^{1}

^{1}

^{1}

Green cognitive radios are promising in future wireless communications due to high energy efficiency. Energy efficiency maximization problems are formulated in delay-insensitive green cognitive radio and delay-sensitive green cognitive radio. The optimal resource allocation strategies for delay-insensitive green cognitive radio and delay-sensitive green cognitive radio are designed to maximize the energy efficiency of the secondary user. The peak interference power and the average/peak transmit power constraints are considered. Two algorithms based on the proposed resource allocation strategies are proposed to solve the formulated problems. Simulation results show that the maximum energy efficiency of the secondary user achieved under the average transmit power constraint is higher than that achieved under the peak transmit power constraint. It is shown that the design of green cognitive radio should take the tradeoff between its complexity and its achievable maximum energy efficiency into consideration.

The unprecedented increase of mobile devices and escalating high data rate requirements have resulted in the rapid growth of energy consumption and greenhouse gas emission. It is reported in [

In CR, resource allocation is of great importance and has received wide attention [

Since the operation of a CR should protect the quality of service (QoS) of the PU, a metric that evaluates the performance of the protection of the PU should be imposed. Basically, there are three metrics for protecting the PU from intolerance interference caused by the SU, namely, a peak interference power constraint (PIP), an average interference power (AIP) constraint, and an outage probability (OP) constraint [

The optimal resource allocation strategies have been well studied in CR with the spectrum sharing paradigm [

There are some investigations of the design of the optimal resource allocation strategies for green CR [

Recently, the EE maximization problems were studied in delay-insensitive CR, delay-sensitive CR, and simultaneously delay-sensitive and delay-insensitive CR in [

Different from the works in [

The optimal resource allocation strategies for delay-insensitive green CR and delay-sensitive green CR that maximize the EE of the SU are found. Different from the work in [

Two algorithms based on the proposed optimal resource allocation strategies are presented. One is proposed to solve the EE maximization problem when the ATP constraint and the PIP constraint are applied. The other one is given for solving the EE maximization when the PTP constraint and the PIP constraint are imposed. It is shown that the complexity of the proposed algorithm for the EE maximization problem subject to the ATP constraint is higher than that of the proposed algorithm for the EE maximization problem subject to the PTP constraint.

Simulation results show that the maximum EE of the SU achieved under the ATP constraint is larger than that achieved under the PTP constraint. The design of a green CR system should take the tradeoff between the achievable maximum EE and the implementation complexity into consideration.

The rest of this paper is organized as follows. Section

As shown in Figure

The system model.

In this section, EE maximization problems are formulated in delay-insensitive green CR and delay-sensitive green CR. Different from the works in [

In CR, from the perspective of the PU, the interference caused by the SU should not be beyond the tolerable interference threshold of the PU. The PIP constraint is chosen as the protection metric of the PU since CR with PIP constraint has low complexity and facilitated implementation. In addition, the long-term power budget of the SU should be considered and can be evaluated by the ATP. From the perspective of the SU, the ATP should be below a threshold. Thus, the constraints on the PIP and ATP can be given as

In delay-insensitive CR, the EC is appropriately used to evaluate the performance of the SU [

Problem

See Appendix

Based on Theorem

The global optimization solution of problem

See Appendix

Thus, on the one hand, problem

For a given

The optimal resource allocation strategy of

In delay-insensitive green CR, the optimal power allocation strategy for EE maximization should take the achievable EE of the SU and the power amplifier coefficient of the SU-Tx into consideration, which is different from the optimal power allocation strategy for EC maximization in the conventional delay-insensitive CR proposed in [

For a given

Flowchart of Algorithm 1 for EE maximization subject to the ATP constraint and the PIP constraint.

In this subsection, the EE maximization problem is analyzed in delay-sensitive green CR, subject to constraints on the PIP and the ATP. In delay-sensitive green CR, the SU is sensitive to the delay, such as voice and video applications. In delay-sensitive CR, the OC that evaluates the achievable constant rate for all fading states is a more appropriate metric. Thus, the EE definition in this green CR should be related to the OC of the SU.

According to the work in [

In this case, when the SU transmits with the minimum power required to maintain the OC

In this case, the maximum of

Theorem

The optimal resource allocation strategy of

It is seen from (

It is seen that problem

In this section, EE maximization problems subject to constraints on the PIP and the PTP are studied in delay-insensitive green CR and delay-sensitive green CR. The PTP constraint is related to the nonlinearity of power amplifiers. Another algorithm based on the derived optimal power allocation strategies is proposed to solve EE maximization problems under the PIP constraint and the PTP constraint.

In this subsection, the peak transmit power constraint is considered, given as

The optimal resource allocation strategy of

When

For a given

Flowchart of Algorithm 2 for EE maximization subject to the PTP constraint and the PIP constraint.

In this subsection, the EE maximization problem in delay-sensitive green CR subject to constraint on the PIP and the PTP is studied. In this case, the EE maximization problem in delay-sensitive green CR, denoted by problem

In this case, when

In this case,

Theorem

The optimal resource allocation strategy of

In delay-sensitive green CR, under constraints on the PIP and the PTP, the optimal power allocation strategy for maximizing the EE given in Theorem

For a given

As shown in Algorithms 1 and 2, a nonnegative dual variable related to the ATP is required to be updated by using the subgradient method when the ATP constraint is applied, whereas the for-loop is only activated when the PTP constraint is used. Let

In this section, we give simulation results to evaluate the achievable maximum EE of the SU with the proposed optimal power allocation strategies in delay-insensitive green CR and delay-sensitive green CR. The achievable maximum EE with the proposed optimal power allocation strategies is compared with that achieved with the conventional power allocation strategies given in [

Figure

The EE of the SU versus the ATP/PTP constraint for different fading channel models with

Figure

(a) The EE of the SU versus the PIP constraint for EE maximization or EC maximization under the PTP/ATP constraint,

Figure

(a) The EE of the SU versus the PIP constraint and the ATP constraint in delay-insensitive green CR. (b) The EE of the SU versus the PIP constraint and the PTP constraint in delay-insensitive green CR.

Figure

The EE of the SU versus the ATP/PTP constraint for different fading channel models with

Figure

(a) The EE of the SU versus the PIP constraint for EE maximization or OP minimization under the PTP/ATP constraint in delay-sensitive green CR,

Figure

The EE of the SU versus the PTP constraint for EE maximization or OP minimization under the PTP constraint with

Table

The comparison of time (s) taken by Algorithm 1 with time taken by Algorithm 2.

Green CR | Transmit power | ||||||||
---|---|---|---|---|---|---|---|---|---|

20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | ||

Delay-insensitive | Average | 535.162 | 313.368 | 212.008 | 155.220 | 119.644 | 95.025 | 77.328 | 63.751 |

Peak | 0.198 | 0.203 | 0.199 | 0.199 | 0.208 | 0.200 | 0.199 | 0.198 | |

| |||||||||

Delay-sensitive | Average | 856.223 | 733.604 | 242.051 | 198.239 | 130.344 | 81.732 | 61.740 | 50.934 |

Peak | 0.170 | 0.168 | 0.182 | 0.177 | 0.177 | 0.180 | 0.175 | 0.177 |

Energy efficiency maximization problems were studied in delay-insensitive green CR and delay-sensitive green CR. Optimal power allocation strategies for delay-insensitive green CR and delay-sensitive green CR were designed to maximize the achievable EE of the SU. Two algorithms based on the proposed optimal resource allocation strategies were proposed. It is shown that CR with the instantaneous metric constraint can achieve implementation with low complexity in contrast with CR with the average metric constraint. Simulation results illustrated that the SU can achieve EE gain under the ATP constraint compared with that achieved under the PTP constraint in terms of EE maximization. The design of a green CR system should take the tradeoff between its complexity and its achievable maximum EE into consideration.

A strictly quasiconcave function is defined as follows. Let

Let

On the other hand, since

Let

The underlying data is not provided since it can be easily obtained by using the algorithms proposed in this article.

The authors declare that they have no conflicts of interest.