cognitive radio aware network.

Based on the results obtained in Figure

In this network configuration, the cognitive radio nodes are supposed to be 20 nodes. It is assumed that there are 5-user communication sessions in the entire network. This configuration is studied in two cases:

Frequency channel availability for each node is arbitrarily chosen as listed in Table

It is assumed that there are 5-user communication sessions. For each session, source and destination, as well as the associated minimum flow rates, are arbitrarily chosen as listed in Table

Link scheduling assignment.

Band | Scheduling | Band | Scheduling |
---|---|---|---|

1 | _{7,3}, _{16,12} | 6 | _{15,19} |

2 | _{8,2} | 7 | _{14,17 }, _{20,1} |

3 | _{13,14} | 8 | _{12,11, } _{5,4} |

4 | _{1,7}, _{2,10} | 9 | _{12,8 }, _{19,6} |

5 | _{11,10, } _{4,9} | 10 | _{18,20} |

Session and link flow rate assignment.

Session | Session flow rate (Mbps) | Assigned link flow rate (Mbps) |
---|---|---|

1 | 133.4 | _{16,12}= 133.40, _{12,11 }= _{11,10}=17.34, _{12,8 }= _{8,2}= _{2,10}= 116.06 |

2 | 67.5 | _{18,20 }= _{20,1 }= _{1,,7 }= _{7,3 }= 13.5 |

3 | 13.5 | _{5,4 }= _{4,9 }= 13.5 |

4 | 94.5 | _{13,14 }= _{14,17 }= 94.5 |

5 | 81 | _{15,19 }= _{19,6 }= 13.5 |

20-node power level assignment.

Band | Assigned power level | Band | Assigned power level |
---|---|---|---|

1 | _{7,3 }= 1, _{16,12 }= 10 | 6 | _{15,19 }= 9 |

2 | _{8,2 }= 2 | 7 | _{20,1 }= 1, _{14,17 }= 1 |

3 | _{13,14 }= 2 | 8 | _{ 5,4 }= 3 |

4 | _{2,10 }= 2, _{1,7}= 6 | 9 | _{19,6 }= 4, _{12,8 }= 1 |

5 | _{ 4,9 }= 4 | 10 | _{18,20 }= 1 |

Connectivity graph for N=20 nodes, Case I.

To verify flow balance, for example, Session 1 which is the

Flow splitting and multipath routing appeared for Session 1, which has the largest rate requirement. The same frequency band may be used by concurrent transmissions. For example, since

Subsequently,

By comparing the channel capacity

For further investigation of the solution algorithm performance, the number of available frequency bands is expanded from 10 to 20 bands for the same network configuration. Figure

Connectivity graph for N=20 nodes, Case II.

Connectivity graph in Figure

In this network configuration, the cognitive radio network is supposed to consist of 30 nodes. It is assumed that there are 5-user communication sessions in the entire network. Two cases are assumed:

Frequency channel availability for each node is arbitrarily chosen as listed in Table

30-node position and 10-frequency channels.

Node | Position | Available frequency bands | |
---|---|---|---|

| | ||

N1 | 2.84 | 11.77 | 1,2,4,7,16,17,19,20 |

N2 | 31.94 | 33.57 | 3,5,9,12,14,15 |

N3 | 5.74 | 32.97 | 1,2,6,7,8,11,16,17,19,20 |

N4 | 27.74 | 6.87 | 1,2,6,7,16,20 |

N5 | 18.54 | 11.57 | 9.5,17 |

N6 | 19.04 | 21.37 | 1,2,6,7,8,16,20 |

N7 | 7.34 | 5.27 | 3,4,5,9,12,14 |

N8 | 25.34 | 42.77 | 3,4,12 |

N9 | 38.04 | 12.17 | 10,18 |

N10 | 34.64 | 21.47 | 3,4,5,9,14 |

N11 | 30.84 | 27.47 | 1,6,7,8,11,16,17,19,20 |

N12 | 34.94 | 39.87 | 10,13,18 |

N13 | 49.94 | 4.47 | 1,2,6,8,11,19 |

N14 | 47.44 | 16.87 | 3,5,9,14 |

N15 | 47.44 | 25.87 | 4,9,12,14 |

N16 | 50.64 | 45.67 | 7,8,11,16,17,19,20 |

N17 | 49.14 | 18.67 | 7,11,16,17,19,20 |

N18 | 14.24 | 14.07 | 3,4,5 |

N19 | 30.94 | 16.67 | 3,12,15 |

N20 | 5.24 | 16.37 | 5,9 |

N21 | 2.84 | 11.77 | 1,2,6,7,8,11,16,17,19,20 |

N22 | 31.94 | 33.57 | 9,12,14,15 |

N23 | 5.74 | 32.97 | 3,4,5,9,10,12,13,14,15,17 |

N24 | 27.74 | 6.87 | 1,2,11,16,17,20 |

N25 | 18.54 | 11.57 | 3,4,5,9,12,14 |

N26 | 19.04 | 21.37 | 3,5,9,15 |

N27 | 7.34 | 5.27 | 1,16,20 |

N28 | 25.34 | 42.77 | 1,2,6,7,8,11,16,17,20 |

N29 | 38.04 | 12.17 | 3,4,5,9,10,12,14,15,18 |

N30 | 41.6 | 19.14 | 1,2,6,7,8,11,16,17,19,20 |

30-node source-destination minimum flow rate.

Session | Source | Destination | Minimum flow rate |
---|---|---|---|

1 | N16 | N28 | 4 |

2 | N24 | N11 | 5 |

3 | N13 | N1 | 1 |

4 | N19 | N29 | 7 |

5 | N26 | N15 | 6 |

Connectivity graph for N=30 nodes, Case I and Case II.

For this network configuration which contains 30 nodes,

In this case, the solution algorithm is examined on large number of sessions. So, the number of network nodes is set to N=50, and the number of sessions is 10. Nodes are arbitrarily positioned as shown in Table

50-node positions and frequency availability, Case III.

Node | Position | Available Bands | |
---|---|---|---|

| | ||

N1 | 11.1 | 21.7 | 2, 3, 4, 8, 25 |

N2 | 0.1 | 4 | 6, 7, 10, 13, 14, 20, 23, 24, 26, 28 |

N3 | 7.2 | 16.6 | 6, 10, 14, 20, 23, 24, 26 |

N4 | 11 | 32.2 | 6, 7, 10, 13, 14, 20, 23, 24, 26, 28 |

N5 | 16.3 | 3.6 | 10, 13, 14, 20, 23 |

N6 | 14.5 | 24.7 | 8, 11, 25 |

N7 | 14.9 | 13.7 | 5, 9, 12, 16, 17, 18, 22, 27, 29, 30 |

N8 | 19.5 | 14.9 | 7, 24, 28 |

N9 | 26.6 | 13.4 | 1, 19, 21, 25 |

N10 | 22.5 | 29.3 | 1, 3, 4, 8, 11, 15, 19 |

N11 | 24.6 | 40.5 | 3, 8, 25 |

N12 | 38.4 | 13.1 | 2, 8, 11, 15 |

N13 | 4 | 3.9 | 9, 12, 16, 22, 27, 29, 30 |

N14 | 6.1 | 18.6 | 9, 12, 16, 17, 18, 22, 27, 30 |

N15 | 38.5 | 22.6 | 2, 4, 11, 15, 19, 21, 25 |

N16 | 1.2 | 24.3 | 5, 9, 12, 17, 22, 29, 30 |

N17 | 4.9 | 42.3 | 5, 27 |

N18 | 18.5 | 1.4 | 5, 9, 12, 17, 18, 27, 30 |

N19 | 16.9 | 29.1 | 3, 4, 10, 11, 12, 15 |

N20 | 33.5 | 10.4 | 7, 13, 14, 20, 23, 24, 26, 28 |

N21 | 25.6 | 12.8 | 6, 7, 20, 23, 24, 28 |

N22 | 45.2 | 45.5 | 2, 8, 15, 19 |

N23 | 43.6 | 22.7 | 1, 2, 3, 4, 11, 15, 19, 21 |

N24 | 10.6 | 40.5 | 4, 15, 19, 21, 25 |

N25 | 18.2 | 32.7 | 9, 12, 18, 22, 27 |

N26 | 25.2 | 27.2 | 10, 14, 20, 24, 26 |

N27 | 22.5 | 42.2 | 5, 9, 12, 16, 18, 27, 29, 30 |

N28 | 30 | 31.5 | 6, 13, 24, 26, 28 |

N29 | 35 | 22.1 | 6, 10 |

N30 | 25.7 | 6.2 | 5, 9, 12, 17, 18, 22, 27, 29, 30 |

N31 | 34.1 | 12.4 | 9, 12, 16, 17, 30 |

N32 | 26.4 | 30 | 5, 9, 12, 16, 17, 18, 22, 27, 29, 30 |

N33 | 14.1 | 40.7 | 1, 2, 25 |

N34 | 34.4 | 46.5 | 9, 17, 18, 30 |

N35 | 19 | 22.5 | 1, 6, 7, 10, 13, 14, 20, 23, 24, 28 |

N36 | 39.9 | 25.1 | 6, 13, 14, 20, 23, 24, 26, 28 |

N37 | 20.3 | 18.2 | 1, 2, 3, 4, 8, 11, 15, 19, 21, 27 |

N38 | 10 | 20.5 | 6, 7, 10, 13, 14, 20, 23, 24, 26, 28 |

N39 | 20.5 | 21.4 | 1, 2, 3, 4, 8, 11, 15, 19, 21, 25 |

N40 | 37.1 | 28.6 | 7, 10, 13, 14, 20, 23, 24, 26 |

N41 | 44.1 | 16.1 | 1, 15, 21 |

N42 | 41.1 | 6 | 9, 29 |

N43 | 43 | 18.8 | 5, 9, 12, 16, 18, 22 |

N44 | 45.4 | 24.2 | 9, 12, 16, 17, 18, 30 |

N45 | 36.2 | 41.2 | 5, 9, 17, 27, 29, 30 |

N46 | 27.5 | 32.3 | 12, 16, 17, 18, 29, 30 |

N47 | 47.8 | 13.8 | 22, 27, 29, 30 |

N48 | 8.9 | 14.8 | 5, 30 |

N49 | 6.8 | 6.2 | 5, 9, 12, 16, 17, 27, 30 |

N50 | 11.7 | 35.8 | 1, 2, 3, 4, 8, 11, 15, 19, 21, 25 |

50-node source-destination minimum flow rate, 10 sessions.

Session | Source | Destination | Minimum flow rate |
---|---|---|---|

1 | N21 | N4 | 4 |

2 | N5 | N26 | 7 |

3 | N19 | N20 | 6 |

4 | N33 | N6 | 10 |

5 | N37 | N10 | 9 |

6 | N23 | N11 | 2 |

7 | N25 | N46 | 3 |

8 | N42 | N43 | 9 |

9 | N44 | N27 | 8 |

10 | N47 | N30 | 1 |

In this case, there are 20 frequency channels for the entire network. Then, there are more available links. The solution algorithm could not establish all communication links properly.

When there are 30 frequency channels for the entire network, the solution algorithm has more rooms to choose between available links and then it could establish all communication links properly. In addition, it is observed that all communication sessions contain only single path routing. Figure

Connectivity graph for N=50 nodes, Case III.

The numerical results proved that the original constraints are achieved. In the first part of the study, the numerical results depicted that the optimum number of power levels

For comparison, the work in [

The objective function: It considers the network resource usage minimization including bandwidth usage minimization. Bandwidth usage cannot characterize the interference of radio transmission [

Linear relaxation: The utilized relaxation implements the convex hull theory but on a different variable than that proposed in our work. In our work, the relaxation is based on the channel capacity linear relaxation which characterizes the actual levels of interference.

By comparing the objective function related to the change of the available power levels in both methods as shown in Figure

Objective value as a function of number of power levels [

In this paper, a cross-layer routing framework for distributed multihop cognitive radio networks was studied. The problem formulated under the SINR physical model captures the physical layer characteristics precisely. The proposed solution provided a tailored Branch-and-Bound solution algorithm via linear relaxation, local search algorithm, and problem specific branching variables selection. Numerical results depicted that the optimum scaling factor is affected by the number of power levels available to SUs. Thus, the conducted scenarios depicted that optimum achieved scaling factor can be optimum when the number of power levels is equal to 10. This value achieves better performance power without sacrificing better flow rate scaling factor and avoids increasing the search space without significant improvement in the flow rate scaling factor. In addition, the algorithm could achieve the multipath routing when it is possible where local search algorithm tries to assign power to unused frequency channels taking into consideration the interference levels. However, using this framework in applications with small to medium networks to avoid the complexity raised by increasing the number of variables to the Branch-and-Bound algorithm is recommended.

The authors declare that there are no conflicts of interest regarding the publication of this paper.