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Conventional designs on OFDM-based underlay cognitive radio (CR) networks mainly focus on interference avoidance and spectral efficiency (SE) improvement. As green radio becomes increasingly important, this paper investigates energy efficient power allocation. Our aim is to maximize energy efficiency (EE), subject to the constraints on the total transmit power, the peak interference power, and the minimum data rate requirement. We first analyze the relationship between SE and EE and solve this optimization problem with the help of bisection search technique. However, the accuracy of the power allocation solution is dependent on the number of iterations. In order to achieve the exact optimal solution, a new energy efficient power allocation scheme is proposed to balance the tradeoff between SE and EE. Simulation results are provided to demonstrate the effectiveness of the proposed schemes.

The rapid development of wireless communication applications has given rise to a tremendous demand for scarce spectrum resources and energy conservation [

Orthogonal frequency division multiplexing (OFDM), which has been regarded as a leading technique for high-data rate transmission due to its inherent resistance to multipath fading and the flexibility in resource allocation, has received wide attention in the evolution and development of CR technology [

Power allocation is a critical design issue for CR networks. Conventional power allocation for OFDM-based CR networks mainly focused on SE [

Although the above power allocation schemes are very efficient, they require to know perfect intersystem channel state information (CSI) and intrasystem CSI. The acquisition of the instantaneous intersystem CSI is difficult to obtain due to not only the lack of cooperation, but also wastes of network resources.

In this paper, we study the EE optimization problem for OFDM-based CR networks with partial intersystem CSI while ensuring a certain data rate of SU. We first analyze the relationship between SE and EE and solve this optimization problem with the help of bisection search technique. However, the accuracy of optimal solution is dependent on the number of iterations. In order to derive the exact optimal solution, we propose a new algorithm to maximize EE, which is different from all existing methods.

The remainder of the paper is organized as follows. Section

Consider an OFDM-based CR network where an SU coexists with a PU over the same spectrum band with

For a spectrum sharing scenario, the PU and SU will interfere with each other. In a practical network with a sufficiently large number of subchannels, the interference introduced by PU-Tx into SU-Rx can be modeled as an additive white Gaussian noise (AWGN). This assumption is widely treated and justified in [

Consequently, the overall data rate

In the transmission mode of SU-Tx, the energy consumption consists of two parts: the energy consumption of power amplifier related to transmit power and the circuit energy consumption incurred by signal processing and active circuit blocks. According to [

In order to prevent the PU from severe performance degradation, the interference power should be restricted by

Since the random variable

To maximize the EE of the CR network while guaranteeing that the interference to the PU receiver is maintained below a predefined threshold, we formulate a transmit power allocation optimization problem under some practical constraints. The optimization problem is formulated as follows:

It is possible that problem P1 does not have any feasible solution if

After formulating the EE optimization problem, we investigate the relation between EE and SE and then propose two optimal power allocation schemes to maximize EE.

First we define a data rate-adaptive (RA) optimization problem for the OFDM-based CR network as

It can be seen that the objectives in (

Since

For problem P2 without peak interference power constraint (

Please see Appendix

Based on Lemma

If the overall data rate is fixed, the objective of problem P1 is equivalent to a transmit power-adaptive (PA) optimization problem. The optimization problem can be formulated as follows:

For problem P3 without peak interference power constraint (

Please see Appendix

According to Lemma

For problem P1 without constraints (

Please see Appendix

Since EE is a quasiconcave function of

Based on the above discussion, both

The optimal water level

and set

(e.g.

convergence accuracy.

The key work of Algorithm

Although the optimization problem P4 can be easily solved by the search algorithm, the accuracy of solution is primarily dependent on

For problem P4 without constraints (

Please see Appendix

However, the optimal unconstrained water level

optimal unconstrained water level as

and

Simulation results are provided to corroborate our analysis and to demonstrate the performance of the proposed scheme. We evaluate the EE and SE performance of proposed schemes and compare them with conventional RA and PA power allocation schemes. The minimum SE requirement is 0.5 bits/s/Hz. The other simulation parameters are set as follows:

Figure

EE-versus-channel gain ratio

SE-versus-channel gain ratio

Figures

EE-versus-interference tolerance

SE-versus-interference tolerance

In Figures

EE-versus-the minimum SE requirement

SE-versus-the minimum SE requirement

We consider the energy efficient power allocation problem of OFDM-based CR systems with statistical intersystem CSI available. We first introduce two conventional optimization problems: rate-adaptive (RA) problem and power-adaptive (PA) problem. After analyzing the relationship between EE and SE, an efficient power allocation scheme with the help of bisection search method has been proposed to maximize EE. However, the accuracy of the solution is dependent on the number of iterations. To derive the exact optimal performance, we also propose a new power allocation algorithm which is different from all existing methods. Simulation results confirm considerable EE improvement by the proposed schemes.

In future, the energy efficient resource allocation problems for more complicated CR networks (e.g., multiuser scenario with imperfect channel state information) should be considered. We may jointly extend the proposed schemes and the methods in [

From problem P1, the objective of EE optimization is modeled as

According to [

According to Lemma

Denote that

Thus the objective function, (

Differentiating the objective function, (

It is obvious that

Let

Here Lemma

The authors declare that there is no conflict of interests regarding the publication of this paper.

The work in this paper has been supported by funding from Beijing Natural Science Foundation under Grant no. 4122009.