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Energy efficiency (EE) capacity analysis of the chunk-based resource allocation is presented by considering the minimum spectrum efficiency (SE) constraint in downlink multiuser orthogonal frequency division multiplexing (OFDM) systems. Considering the minimum SE requirement, an optimization problem to maximize EE with limited transmit power is formulated over frequency selective channels. Based on this model, a low-complexity energy efficient resource allocation is proposed. The effects of system parameters, such as the average channel gain-to-noise ratio (CNR) and the number of subcarriers per chunk, are evaluated. Numerical results demonstrate the effectiveness of the proposed scheme for balancing the EE and SE.

The unprecedented expansion of high data rate wireless networks has triggered steadily increase in energy consumption and left a significant environmental footprint. It is reported that the energy usage for radio access can account for up to more than 70 percent of the total energy bill for a mobile operator [

Orthogonal frequency division multiplexing access (OFDMA) has become a promising technique due to its improved immunity to fast fading and flexibility in resource allocation [

In previous works, chunk-based resource allocation schemes for OFDMA systems mainly intend to increase the system capacity or spectrum efficiency (SE) [

Besides the capacity improvement, the energy efficiency (EE) has been becoming equally or even more important than SE for green radio. Energy efficient design has received much attention from both industry and academia [

The above discussions motivate us to investigate the EE optimization for chunk-based OFDMA systems. In this paper, we formulate an optimization problem to balance the tradeoff between SE and EE. The objective function is the EE which is measured by instantaneous “bits-per-Joule.” The SE is assured by imposing a required minimum data rate into the optimization problem. This paper proposes a low-complexity algorithm to obtain high EE for each channel realization. Furthermore, for a fixed chunk assignment, an optimal power allocation with closed-form expression is also derived.

The rest of this paper is organized as follows. In Section

Consider a single cellular downlink OFDMA system consisting of

The broadband channel is frequency selective and the normalized correlation coefficient between

Let

To guarantee the quality-of-service (QoS), the overall data rate

According to [

For a practical system, the total transmit power

Our objective is to optimize the chunk and power allocation in order to obtain the maximum EE under the required minimum rate constraint. Hence, the optimization problem can be formulated as

The optimization problem in ((

For any given maximum total transmit power

The dual problem is defined as

The optimal power distribution should maximize

The optimal transmit power for user

The core principle of the chunk allocation scheme is to assign the chunk with high capacity as much as possible for each user. Since both the throughput and the EE are nondecreasing with the number of subcarriers. In order to achieve high EE, we can set

According to the above discussion, the data rate is maximized when the power is distributed among the subcarriers using water-filling algorithm. For a given chunk allocation, the optimal power distribution and system throughput continuously change as the power level varies. Then, the optimization problem can be reformulated as

It can be seen that the system data rate

The minimum power level

Please see Appendix

The maximum power level

Please see Appendix

Since we assume that the required minimum data rate can be achieved under the constraint (

The primal variable of problem ((

To a certain determined chunk allocation, the EE is a quasiconcave function of power level

Please see Appendix

According to Lemma

Figure

EE-power level relation in downlink OFDMA.

In this section, we provide some simulation results to verify the effectiveness of the algorithm proposed in the previous sections. The system parameters are assumed as follows. The number of active users is 6 and the system bandwidth is divided into 256 subcarriers, each with bandwidth

Figure

System EE versus average CNR in the case that

System SE versus average CNR in the case that

Figure

System EE versus average CNR in the case that

System SE versus average CNR in the case that

In this paper, the EE-SE relation in a single cell downlink OFDMA system is investigated and the performance analysis of the chunk-based resource allocation is presented with energy-efficient design under the constraints on the minimum SE requirement and total available power. When the number of subcarriers per chunk is given, both EE and SE increase when the coherence bandwidth increase from a very small value. The performance of chunk-based resource allocation is very close to that of single-subcarrier-based allocation scheme when the bandwidth of each chunk is smaller than coherence bandwidth.

Simulation results verify the effectiveness of the proposed scheme in practical and demonstrate that it is much more suitable to green communications. Furthermore, the impact of the number of users and minimum SE requirement to the EE are also analyzed.

For arbitrary

Since

For arbitrary

Hence, the true power level

Since

For arbitrary

According to [

This work is partially supported by the Beijing Municipal Natural Science Foundation (no. 4122010).