6G Communication Systems Utilizing Intelligent Reflective Surfaces for Improved Data Rates Based on AI

2.1. System Model

Here, we focus on one-to-one transmissions, where the source and destination each have a single antenna, where $h_{sd}\in \mathbb{C}$ represents the deterministic flat-fading channel, while the destination receives a signal as in (1).

A higher transmission capacity during wireless communication can be achieved by using additional technologies. An IRS is one such technology that can enhance the data transmission capacity of wireless communication systems. IRSs can outperform relays at processing deterministic flat-fading channels, channel estimation, and frequency-selective fading. In terms of performance, deterministic flat-fading channels achieve the best performance [27].

For clarity and ease of mathematical manipulation, we employ deterministic flat-fading channels in our simulations and analysis. However, real-world wireless environments frequently experience frequency-selective fading. This makes it more difficult to compare the performance of IRS and relays.

One of the best features of relays is their ability to perform tasks like equalization and amplification, which can reduce inter-symbol interference brought on by fading that only impacts specific frequencies. An IRS cannot perform this type of active equalization since it is passive. It works well in wideband systems if it can make a frequency-flat response or if it uses more advanced, frequency-selective phase shift designs, which is an area of active research. So, even though IRS technology has big benefits in terms of power efficiency and possible spatial gain over relays in flat-fading channels, using it in environments with strong frequency selectivity needs to be thought about carefully and may involve trade-offs compared to active relays. This indicates a promising avenue for future research.

This paper examines IRS properties and develops an optimized IRS model. Subsequently, we compare the standard and ( ${IRS}^o$ ) models to ascertain their strengths and weaknesses. To conduct this study, we created a comprehensive transmission diagram in the wireless communication system using either the standard IRS or the proposed ( ${IRS}^o$ ), as shown in Figure 1.

2.2. Performance of Analytics

Here, we analyze the three achievable rates discussed in the previous section. Uniquely, the phases of the channel elements ignore only the amplitudes used in the expressions. From now on, the notation $\left|h_{sd}\right|=\sqrt{{\beta }_{sd}}, \left|h_{sr}\right|=\sqrt{{\beta }_{sr}}, \left|h_{rd}\right|=\sqrt{{\beta }_{rd}}$ , and ${\displaystyle \frac{1}{N}}{\sum }_{n=1}^N \left|{\left[{ h}_{sr}\right]}_n{\left[{ h}_{rd}\right]}_n\right|=\sqrt{{\beta }_{IRS}}$ , will be introduced as a means of brevity within the IRS. However, the same notations will have different values with the ${IRS}^o$ compared to the IRS, as follows $\left|h_{sd}^o\right|=\sqrt{{\beta }_{sd}^o}, \left|h_{sr}^o\right|=\sqrt{{\beta }_{sr}^o}, \left|h_{rd}^o\right|=\sqrt{{\beta }_{rd}^o}$ , and ${\displaystyle \frac{1}{N^o}}{\sum }_{n^o=1}^{N^o} \left|{\left[h_{sr}^o\right]}_{n^o}{\left[h_{rd}^o\right]}_{n^o}\right|=\sqrt{{\beta }_{{IRS}^o}^o}$ , where these notations are used to represent the ${IRS}^o$ . The equations (2), (6), and (10) must be reformulated for more compact forms.

Equality will be obtained for $N=0$ with the IRS and for $N^o=0$ with ${IRS}^o$ , where $R_{\mathrm{IRS} }\left(N\right)$ is an increasing function of $N$ , while $R_{{IRS}^o}^o\left(N^o\right)$ is an increasing function of $N^o$ . It is evident that $R_{{IRS}^o}^o\left(N^o\right)>R_{\mathrm{IRS} }\left(N\right)\ge R_{\mathrm{SISO} }$ . As mentioned in [29] and elaborated on in [27,34], the rate increases as $\mathcal{O}\left({log}_2\left(N^2\right)\right)$ when $N$ becomes large. For this reason, for values of $N$ , the exponential growth rate presented in this paper is $\mathcal{O}\left({log}_2\left({N^o}^2\right)\right)$ . Consequently, it is not simple to evaluate the two cases of the IRS and the ${IRS}^o$ .

The radio transmission will work enhanced within this paper’s ( ${IRS}^o$ ) model compared to the IRS described in the previous literature. The transmission supported by the ( ${IRS}^o$ ) model has the highest rate for any $N>N^o\ge 1$ if ${{\beta }_{\mathrm{s}\mathrm{d}}>\beta }_{sd}^o>{\beta }_{sr}^o$ ; because the IRS-supported transmission provides the highest rate for $N\ge 1$ if ${\beta }_{sd}>{\beta }_{sr}$ compared to transmissions supported with any additional communications equipment [27], in which the ${IRS}^o$ model achieves the highest rate in the case of ${\beta }_{sd}^o\le {\beta }_{sr}^o<{\beta }_{sd}$ , while the IRS achieves the highest rate in the case of ${\beta }_{sd}\le {\beta }_{sr}$ .

As for the distinction between the transmission supported by the ( ${IRS}^o$ ) and IRS; the IRS supports the case that $R_{IRS}\left(N\right)>R_{\mathrm{SISO}}$ for $N\ge 1,$ yield the highest rate if $R_{\mathrm{I}\mathrm{R}\mathrm{S}}\left(N\right)>$   $R_{ace}$ ; where any additional communications equipment will be represented by $R_{ace}$ . Because the IRS supports multiple transmissions. $R_{SISO}>R_{ace}$ will cause this for ${\beta }_{sd}>{\beta }_{sr}$ . As a consequence of this, the result will be ${R_{IRS}\left(N\right)>R}_{SISO}>R_{ace}$ . But, this paper shows that, $R_{{IRS}^o}^o\left(N^o\right)>R_{\mathrm{SISO}}$ for $N>N^o\ge 1$ , in the case supported by the ${IRS}^o$ , yields the highest rate if and only if $R_{{IRS}^o}^o\left(N^o\right)>R_{IRS}\left(N\right)$ achieves. Due to transmission supported by the ${IRS}^o$ , ${{\beta }_{\mathrm{s}\mathrm{r}}>\beta }_{sd}^o>{\beta }_{sr}^o$ always occurs when $R_{SISO}<R_{IRS}\left(N\right)$ . Therefore, the result will be ( ${{R_{{IRS}^o}^o\left(N^o\right)>R}_{IRS}\left(N\right)>R}_{SISO}$ ) in this case. It can reduce the inequality, $R_{IRS}\left(N\right)>$   $R_{ace}$ by using (12), if the situation of ${\beta }_{sd}\le {\beta }_{sr}$ , with the IRS supporting the transmission. Furthermore, if the case of ${\beta }_{sd}^o\le {\beta }_{sr}^o<{\beta }_{sd}$ transmission supported by the ${IRS}^o$ , the inequality ${R_{{IRS}^o}^o\left(N^o\right)>R}_{IRS}\left(N\right)$ can be simplified by using (13).

A LOS between the ${IRS}^o$ , and IRSs are required to interpret the results correctly ${IRS}^o$ . Since any element in $h_{sr}$ has the same magnitude as any element in $h_{\mathrm{s}\mathrm{r}}$ , and any element in $h_{rd}$ has the same magnitude as any element in ${(h}_{rd}$ ), it follows that the ( ${IRS}^o$ ) elements all have the same magnitude as the essential IRS model elements. As a consequence of this, ${\beta }_{IRS}={\beta }_{sr}{\beta }_{rd}$ , and ${\beta }_{IRS}^o={\beta }_{sr}^o{\beta }_{rd}^o$ .

The higher rate of ( ${\beta }_{sd}>{\beta }_{sr}$ ) is provided by transmissions supported by the standard model of the IRS, as in [27]. It is contrary to what is in this paper; the highest rate of ${\beta }_{sd}>{\beta }_{sr}$ is provided by transmissions supported by the optimized model of the IRS.

The difference between $R_{IRS}\left(N\right)$ and $R_{\mathrm{S}\mathrm{I}\mathrm{S}\mathrm{O}}$ is negligible for most actual values of $N$ when the value is small for ${\beta }_{rd}$ , since $\sqrt{{\beta }_{sd}}\gg N\alpha \sqrt{{\beta }_{IRS}}=N\alpha \sqrt{{\beta }_{sr}{\beta }_{rd}}$ . However, the difference in this paper is between $R_{\mathrm{I}\mathrm{R}\mathrm{S}}\left(N\right)$ , $R_{SISO}$ and $R_{{IRS}^o}^o\left(N^o\right)$ is the smallest since $\sqrt{{\beta }_{sd}^o}\gg N^o\alpha \sqrt{{\beta }_{IRS}^o}=N^o\alpha \sqrt{{\beta }_{sr}^o{\beta }_{rd}^o}$ for most practical values of $N^o$ while ${\beta }_{rd}^o$ is the smallest number for the most practical values of ${\beta }_{rd}^o< {\beta }_{rd}$ . It should be noted that in wireless communications, −50 dB is considered a “large” channel gain. In cases where ${\beta }_{sd}\le {\beta }_{sr}$ , an IRS can result in a noticeable performance improvement. Conversely, when ${\beta }_{sd}^o\le {\beta }_{sr}^o<{\beta }_{sd}$ , an ( ${IRS}^o$ ) can offer a significantly better performance boost.

The coefficient $\alpha$ of the amplitude reflection, the channel gains ${\beta }_{sd},{\beta }_{sr}$ , and ${\beta }_{rd}$ , and the transmit SNR $p/{\sigma }^2$ from the right-hand side of (14), where we recall that ${\beta }_{IRS}={\beta }_{sr}{\beta }_{rd}$ . It is noted that $p\to \mathrm{\infty }$ (on the right) is essential $-\sqrt{{\beta }_{sd}}/\alpha \sqrt{{\beta }_{sr}{\beta }_{rd}}$ (on the left). However, the transmitted SNR $p^o/{\sigma }^2$ , the coefficient $\alpha$ of amplitude reflection, and the enhanced channel gains ${\beta }_{sd}^o,{\beta }_{sr}^o$ , and ${\beta }_{rd}^o$ , determine the enhanced value on the right-hand side of (15), where we recall that ${\beta }_{IRS}^o={\beta }_{sr}^o{\beta }_{rd}^o$ . It noted $-\sqrt{{\beta }_{sd}^o}/\alpha \sqrt{{\beta }_{sr}^o{\beta }_{rd}^o}$ (on the right) gets close to ${\beta }_{IRS}^o={\beta }_{sr}^o{\beta }_{rd}^o$ (on the left). It means that for each given, $p^o\to \mathrm{\infty }$ , the most significant rate at a high SNR ( $p/{\sigma }^2$ ) is achieved by the transmission supported by the IRS for any N. Conversely, the inequality in (14) reduces to (16).

Also, for any ( $N^o$ ), it stands to reason that the transmission with the ( ${IRS}^o$ ) will transmit at the most significant rate when the SNR ( $p^o/{\sigma }^2$ ), is high. Conversely, the inequality in (15) simplifies to (17).

The numbers $p\to 0$ and $p^o\to 0$ have different values, given that $p\to 0$ achieved with ${\beta }_{sd}⩽{\beta }_{sr}$ , while $p^o\to 0$ is achieved with ( ${\beta }_{sd}^o⩽{\beta }_{sr}^o<{\beta }_{sd}$ ), it can result in huge numbers. As an illustration, if $\alpha =1$ , ${\beta }_{rd}=-60 \mathrm{d}\mathrm{B}$ , ${\beta }_{sr}=-80 \mathrm{d}\mathrm{B}$ , and ${\beta }_{sd}=-110 \mathrm{dB}$ , the result is that (16) becomes $N>963$ .

Accordingly, the SNR and the number of elements determine whether a standard model for the IRS or an optimized model for the IRS is selected. It assumes throughout this study that both, ${\beta }_{IRS}$ and ${\beta }_{{IRS}^o}^o$ are independent of $N$ and $N^o$ , respectively.

In most cases, the ideal number of elements in Equations (18) and (19) is not a whole number. Hence, the closest integer, whether greater or smaller, can be used to approximate the true optimum. The SISO situation with N = 0 is the actual ideal value because the best value might potentially be damaging. So, $N^{opt\left(SISO\right)}=0$ .

Maximizing energy efficiency while adhering to the data rate ( $R_d$ ) limits may be accomplished with the assistance of the SISO, IRS, and ${\mathrm{I}\mathrm{R}\mathrm{S}}^{\mathrm{o}}$ , as shown by the findings from [27], where EE of SISO ( ${EE}_{SISO}$ ), EE of IRS ( ${\mathrm{E}\mathrm{E}}_{IRS}$ ) and EE of ${\mathrm{I}\mathrm{R}\mathrm{S}}^{\mathrm{o}}$ ( ${EE}_{{IRS}^o}^o$ ) determined by Equations (20)–(22).

Suppose the destination demands a particular $R_d$ . Then, suppose we use the formulas for the $R_{d}s$ in (11), (12), and (13). In that case, we can determine the transmission power requirements for each of the three possible communication setups.

Consequently, (22) is a non-convex optimization problem for the IRS. Since this optimization problem is non-convex, there is no conventional solution. Consequently, in this paper, we propose a novel artificial intelligence algorithm based on the DS-PSO technique, which will be discussed in the next section.

2.3. The Proposed AI Algorithm to Improve Performance

At (27), the IRS addresses the non-convex optimization problem via an AI algorithm based on the DS-PSO technique. It is a hybrid particle swarm optimization algorithm that integrates both static and dynamic methods. The conventional Particle Swarm Optimization (PSO) methodology employs a search space to commence the particle swarm. To keep an eye on the swarm’s behavior, each particle has a swarm subset, a neighborhood, a speed, and a randomly chosen position. In each iteration, every particle evaluates its current objective function value. Once the fitness of the current solution exceeds that of the particle’s current personal best ( ${Pos}_{best}$ ), the current position is deemed the new personal best ( ${Pos}_{best}$ ). The particle’s position and velocity are updated utilizing Equations (31) and (29) provided below. DS-PSO has a notable similarity to PSO algorithms since it amalgamates the topologies of both static and dynamic iterations of traditional PSO.

The distinguishing feature of DS-PSO is the implementation of two distinct topologies for particles: one for their dynamic neighborhood and another for their static neighborhood. Conversely, the additional dynamic designs prioritize the exploration of the search space over early convergence. A completely random topology is generated concurrently with the execution of the operation. Conversely, alternative dynamic PSO algorithms lose the exploitative characteristics of traditional PSO while employing static topologies.

Swarm particles are modifying their velocities ( $V$ ) and positions ( $Pos$ ) in accordance with Equations (30) and (31), influenced by the neighborhood bests ( $N_{pbest}$ ) across all topologies of the DS-PSO.

The velocity is denoted as $V_{par}\left(i\right)$ in the preceding equations, whereas $X_{par}\left(i\right)$ , signifies the particle’s (par) position at the current iteration. The particle, individual, dynamic, and static enhanced solutions identified to date in iteration (i) are denoted by ${Pos}_{par}\left(i\right)$ , $D_{parbest}\left(i\right)$ and $S_{parbest}\left(i\right)$ .

The DS-PSO algorithm’s main new idea, and what makes it different from other optimization methods like standard PSO or Genetic Algorithms (GA), is its hybrid topology. In traditional PSO, there is only one social network (like a global best). This can cause problems to converge too quickly when they are complex and have more than one mode, like IRS phase-shift optimization. DS-PSO, on the other hand, keeps two separate social networks for each particle at the same time: a stable static topology ( $S_{parbest}$ ) that preserves reliable social information and promotes consistent exploitation, and a randomly changing dynamic topology ( $D_{parbest}$ ) that injects novelty into the search process, preventing stagnation in local optima. This hybrid approach is designed to strike the ideal balance between exploitation (improving known good solutions) and exploration (searching for new areas of the solution space). Unlike other algorithms, DS-PSO adapts its search strategy naturally, making it ideal for the high-dimensional, non-convex optimization problem presented by IRS, where determining the optimal phase-shift configuration is crucial to achieving maximum energy efficiency.

The hybrid nature of DS-PSO, combining both static $S_{parbest}\left(i\right)$ and dynamic $D_{parbest}\left(i\right)$ Social topologies are its key adaptive strength. A major issue with metaheuristics is directly addressed by this design: striking a balance between exploration (finding new areas) and exploitation (improving areas that are already good).

Purely static topologies, such as ring structures, facilitate stable convergence, making them ideal for exploitation. However, it could cause convergence to a local optimum too quickly in challenging, multi-modal problems like IRS phase-shift optimization. Conversely, a purely dynamic topology is highly exploratory but may be aimless, which causes instability and slow convergence.

By not requiring you to select between these two plans, DS-PSO transforms the situation. By providing a consistent, long-range source of social information, the static topology helps people stay on course and prevents them from acting irrationally. In contrast, the dynamic topology adds interest and randomness to the search process. By allowing particles to receive assistance from various randomly assigned neighbors, this aids them in leaving local optima. The algorithm’s behavior is determined by the acceleration coefficients ( $C_1$ , $C_2$ and $C_3$ ). In situations where the fitness landscape is simpler and convex, the static component ( $C_3$ ) will provide consistent guidance, which will lead to fast and stable convergence. In very complicated, non-convex situations like our IRS optimization problem, the dynamic component ( $C_2$ )’s ability to explore becomes even more important. This lets the swarm find better phase-shift configurations that a purely static approach might miss.

To keep speeds from getting too fast, the constriction coefficient, ( $C_{\mathrm{c}}$ ), is usually set at about 0.7298438. In Equation (29), the acceleration coefficients ( $C_1$ ) and ( $C_2$ ) make particles more likely to be drawn to ${Pos}_{par}$ and $N_{parbest}$ , respectively. The total acceleration coefficient for standard PSO is 4.1, and the individual coefficients ( $C_1$ ) and ( $C_2$ ) are both 2.05. Also, the acceleration coefficients ( $C_1$ , $C_2$ and $C_3$ ) are used in Equation (30) to make particles more attracted to ${Pos}_{par}\left(i\right)$ , $D_{parbest}\left(i\right)$ and $S_{parbest}\left(i\right)$ , respectively. Each particle will attain optimal static, dynamic, and individual performance. Because of this, DS-PSO finds three acceleration coefficients instead of the two that the traditional PSO algorithm finds. The acceleration coefficients ( $C_1$ , $C_2$ and $C_3$ ) each give a value of 1.366666667, and they are set at 4.1/3.

To make research easier, the components of the velocity equation are multiplied by a vector of random values, $R_1$ , $R_2$ , and $R_3$ , that are limited to the range [0,1]. The search space is defined by the interval [ $V_{min}$ ; $V_{max}$ ], which shows the minimum and maximum values of the search space. Each element of $V_{par}$ must be within this range. The particle exhibits a preference for $D_{parbest}$ and $S_{parbest}$ , over $N_{parbest}$ , the optimal neighbors. Therefore, while evaluating the static and dynamic topologies of particles, this is the ideal solution [35,36,37].

The pseudocode flow of the sequence of operations of the DS-PSO algorithm is shown in [37] as a reference for implementation details.

Below is a pseudocode that visually represents the dual influence of static and dynamic topologies in DS-PSO. This format is designed to provide a step-by-step guide to the operation of the DS-PSO algorithm. The pseudocode has been streamlined to focus on explaining the intuition behind the hybrid topology and the key equations for IRS Phase-Shift Optimization, illustrating the process flow. The parameters used in simulating the algorithm are as shown in Table 1.

Traditional PSO employs a single social topology (e.g., a global best) to guide the swarm; this can lead to premature convergence in complex problems, such as IRS phase-shift optimization, where the search space is highly multimodal. The DS-PSO algorithm hybridizes this approach by maintaining two distinct social networks for each particle: a static topology (e.g., a ring or star structure) that preserves stable, long-range social information and promotes exploration, and a dynamic topology that randomly changes neighbors over iterations, preventing premature stagnation.

In the context of optimizing an IRS with N elements, each particle’s position represents a candidate set of phase shifts (θ₁, θ₂, ..., θ_N). A traditional PSO might become trapped in a local optimum, failing to find the optimal phase configuration that maximizes the SNR at the destination. On the other hand, the dynamic part of DS-PSO lets a particle get help from a random, different part of the swarm from time to time, which lets it "jump" out of a local valley. The static part makes sure that it still follows a stable path from its stable neighbors. This hybrid strategy works especially well for IRS optimization because it strikes a good balance between the need to thoroughly search the large phase-shift space (exploration) and the need to improve and focus on the best solution found (exploitation).

3.1. Transmit Destination

The 3GPP Urban Micro (UMi) model, as described in reference [38]. The carrier frequency is set at 3 GHz to depict the channel gains accurately. The line-of-sight (LOS) and non-line-of-sight (NLOS) Urban Microcell (UMi) models, specified for distances of 10 m or greater, are employed. Let us say that the antenna gains for the transmitter and receiver, measured in dBi, are $G_t$ and $G_r$ , respectively. It is possible to use UMi at both LOS and NLOS distances.

For the simulations in this study, we assume that the transmitter and receiver antennas ( $G_t$ and $G_r$ ) located between the source and the IRS have equal gains of 5 decibels of isotropic radiated power (dBi) within a distance of 100 m while disregarding shadow fading. Upon reaching the desired destination, the individual possesses a telephone with an omnidirectional antenna with a gain of 0 dBi.

The transmission in wireless communication networks is influenced by factors such as channel gain and distance. We made a detailed channel gain and distance diagram to study and model a wireless communication system that uses an IRS. This diagram is shown in Figure 2 for the wireless communication system supported by the IRS. The communication system model proposed in this study closely resembles the configuration depicted in Figure 2. However, it utilizes the improved IRS model instead of the standard IRS model and adopts the improved LOS. Figure 2 depicts the stationary positions of both the source and the IRS or ( ${IRS}^o$ ) proposed in this study. The simulations for this study assume the distances between the source and the standard IRS or ${IRS}^o$ , as depicted in Figure 2, respectively. The proposed distance between the source and the IRS d₁ is 70 m. The user/destination can be located within the range of the source as long as the distance between them (d₂) is greater than or equal to 10.

Figure 2 illustrates the support of the IRS in facilitating transmission within the wireless communication system by generating line-of-sight (LOS) channels. A standard LOS version generates two distinct line-of-sight (LOS) channels. The LOS between the source and the IRS is denoted as ${\beta }_{sd}$ , while the LOS between the IRS and the user or destination is denoted as ${\beta }_{rd}$ . Conversely, the NLOS version between the source and the user or destination generates a channel denoted as ${\beta }_{sd}$ . The Equation ${\beta }_{IRS}={\beta }_{sr}{\beta }_{rd}$ is used to represent the relationship between ${\beta }_{IRS}$ , ${\beta }_{sd}$ , and ${\beta }_{rd}$ .

In the NLOS case, the weak channel gain between the source and the user (or destination) means that an Intelligent Reflecting Surface (IRS) needs to be used to improve signal transmission in next-generation wireless communication networks. The IRS makes LOS channels that work better than NLOS channels. Also, as the distances get longer, the channel gain values with LOS go down, but they are still better than those with NLOS. This is why LOS properties were used in the design of a wireless communication system that was made easier by using an IRS, which had a lot of benefits.

As a result, using IRS in wireless communication networks has created two LOS channels. There is one channel that goes from the source to the IRS. On the other hand, the link between the IRS and the user or destination makes these networks work better when sending data.

The LOS channels within the model of ( ${IRS}^o$ ) will consist of two channels. The initial channel connecting the source and the model of ${IRS}^o$ is denoted as ${\beta }_{sr}$ . This channel’s channel is optimized by maximizing the LOS between the source and the ( ${IRS}^o$ ), denoted as ${\beta }_{sr}$ . The second channel between the ( ${IRS}^o$ ) and the user or destination is created by optimizing the LOS channel between the ( ${IRS}^o$ ) and the user or destination, denoted as ${\beta }_{rd}$ . The Equation can be simplified as ${\beta }_{{IRS}^o}^o$ = ${\beta }_{sr}^o$ and ${\beta }_{rd}^o$ .

The initial step in the simulation involves calculating the channel gain value ( ${\beta }_{sd}$ ) for the SISO case in the communication system depicted in Figure 2. This calculation uses Equation (32) due to its NLOS nature. The channel gains values ( ${\beta }_{rd}$ and ${\beta }_{sr}$ ) with the standard IRS of the communication system in Figure 2 can be calculated using Equation (32). These values are determined based on the distance d1 and the antenna gains ( $G_t$ , and $G_r$ ), between the source and the IRS; this is to determine the values of ${\beta }_{sd}$ and ${\beta }_{sr}$ . Furthermore, the channel gain values ( ${\beta }_{sr}^o$ and ${\beta }_{rd}^o$ ) are calculated using Equation (33) for the proposed ( ${IRS}^o$ ) model for the communication system. The channel gain using the improved IRS is the improved LOS version.

Given the superior performance of the optimized LOS configuration relative to the standard LOS version, it is reasonable to expect that the proposed IRS model in this study will achieve improved performance compared to the conventional IRS model. Thus, this study’s proposed ( ${IRS}^o$ ) can enhance the performance of 6G communication systems. This claim can be supported in this paper by using an IRS system performance evaluation measure. Therefore, this paper suggests implementing (energy efficiency compared to data rate) evaluation measures for IRS systems, specifically focusing on the standard IRS model and the proposed ( ${IRS}^o$ ) model that is optimized in this paper. A comparative analysis is then performed to compare the findings of this research with previous studies on (energy efficiency compared to data rate) in alternative IRS models.

3.2. Energy Efficiency Compared to Data Rate

The simulation involves evaluating the performance of the SISO case, the standard IRS model, and the proposed ( ${IRS}^o$ ) model based on their energy efficiency. In this paper, we determined the parameters associated with energy efficiency, including the quantity of the data rate, which is attributed to the significance of these parameters in enhancing the performance of the IRS. In this section, we aim to calculate energy efficiency values using the parameters from Table 2.

In the simulations presented in this paper, we will utilize the proposed algorithm, in addition to the LOS version discussed in Section 3.1, which has been improved.

Simulations were performed for the SISO case, the standard IRS model, and the proposed IRS model that is optimized in this study. The simulations compared energy efficiency in terms of data rate. Next, the findings of this study will be compared to previous research on energy efficiency, particularly in terms of data.

Calculating energy efficiency requires determining the total transmission power, which in turn requires calculating the needed transmission capacity and the number of elements within the IRS. Calculating the number of elements needed in the IRS involves determining its channel gain values, which provide an estimate of the overall channel performance. ( ${\beta }_{r\mathrm{d}}$ and β_sr) related to the IRS are essential in determining the number of reflective elements within the IRS. Therefore, we sought to use improved channel gain values. The proposed algorithm relates ( ${\beta }_{sr}^o{ \mathrm{a}\mathrm{n}\mathrm{d} \beta }_{rd}^o$ ) to the ( ${IRS}^o$ ) proposed in this paper.

To obtain the results of this study, the energy efficiency values for the SISO case, the standard IRS, and the ( ${IRS}^o$ ) proposed in this paper are calculated using Equations (20)–(22), respectively. Equations (23)–(25) are used to find the total transmission power values for the SISO cases, the standard IRS, and the ( ${IRS}^o$ ) proposed in this paper. Equations (26)–(28) are used to figure out how much power each SISO case needs, including the standard IRS and the ( ${IRS}^o$ ) proposed in this paper. Equations (18) and (19) can be used to figure out how many reflective elements are in both the standard IRS and the proposed ( ${IRS}^o$ ) model. It’s important to note that there are no reflective elements in the SISO case. The channel gains ( ${\beta }_{r\mathrm{d}}$ and β_sr) with the standard IRS of the communication system depicted in were determined using Equation (32). The channel gains values ( ${\beta }_{sr}^o$ and ${ \beta }_{rd}^o$ ) with the ( ${IRS}^o$ ). The performance of the communication system was determined using Equation (33). The channel gain values obtained from Equations (32) and (33) are included in Equations (18) and (19), respectively.