In this paper, EE and SE conditions and boundaries for data transmission are mainly being studied (Ibrahim Salah et al. 2021). The proposed system model consists of a single-cell (Wyner 1994; Xiao, et al. 2015) where one Massive-MIMO antenna BS simultaneously serving a set of User Equipment UE as shown in Fig. 1.
Impact of multiple BS antennas and users
While using Maximum Ratio (MR) combining with perfect channel information at the BS (Miao et al. 2016), the uplink (UL) SE of each UE is calculated according to Eq. (3)
$$SE_{0} = \log_{2} \left( {1 + \frac{M - 1}{{\left( {K - 1} \right) + K\overline{\beta } + \frac{{\sigma^{2} }}{{p\beta_{0}^{0} }}}}} \right)$$
(3)
where, M is the number of antennas per each base station, K is the number of user equipment’s UEs, p defines the transmit power, σ2 means the noise power, and β signify the average gain of channel of the active UE and it is assumed to be constant for all UEs in cell j. The corresponding EE of cell 0 is defined (Björnson et al. 2015) according to Eq. (4)
$$EE_{0} = \frac{{BKSE_{0} }}{{K\left( {\frac{M - 1}{{2^{{SE_{0} }} - 1}} - K\overline{\beta } + 1 - K} \right)^{ - 1} \nu_{0} + CP_{0} }}$$
(4)
where, B denotes the bandwidth, and \(v_{0}\) is evaluated according to Eq. (5)
$$v_{0} = \frac{{\sigma^{2} }}{{\mu \beta_{0}^{0} }}$$
(5)
where, \(\mu\) is a factor accounts for the Effective Transmit Power (ETP), \(0 < \mu < 1\).
The Circuit Power (CP) model consumed by single UE is estimated according to:
$$CP_{0 } = P_{FIX} + MP_{BS }$$
(6)
where, PFIX is the fixed power and PBS refers to the power utilized by the circuit components (e.g., DACs, ADCs, Q mixers /filters, Local Oscillator, OFDM modulation/demodulation), and I in which they are needed for the operation of each BS antenna.
In order to calculate the additional Circuit Power (CP) consumed by all the active UEs (Miao et al. 2016), CP0 is estimated according to Eq. (7)
$$CP_{0 } = P_{FIX} + MP_{BS} + KP_{UE}$$
(7)
where, PUE, refers to the power required by all circuit components (e.g., I/Q mixer, DAC, filter, and so forth) of each UE’s single-antenna.
Derivative of Eq. (4), is obtained to get the Maximum Energy Efficiency (Max EE), (Björnson et al. 2015) yields the expression:
$$\begin{gathered} \max EE = \frac{d}{dSE0} EE_{0} \hfill \\ \max EE \approx \frac{eB}{{\left( {1 + e} \right)}}\frac{{\log_{2} \left( {MP_{FIX} } \right)}}{{P_{FIX} }} \hfill \\ \end{gathered}$$
(8)
Equation (8) proves that, the maximum EE enhances logarithmically with the number of antennas per base station (M) and has an almost linear decreasing function with increasing PFIX.
The block diagram of the proposed system is depicted in Fig. 2. The Maximum Energy Efficiency Estimator block is firstly supplied by the number of active users (Ibrahim Salah et al. 2021; Mabrook et al. 2019) served by the cell (Zhong et al. 2020) using the base station database or using spectrum sensing techniques (Mabrook et al. 2019, 2020). Then, Eq. (4) is used to estimate Max. EE values for different M antennas. Secondly, an Antenna selector-based Genetic optimizer is initiated to evaluate the optimum number of active antennas according to the Genetic algorithm optimization technique.
Finally, the RF chain switch operates the pre-evaluated number of active antennas and switches off the unnecessary antennas to maximize EE.
EE optimization based on Genetic Algorithm Artificial intelligence
In order to get the optimum number of massive MIMO antennas corresponding to the active users served by 5G cell, many optimization techniques are proposed [ 21]. However, GA optimization technique is mostly enrolled in massive MIMO networks as (Mabrook et al. 2020). GA technique supports selection, crossover, and mutation processes. GA's main concepts are focused on Charles Darwin's theory of evolution.
These concepts are then applied to a computational algorithm to find solutions to optimization problems with a given objective function. (Chou and Cheng 2017). A chromosome is a solution to such an optimization problem. Whereas a Population is a set of chromosomes.
The algorithm starts with an initial population of abnormal chromosomes, which are then determined using the fitness function (objective function) to choose the best ones, known as Parents Élite children have genes that donate the highest fitness value and are chosen to participate in the next generation. The remaining chromosomes would then be subjected to crossover and mutation processes to produce the next generation.
Regarding this mechanism, the target of the proposed technique is to optimize the EE in M-MIMO and improve the performance of 5G networks, as shown in Fig. 3 and Table 1.Then, the mentioned steps are refined till the optimum value of EE (the fitness function) is obtained. The number of antennas in M-MIMO grid is adopted to achieve the optimum EE in each cell. Therefore, we can reformat the optimization problem from Eq. (8) as,
$$\begin{gathered} {\text{Optimize }}\left\{ {{\text{max EE }}\left( {{\text{M}},{\text{ K}}} \right)} \right\} \hfill \\ {\text{Subjected to }}\left( {\text{no of active users in the cell K}} \right) \hfill \\ \end{gathered}$$
(9)
GA is mainly used to get the optimization of its input objective functions. Therefore, in this work, EE and the number of users’ K are considered. The GA optimizers are used to optimize the consumed energy per cell and improve the M-MIMO system's EE in 5G networks.