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# Energy efficient power allocation strategy for 5G carrier aggregation scenario

- Weidong Gao
^{1}Email authorView ORCID ID profile, - Lin Ma
^{1}and - Gang Chuai
^{1}

**2017**:140

https://doi.org/10.1186/s13638-017-0924-1

© The Author(s). 2017

**Received:**24 June 2017**Accepted:**2 August 2017**Published:**18 August 2017

## Abstract

Carrier aggregation (CA) is considered to be a potential technology in next generation wireless communications. While boosting system throughput, CA has also put forward challenges to the resource allocation problems. In this paper, we firstly construct the energy efficiency optimization problem and prove that the function is strictly quasi concave. Then we propose a binary search-based power allocation algorithm to solve the strictly quasi concave optimization problem. Simulation results show that the proposed algorithm can greatly improve the system energy efficiency while keeping low computation complexity.

## Keywords

- Carrier aggregation
- Power allocation
- Binary search
- Strictly quasi concave
- Optimization

## 1 Introduction

The next generation wireless communication system should meet the characteristic of 1G+ bits per second data rate to meet the requirements of various high-speed multimedia applications. To achieve this goal, the use of a larger bandwidth for transmission becomes the most direct way to boost transmission rate. But a large segment of continuous spectrum is not available easily for most of the wireless network operators due to the practical constraints, which makes the effective use of a plurality of non-continuous frequency spectrum a viable alternative option. The international standardization organization, for example 3GPP, has carried out research on spectrum expansion technologies, which is called carrier aggregation (CA) [1]. With CA, multiple spectrum fragments, whether continuous or not, can be aggregated together to be used by single user, which can substantially improve single user’s peak data rate. Thanks to its high spectral efficiency, except for cognitive radios [2, 3], millimeter-wave communication [4], it is likely that carrier aggregation technology will also play an important role in future 5G wireless networks.

Though CA technology has significantly improved the system throughput, it has also increased the complexity of resource scheduling for the network. In addition, due to that multiple component carriers are used by the UE simultaneously, more transmission power will be consumed by the eNodeB as well as by the UE [5]. Therefore, energy-saving problem cannot be ignored for carrier aggregation and it is necessary to reduce the extra energy consumed by CA operation, thus reduce the carbon emission and contribute to green communication. Up to now, there are few researches on energy efficiency optimization algorithm focusing on power allocation in carrier aggregation systems. With respect to energy efficiency optimization for CA systems, there are mainly two kinds of algorithms. For the first one, it is assumed that the collection of resource blocks occupied by each user is known [6] and then the power allocation is performed. For the second one, the users’ target data rate is constraint, and then the power and resource block are jointly allocated [7]. Because of these non-practical assumptions, these two kinds of optimization methods cannot be applied to the practical systems.

In this paper, we have proposed a binary search-based power allocation scheme for CA systems, which can greatly improves the energy efficiency of carrier aggregation system while keep low computation complexity at the base station.

## 2 System model and problem formulation

### 2.1 System model

Consider a single cell network model with a total of *K* users and *N* CCs. Each CC is composed of *M* PRBs each with bandwidth *B*. Define \( \mathcal{K}=\left\{1,2,\dots, K\right\} \), \( \mathcal{N}=\left\{1,2,\dots, N\right\} \), and *ℳ* = {1, 2, … , *M*} as the user set, CC set, and PRB set, respectively. Indicator variable *c*
_{
k , n , m
} ∈ {0, 1} is used to indicate the relationships among the CCs, the users, and the PRBs, where value “1” indicates that PRB # *m* of CC # *n* is allocated to user # *k* and value “0” indicates the opposite. There is a rule that each PRB can only be assigned to single user at any moment.

*k*can obtain from PRB #

*m*of CC #

*n*can be written as:

*p*

_{ k , n , m }≥ 0 is the transmit power of the base station,

*g*

_{ k , n , m }is the channel gain, and

*N*

_{0}is additive white Gaussian noise(AWGN) power spectral density.

*c*

_{ k , n , m }, we can obtain the total system throughput by summing up the transmission rate of all the users as following:

*p*

_{ k , n , m }is the base station’s transmit power on PRB #

*m*of CC #

*n*for user

*k*

_{.}

*P*

_{ C }. Without losing generality, the energy efficiency is defined as the number of bits that are transmitted per joule:

*P*:

*P*

_{max}is the maximum transmit power of the base station. Function

*τ*(

*x*) is defined as following:

The constraint condition C2 limits the maximum number of CCs that each user can aggregate simultaneously. It is specified that by 3GPP that the largest number of CCs each user can aggregate should be no more than 5 [1]. Therefore, throughout this paper, the value of *T* is set to less than or equal to 5. The constraint condition C4 guarantees the effectiveness of the indicator variable as well as the transmit power.

### 2.2 Problem analysis

Because of the existence of 0–1 indicating variables, the scope of the constrained optimization problem presented in 5 is not convex. At the same time, since the base station’s transmit power, *P*
_{BS}, appears both in the numerator and in the denominator of the optimization objective function, the optimization objective function is not convex. According to the above observations, the optimization problem as given in Eq. 5 is not a convex optimization problem, and it is not solved by convex optimization theory.

To solve this kind of non-convex optimization problem, reference [8] adopted a fixed value of base station transmission power and expanded the range of indicator variable *c*
_{
k , n , m
} from discrete value of 0 or 1 to continuous real numbers that range in [0, 1], and then convex optimization theory was used to solve the problem [9]. Since too many approximate operations are used in the above schemes, the accuracy of the solution is not fine enough. Furthermore, the total number of resource blocks is much larger for 5G carrier aggregation systems than that of the LTE systems, so the computing complexity of the scheme is too high and it cannot be effectively applied in the realistic 5G communication systems.

*P*

_{BS}, then the optimization problem presented by Eq. 5 is reduced to a resource allocation optimization problem that under fixed given transmit power value.

*R*

_{max}(

*P*

_{BS}) represents the maximum data rate of the carrier aggregation system under determined

*P*

_{BS}value. The definition of

*c*

_{ k , n , m },

*r*

_{ k , n , m,}and

*τ*function are the same with that of optimization problem (Eq. 5).

*P*

_{BS}, which is:

## 3 Power allocation scheme

Considering that the base station’s transmission power, *P*
_{BS}, has real value, if we aim at traversing all *P*
_{BS} values at equal intervals in [0, *P*
_{max}], the step must be set small enough to ensure sufficient accuracy. That is to say, we should solve the optimization problem for a large number of transmit power values. Obviously, the complexity of the algorithm is too high, so we need to optimize it with low complexity method.

Through in-depth analysis of the optimization problem (Eq. 9), we find that \( {\eta}_{\mathrm{EE}}^{\mathrm{max}}\left({P}_{\mathrm{BS}}\right) \) is a strictly quasi concave function on *P*
_{BS} (please see Appendix for the proof). It means that \( {\eta}_{\mathrm{EE}}^{\mathrm{max}}\left({P}_{\mathrm{BS}}\right) \) has only one local optimal solution, and the local optimal solution is also global optimal. For this kind of optimization problems, the literature [8] proposed an iterative algorithm based on extreme point idea, which adopted a large number of approximate operations that greatly increased the algorithm’s time and space overhead. Considering this, we in this paper propose a binary search-based power allocation algorithm (BSPAA), which can provide high precision without too much iterations.

Assume that the number of users in the system is *K* and the user set is \( \mathcal{K}=\left\{1,2,\dots, K\right\} \). Since the resource allocation scheme has already been determined, it is not necessary to distinguish which component carrier each resource block belongs to, i.e., we can consider all of the resource blocks as a set, which is denoted as \( \mathcal{N}=\left\{1,2,\dots, N\right\} \). Defined *p*
_{
k , n
} as the transmission power allocated to user #*k* on resource block #*n* and *c*
_{
k , n
} as the indication whether the resource block #*n* is assigned to user #*k*, where value 1 represents “yes” and value “0” represents “no”.

*k*on the resource block #

*n*can be represented by the following formula:

*g*

_{ k , n }is the channel gain of user #

*k*on resource block

*n*.

*B*is the bandwidth of a single resource block and

*N*

_{0}is the Gauss white noise.

*r*

_{ k , n }is given by Eq. 10. Constraint C1 shows that one resource block can only be assigned to at most one user. Constraint C2 shows that the total transmit power of the base station is equal to the sum of the transmit power on all of the resource blocks.

*λ*

_{ k }as the Lagrange multiplier of user #

*k*, then we can get the transmission power allocated to user #

*k*on resource block #

*n*:

*x*

^{+}equals to

*x*when

*x*is larger than 0, and

*x*

^{+}equals to 0 when

*x*is less than or equal to 0. The Lagrange multiplier,

*λ*

_{ k }, must satisfy the following inequality:

It can be seen from Eqs. 14 and 15 that the optimal power allocation scheme can be solved as long as the value of Lagrange multiplier is determined. The solution of the Lagrange multiplier is usually achieved by binary search method, and the specific steps can be found in [10], which is not addressed in detail here.

- step1.
Use GCSRAA algorithm to get the optimal resource allocation scheme \( \mathcal{A} \)

_{.} - step2.
Initialize all the parameters, including the lower limit of transmission power

*P*_{lo}= 0, the upper limit of transmission power*P*_{hi}= 0, and the transmit power adjustment step Δ. - step3.
Set the initial transmit power of the base station to

*P*_{cur}= (*P*_{hi}+*P*_{lo})/2. - step4.
Using water-filling based power allocation algorithm to calculate

*η*_{EE}(*P*_{cur}− Δ),*η*_{EE}(*P*_{cur}), and*η*_{EE}(*P*_{cur}+ Δ), i.e., the energy efficiency under the condition that the base station transmit power is*P*_{cur}− Δ,*P*_{cur}, and*P*_{cur}+ Δ, respectively. - step5.
If the energy efficiency values obtained in step3 satisfy the following inequality:

*P*

_{cur}is higher than that under transmit power

*P*

_{cur}− Δ and

*P*

_{cur}+ Δ, so it can be declared that

*P*

_{cur}is the global optimal solution if the adjustment step Δ is fine enough, then jump to step6.

*P*

_{cur}, i.e., the local optimal solution is larger than

*P*

_{cur}, so we can update the lower limit of the transmission power to

*P*

_{cur}and then jump to step3.

*P*

_{cur}, i.e., the local optimal solution is smaller than

*P*

_{cur}, so we can update the upper limit of the transmission power to

*P*

_{cur}and then jump to step3.

- step6.
The algorithm ends. The current base station transmit power is the optimal value, and the corresponding power allocation scheme and resource allocation scheme are also the optimal strategy.

## 4 Numerical results

Simulation parameters

Parameters | Value |
---|---|

Carrier frequency | 3.5 GHz |

Cell layout | 1 layer, 3 sectors |

Channel model | SCME model |

Scenario | Urban macro |

Carrier bandwidth | 20 MHz |

Maximal transmit power | 49 dBm |

Minimum BS-UE distance | 35 m |

Cell range expansion parameter | 0 dB |

Service type | Full buffer |

TTI length | 1 ms |

TTI number | 5000 |

## 5 Conclusions

This paper presents the problem of power allocation in carrier aggregation systems. Energy efficiency is adopted as the evaluation metric, and it is found that the function of energy efficiency optimization is strictly quasi concave, which cannot be solved easily with traditional optimization method. We propose a binary search-based power allocation scheme, which can significantly improve the system energy efficiency while keeping low computation complexity. Future work will consider jointly optimization of component carrier selection, radio resource allocation, and power allocation to further improve the system performance.

## Declarations

### Funding

This work is supported by Major National Scientific and Technological Specific Project of China under grant number 2016ZX03001009-003.

### Authors’ contributions

WG conceived and designed the study. LM performed the experiments. GC reviewed and edited the manuscript. All authors read and agreed the manuscript.

### Competing interests

The authors have declared that no competing interests exist.

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## Authors’ Affiliations

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