Energy efficiency (EE) is a critical design when taking into account circuit power consumption (CPC) in fifth-generation cellular networks. These problems arise because of the increasing number of antennas in massive multiple-input multiple-output (MIMO) systems, attributable to inter-cell interference for channel state information. Apart from that, a higher number of radio frequency (RF) chains at the base station and active users consume more power due to the processing activities in digital-to-analogue converters and power amplifiers. Therefore, antenna selection, user selection, optimal transmission power, and pilot reuse power are important aspects in improving energy efficiency in massive MIMO systems. This work aims to investigate joint antenna selection, optimal transmit power and joint user selection based on deriving the closed-form of the maximal EE, with complete knowledge of large-scale fading with maximum ratio transmission. It also accounts for channel estimation and eliminating pilot contamination as antennas

Massive multiple-input multiple-output (MIMO) systems are an increasingly interesting area of study. They have become an essential technology for fifth-generation (5G) cellular networks that support big rate traffic. The 5G and beyond-5G based on cognitive radio technologies are helpful to use the available spectrum to achieve the QoS and increase the overall quality of the network [

One of the major challenges facing massive MIMO systems is pilot contamination (PC), which arises from a large number of pilot reuse sequences (PRSs) due to non-orthogonal pilot sequences between neighboring cells. This problem requires a finite number of PRS due to the limited channel coherence intervals. The interference of active users (UEs) in neighboring cells is largely determined based on the evaluation of large-scale fading involved in the joint channel processing [

In both the BS and UE, a larger number of RF chains consume more power because of the processing performance in the digital-to-analogue converter (DAC), power amplifier, multiplexer and filter. Moreover, all antennas at the BS must connect with the RF chains. It is estimated that about a third of the total electricity has been consumed, and 30 million tonnes of carbon dioxide

The EE metric becomes an important design when taking into account CPC. The optimal transmit power allocation highly depends on selection of the optimal antenna and of flexible users to improve the EE in the cellular system. More transmit antennas are required to serve a number of allocated UEs, in which case the RF chains and high CPC are involved in signal transmission from BS to UEs. Prior work [

In this work, the energy-efficient massive MIMO system focused not only on joint antenna selection, optimal transmit power, and joint user selection, but also analyzed a CPC to balance the radiated EE and adjust the length of the pilot sequences to improve channel estimation as shown in

To investigate the lower bounds of the achievable downlink (DL) data rate and SINR based on relative channel estimation with full knowledge of large-scale fading by using PRS and performance analysis of maximum ratio transmission (MRT) to eliminate different levels of PC.

To minimise the consumption circuit power for antenna selection and obtain a high-quality channel estimate based on correlates of the training signal with the established PRS of every UE for the linear processing MRT to mitigate interference.

To analyse the exact power consumption based on a proposed novel power consumption model for each antenna based on the analysis of the power amplifier and CPC that enable the use of low-cost RF amplifiers that exploit antenna selection.

To propose a novel iterative low-complexity algorithm (LCA) for optimal antenna selection, joint optimal transmit power, and joint user selection under the impact of PRS to achieve optimal EE.

The EE metric becomes an important design criterion, because it allows operations to remain practically affordable through regulated energy consumption levels. The orthogonal pilot sequences for all UEs in the same cell prevent channel estimation from being affected by the interference of other UEs. Prior work [

Ref. No. | Year | Problem | Features | Limitation | |
---|---|---|---|---|---|

[ |
2016 | • Large cost of RF circuits. | • Used energy-efficient (EEHP-MRFC) algorithm. | • EE Hybrid Precoding zero forcing (ZF). | |

• Used the critical NoA searching (CNAS) to reduce CPC. | |||||

[ |
2015 | • Pilot assignment problem. | • Used joint pilot assignment and resource allocation. | • Proposed algorithm | |

• Number of activated antennas and power allocation units. | • Used an iterative algorithm to solve the transformed problem. | • Conventional scheme. | |||

[ |
2011 | • Problem of pilot contamination in multi-cell systems. | • Used training pilot sequences. | • ZF and MMSE. | |

• Achievable data rate by developing a multi-cell MMSE. | |||||

[ |
2013 | • Pilot contamination effect, the equivalent system model. | • Used equivalent channel with pilot. | • Infinite NoA. | |

• Derived the rate in the lower bound. | |||||

[ |
2013 | • More circuit power dissipated by analogue devices and a power amplifier. | • Proposed a practical power consumption model to maximise EE. | • Large NoA. | |

• Proposed CPC. | |||||

[ |
2016 | • Pilot contamination. | • Maximised EE under optimised NoA, number of users, and pilot sequences. | • Proposed (AO-BS) algorithm. | |

• Increased CPC. | |||||

[ |
2019 | • Inter-cell interference. | • Maximised EE under optimal NoA selection, and user scheduling. | • Adaptive Markov Chain. | |

• High computational complexity. |

Many works have investigated the progress of actual models and efficient algorithms user selection. Optimal performance EE is achieved by applying lower computational complexity by employed equal transmit power allocated to every UE. The authors in [

In this research, the problem arises due to the increasing NoAs in the massive MIMO system, due to inter-cell interference for CSI. Moreover, a higher number of RF chains at the BS and UEs consume more power, due to the processing activities in the DAC and power amplifier. Therefore, antenna selection, user selection, optimal transmission power, and PRS are vital aspects in improving EE. In this work, we propose channel estimation with comprehensive knowledge of large-scale fading to eliminate PC. The channel estimation was evaluated at the received signal based on the BS correlating the training signal with the recognised PRS of each UE, to achieve a high-quality channel estimate. This work also investigated the performance of a joint optimal antenna selection, optimal transmit power, and joint user selection with minimum PRS, based on proposing a novel LCA algorithm by applying Newton’s method and Lagrange multiplier. Whereas the purpose of using LCA is to improve the joint optimal antenna selection, optimal transmit power allocation and joint user selection for optimisation problems under the impact of PRS to maximise EE.

In a DL multi-cell network, every cell contains one BS. Each BS contains several transmit antennas,

The DL assumed that the BS is working with an imperfect CSI. The received signal of the

where

Based on the correlated received pilot sequences and channel estimation, the interference is reduced to achieve low-complexity in channel estimation, which is expressed as follows:

where

The MMSE estimate of the channel depends on

By substituting

The achievable data rate for transmission from BS

According to several studies [

The uncorrelated noise power can be written as follows:

The SINR of UEs is calculated in

From the received signal in

The noise variance was obtained from the large fading. The properties of the variance channels were used from [

Following the asymptotic analysis by [

According to

The second term

The third term

From

where

The improved EE based on the proposed methods for the joint antenna selection, transmit power allocation and joint user selection by utilizing LCA to reduce the CPC and power consumption.

The power consumed for DL transmission comprises the power consumed by the circuit and the power used for pilot transmission. Due to a reduction in energy consumption, a large numbers of antennas,

The peak-to-average power ratio (PAPR) followed

where _{c}_{RF}_{c}_{BB}_{RF}_{c}_{BB}_{RF}

In this process, it is complicated to design the joint antenna selection, joint power allocation and joint user selection that maximises EE if only using the ratio of achievable data rates to overall consumed power at the BS for a significant number of transmit antennas.

The maximum of EE depends on calculating the optimisation PRS,

Energy-efficient power allocations maximise the EE by evaluating the transmit power, CPC and minimum rate constrained with imperfect channel estimation. The EE depends on distributed users in multi-cell by using a LCA for joint user selection that generates low-complexity at the BS, and improves the system performance. The conception of the data rate for joint user selection is denoted by the sum of the products between the binary association and data rate

According to the optimisation theory [_{max}

where _{max}_{c}

where

where

where _{1} and _{2} represent the concave,

where ^{*} is the optimal value of _{c}^{*} was proved, which is proportional to the distributed number of users ^{*} updates the iteration for every UE to obtain the optimal value of _{c}_{c}

In this process, the problem in

From [

where _{m}_{m}

The maximum EE depends on the updated value of EE,

The relaxed problem

where

The transmit power should be allocated to every user by using a high-channel gain. From

where

where

In this section, the proposed low-complexity algorithm jointly realises a determined scheduled user selection. The network EE is maximised based on an investigation of the relaxed problem of transmit power allocation and joint user selection. The nonlinear problem in

The relaxed problem was converted into a convex optimisation one by using the non-negative Lagrange dual-decomposition method for joint selection users can be expressed as follows:

where

The LCA is improved by assigning the user direction to antennas arrays at the BS. Every user must achieve a data rate with the smallest transmit power allocation by satisfying the minimum rate requirement, and adopting user selection

The

where

Energy-efficient user selection is enhanced to decrease the total power consumption. In order to denote the joint user selection, the user selection employs _{m, k} and selecting the optimal of joint UEs. The optimal solution is obtained by applying the Karush-Kuhn-Tucker (KKT) conditions to solve a nonlinear problem to be optimal and set the partial derivative

The dual problem is guaranteed with respect to conventional user selection if

In this section, we apply a series of Monte Carlo simulations to evaluate the maximal EE performance of the proposed LCA. The performance presents the proposed channel model that accounts for imperfect channel estimation using MMSE. The proposed LCA are evaluated as shown in

Terms | Remark | Number of UEs K | Number of M | Value of EE Mb/j | Value of |
---|---|---|---|---|---|

EE with User | LCA offer optimal users by employing a training signal with the established of every UE to obtain a high-quality channel estimate, and support high transmit data channels. | 80 | 100 | 44.776 | 42.5 |

EE with Antenna | The LCA provide joint optimal antenna with uniformly good services, this is because LCA clips the transmit power at the BS to maximize the system EE. | 20 | 100 | 88 | 12 |

EE with Power | The LCA algorithm offers good tradeoff a constant power consumption, and tends to use the minimum NoAs based on |
20 | 100 | 93 | 60 |

Antenna selection in a massive MIMO system was investigated from the large-scale fading for channel estimation under PRS. More antennas are equipped for relative channel estimation with complete knowledge of large-scale fading by using PRS to eliminate PC. In terms of the relationship between EE and the number of transmitting antennas from the proposed LCA, the EE values increased when the NoA increased. According to

According

From

According to

In this work, to maximise the EE, a novel iterative low complexity algorithm was proposed for joint optimal antenna selection, optimal transmit power allocation and joint user selection under minimised PRS. Our simulation results demonstrate that the proposed iterative low complexity algorithm was used to maximise the EE based on a reasonable maximum transmit power in the case the noise power is less than the power of the received pilot sequence. The optimal antenna selection occurs when the transmission power is practical. The EE is affected by the use of minimised PRS at high SINRs. The proposed LCA prevented repeated searching for joint optimal antenna selection, optimal transmission power and joint user selection, in order to reduce the complexity caused by the increasing NoA. The hybrid precoding technique meets the anticipate emerging as key solutions and growth of traffic demands for high-data-rate multimedia of millimetre wave frequency-based for 5G and beyond-5G. This technique of hybrid precoding equipped with fully-connected and partially-connected structures that are able to reduce hardware complexity and energy consumption for high-frequency designs.