Related work

Routing electromagnetic beams through a coordinated network of hypersurfaces, namely reconfigurable/large intelligent surfaces (RIS/LIS) in an outdoor environment. To enable energy savings and improve security in wireless communications by providing a solution to achieve complete control of the wireless channel by confining most of the energy transmitted between the surfaces of the RIS by Optimized focal plane placement of RIS systems to maximize pointing hop distance and minimize energy loss [Reference Salah, Elsherbini and Omer24]. The benefits of FD transmission and RISs in a two-way communication system are investigated. The focus is on the mathematical expressions of outage probability and ergodic capacity of an RIS-FD system with a direct link between two stations and multiple reflective paths established by RIS stations over a Rayleigh fading channel. The influence of system parameters such as the number of RISs and the number of reflective elements is used to fully consider the performance of the system [Reference Nguyen, TM, PT and TN25]. In [Reference Yang, Cao, Huang, Yuen, Qian and Di Renzo26], The study introduced the concept of intelligent spectrum learning which uses a convolutional neural network to help RISs infer interfering signals from incident signals. The goal was to maximize SINR by dynamically configuring the binary active/inactive state of the RIS elements. Emphasis has been placed on enhancing wireless communications using RIS to improve the SINR for users. Multiple IRSs Auxiliary systems are designed to improve the UE signal-to-noise ratio (SNR) of millimeter-wave (mm-Wave) wireless systems in densely blocked areas. Maximizing the SNR received for the UE was the goal by optimizing the PSs at successive IRS stations and precoding vectors at the BS, see [Reference Liang, Fan and Yue27]. The study was about enhancing physical layer security in wireless communications using IRS in challenging radio environments. The co-design of beamformers and an artificial noise covariance matrix at access points and phase shifters at IRS stations were investigated to maximize the system sum rate while limiting information leakage to potential eavesdroppers [Reference Yu, Xu, Sun, Ng and Schober28]. In [Reference Wang and Peng29], the concept of an active RIS is proposed to increase the capacity of a conventional cell-free network with the help of RIS. The study focuses on analyzing the energy-efficacy fairness (EEF) of a RIS-supported active cell-free network and formulating a problem to maximize the EEF. To address this, a joint beamforming and resource allocation (JBRA) using alternating optimization (AO). and fractional programming (FP) is proposed. In [Reference Papazafeiropoulos, Kourtessis and Chatzinotas10], The lowest possible SINR was studied, as was the impact of hardware impairments (HWIs), showing the better results of STAR-RIS compared to conventional RIS and highlighting the effects of HWIs. The others introduce the concept of Beyond Diagonal RIS (BD-RIS) as an advancement beyond the conventional RIS with diagonal PS matrices. They explain the modeling of BD-RIS based on the scattering parameter network analysis and classify BD-RIS by the mathematical characteristics of the scattering matrix, supported modes, and architectures. Then, they provide simulations to evaluate the sum-rate performance with different modes of BD-RIS. The BD-RIS aims to enhance wireless communications by providing high flexibility in wave manipulation, expanding coverage, facilitating deployment, and requiring fewer resolution bits and scattering elements [Reference Li, Member, Shen and Member30]. The impact of interference on SNR and signal quality was examined. It was observed that the SINR improved when multiple users were in close proximity, as noted in reference [Reference Alsawaf and Ayoob31].

The proposed model was based on several smart surfaces placed horizontally in two-dimensional. The transmitter connects directly to the first RIS and has no connection to the other RISs. The signal is sent from the transmitter to the first RIS, and then the signal is reflected to nearby users, or to the second RIS, which reflects the signal to nearby users, or to the third RIS, and so on. In other words, there is no direct transmission between the transmitter and the second and third RIS, and this leads to a defect in any RIS meaning that the signal does not reach the users. Increasing the distance traveled by the signal means significantly increasing path losses, especially when using mm-Wave frequencies [Reference Ma, Fang, Zhang, Guo and Yuan32].

The previous problems in [Reference Ma, Fang, Zhang, Guo and Yuan32] were solved through the model proposed in this work, which is based on three-dimensional (3D), the effect of the site of the RIS on the SINR of several users was examined. First, the effect of the distance of the RIS on the TX-User line, the effect of the height of the RIS, and the proposal of multiple RIS to improve the SINR for users were studied. Finally, the effect of SINR on the size of the RIS was tested.

System model

A wireless communication model with RIS in a mm-Wave environment is proposed. The proposed model contains one transmitter and five users at the receiving end. The LOS path between the transmitter and each user is non-existent (Rayleigh channel) due to blocking or any barriers. New paths are created between the transmitter and users using the IRS, which changes a non-LOS (NLOS) path to LOS for communication. IRS reflects the transmitted signal falling on it; in other words, it redirects the signal sent to the receiver. The IRS is rectangular and consists of passive elements (Nx × Ny). These elements are placed on the x–y axis and separated by dx and dy as shown in Figure 1. An intelligent surface is composed of numerous passive reflective elements. Essentially, it is an energy-free, inert, rectangular reflective surface that reflects electromagnetic signals from the transmitter back to the users without providing any additional gain. According to Fig. 1, the system model’s specifics, including basic dimensions and symbols, are as follows: The horizontal distance between Tx and RIS is R1. Symbols R21, R22, R23, R24, and R25 represent the horizontal distance between RIS and diverse users. The symbol Rts represents the TX-RIS diagonal dimension. Finally, the symbol Rsr represents the diagonal dimension between RIS and user sites, and the symbol x represents the distance between the RIS location and the TX-Users line. The model significantly depends on the TX, RIS, and user heights, denoted as ht, hs, or L ₁, and hu, respectively. The transmitted signal in NLOS is subjected to incidence and reflection angles θi and θr, respectively. We proposed three RISs to improve the SINR. Figure 2 shows different interspaces separate multiple RIS sites, namely L ₁, L ₂, and L ₃. L ₁ acts as the distance between the ground and the first RIS, meaning the height of the first RIS; L ₂ refers to the interspace between the first RIS and the second RIS; and L ₃ depicts the interspace between the second RIS and the third RIS. In other words, it uses the RISs at three different heights. The proposed model assumptions including:

1. a) Three vertically placed RIS communicate directly with both the transmitter and receiver.

2. b) The proposed model works in 3D.

3. c) The effective area of the RIS was taken into the model and represents the number of elements, and this is what several previous researches have relied on [Reference Trichopoulos, Theofanopoulos, Kashyap, Shekhawat and Modi33, Reference Brancati, Chukhno, Chukhno and Araniti34].

4. d) SINR of 15 dB is certified and supports QAM256 modulation type as per international standard.

Figure 1. System model supported by a single RIS.

Figure 2. The proposed system model supported by three RIS.

The validity of the proposed system and the optimal RIS location are verified if the maximum value of the SINR is determined. In the light of the analytical calculations, it is easy to find that:

(1)\begin{equation}Rts = \sqrt {R{1^2} + {x^2} + {{\left( {hs - ht} \right)}^2}} \end{equation}

(2)\begin{equation}Rsr = \sqrt {R{2^2} + {x^2} + {{\left( {hs - hu} \right)}^2}} \end{equation}

(3)\begin{equation}\theta i = {\tan ^{ - 1}}\left( {\frac{{\sqrt {R{1^2} + {{\left( {hs - ht} \right)}^2}} }}{x}} \right)\end{equation}

(4)\begin{equation}\theta r = {\tan ^{ - 1}}\left( {\frac{{\sqrt {R{2^2} + {{\left( {hs - hu} \right)}^2}} }}{x}} \right).\end{equation}

When positioning the RIS between TX and RX, the received power will be determined using the formula below [Reference Trichopoulos, Theofanopoulos, Kashyap, Shekhawat and Modi33]:

(5)\begin{equation}Pr = \frac{Pt \gt Gr{\lambda ^2}\sigma}{{{{\left( {4\pi } \right)}^3}Rt\,{s^2}Rs\,{r^2}}}\end{equation}

where Pt is the transmitted power of TX, the gains of the TX and RX antennas are denoted as Gt and Gr, respectively. The transmitted electromagnetic wave has a wavelength of λ. TX-RIS and RIS-User have different dimensions, which are Rts and Rsr. The cross-section of the RIS that resembles a planar or rectangular surface is σ, which can be calculated as follows:

(6)\begin{equation}\sigma = \frac{{4\pi \eta Cos\theta iCos\theta r{A^2}}}{{{\lambda ^2}}}.\end{equation}

The relative power of signals received by the RIS compared to signals transmitted by it is η, which represents the efficiency of the RIS [Reference Trichopoulos, Theofanopoulos, Kashyap, Shekhawat and Modi33]. In RIS, A is the area. For the signal transmitted, θi and θr denote the incidence and reflected angles, respectively. The RIS is considered to be composed of passive elements with η = 1 in this paper [Reference Qeryaqos and Ayoob21]. The form of the first equation is as follows when (2) is substituted into (1):

(7)\begin{equation}Pr = \frac{{Pt{\text{ }} \gt {\text{ }}Gr{\text{ }}\eta {\text{ }}{A^2}Cos\theta i{\text{ }}Cos\theta r{\text{ }}}}{{{{\left( {4\pi } \right)}^2}Rt\,{s^2}Rs\,{r^2}}}.\end{equation}

IUI is the term used to describe the interference that multiple users in one region cause to a single user’s received signal. IUI is the overlap between a user and another user close to him only and not with all users. IUI happens when the RIS sends signals to several users. The main beam of another user may be interfered with by the Side-Lobe Level of that user’s radiation pattern [Reference Tahkoubit, Cassiau, Demmer and Doré35]. For this reason, the overlap of the user on the right side and the one on the left side was taken only. In this case, the signal is directed specifically at a certain receiver through the use of beamforming technology. When this technology is employed, user interference is reduced. However, the consequence of bringing users closer together still results in IUI. The idea of deploying the RIS at three different heights can help to resolve this issue. In the case of a single RIS, the beam coverage for users close to each other is almost equal, meaning the beam coverage is overlapping. When three RIS is installed, the beam coverage for users changes in proportion to their distance and the height of the RIS. Thus, the beam coverage for users becomes different, which reduces interference. According to the Fig. 3 below:

Figure 3. Inter-user interference (IUI) in RIS.

The transmitting antenna is a planar array antenna, with M × N elements oriented toward the x and y axes, and the distance between antenna elements is represented by the values dx and dy, which are equal to λ/2. Let λ be the wavelength and k = 2π/λ. The excitation current for the matrix factor elements for the transmitter antenna was calculated using Taylor’s method for analyzing and designing antennas. The current amplitudes are Im and In. If the distribution pattern of the excitation current in every row is the same, then the array radiation factor in every direction can be expressed as follows [Reference Balanis36]:

\begin{equation*}A{F_n} = A{F_X}.A{F_y}\end{equation*}

(8)\begin{equation} = \left( {\frac{1}{M}{\text{ }}\frac{{{I_m}{\text{ }}sin\left( {\frac{M}{2}{\text{ }}{\psi _x}} \right)}}{{sin\left( {\frac{{{\psi _x}}}{2}{\text{ }}} \right)}}} \right){\text{ }}\left( {\frac{1}{N}{\text{ }}\frac{{{I_n}{\text{ }}sin\left( {\frac{N}{2}{\text{ }}{\psi _y}} \right)}}{{sin\left( {\frac{{{\psi _y}}}{2}{\text{ }}} \right)}}} \right)\end{equation}

where

\begin{equation*}{\psi _x} = K{\text{ }}{d_{x{\text{ }}}}\sin \theta \cos \phi + {\beta _x}\end{equation*}

\begin{equation*}{\psi _y} = K{\text{ }}{d_{y{\text{ }}}}\sin \theta \cos \phi + {\beta _y}\end{equation*}

And

\begin{equation*}{\beta _x} = - K{\text{ }}{d_{x{\text{ }}}}\sin {\theta _o}\cos {\phi _o},\end{equation*}

\begin{equation*}{\beta _y} = - K{\text{ }}{d_{y{\text{ }}}}\sin {\theta _o}\sin {\phi _o}\end{equation*}

The following formula determines the interference power between users:

(9)\begin{equation}Pi = \frac{{Pt{\text{ }} \gt {\text{ }}Gr{\text{ }}\eta {\text{ }}{A^2}Cos\theta {\text{ }}Cos\theta r}}{{{{\left( {4\pi } \right)}^2}Rt\,{s^2}Rs\,{r^2}}}.\end{equation}

The preceding equation defines Gt and Gr as transmitted and received gains, respectively, and Gt is calculated using Gt = AF ² Gtmax. As a result, the corresponding end-to-end SINR of the receiver may be determined as follows [Reference Alsawaf and Ayoob31, Reference Tahkoubit, Cassiau, Demmer and Doré35, Reference Zuo, Li, Yan, Xue and Yang37]:

(10)\begin{equation}SINR = \frac{{Pr}}{{{N_0} + Pi}}.\end{equation}

Finally, take into account the presence of additive white Gaussian noise in the received signal [Reference Ntontin, Boulogeorgos, Selimis, Lazarakis, Alexiou and Chatzinotas38], which is calculated using the following equation and denoted by N ₀.

(11)\begin{equation}{N_o} = - 174 + 10{\text{ }}lo{g_{10}}\left( w \right) + {\text{ }}{F_{dB}}.\end{equation}

The noise figure in decibels is represented by F _dB, and the transmission bandwidth is denoted by w.

Results and discussion

The results are divided into two sections: the first considers the impact of the distance between the RIS and the TX-User line, and the second illustrates the effect of the difference in RIS heights on interference between users in the mm-Wave environment through the use of eq. (10). To ensure the validity of the proposed system, as shown in Fig. 4. The specific simulation parameters used in the proposed model are listed in Table 1.

Figure 4. The effect of SINR by changing the height of the RIS at different user locations.

Table 1. Parameters of the proposed model

Multiple RIS

We propose three different RIS heights to study the effect of these heights on the SINR as can be seen in Fig. 2. As can be seen in Fig. 2. Firstly, the single RIS height effect is examined on various users’ locations and the signal level of these users, on the other hand. Figure 5 shows the coverage area of the first RIS station at an altitude of 35 m. The signal level for users whose distance from the RIS midpoint is up to 8 m is good, but a sharp drop in signal level is observed when the user distance increases more than 8 m from the midpoint.

Figure 5. SINR with the horizontal distance between the RIS and the user at L ₁ = 35 m.

It is clear by comparing Fig. 3 and Fig. 4 that the number of users that a single RIS can serve in Fig. 3 (e) at a height of 35 is 3 users, while in Fig. 5 it is very easy to notice that the number of users has become 8, and they are the users who have a SINR greater than or equal to 15 dB. Therefore, the improvement rate is 62.5%.

Secondly, another RIS is added with a height of 5 m higher than the first RIS to provide coverage for users at a distance of 6–12 m from the middle of the distance. The distance between the first RIS and the second RIS increases to 10 m instead of 5 m (L ₂ = 10 m) to increase the coverage. The SINR is satisfied for users at 8 m to 14 m from the middle of the distance, and if the increase in the distance between the first RIS and the second RIS is 15 m instead of 10 m and 5 m, then the coverage range domain will be perfect for users who are from 10 m to 16 m from the middle distance, as shown in Fig. 6.

Figure 6. The effect of the interspace between RIS1 and RIS2 on the users’ SINR.

It turns out that when the distance between the RIS1 and RIS2 is equal to 15 m, there are users who do not have good coverage, and they are those whose location is between 8 m and 10 m. Therefore, the distance between the RIS1 and RIS2 equal to 10 m is better, as the coverage domain of the second RIS is complementary to the coverage domain of the first RIS without leaving any distance, but with a severe decline in the signal level for farther users.

The third RIS is added at a height higher than the height of the second RIS and the height of the first RIS, and the distance between the third RIS and the second RIS is equal to 5 m, L ₃ = 5 m, the coverage domain of this RIS is for distance from 10 m to 16 m from the middle of the distance between the TX and the user, where there appears to be an intersection between covering the second RIS and the coverage domain of the third RIS, meaning they provide coverage domain for the same users.

For this reason, the interspace distance, L ₃, was increased from 5 m to 10 m. In this case, the coverage intersection between the second RIS and the third RIS decreased, and the SINR became good until it reached users 15 m from the middle of the distance between the TX and the user. The L ₃ interspace distance increased to 15 m, there does not appear to be any intersection between the coverage domain of the second RIS and the third RIS, and the coverage domain of the third RIS increases to reach a distance of 20 m from the middle of the distance, see Fig. 7.

Figure 7. The effect of the interspace between RIS2 and RIS3 on the users’ SINR.

Several RIS were used to reduce the interference, and the best results were obtained using 3 RIS, and the best distances were obtained in the results that gave the best values for SINR (Peak), as shown in the Fig. 7(c). Interference between users was reduced through the model proposed in “Related work” section and by comparing the SINR value for users before and after adding 3 RIS. From Fig. 7(c), the improvement percentages for SINR for the second and third heights of the RIS can be obtained, as the improvement percentage was 48.46% provided by the second RIS that has a height of 45 m, while the third RIS that has a height of 60 m has an improvement rate of 77.38%.

It is worth mentioning that the level of the SINR decreased due to the increase in the distance of the user from the TX, the increase in the height of the RIS, and the distance of its location from the TX-User line. In other words, the problem appears through the increasing distance traveled by the transmitted signal, see Fig. 7. One solution to this problem is to enlarge the size of the RIS and increase the gain to reduce transmitted signal losses due to the long distance traveled. Figure 8 shows maintaining one level of the transmitted signal with different heights of the RIS and different user locations by deploying the RIS in three different sizes in addition to the various heights. The size of the three RISs was the same in all previous figures. A was equal to 0.044. Now, after changing its sizes, A became equal to 0.044, 0.0616, and 0.11, respectively, which means the size of the three RISs was the same in all previous figures. A was equal to 0.044. Now, after changing its sizes, A became equal to 0.044, 0.0616, and 0.11, respectively, which means the first RIS is the smallest, the second is larger than the first, and the third very high surface is larger than the two.

Figure 8. SINR with different user locations at different RISs sizes.

The IUI value decreased significantly after using three RIS, which led to improved SINR. If the value of interference power (pi) for the fourth user who is at 15 meters away is equal to −76.36 dB when using single RIS, and in the case of using two RIS, the value of pi decreased to −82.78 dB and its value became equal to −94.64 dB when adding the third RIS.