Transmit antenna selection in M-MIMO system using metaheuristic aided model

Abstract

Massive MIMO (M-MIMO) devices are the key tool to meet the performance stards established for 5G-wireless communication. However, more Radio Frequency (RF) chains needed in base station (BS) with a huge count of transmitting antennas, involve expensive hardware and computing complexities. In order to decrease the RF chains needed in BS, this work intended to use the optimal transmit antenna selection (TAS) strategy. This strategy is gaining a lot of interest since the optimization algorithm aids in the ability to enhance the system performance considerably the efficiency and secrecy rate. This work proposes a novel Coati Adopted Pelican Optimization (CA-PO) for choosing the optimal TA by considering efficiency as well as secrecy rate. In addition, the CA-PO algorithm makes the decision on which antenna to be elected. At last, the supremacy of CA-PO-based TAS is proven from the analysis regarding secrecy rate and EE analysis. Accordingly, the proposed CA-PO method for MF for set up 2 has attained a higher EE of 0.976; whereas, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively lower EE of 0.968.

Keywords

M-MIMO Optimal TAS efficiency secrecy rate CA-PO Algorithm

Table 1
Nomenclature

Abbreviation Description

AS Antenna Selection

AWGN Additive white Gaussian noise

BEA Blad Eagle Search Algorithm

COA Coati Optimization Algorithm

CSA Cat Swarm Algorithm

CA-PO Coati Adopted Pelican Optimization

CSI Channel State Information

DMOA Dwarf Mangoose Optimization

EPGA Elite Preservation Genetic Algorithm

GBDT Gradient Boosting Decision Tree

G-OTAS Greedy Search-Based Optimum TAS

IUI Inter User Interface

JTRAS Joint Transceiver Antenna Selection

LS-MIMO Large Scale-MIMO

MRFO Manta ray foraging optimization

M-MIMO Massive Multiple Input Multiple Output

NYUSIM New York University Simulator

NCIP Nonconvex Challenging Integer Programming

PDL Probability Distribution Learning

PSO Particle Swarm Algorithm

POA Pelican Optimization Algorithm

RSNR Received Signal-To-Noise Ratio

RSM Receive Spatial Modulation

RFCM Rayleigh Fading Channel Matrix

SIC Successive Interference Cancellation

SISO Single Input, Single Output

Abbreviation	Description
AS	Antenna Selection
AWGN	Additive white Gaussian noise
BEA	Blad Eagle Search Algorithm
COA	Coati Optimization Algorithm
CSA	Cat Swarm Algorithm
CA-PO	Coati Adopted Pelican Optimization
CSI	Channel State Information
DMOA	Dwarf Mangoose Optimization
EPGA	Elite Preservation Genetic Algorithm
GBDT	Gradient Boosting Decision Tree
G-OTAS	Greedy Search-Based Optimum TAS
IUI	Inter User Interface
JTRAS	Joint Transceiver Antenna Selection
LS-MIMO	Large Scale-MIMO
MRFO	Manta ray foraging optimization
M-MIMO	Massive Multiple Input Multiple Output
NYUSIM	New York University Simulator
NCIP	Nonconvex Challenging Integer Programming
PDL	Probability Distribution Learning
PSO	Particle Swarm Algorithm
POA	Pelican Optimization Algorithm
RSNR	Received Signal-To-Noise Ratio
RSM	Receive Spatial Modulation
RFCM	Rayleigh Fading Channel Matrix
SIC	Successive Interference Cancellation
SISO	Single Input, Single Output

1. Introduction

Massive Multiple Input Multiple Output (M-MIMO) technology has got the most attention in recent times due to its remarkable ability to offer faster data rates, improved connection stability, and considerable power savings for systems that will replace 4G in the future [16,32,37]. Rich scattering environments that once made it difficult to use conventional MIMO systems are no longer an issue with the use of hundreds or even more low-power antennas at the Base station (BS), as there are undoubtedly enough independent channels to be found in such a vast channel space [6,21,22]. However, as the antenna count rises, the hardware and signal processing costs become a significant burden. It has been demonstrated that performance increases as the amount of receive antennas rises. The primary goal is to increase Spectral Efficiency (SE) and Energy Efficiency (EE), which is accomplished by adding more antennas and Radio Frequency (RF) chains [2,4,24]. The TAS method uses less RF chain, which raises the intricacy of the network and energy consumption of hardware. The TAS approach may be used to utilize fewer RF components than the total number of accessible antennas to lower hardware expenses and computing challenges whilst maintaining the majority of the variety or multiplex advantages of every antenna [34,35,39].

It is well known that thorough searching can lead to the discovery of the ideal antenna subset. However, as the count of accessible antennas increases, the computing cost of exhaustive search increases exponentially [5,10]. Because so many antennas are used in huge MIMO systems, it is therefore impracticable to do an exhaustive search [28–30]. Many low-complexity TAS methods were already in use, like beam forming and Space-Time Coding (STC), which were presented to get a suboptimal solution in traditional MIMO technology. Nevertheless, the techniques are not appropriate for M-MIMO systems’ real-time TAS implementation [17,20,35]. Nomenclature is depicted in Table 1.

The literature has recently examined the use of antenna selection techniques in huge MIMO systems [12,19,27]. However, they only paid attention to systems that had users of a single antenna, and the amount of available antennae was not as great as “massive” [9]. Additionally, a variety of methods, including the bidirectional branch method, limit searching and others, were developed for M-MIMO TAS, but the problem of the RF chains’ increasing cost and complexity has not been resolved [1,18,35]. As a result, the TAS for M-MIMO networks was not extensively studied, and it is difficult to develop a TAS method for M-MIMO systems that is low in complexity and memory-intensive [25,26].

The contributions are mentioned as follows:

This work intended to use the optimal Transmit Antenna Selection (TAS) strategy in order to decrease the RF chains needed in BS.

As a novelty, this work proposed novel Coati Adopted Pelican Optimization for choosing the transmit antenna in an optimal manner that ensures efficiency as well as secrecy rate.

The CA-PO algorithm makes the decision on which antenna to be elected.

Here, Section 2 reviews the conventional TAS in M-MIMO systems. Section 3 portrays the system model. Section 4 portrays the CA-PO-based selection of TA in M-MIMO. Section 5 describes the outcomes and Section 6 concludes the research.

2. Literature survey

2.1. Related works

Seo and Son [23] in 2021 focused on the selection of optimal TAs from a certain amount of available TAs. The TAS must be optimized by taking into account the quantity of TAs to maximize the confidentiality capacity. By pursuing the ideal amount of TAs in M-MIMO channels, the G-OTAS method was presented to maximize the secrecy capacity. It was shown via simulation that the suggested G-OTAS algorithm efficiently decreased computational complexity when compared to the reference methods and improved confidentiality capacity.

For RSM-oriented MIMO, Kim et al. [15] in 2020, suggested two effective TAS techniques. To choose active TAs from the available TAs, an incremental TAS method was first described based on the maximizing of the RSNR. The updated TAS algorithm then ran two consecutive selection steps to further reduce complexity. In the pre-processing step, active TAs were chosen that were equivalent to or more numerous than receive antennas and less numerous than the total number of TAs to be chosen. The other operable antennas were then picked in the post-processing phase. A basic norm-based approach was used in the initial stage to drastically minimize the complexity. Finding more TAs was done in the second step using an incremental selection technique. Additionally, the simulation results demonstrated that when there was a big disparity between the amount of chosen TAs and the total TAs, the suggested TAS schemes offered much less complexity than the decremental TAS.

In 2023, Yang et al. [33] characterized the TAS issue as a multi-class categorization issue and suggested an effective TAS algorithm based on GBDT taking into account the system’s safe transmission. Here, the network safety and computing complexity were taken into account as the optimizing goals. Accordingly, the system reliability was enhanced as the attainable security capacity was very similar to the conventional exhaustive search method. Accordingly, when complexity increased, GBDT’s training effectiveness considerably increased. Additionally, the effectiveness of the suggested algorithm in an M-MIMO system was assessed using the NYUSIM approach that was based on actual channel measurements. Performance investigation demonstrated that the suggested GBDT-based strategy may greatly lower the computing complexity while improving the secrecy capability of the system.

A TAS method to overcome SE issues was suggested by Zhu et al. [38] in 2022. The TAS problem was specifically framed as an optimization issue of enhancing the network’s total SE. As it was an NCIP issue, an EPGA, which used an elite preservation tactic, was deployed to make sure that there were no losses during mutation or crossover. The simulated results revealed that the EPGA achieved significantly better than random selection and was almost similar to an exhaustive search.

A computationally effective and ideal technique based on PDL for TAS was suggested by Salman et al. in 2021 [13]. The suggested approach can produce an optimal result for the real-time TAS issue and is computationally effective. After TAS, a consecutive interference cancellation method was used for pre-coding with chosen antennas since beam forming and pre-coding were also seen as crucial strategies to mitigate route loss brought on by high-frequency communications. The suggested combined TAS and pre-coding approach was computationally effective and almost optimum on SE when compared to an exhaustive search strategy as per the simulation findings. The suggested technique also optimized the EE of the network, which improved the performance of M-MIMO systems.

A new Augment TAS method based on the maximum flow minimal cut theory was suggested by Daphney et al. [7] in 2022. It captured the best antennas depending on the combined capacity of all potential antenna combinations. This algorithm’s first step suggested a subset of antennae to calculate enhanced pathways, and its second step selection takes into account the remaining antenna capacity to calculate the highest flow in a network. To increase spectrum and energy efficiency, this system chooses ideal antennas with improved channel conditions. The simulation findings have shown the efficacy of the developed work.

In 2022, Yiwen et al. [36] investigated and contrasted the accuracy, cost, and complexity of 3 intelligent algorithms: the Genetic Algorithm (GA), CSA, and PSO. Additionally, the algorithms were suggested using Fractional Coding (FC) rather than binary coding. The simulation results showed that all three methods were capable of completing the TAS successfully. PSO offered the most stability and accuracy, yet it also had the highest level of complexity. When considering total performance, CSO was the best option, especially for practical implementation. Additionally, FC performed more effectively than binary coding.

In 2022, Salman et al. [14] targeted to increase EE with no apparent performance deterioration on SE owing to the dependence of SE and energy on RF chains. In this article, RF chain selection utilizing evolutionary schemes was used to examine this trade-off. A hybrid heuristic strategy was described that combined Successive Interference Cancellation (SIC) for pre-coding with low computationally demanding algorithms for the selection of RF chains. Additionally, it was demonstrated that the analogue pre-coding was the most energy-efficient option for lower Signal to Noise Ratio (SNR) environments, whereas the RF chain selection method was the most effective option for higher SNR environments. Additionally, the channel anomalies have no impact on the suggested plan.

2.2. Problem gaps

The problems in conventional TAS in M-MIMO systems are as follows:

Each antenna element in traditional MIMO systems with fewer TAs is given an individual RF chain. While RF chains are expensive, heavy, and power-intensive, antenna elements are rather cheap and tiny.

Because there are so many BS antennas, it is therefore nearly impossible to give a distinct RF chain to each antenna element in huge MIMO systems.

Therefore, a well-motivated task for massive MIMO is the design of transmit pre-coders that require a small number of RF chains to get a good balance between efficiency and hardware performance.

The exhaustive Algorithm (EA) model that analyzes every feasible combination of antenna subsets is frequently used for selecting the antenna subset that will result in the best system performance. Nevertheless, the EA method also significantly increases computational complexity.

This is especially true for large-scale antennas, where the EA computation period is excessively long and its computing volume is rapidly growing, making it challenging to get resultants in a constrained amount of time and ultimately decreasing its applicability.

A JTRAS method is suggested for enhancing the performances of the AS system further and producing effective channel capacity results.

However, the algorithm’s computational cost is still quite high, and its performance remains unsatisfactory in applicability.

Hence, to overcome the aforementioned issues, this paper proposes a novel transmit antenna selection in an M-MIMO system using the metaheuristic-aided model for optimally choosing the transmit antenna and thereby ensuring efficiency as well as secrecy rate.

3. System model

This work suggests a novel optimal TAS scheme by considering efficiency and secrecy rate. Secrecy capacity is the rate of communicating secret information from one node to another node. The safer rate of communication among authoritative nodes with no leakage of information to an eavesdropper is described by secrecy capacity that depends upon relevant attenuations in the channel. Eavesdropping attack occurs when the hacker enters, delete, or changes data transmitted between 2 devices. For accessing transmitted data among devices, eavesdropping is termed as snooping or sniffing. So as to progress the network performance, it is obligatory to select the optimal TA. Selecting the optimal TA is performed with a new CA-PO algorithm. Figure 1 shows the developed TAS in the M-MIMO scheme.

Fig. 1.

General diagram of developed optimal TAS in M-MIMO system.

3.1. System model

Presume a cell containing a BS with B terminal. The TX in $E_{t}$ counts is integrated in BS and each B contains individual RX antennas. Equation (1) specifies the signal received at B, here O corresponds to $B \times E_{t}$ smaller scale RFCM, y corresponds to $B \times 1$ signal vector attained for all B, $p_{tx}$ corresponds to the whole TX power at uplink and, ς corresponds to TX power normalizing term as exposed in $ς \approx \sqrt{\frac{E_{t}}{B}}$ . $y u$ corresponds to $B \times 1$ , $nv$ corresponds to AWGN of $B \times 1$ , and V corresponds to $E_{t} \times B$ pre-coded matrix that lessens IUI. Here, 2 pre-coders are calculated for LS-MIMO, like Match Filtering (MF) $(MF : U = E_{t}^{- 1} O^{O})$ , and ZF $(ZF : U = O^{O} {(O O^{O})}^{- 1})$ . $\begin{matrix} (1) & S = \sqrt{P_{tx}} O ς U y u + n u \end{matrix}$

The system will be said to be LS-MIMO when the transmitter contains an idle CSI. To evaluate the EE, there has to be a suitable model for power exploitation. Equation (2) shows the summation of power, $p_{sm}$ , in which, $p_{BA}$ and $p_{PA}$ corresponds to the power consumption of Base Band (BB) and PA, and the RF power consumption at the front-end is implied by $p_{{RF}_{front}}$ , $C_{t}$ corresponds to the TA count. $\begin{matrix} (2) & p_{sm} = p_{BA} + p_{PA} + C_{t} p_{{RF}_{front}} \end{matrix}$

The power consumption $p_{c p}$ is calculated and it rises with rise $E_{t}$ as exposed in Eq. (3). Thus, Eq. (3) is remodelled as in Eq. (4). $\begin{array}{c} (3) & p_{c p} = (p_{BA} / E_{t} + p_{{RF}_{front}}) \\ (4) & p_{sm} = p_{PA} + E_{t} p_{c p} \end{array}$

In addition, consider an OFDM system with 1024 subcarriers, 10 MHz frequency, and 78.5% efficiency with 11 dB IBO. In this case, the efficiency of Power Amplifier (PA) is said to be 22%. The relationship amid $p_{tx}$ and $p_{PA}$ is specified in Eq. (5). $\begin{matrix} (5) & p_{tx} = η p_{PA} \end{matrix}$

The assessment of the LSMIMO BB model $y u (V flops) p_{BA}$ is specified in Eq. (6) [3]. $\begin{matrix} (6) & z = B_{t} X . [\begin{array}{l} (\frac{R_{g i}}{R_{s d}}) {log}_{2} (R_{g i} X) + (\frac{R_{g i}}{R_{s d}}) (1 - \frac{R_{p t}}{R_{s t}}) B + (\frac{R_{g i}}{R_{s d}}) \\ (\frac{R_{p t}}{R_{s t}}) {log}_{2} (\frac{R_{g i} R_{p t}}{R_{s d} R_{d l}}) + (\frac{R_{d l}}{R_{s t}}) B^{2} \end{array}] \end{matrix}$

Here,

X corresponds to the bandwidth that utilizes 10 MHz power.

$R_{s t}$ corresponds to slot length that utilizes 0.5 ms power.

$R_{p t}$ corresponds to the pilot length that utilizes 0.214 ms power.

$R_{s d}$ corresponds to symbol duration that utilizes 0.214 ms power.

$R_{c o}$ corresponds to Graphical Interface (GI) that utilizes 4.7 μs power.

$R_{g i}$ corresponds to GI that utilizes 66.7 μs power.

$R_{d l}$ corresponds to the delay of GI that utilizes 4.7 μs power.

The relationship amid $p_{BA}$ and $y u (V flops)$ is depicted in Eq. (7), in which, ϖ points out VLSI efficiency and $ϖ = 5 V flop / A$ and $50 V flop / A$ is elected. $\begin{matrix} (7) & p_{BA} = \frac{y u (V flops)}{ϖ (V flops / A)} \end{matrix}$

3.2. Optimal TAS

The signal received by hth user is exposed in Eq. (8), here $g_{k}$ ,: corresponds to $1 \times C_{t}$ channel vector of hth user and P:,_k corresponds to the pre-coded vector. The last term in Eq. (8) is said to be IUI. $\begin{matrix} (8) & q_{k} = \sqrt{\frac{p_{tx} C_{t}}{O}} g_{k}, : P :,_{k} z_{k} + e_{k} + \sqrt{\frac{p_{tx} C_{t}}{O}} \sum_{l \neq k} g_{k}, : P :,_{l} z_{l} \end{matrix}$

The size of a remote cell is given in Eq. (9), in which, α corresponds to the scaling term, $E_{0} X$ corresponds to noise power with X. $\begin{matrix} (9) & H = α X . \sum_{k = 1}^{K} D [{log}_{2} (1 + \frac{\frac{p_{tx} E_{t}}{B} | g_{k}, : P :,_{k} |^{2}}{\frac{p_{tx} E_{t}}{B} | \sum_{l \neq k} g_{k}, : P :,_{l} |^{2} + E_{0} X})] \end{matrix}$

Equation (9) is rewritten as given by Eq. (10), when $E_{t} > 10 B$ , in which S corresponds to IUI. Accordingly, Eq. (11) shows the formulation of EE. In addition, the optimum TX antenna counts $E_{t}^{opt}$ have to gratify Eq. (12). $\begin{array}{c} (10) & X_{app}^{LS - MIMO} \approx α X B . [{log}_{2} (1 + \frac{p_{tx} E_{t}}{(S + E_{0} X) B})] \\ (11) & EE = H / p_{sm} \end{array}$ $\begin{aligned} \frac{\partial}{\partial E_{t}} EE & = \frac{\partial}{\partial E_{t}} (\frac{H_{app}}{\frac{1}{η} p_{tx} + E_{t} p_{c p}}) \\ = \frac{X B p_{tx}}{(S + E_{0} X) B (1 + \frac{p_{tx} E_{t}}{(L + E_{0} X) B}) p_{sm} {log}_{2} P} \\ - \frac{X B p_{c p} . {log}_{e} (1 + \frac{p_{tx} E_{t}}{(S + E_{0} X) B})}{p_{sm}^{2} {log}_{2} P} \\ (12) & = 0 \end{aligned}$

Thus, $B_{t}^{opt}$ is computed as in Eq. (13), in which $Γ = \frac{p_{tx}^{2} - B E_{0} X p_{c p} - B S p_{c p}}{B (S + E_{0} X) p_{c p} exp (1)}$ and A refers to Lambert function and is given by $Γ = A (Γ) exp (A (Γ))$ . $\begin{matrix} (13) & E_{t}^{opt} \approx \frac{(S + E_{0} X) B}{p_{tx}} (- 1 + exp (1 + A (Γ))) \end{matrix}$

$E_{t}^{opt}$ is modelled as in Eq. (13), however, the issue is ‘how to select the $E_{t}^{opt}$ antennas from the total number of antennae $B_{t}^{total}$ ’. The channel capacity of $E_{t}^{opt}$ while choosing the columns of O are ${q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}$ . Equation (14) shows $H_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}}$ , wherein $1 \times E_{t}^{opt}$ channel vector for hth user is given by $g_{k, {q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}}$ , $1 \times E_{t}^{opt}$ the pre-coded vector is given by $P_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}, k}$ while electing ${q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}$ th. $\begin{matrix} (14) & H_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}} = α X . D [{log}_{2} (1 + \frac{\frac{p_{tx} E_{t}}{R} | d_{k, {q_{1}, q_{2}, \dots q_{E_{t}^{opt}}} p_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}, k}} |^{2}}{\frac{p_{tx} E_{t}}{B} | \sum_{l \neq k} g_{k, {q_{1}, q_{2}, \dots q_{E_{t}^{opt}}} P_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}, l}} |^{2} + E_{0} X})] \end{matrix}$

In Eq. (11), the optimum AS for the capacity of the channel as well as EE were equivalent, since $E_{t}^{opt}$ was formerly elected from Eq. (13). Consequently, $p_{sm}$ is not dependent on AS. For the finest TAS, $E_{t}^{opt}$ column with better EE is elected as shown by Eq. (15), in which, each possible amalgamation of $E_{t}^{opt}$ antenna is given by L. $\begin{matrix} (15) & {q_{1}, q_{2}, \dots q_{E_{t}^{opt}}} = {arg max}_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}} \frac{H_{{q_{1}, q_{2}, \dots q_{E_{t}^{opt}}}}}{p_{sum}} \end{matrix}$

3.3. Computation of secrecy rate

The maximum rate of broadcast to target from source, where, a hacker is not capable of getting the data is termed as secrecy capacity $(A_{s})$ . $A_{s}$ is calculated as exposed in Eq. (16), in which, ${[x]}^{+} = max {0, x}$ , $A_{h}$ specifies the attainable rate above the major channel as exposed in Eq. (17), in which, $ρ_{m}$ corresponds to mean SNR at every receiving antenna, $M_{h}$ corresponds to major channel matrix, $Q_{h \times h}$ corresponds to the power controller matrices. Equation (16), $A_{e}$ corresponds to the reachable rate against the eavesdropped channel as exposed in Eq. (18), wherein $M_{e}$ corresponds to the eavesdropper channel matrix. $\begin{array}{c} (16) & A_{s} = {[A_{h} - A_{e}]}^{+} \\ (17) & A_{h} = log | I + ρ_{m} M_{m} Q M_{h}^{M} | \\ (18) & A_{e} = log | I + ρ_{e} M_{e} Q M_{e}^{M} | \end{array}$

Therefore, the achievable rate of secrecy $A_{s} (X)$ is revealed in Eq. (19), wherein, S corresponds to the dependence of $A_{s} (X)$ on TAS protocol, ${\tilde{M}}_{e}$ and ${\tilde{M}}_{h}$ corresponds to an eavesdropper and major channels in that order. ${\tilde{M}}_{h}$ corresponds to $N \times L$ matrix with column $m_{w 1, h}, \dots m_{w L, h}$ . $\begin{matrix} (19) & A_{s} (X) = {[log \frac{| I + ρ_{h} {\tilde{M}}_{h} {\tilde{M}}_{h}^{M} |}{| I + ρ_{e} {\tilde{M}}_{e} {\tilde{M}}_{e}^{M} |}]}^{+} \end{matrix}$

4. CA-PO based optimal selection of TA in M-MIMO

Solution Encoding: The suggested approach chooses the optimal TAs via the CA-PO algorithm and it analyses ‘which antenna should be selected. For optimum TAS, the antenna selection vector q is given as input to CA-PO, and its length relies upon the count of the antenna $C_{t}$ . In addition, the objective $(Oj)$ set for CA-PO is exposed in Eq. (20), in which, $Ef$ corresponds to efficiency and $N (A_{s})$ corresponds to standardized secrecy rate. $\begin{matrix} (20) & Oj = Minimize (\frac{1}{Ef + N (A_{s})}) \end{matrix}$

4.1. Procedure of CA-PO algorithm

The POA results from inconsiderable solutions, simple execution and few parameters, however, the exactness is somewhat low [31]. Further, coatis have more escape alternatives while pursuing a physical effort approach, which improves the algorithm’s exploratory power and its capacity to escape local optima. Thereby, we combine the theory of COA [8] with POA to lessen the limitations of conservative POA. The hybrid optimization strategy enhances the ability to problem-solve with an increased convergence rate than the single model.

POA is an optimization that depends on the populations of pelicans. Every character in a populace offers a feasible solution. The POA members are assigned as in Eq. (21). $\begin{matrix} (21) & N_{i, j} = f_{j} + ran ({up}_{j} - {lp}_{j}), i = 1, 2, \dots G, j = 1, 2, \dots W \end{matrix}$

In Eq. (21), $N_{i, j}$ corresponds to jth variable offered by ith solution, G corresponds to member count, W corresponds to problem variable count, $ran$ corresponds to random numeral, ${lp}_{j}$ and ${up}_{j}$ corresponds to upper and lower limits.

The hunting method of POA has the following steps:

Exploration Phase:

The location of prey is arbitrarily created which is considered a vital element of POA. This enhanced the POA’s capability to accurately assess the issue-resolving domain. Equation (24) characterizes the immigration of the pelican to its targeted prey. $\begin{matrix} (22 a&b) & N_{new 2} = N_{i, j}^{κ_{1}} = \{\begin{array}{ll} N_{i, j} + ran (κ_{j} - I . N_{i, j}), & T_{κ} < T_{i}; \\ N_{i, j} + ran (N_{i, j} - κ_{j}), & else \end{array} \end{matrix}$

As per CA-PO, Eq. (22 a&b) is modified by combining the concept of COA as shown in Eq. (23 a&b). As per CA-PO, if $T_{κ} < T_{i}$ , update is done using improved POA Eq. (23 a&b)(a), else, the update is done using improved COA as in Eq. (23 a&b)(b). In Eq. (23 a&b)(b), r corresponds to random integer, ${Iguana}_{i}^{G}$ corresponds to iguana location. $\begin{matrix} (23 a&b) & N_{new 2} = N_{i, j}^{κ_{1}} = \{\begin{array}{ll} N_{i, j} + ζ . ran (κ_{j} - I . N_{i, j}), & T_{κ} < T_{i}; \\ N_{i, j} + r (N_{i, j} - {Iguana}_{i}^{G}) - Y . D ζ, & else \end{array} \end{matrix}$ $\begin{array}{c} (24) & ζ = 5 - (t \times (\frac{5}{t_{max}})) \\ (25) & Y = 2 ζ . r d_{2} - θ \\ (26) & θ = sin (\frac{π . t}{2 . t_{max}} + π) . r \\ (27) & D ζ = | G . N_{i, j} - N_{best} | \\ (28) & G = 2 . r d_{2} \end{array}$

In Eq. (23 a&b), I lies among 1 or 2, $N_{i, j}^{κ_{1}}$ corresponds to new ith pelican position, $T_{κ}$ corresponds to objective and $κ_{j}$ corresponds to the location of prey. Here, I is randomly chosen. A new position is allowable in the suggested POA if the goal is met. This update is shown in Eq. (29). $\begin{matrix} (29) & N_{i} = \{\begin{array}{ll} N_{i}^{κ_{1}}, & T_{i}^{κ_{1}} < T_{i}; \\ N_{i}, & else \end{array} \end{matrix}$

In Eq. (29), $N_{i}^{κ_{1}}$ corresponds to the novel position and $T_{i}^{κ_{1}}$ corresponds to the objective.

Exploiting phase:

The hunting behavior during the exploitation stage is provided in Eq. (30), wherein, $N_{i, j}^{κ_{2}}$ corresponds to the new position, Z = 0.2, $Z (1 - \frac{t}{t_{max}})$ corresponds to neighboring radii of $N_{i, j}$ , t and $t_{max}$ corresponds to iteration counts, and utmost iteration counts. $\begin{matrix} (30) & N_{i, j}^{κ_{2}} = N_{i, j} + Z (1 - \frac{t}{t_{max}}) . (2 . ran - 1) N_{i, j} \end{matrix}$

Equation (31) shows the novel position of the pelican, wherein, $T_{i}^{κ_{2}}$ corresponds to the objective at this phase. $\begin{matrix} (31) & N_{i} = \{\begin{array}{ll} N_{i}^{κ_{2}}, & T_{i}^{κ_{2}} < T_{i}; \\ N_{i}, & else \end{array} \end{matrix}$

Hybrid Mutation strategy [ 11 ]: This strategy involves the combination of Gaussian and Cauchy mutation. The Gaussian mutation is modelled as in Eq. (32). $\begin{matrix} (32) & N_{i, j} (t + 1) = N_{i, j} (t + 1) + C_{i, j}^{1} . {Gau}_{i, j} (φ_{i, j}, γ_{i, j}) \end{matrix}$

Cauchy mutation is modelled as in Eq. (33), $\begin{matrix} (33) & N_{i, j} (t + 1) = N_{i, j} (t + 1) + C_{i, j}^{2} . {Cau}_{i, j} (φ_{i, j}, γ_{i, j}) \end{matrix}$

The resulting hybrid mutation strategy is modelled as in Eq. (34), $\begin{aligned} K_{i, j} (t + 1) & = N_{i, j} (t + 1) + w e_{i, j}^{1} C_{i, j}^{1} . {Gau}_{i, j} (φ_{i, j}, γ_{i, j}) \\ (34) & + w e_{i, j}^{2} C_{i, j}^{2} . {Cau}_{i, j} (φ_{i, j}^{1}, γ_{i, j}^{1}) \end{aligned}$

Here, ${Gau}_{i, j} (φ_{i, j}, γ_{i, j})$ and ${Cau}_{i, j} (φ_{i, j}^{1}, γ_{i, j}^{1})$ denotes Gaussian as well as Cauchy distribution, $(φ_{i, j}, γ_{i, j})$ and $(φ_{i, j}^{1}, γ_{i, j}^{1})$ denotes mean and variance of Gaussian as well as Cauchy respectively and $w e_{i, j}^{1} + w e_{i, j}^{2} = 1$ . Algorithm 1 shows the pseudo-code of CA-PO. $\begin{array}{c} (35) & C_{i, j}^{1} = ϕ_{i, j} . e^{(α . Υ (0, 1) + β . Υ_{j} (0, 1))} \\ (36) & C_{i, j}^{2} = γ_{i, j} . e^{(α^{'} . Υ (0, 1) + β^{'} . Υ_{j} (0, 1))} \\ (37) & α = \frac{1}{\sqrt{2 n}} \\ (38) & β = \frac{1}{\sqrt{2 \sqrt{n}}} \end{array}$

Algorithm 1:

Pseudocode for CA-PO

4.2. Complexity analysis

This subsection computes the suggested hybrid CA-PO computational complexity. Four aspects emphasize the computational complexity of the proposed POA: initializing the algorithm, assessing the fitness function, generating prey, and updating the solution. The initialization steps of the algorithms have an $O (N)$ computational complexity. Every member of the population assesses the objective function in both stages during every iteration. Therefore, $O (2 \cdot T \cdot N)$ is the computing complexity of the fitness function assessment. The computational complexity of generating prey is $O (T) + O (T \cdot m)$ , since prey is created and assessed at each iteration. The number of N population members with m dimensions needs to be updated twice in each cycle. As a result, the solutions of COA is given to POA and the updated computational complexity is $O (2 \cdot T \cdot N \cdot m)$ . Thus, the overall computational complexity of the proposed hybrid CA-PO is equal to $O (N + T \cdot (1 + m) \cdot (1 + 2 \cdot N))$ .

5. Results and discussions

5.1. Simulation setup

The developed CA-PO-based TAS for the M-MIMO system was done in MATLAB. Consequently, the examination was done using 2 setups.“The first setup was $p_{tx} = 40 W$ , $y u (V flop / A) = 5 V flop / A$ , $p_{{RF}_{front}} = 975 m W$ and the 2nd setup was $p_{tx} = 10 W$ , $p_{sum 1} y u (V flop / A) = 50 V flop / A$ , $p_{{RF}_{front}} = 97.5 m W$ ”. The developed CA-PO approach was evaluated over DMOA, COA, MRFO, POA and BEA. The algorithm parameters is illustrated in Table 2.

Table 2
Algorithm parameters

Algorithm Parameters and values

DMOA Variables Lower Bound $= - 10$

Variables Upper Bound = 10

D = 0.16;

Maximum Number of Iterations = 25

Population Size = 100

nBabysitter = 2

COA population size = 10;

chromosome length = 1000

itermax = 50;

MRFO Maximum Iterations = 1000

PopSize = 50

FunIndex = 5

POA population size = 10

setting minimum = 0.1

itermax = 50

BEA C = 0.955;

population size = 10;

itermax = 50

CA-PO No of transmiter = 1000

population size = 10

chromosome length = nt

setting minimum = 0.1*ones(1,ch_len)

Setting maximum bound = ones(1,ch_len)

itermax = 50

Algorithm	Parameters and values
DMOA	Variables Lower Bound $= - 10$
Variables Upper Bound = 10
D = 0.16;
Maximum Number of Iterations = 25
Population Size = 100
nBabysitter = 2
COA	population size = 10;
chromosome length = 1000
itermax = 50;
MRFO	Maximum Iterations = 1000
PopSize = 50
FunIndex = 5
POA	population size = 10
setting minimum = 0.1
itermax = 50
BEA	C = 0.955;
population size = 10;
itermax = 50
CA-PO	No of transmiter = 1000
population size = 10
chromosome length = nt
setting minimum = 0.1*ones(1,ch_len)
Setting maximum bound = ones(1,ch_len)
itermax = 50

5.2. Analysis of capacity of CA-PO vs conventional algorithms

Figure 2 shows the analysis of capacity (bps/w) using the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA. Here, analysis is performed under 2 setups for Zero Forcing (ZF) and MF by changing the user counts from 5 to 40. The capacity of the developed CA-PO technique should be high for better system performance. When the count of user is less, the capacity of the system is less for developed CA-PO as well as existing DMOA, COA, MRFO, POA and BEA. However, with the increase in user count, the system capacity increased gradually. However, developed CA-PO shows high capacity over DMOA, COA, MRFO, POA and BEA. For set up 1, the ZF shows a high capacity of 4.1 × $10^{8}$ , while, DMOA, COA, MRFO, POA and BEA show a relatively lower capacity of 2.1 × $10^{8}$ , 2.1 × $10^{8}$ , 2.1 × $10^{8}$ , 2.2 × $10^{8}$ and 2.1 × $10^{8}$ , when count of user = 40.

Likewise, the system capacity of the adopted CA-PO technique over DMOA, COA, MRFO, POA and BEA for ZF and MF for 2nd set-up is revealed in Fig. 2(c and d). In Fig. 2(d), the developed CA-PO technique for MF has a higher capacity of 8.8 × $10^{8}$ . On the other hand, the DMOA, COA, MRFO, POA and BEA techniques show a relatively lower capacity of 5.8 × $10^{8}$ when the count of users = 40. The result shows that the capacity of the proposed system is improved. The better system capacity is due to the newly introduced hybrid CA-PO algorithm, which helps in optimally choosing the transmit antenna.

Fig. 2.

Analysis of capacity for optimal TAS in M-MIMO systems for (a) ZF (b) MF for setup 1 and (c) ZF (d) MF for setup 2.

5.3. Analysis of EE of CA-PO vs conventional algorithms

The EE analysis attained by means of the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA is explained here. The estimation is done for varied users from 5 to 40. In Fig. 3, the developed CA-PO technique has attained higher EE for both ZF and MF over DMOA, COA, MRFO, POA and BEA techniques. When the user count is 5, EE of the system is less for developed CA-PO as well as existing DMOA, COA, MRFO, POA and BEA. However, with the increase in user count, the EE gets increased gradually. However, developed CA-PO shows high EE over DMOA, COA, MRFO, POA and BEA.

Particularly, the developed CA-PO technique for ZF for set up 1 has a high EE of 0.975; whereas, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively lower EE of 0.976 when the user count is 40. Also, the developed CA-PO technique for MF for set up 2 has got a high EE of 0.976; whereas, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively lower EE of 0.968. In addition, for ZF for set up 2, the EE of the developed CA-PO technique has got a higher value of 0.98, whereas DMOA, COA, MRFO, POA and BEA also gained a high EE of 0.98 when the user count is 40. The better EE is owing to the introduction of a novel hybrid CA-PO that helps in selecting the transmit antenna optimally. Thus the proposed model helps in reducing power consumption.

Fig. 3.

Analysis of relative EE for optimal TAS in M-MIMO systems for (a) ZF (b) MF for setup 1 and (c) ZF (d) MF for setup 2.

5.4. Analysis of TAS count of CA-PO vs conventional algorithms

Table 3 and Table 4 present the optimal count of TAs chosen using the developed CA-PO technique and existing DMOA, COA, MRFO, POA and BEA techniques for MF and ZF respectively. The analysis is done for varied user counts from 5, 10, 15, 20, 25, 30, 35 and 40. The finest count of TAs chosen by the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA for MF and ZF. In addition, Table 3 shows the finest count of TAs chosen by the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA for MF and ZF for 2nd set-up. This betterment is due to the deployment of CA-PO method, which helps in optimally selecting the transmit antenna.

Table 3
Optimal TA count in M-MIMO systems for setup 1

Methods 5 10 15 20 25 30 35 40

Match filtering

DMOA 4932 5031 4966 4991 4985 4917 5027 4961

COA 5028 4999 5006 4994 5089 5060 5051 4974

MRFO 4110 4094 3998 4054 4030 4126 4087 4002

POA 4646 4988 4992 5027 5068 5044 4947 5018

BEA 4993 4999 5059 5016 4970 5044 5037 5011

CA-PO 5045 5766 6834 6826 5973 6899 6955 6804

Zero forcing

DMOA 5067 4998 4916 5032 5000 4986 4974 4939

COA 4967 5025 4926 5024 5031 5097 5045 5014

MRFO 4223 4692 4127 4019 3971 4155 4111 4016

POA 4993 4873 5034 5048 4975 5022 5029 5027

BEA 5017 5053 5011 5018 4876 5093 5016 4937

CA-PO 5074 5065 6862 6835 6952 6011 7086 6773

Methods	5	10	15	20	25	30	35	40
Match filtering
DMOA	4932	5031	4966	4991	4985	4917	5027	4961
COA	5028	4999	5006	4994	5089	5060	5051	4974
MRFO	4110	4094	3998	4054	4030	4126	4087	4002
POA	4646	4988	4992	5027	5068	5044	4947	5018
BEA	4993	4999	5059	5016	4970	5044	5037	5011
CA-PO	5045	5766	6834	6826	5973	6899	6955	6804
Zero forcing
DMOA	5067	4998	4916	5032	5000	4986	4974	4939
COA	4967	5025	4926	5024	5031	5097	5045	5014
MRFO	4223	4692	4127	4019	3971	4155	4111	4016
POA	4993	4873	5034	5048	4975	5022	5029	5027
BEA	5017	5053	5011	5018	4876	5093	5016	4937
CA-PO	5074	5065	6862	6835	6952	6011	7086	6773

Table 4

Optimal TA count in M-MIMO systems for setup 2

Methods	5	10	15	20	25	30	35	40
Match filtering
DMOA	4932	5031	4966	4991	4985	4917	5027	4961
COA	5028	4999	5006	4994	5089	5060	5051	4974
MRFO	9138	9075	9053	9042	9035	9030	9026	9024
POA	5045	4988	4992	5027	5068	5044	4947	5018
BEA	4993	4999	5059	5016	4970	5044	5037	5011
CA-PO	9144	9082	9059	9045	9036	9031	9027	9024
Zero forcing
DMOA	5074	4998	4916	5032	5000	4986	4974	4939
COA	4967	5025	4926	5024	5031	5097	5045	5014
MRFO	5067	9078	9054	9042	9035	9030	9027	9024
POA	4993	5065	5034	5048	4975	5022	5029	5027
BEA	5017	5053	5011	5018	4876	5093	5016	4937
CA-PO	9140	9078	9059	9045	9037	9031	9027	9024

5.5. Analysis of secrecy rate of CA-PO vs conventional algorithms

The analysis of the secrecy rate using the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA techniques is described in Fig. 4. The secrecy rate should be high for better efficiency of the system. Diverse secrecy rates were achieved for diverse user counts. At the initial count of users, the secrecy rates are less for both setups, however, the secrecy rates are increased with the rise in user count.

Particularly, the developed CA-PO technique for MF for set up 1 has got a high secrecy rate of 7.6323; whereas, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively less secrecy rate of 7.6319 when the user count is 40. Also, the developed CA-PO technique for MF for set up 2 has got a high secrecy rate of 7. 6323, while, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively less secrecy rate of 7.6319. Hence, it is evident that the proposed model is highly secure in MIMO communications. The high secrecy rate is owing to the introduction of a novel hybrid CA-PO that aids in optimally selecting the transmit antenna.

Fig. 4.

Analysis on secrecy rate for optimal TAS in M-MIMO systems (a) ZF (b) MF for setup 1 and (c) ZF (d) MF for setup 2.

5.6. Convergence analysis

The analysis on convergence using the developed CA-PO technique over DMOA, COA, MRFO, POA and BEA techniques is described in Fig. 5. In Fig. 5(a), the convergence probability for set up 1 is high for the developed CA-PO algorithm over other compared algorithms. Likewise, in Fig. 5(b), the convergence probability is high for the developed CA-PO algorithm over others for set-up 2. The convergence probability for both setups lies between 0.92 and 0.93 approximately. This shows that the convergence probability of the developed CA-PO algorithm is high to get minimum fitness as specified in Eq. (20).

Fig. 5.

Convergence analysis in M-MIMO systems (a) setup 1 and (b) setup 2.

5.7. Analysis of computational time

The computational time of the proposed CA-PO method in comparison to the existing algorithms is portrayed in Table 5. On seeing the results in Table 5 it is noticed that the adopted CA-PO method takes very less time to compute when compared with the traditional models. The computational time of the suggested method is 54.20%, 19.14%, 41.82%, 12.61%, and 32.28% better than DMOA, COA, MRFO, POA and BEA techniques. The computational analysis of hybrid CA-PO is lower because in this work the updation of COA is replaced by POA. Hence for a hybrid CA-PO algorithm, the computational time is high.

Table 5
Computational time

Algorithms Time (sec)

DMOA 210.10

COA 119.01

MRFO 165.410

POA 110.120

BEA 142.102

CA-PO 96.23

Algorithms	Time (sec)
DMOA	210.10
COA	119.01
MRFO	165.410
POA	110.120
BEA	142.102
CA-PO	96.23

6. Conclusion

This work developed a novel CA-PO for selecting the optimal TA by considering efficiency as well as secrecy rate. Together with this, the CA-PO algorithm makes the decision on which antenna to be elected. At last, the supremacy of CA-PO-based TAS was proven from the analysis regarding secrecy rate and EE analysis. At the initial count of users, the secrecy rates are less for both setups, however, the secrecy rates were increased with the rise in user count. Particularly, the developed CA-PO technique for ZF for set up 1 has a high secrecy rate of 7.6323; whereas, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively less secrecy rate of 7.6319 when the user count was 40. Also, the developed CA-PO technique for ZF for set up 2 has got a high secrecy rate of 7.6323, while, the DMOA, COA, MRFO, POA and BEA techniques have got a relatively lower secrecy rate of 7.6319. In the future, massive antenna arrays can be attained with excellent spatial multiplexing and array gains. This trend is being further accelerated by new concepts such as intelligent surfaces and cell-free massive MIMO.

Conflict of interest

The authors have no conflict of interest to report.

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Transmit antenna selection in M-MIMO system using metaheuristic aided model

Abstract

Keywords

2. Literature survey

2.1. Related works

2.2. Problem gaps

3. System model

3.2. Optimal TAS

3.3. Computation of secrecy rate

4. CA-PO based optimal selection of TA in M-MIMO

4.1. Procedure of CA-PO algorithm

5. Results and discussions

5.1. Simulation setup

Table 5 Computational time Algorithms Time (sec) DMOA 210.10 COA 119.01 MRFO 165.410 POA 110.120 BEA 142.102 CA-PO 96.23

Conflict of interest

References

Table 5
Computational time

Algorithms Time (sec)

DMOA 210.10

COA 119.01

MRFO 165.410

POA 110.120

BEA 142.102

CA-PO 96.23