Performance Analysis of Reconfigurable Intelligent Surface-Assisted Millimeter Wave Massive MIMO System Under 3GPP 5G Channels

Abstract

Reconfigurable intelligent surfaces (RIS) and massive multiple input and multiple output (M-MIMO) are the two major enabling technologies for next-generation networks, capable of providing spectral efficiency (SE), energy efficiency (EE), array gain, spatial multiplexing, and reliability. This work introduces an RIS-assisted millimeter wave (mmWave) M-MIMO system to harvest the advantages of RIS and mmWave M-MIMO systems that are required for beyond fifth-generation (B5G) systems. The performance of the proposed system is evaluated under 3GPP TR 38.901 V16.1.0 5G channel models. Specifically, we considered indoor hotspot (InH)—indoor office and urban microcellular (UMi)—street canyon channel environments for 28 GHz and 73 GHz mmWave frequencies. Using the SimRIS channel simulator, the channel matrices were generated for the required number of realizations. Monte Carlo simulations were executed extensively to evaluate the proposed system’s average bit error rate (ABER) and sum rate performances, and it was observed that increasing the number of transmit antennas from 4 to 64 resulted in a better performance gain of ∼10 dB for both InH—indoor office and UMi—street canyon channel environments. The improvement of the number of RIS elements from 64 to 1024 resulted in ∼7 dB performance gain. It was also observed that ABER performance at 28 GHz was better compared to 73 GHz by at least ∼5 dB for the considered channels. The impact of finite resolution RIS on the considered 5G channel models was also evaluated. ABER performance degraded for 2-bit finite resolution RIS compared to ideal infinite resolution RIS by ∼6 dB.

1. Introduction

With the rapid proliferation of wireless devices, the increasing demand for ultra-high data rates, and the emergence of new applications like augmented reality (AR), Internet of Everything, and autonomous vehicles, the future of communication networks is rapidly approaching the era of 6G networks. The journey towards 6G is marked by a series of evolutionary leaps, each building upon the foundations of its predecessor. As we transition from fourth-generation (4G) and fifth-generation (5G) networks to the next generation, 6G networks promise to redefine the boundaries of wireless communications, ushering in a new era of hyper-connectivity, massive data exchange, and seamless integration of physical and virtual worlds. While 4G networks provided significant improvements in data rates and network capacity, 5G networks introduced revolutionary technologies such as M-MIMO, beamforming, flexible frame structure for orthogonal frequency division multiplexing, non-orthogonal multiple access (NOMA), reconfigurable intelligent surfaces (RIS), and network slicing, enabling enhanced user experiences and supporting a diverse range of services [1,2,3].

Compared with 5G, 6G networks aim to exhibit substantial enhancements in peak data rate, latency, SE, EE, reliability, and security. Applications and technologies driving 6G, target requirements, and potential services that 6G can offer are briefly discussed in [1]. 6G is projected to achieve peak data rates of up to 1 Tbps and reduce air-interface latency to as low as a few hundred nanoseconds. This is essential for real-time and mission-critical applications, including industrial automation, AR, remote healthcare, and tactile internet. 6G aims to enhance SE and EE gains by 100 times in bps/Hz/m³/Joules compared to current 5G networks. 6G networks are envisioned to enhance end-to-end reliability significantly, by 99.99999%. 6G networks are expected to incorporate stronger security measures, such as post-quantum cryptography and quantum key distribution, to mitigate the evolving threat landscape and safeguard critical communication systems [4]. To analyze channel modeling and characteristics in 6G wireless networks effectively, it is imperative to incorporate diverse technologies and disciplines. This integration should address high mobility, uncertain motion trajectories, and the non-stationary time or frequency or spatial domains [5]. The realization of B5G and 6G networks relies on breakthrough advancements in physical layer technologies. Potential technologies that have garnered significant attention include RIS, terahertz communication, and cell-free M-MIMO [4,6,7].

MIMO techniques offer several enhancements, such as spatial multiplexing, spatial diversity, and beamforming, and these have been incorporated into contemporary wireless standards. M-MIMO plays a vital role in 5G physical layer network design. Unlike traditional MIMO, M-MIMO utilizes several hundred antennas at the transmitter and/or receiver. The large number of antennas offers more flexibility to overcome dynamic channel conditions. Additionally, M-MIMO provides benefits like channel hardening, improved reliability, higher SE, EE, reduced multiuser interference, low power consumption, low latency on the air interface, and enhanced security [8,9,10,11]. M-MIMO antenna arrays, featuring hundreds of elements at base stations (BS), can be effectively implemented using millimeter waves (mmWave), which hold the promise of significantly improving performance [12].

RIS is an emerging technology with great promise for revolutionizing wireless communication systems, including B5G and 6G networks. RIS consists of passive electromagnetic surfaces embedded with reconfigurable elements, such as tunable metamaterials or semiconductor devices, which can dynamically control the propagation environment. RIS operates by manipulating the phase and amplitude of impinging electromagnetic waves as they pass through or reflect off the surface. Each element in the RIS can be programmed to configure its reflection and transmission properties based on the desired application requirements or network conditions [7,13,14,15].

The RIS-aided MIMO system presents many advantages compared to conventional MIMO systems that do not integrate RIS. RIS significantly enhances EE by leveraging passive elements without requiring active radio frequency (RF) chains. Unlike traditional MIMO systems, which are limited to performing beamforming at the transmitter, the RIS-aided MIMO system supports joint beamforming at both the transmitter and the RIS. This capability improves signal quality and allows for the dynamic reconfiguration of the communication environment. Furthermore, while conventional MIMO systems can suffer from blockage and exhibit poor performance in non-line-of-sight (NLoS) conditions, the RIS-aided MIMO system excels in these challenging scenarios. Additionally, conventional MIMO systems rely on fully active antenna arrays, which can lead to increased hardware costs and complexity. In contrast, the integration of RIS streamlines these aspects, offering a more cost-effective and efficient solution for B5G.

RIS offers a myriad of advantages that address critical challenges faced by next-generation systems. By intelligently controlling the phase shifts of the reflected waves, RIS can steer, focus, amplify, or attenuate the signals, enabling it to shape the wireless propagation environment effectively. RIS can reshape electromagnetic wavefronts, effectively mitigating path loss and shadowing and improving signal coverage in challenging environments. RIS can selectively reflect and cancel interfering signals, reducing overall interference levels. RIS can adapt its real-time configuration, responding to variations in the wireless channel and user locations. Because RIS is a passive technology, passive RIS elements consume negligible power compared to active radio transmitters and amplifiers, resulting in a more energy-efficient and environmentally friendly alternative for future 6G networks. Leveraging mmWave for unmanned aerial vehicle (UAV) communications can meet the data rate requirements of future networks; however, obstacles like tall buildings and trees often block line-of-sight (LoS) connections. RIS can assist in improving the quality of UAV-integrated mmWave communication [16]. RIS technology finds utility in high-speed trains (HST), where mmWave waves are pivotal in delivering a superior experience for highly mobile passengers [17]. RIS complements other advanced technologies such as M-MIMO [18,19], mmWave frequency communications [20,21], NOMA [22,23], and integrated sensing and communication [24] to achieve unprecedented levels of performance to support a diverse range of applications envisioned for the B5G and 6G era.

One of the significant research challenges in integrating RIS with potential technologies such as M-MIMO and mmWave frequency communications is channel modeling. Few studies have discussed RIS channel modeling for mmWave M-MIMO systems. In [25,26], the authors introduced the SimRIS simulation tool, which provides a system and channel model for RIS according to 3GPP 5G standards. These works emphasize channel modeling but fail to include practical performance assessments like ABER. Ref. [27] conducted an ABER analysis and quantified performance comparisons between 28 GHz and 73 GHz frequencies in RIS-assisted MIMO configurations for both InH and UMi models. However, it did not adequately examine the influence of the size of the RIS array on system performance at mmWave frequencies. Studies conducted thus far have not investigated the effects of discrete versus continuous phase resolution of RIS on ABER performance. Ref. [27] also did not examine multi-user MIMO setups.

Table 1. Proposed framework vs. Existing SimRIS implementations.

Components/Works	[25]	[26]	[27]	[28]	Proposed
mmWave channel modeling framework	✓	✓	✓	✓	✓
3GPP-based RIS simulation	✓	✓	✓	✓	✓
Discrete vs. continuous phase RIS analysis	✓	✗	✗	✗	✓
Quantified ABER impact for indoor/outdoor scenarios (28/73 GHz)	✗	✗	✓	✗	✓
Analysis on impact of increasing N and $N_t$	✗	✗	✓	✓	✓
Analysis on impact of size of RIS array	✓	✗	✗	✓	✓
Multi-user scenarios	✗	✗	✗	✗	✓
Sum rate analysis	✓	✓	✗	✓	✓

outlines the differences between our proposed framework and prior SimRIS implementations [25,26,27,28]. Here, the proposed framework and previous works indicate included factors with a tick mark and excluded factors with a cross.

Building on the research found in [27], which combined M-MIMO, mmWave, and RIS to enhance wireless communication at frequencies of 28 GHz and 73 GHz, this study explores the effects of increasing the size of the RIS array. The initial findings highlighted how M-MIMO can manage multiple data streams concurrently, how mmWave technology benefits from high-frequency capabilities, and the role of RIS in improving signal dissemination. This combination led to better coverage, minimized interference, and enhanced EE, providing important insights for advancing B5G. The current research will investigate the impact of adding more RIS elements on system performance. Many traditional studies on mmWave communication emphasize channel coefficients that may not accurately reflect the true characteristics of mmWave channels. In this research, we utilized the SimRIS channel simulator to generate realistic channel coefficients tailored for both indoor and outdoor settings. As a result, we achieved the desired ABER by employing higher signal-to-noise ratio (SNR) values. Additionally, this performance can be improved by increasing the RIS array size. This study primarily focuses on this aspect.

The proposed work’s contributions are as follows:

• This study thoroughly analyzes ABER and sum rate performance in RIS-assisted mmWave M-MIMO systems utilizing standardized 5G channel models defined by 3GPP. It serves as a practical benchmark for performance evaluation.
• A comprehensive comparison between indoor (InH–Office) and outdoor (UMi–Street Canyon) settings at frequencies of 28 GHz and 73 GHz, demonstrating that the 28 GHz band yields better ABER performance in indoor environments.
• Furthermore, this research evaluates continuous phase RIS against discrete phase configurations (1-bit and 2-bit), emphasizing the performance trade-offs and quantization effects crucial for real-world implementations.
• This study also highlights critical aspects overlooked in previous research, such as performance in multi-user scenarios and the effects of increasing RIS elements. The findings reveal that a higher RIS array size can significantly improve ABER performance.

The upcoming sections of this paper are ordered as follows: Section 2 covers recent works in the literature related to M-MIMO, mmWave M-MIMO, RIS, and RIS integrated with mmWave M-MIMO. The system model for RIS-assisted mmWave M-MIMO is presented in Section 3. Section 4 describes corresponding 5G channel models for indoor and outdoor scenarios. The outcomes from the Monte Carlo simulation, demonstrating the ABER performance of RIS-assisted mmWave M-MIMO, are exemplified in Section 5. Section 6 concludes this study and emphasizes potential directions for future research.

2. Related Works

In [29], a real-time testbed for M-MIMO named LuMaMiis developed by researchers at Lund University. It employs 100 antennas to serve 10 users simultaneously. The system achieves a throughput of 384 Gbps. Similarly, in [30], researchers at Bristol University developed a 128-antenna M-MIMO testbed that serves 22 users simultaneously in an indoor environment, achieving a SE of 145.6 bits/s/Hz.

To address pilot contamination, several mitigation techniques have been developed. In [31], the pilot sequence reuse technique is designed to avoid pilot contamination within a cell cluster. A blind pilot decontamination scheme is developed, where, without the requirement of pilot data, subspace projection is used for channel estimation [32]. In [33], the interference alignment-based pilot decontamination technique exploits multiple antennas at the user side for pilot decontamination. Precoding allows for multi-stream transmission in M-MIMO systems. Many efficient linear and non-linear precoders have been developed.

The effects of hardware impairments on the performance of M-MIMO systems are extensively studied in [34]. The usage of the machine and deep learning algorithms to address several challenges, such as beamforming, channel estimation, and signal detection, is studied in [35]. The authors of [36] investigated error modeling of the downlink channel and validated computational and experimental results by altering the BS array size.

In the past few years, extensive research has been done on mmWave M-MIMO systems, addressing the various benefits offered and challenges faced. Because of signal processing and hardware architecture constraints, conventional digital precoding techniques and analog beamforming cannot be extended for mmWave M-MIMO systems. Hence, in [37], a hybrid precoding scheme is introduced, an amalgamation of analog and digital precoding. This precoding technique achieves antenna array gain, spatial multiplexing gain, and high sum rate performance with fewer RF chains. Estimating channels in mmWave MIMO systems before beamforming presents difficulties due to the massive antennas and the lower SNR.

To understand the behavior and properties of M-MIMO channels at mmWave frequencies, practical field measurements should be conducted, through which researchers can derive statistical and/or deterministic models to represent the properties and behavior of channels. Sounding, the process of transmitting known waveforms and analyzing the channel-impacted received signals, has become a prevalent approach for wireless channel modeling. Real-world channel measurements were conducted at 28 GHz and 73 GHz frequencies in New York City to develop detailed spatial statistical channel models. These statistically derived models were then leveraged to theoretically evaluate mmWave microcell and picocell networks in a dense urban deployment [38]. Similar work was carried out in Germany by the mmMAGIC group for 10–100 GHz frequencies and in China at 32 GHz [39,40].

Reference [41] presents novel methods for employing ray-tracing (RT) to establish a digital twin representation of radio propagation across various frequency bands, from microwave frequencies to the visible light spectrum. It suggests techniques for characterizing material electromagnetic properties through a combination of material characteristics and field measurements. A super-resolution modeling method is formed by fusing RT and artificial intelligence algorithms. In [17], the electromagnetic and scattering properties of materials are evaluated for HST mmWave communication between 26.5 GHz and 40 GHz. The study involves creating 3D models for outdoor and tunnel HST environments in the mmWave spectrum. The authors establish fundamental HST mmWave channel modeling principles using extensive RT simulations. The system model is validated with six main objects: buildings, tracks, tunnels, etc. In [42], two case studies aim to simulate real-world HST channels in the context of 5G mmWave technology. The first case study focuses on tunnels within the 30 GHz band, while the second examines outdoor HST environments in the 90 GHz band. Both studies include RT simulations, stochastic channel modeling, implementation, and cross-validation.

The authors of [43] assessed the precoding and beamforming of mmWave M-MIMO, focusing on beamforming approaches for the practical application of 5G wireless networks and trade-offs between performance and complexity. The authors of [44] suggested a hybrid beamforming (HBF) approach with good accuracy and low complexity for mmWave M-MIMO. An experimental demonstration was accomplished on an actual 5G mmWave setup following the 3GPP standard with two distinct users. Because of its minimal complexity and high performance, the suggested technology is well-suited for B5G.

In [45], the authors provided a detailed description of the working principles of RIS. They also provided a mathematical model for signal transmission using RIS as a smart reflector (SR) in a dual-hop communication scenario and RIS as a low-complex energy-efficient transmitter. In addition, a system model for multiuser downlink transmission over an RIS was described. Closed-form expressions for symbol error probability (SEP) were also developed for the communication scenarios under consideration. RIS can be integrated with other potential technologies to reap the combined benefits and enhance SE, EE, reliability, and signal coverage. In [23], RIS was integrated with NOMA to improve SE and connectivity. The uplink sum capacity was maximized using optimal power allocation coefficients for NOMA. The intelligent RIS-assisted fixed NOMA is investigated in [46], also assessing outage probabilities and optimizing transmit power allocation. The work in [23] is further developed in [22], which considers blind RIS-assisted ordered NOMA rather than fixed NOMA.

The potential benefits of employing RIS across several frequency bands, from sub-6 GHz to mmWave, for indoor and outdoor setups are studied in [47]. Empirical models are also used to investigate the path loss exponent. Most current RIS-assisted channel models consider NLoS propagation. However, in [48], the authors analyzed the RIS-assisted channel model by considering the LoS path between the transmitter and the receivers. When RIS array size increases, mmWave channels can be modeled as a spatially correlated Rayleigh fading channel, leading to an improved mmWave scattering environment [49]. In [25], a channel model for a system with RIS operating at mmWave frequencies is described, which is usable in various indoor and outdoor environments and covers the physical properties of propagation by taking 3GPP 5G standard radio channel models into account. The authors further developed SimRIS, an open-source channel simulator that generates channel coefficients according to the 3GPP 5G radio standards for indoor and outdoor scenarios. This work is expanded in [28], where the authors developed a channel simulator, SimRIS version 2, which presents a channel model for RIS-assisted mmWave MIMO. The simulation results in [50] show the immense benefits enabled by the RIS compared to increasing the number of BS antennas.

The authors of [51] suggested employing an RIS for MIMO wireless communication by modulating data onto a carrier signal reflected by the RIS. Each RIS element corresponds to a distinct data stream. A non-linear modulation technique is devised to independently regulate harmonic amplitudes and phases under a constant envelope constraint to enable high-order quadrature amplitude modulation (QAM). A prototype was also built for RIS-based 2 × 2 MIMO 16-QAM transmission at 4.25 GHz. They achieved a 20 Mbps data rate with 0.7 W power consumption. A RIS-aided angular-based HBF design for mmWave M-MIMO systems and a three-stage architecture are presented in [52]. Comprehensive simulations show that employing RIS can result in significant rate gains, especially when the direct Tx–Rx link is blocked, and RIS can provide an alternate, reliable path. The amount of RIS elements increases the attainable rate, with PSO-based optimization outperforming random phase selection.

The channel state information (CSI) is essential for RIS to function accurately. RIS-based systems exhibit high sensitivity to CSI errors. The foundational premise of the RIS concept relies on the assumption that RIS elements have complete knowledge of the channels connecting the BS to RIS and from RIS to UE. With this channel information, the RIS can effectively execute both the pre-compensation and post-compensation phases of the channel. However, if the CSI is imperfect, the optimal phase shifts that each RIS element should introduce will be inaccurate. This inaccuracy can compromise the joint beamforming process between the transmitter and the RIS, subsequently hindering the realization of the advantages associated with RIS technology. Deep learning techniques based on compressive sensing are suggested in [53] to estimate channels in RIS-assisted mmWave MIMO systems with limited training overhead. The recommended method takes advantage of joint sparsity in angles and among subcarriers. This proposed work aims to assess the ABER and sum rate performances of the assisted mmWave M-MIMO system under the considered channel models and frequencies for different transmit antenna and RIS configurations.

3. System Model

Consider a single-cell downlink RIS-assisted mmWave M-MIMO system, where a BS with $N_T$ transmit antennas communicates with a $N_r$ antenna UE through RIS containing N RIS elements. It is presumed that the direct channel link between UE and BS is ignored, as it is severely affected by excessive blockage from trees, buildings, etc. Figure 1 and Figure 2 depict sample outdoor and indoor scenarios, respectively. Here, the system model is described for a single-user scenario.

The effective channel between BS and UE is expressed as $\mathbf{D}=\mathbf{G}\mathbf{\Theta }\mathbf{H}$, where $\mathbf{H}$ is an $N\times N_T$ channel matrix between the BS and RIS, and $\mathbf{G}$ is an $N_R\times N$ channel matrix between RIS and UE. Here, $\mathbf{\Theta }=diag\left(\left[e^{j{\varphi }_1},e^{j{\varphi }_2},\dots ,e^{j{\varphi }_N}\right]\right)$ is a diagonal RIS phase shift response matrix. The received signal at the UE reflected from the RIS is expressed as follows:

$$\mathbf{r}=\mathbf{D}\mathbf{x}+\mathbf{n}$$

(1)

where $\mathbf{x}$ is the transmit signal vector that indicates the signals transmitted from the $N_T$ transmit antennas. $\mathbf{n}$ is the noise vector with elements following $C\mathcal{N}\left(0,N_o\right).$ Expression (1) can be expanded as follows:

$$\underset{N_R\times 1}{\underbrace{\mathbf{r}}}=\underset{N_R\times N_T}{\underbrace{\mathbf{G}\mathbf{\Theta }\mathbf{H}}}\underset{N_T\times 1}{\underbrace{\mathbf{x}}}+\underset{N_R\times 1}{\underbrace{\mathbf{n}}}$$

(2)

We presume that all the antennas communicate the same information symbol to achieve spatial transmit diversity gain. To explain more clearly, we consider a simplified scenario where the UE is equipped with a single antenna. Equation (2) can be simplified as follows:

$$r=\underset{1\times N_T}{\underbrace{\mathbf{g}\mathbf{\Theta }\mathbf{H}}}\underset{N_T\times 1}{\underbrace{\mathbf{x}}}+n$$

(3)

Here, we can consider the individual elements of channel matrices as $g_i={\beta }_i{e}^{-j{\psi }_i}$ and $h_{i,k}={\alpha }_{i,k}{e}^{-j{\theta }_{i,k}},i\in \left\{1,2,\dots ,N\right\},k\in \left\{1,2,\dots ,N_T\right\}$. As the same symbol $\left(x\right)$ is transmitted from all the antennas, the expression (3) can be further reduced as follows:

$$r=\left(\sum _{i=1}^N{g}_i\left[\sum _{k=1}^{N_T}{h}_{i,k}\right]e^{j{\varphi }_i}\right)x+n$$

(4)

Let ${\sum }_{k=1}^{N_T}{h}_{i,k}={h_i^s=\alpha }_i^s{e}^{-j{\theta }_i^s}$. Substituting in (4) results in the following:

$$r=\left(\sum _{i=1}^N{g}_i{h}_i^s{e}^{j{\varphi }_i}\right)x+n$$

(5)

The instantaneous SNR at the UE can be composed as follows:

$$\epsilon ={\displaystyle \frac{{\left|{\sum }_{i=1}^N{\beta }_i{{\alpha }_i^{s}e}^{j\left({\varphi }_i-{\psi }_i-{\theta }_i^s\right)}\right|}^2{E}_s}{N_o}}$$

(6)

The RIS phase shift responses ${\varphi }_i$ require optimization to maximize the instantaneous SNR at the UE. In a continuous phase RIS, every reflecting element is considered to produce a uniformly distributed ideal phase shift in [0, $2\pi$], which allows for optimal beamforming. This configuration serves as the theoretical upper bound for RIS-aided systems. The assumption is that RIS elements have complete knowledge of the channels connecting the BS to the RIS and from the RIS to the UE. The optimal choice for RIS phase shifts is attained by considering ${\varphi }_i={\psi }_i+{\theta }_i^s$. With this channel information, the RIS can effectively execute both the pre-compensation and post-compensation phases of the channel. After phase distortion cancellation, the upper bound of the instantaneous SNR attained at UE is as follows:

$${\epsilon }_{max}={\displaystyle \frac{{\left|{\sum }_{i=1}^N{\beta }_i{\alpha }_i^s\right|}^2{E}_s}{N_o}}$$

(7)

The optimal maximum likelihood (ML) detector can be employed for the detection of the transmitted symbol from the received signal at the UE as follows:

$$\widehat{x}=\arg {\underset{x}{\min }\left|r-\left(\sum _{i=1}^N{g}_i{h}_i^s{e}^{j{\varphi }_i}\right)x\right|}^2$$

(8)

The ML detector requires perfect CSI at the UE to detect the transmitted symbol accurately. Although the RIS possesses an ideal CSI, its operation resembles an ON–OFF switch. In practice, it cannot produce all possible phase angles. The practical implementation limits each RIS element’s phase shift to a finite number of discrete phase resolutions. Let $P=2^b$ be the total number of phase shift resolutions the RIS can produce, where b is the number of bits required to represent the number of phase shift levels. The discrete phase shift values can be acquired via uniform quantization from the interval ${\varphi }_i^dϵ[0,2\pi )$ [54,55]:

$${\varphi }_i^dϵ\mathcal{F}=\left\{0,{\displaystyle \frac{2\pi }{P}},2{\displaystyle \frac{2\pi }{P}},\dots ,(2^b-1){\displaystyle \frac{2\pi }{P}}\right\}$$

(9)

For a one-bit discrete phase shifter $(b=1)$, the corresponding two discrete phase levels are 0 and $\pi$. For the two-bit discrete phase shifter $(b=2)$, the corresponding four discrete levels are 0, ${\displaystyle \frac{\pi }{2}}$,$\pi$,${\displaystyle \frac{3\pi }{2}}$. The discrete reflection phase shifter produces a quantized phase corresponding to the total phase shift of the dual-hop channel, which is given as follows [13,56]:

$${\varphi }_i^d=q_b({\psi }_i+{\theta }_i^s),i=1,2,\dots ,N$$

(10)

where $q_b$ is the quantized phase levels. The specific phase angle that needs to be generated should be selected based on the proximity to the angles it can produce. The instantaneous SNR at the UE due to the discrete reflection RIS is given as follows:

$${\epsilon }^{\prime }={\displaystyle \frac{{\left|{\sum }_{i=1}^N{\beta }_i{\alpha }_i^s{e}^{j({\varphi }_i^d{-\psi }_i-{\theta }_i^s)}\right|}^2{E}_s}{N_o}}$$

(11)

Due to the residual phase, there will be a degradation in SNR at UE compared to infinite resolution RIS, i.e., $\left({\epsilon }^{\prime }<\epsilon \right)$ [56]. The ML detector for discrete RIS is similar to (8), replacing ${\varphi }_i$ with ${\varphi }_i^d$.

4. Channel Modeling

This section delivers a comprehensive channel model for an RIS-assisted M-MIMO system, which functions at mmWave frequencies. This narrowband channel model considers a random number of scatterers (clusters), shadowing, sharing between clusters, probability of LoS, etc. Moreover, this considers array responses and realistic channel gains of RIS components. This channel model describes the modeling of amplitude and phase, considering the RIS phase shifts. This is widely used in 3GPP [20,21,57].

4.1. Indoor Physical Channel Model

This model assumes InH—indoor office for 28 and 73 GHz frequencies. The models for the BS-RIS and RIS-UE channels are described in the subsections below:

4.1.1. BS-RIS Channel

Let us consider that M scatterers/reflectors are available between BS and RIS. These M scatterers are grouped into C clusters, each having $S_c$ sub-rays for $c=1,2,\dots ,C$, i.e., $M={\sum }_{c=1}^C{S}_c$. A cluster generally consists of sub-rays with similar spatial and/or temporal characteristics. The BS-RIS channel vector of size $N\times N_T$ is defined as follows [25]:

$$\mathbf{H}=\gamma \sum _{c=1}^C\sum _{s=1}^{S_C}{\beta }_{c,s}\sqrt{G_e\left({\theta }_{c,s}^{BS-RIS}\right)L_{c,s}^{BS-RIS}}\mathbf{a}\left({\varphi }_{c,s}^{BS-RIS},{\theta }_{c,s}^{BS-RIS}\right){\mathbf{a}}^T\left({\varphi }_{c,s}^{BS},{\theta }_{c,s}^{BS}\right)+{\mathbf{H}}_{\mathrm{LoS}}$$

(12)

where $\gamma =\sqrt{{\displaystyle \frac{1}{{\sum }_{c=1}^C{S}_c}}}$ is the normalization factor, and ${\beta }_{c,s}$ is the complex Gaussian distributed small-scale path gain corresponding to $s^{th}$ sub-ray in $c^{th}$ cluster. $G_e\left({\theta }_{c,s}^{BS-RIS}\right)$ is the RIS element gain and $L_{c,s}^{BS-RIS}$ is the large-scale path attenuation associated with the $s^{th}$ sub-ray in the $c^{th}$ cluster. $\mathbf{a}\left({\varphi }_{c,s}^{BS-RIS},{\theta }_{c,s}^{BS-RIS}\right)$ and $\mathrm{a}\left({\varphi }_{c,s}^{BS},{\theta }_{c,s}^{BS}\right)$ are the array response vectors for the elevation arrival angle ${\theta }_{c,s}^{BS-RIS},{\theta }_{c,s}^{BS}$ and azimuth arrival angle ${\varphi }_{c,s}^{BS-RIS}{,\varphi }_{c,s}^{BS}$, respectively. The array response vectors are calculated by following the steps described in [25,58].

The RIS element gain $G_e\left({\theta }_{c,s}^{BS-RIS}\right)$ is modeled as follows [25,59]:

$$G_e\left({\theta }_{c,s}^{BS-RIS}\right)=2\left(2q+1\right)\cos {\left({\theta }_{c,s}^{BS-RIS}\right)}^{2q},-{\displaystyle \frac{\pi }{2}}<{\theta }_{c,s}^{RIS}<{\displaystyle \frac{\pi }{2}}$$

(13)

where

$$q=0.25G_e\left(0\right)-0.5,G_e\left(0\right)=2\pi$$

(14)

The Poisson distribution is commonly used to model the number of clusters in a mmWave communication $C\sim \mathcal{P}\left({\lambda }_p\right)$. Here, ${\lambda }_p$ is the variance, which depends on the operating frequency [60].

$${\lambda }_p=\left\{\begin{array}{c}1.8,f=28GHz\\ 1.9,f=73GHz\end{array}\right.$$

(15)

The cluster size is assessed to ensure a minimum of one cluster exists in the propagation environment.

$$C=\max \left\{1,\mathcal{P}\left({\lambda }_p\right)\right\}$$

(16)

In a given cluster, ${\varphi }_{c,s}^{BS-RIS}$ and ${\varphi }_{c,s}^{BS}$ follow a Laplacian distribution with mean $\mathcal{U}\left[-{\displaystyle \frac{\pi }{2}},{\displaystyle \frac{\pi }{2}}\right].$ Similarly, the ${\theta }_{c,s}^{BS-RIS}$ and ${\theta }_{c,s}^{BS}$ are assumed to be conditionally Laplacian with a mean of $\mathcal{U}\left[-{\displaystyle \frac{\pi }{4}},{\displaystyle \frac{\pi }{4}}\right].$

The path loss $L_{c,s}^{BS-RIS}$ for ${\left(c,s\right)}^{th}$ path can be expressed as follows [25,60]:

$$L_{c,s}^{BS-RIS}=-20{\log }_{10}\left({\displaystyle \frac{4\pi }{\lambda }}\right)-10n\left(1+z\left({\displaystyle \frac{f-f_0}{f_0}}\right)\right){\log }_{10}{d}_{c,s}-X_{\sigma }$$

(17)

This model applies to real-time environments such as UMi and InH. Here, $d_{c,s}$ is the propagation length of the ${\left(c,s\right)}^{th}$ path, which is measured according to the steps followed in [61], n is path loss exponent, and z is the system parameter, whereas $f_o$ is the fixed reference frequency. 5G InH—indoor office is considered for indoor channel modeling, and the corresponding parameters such as $n,z,\sigma$ are tabulated in

Table 2. Path loss attributes for InH [25,61].

Parameters	NLoS	LoS
n	3.19	1.73
$\sigma$ (dB)	$8.29$	$3.02$
z	$0.06$	0
$f_0\left(GHz\right)$	$24.2$	$24.2$

[25,61].

The LoS component of the channel matrix $\mathbf{H}$ can be formulated as follows:

$${\mathbf{H}}_{\mathrm{LoS}}=I_h\left(d_{BS-RIS}\right)\sqrt{G_e\left({\theta }_{\mathrm{LoS}}^{BS-RIS}\right)L_{\mathrm{LoS}}^{BS-RIS}}{e}^{j\eta }\mathbf{a}\left({\varphi }_{\mathrm{LoS}}^{BS-RIS},{\theta }_{\mathrm{LoS}}^{BS-RIS}\right){\mathbf{a}}^{\mathit{T}}\left({\varphi }_{\mathrm{LoS}}^{BS},{\theta }_{\mathrm{LoS}}^{BS}\right)$$

(18)

where $I_h\left(d_{BS-RIS}\right)$ follows a Bernoulli distribution containing values from the set {0,1}, which indicates the presence of a LoS link between BS and RIS separated by a distance of $d_{BS-RIS}$. $\eta \sim \mathcal{U}\left[0,2\pi \right]$ is a random phase term. $L_{\mathrm{LoS}}^{BS-RIS}$ indicates attenuation of the LoS link calculated using (17) for the separation distance $d_{BS-RIS}$. $G_e\left({\theta }_{\mathrm{LoS}}^{BS-RIS}\right)$ is the RIS element gain for the LoS link between BS and RIS. $\mathbf{a}\left({\varphi }_{\mathrm{LoS}}^{BS-RIS},{\theta }_{\mathrm{LoS}}^{BS-RIS}\right)$ and $\mathbf{a}\left({\varphi }_{\mathrm{LoS}}^{BS},{\theta }_{\mathrm{LoS}}^{BS}\right)$ are the corresponding array response vectors for angles ${\varphi }_{\mathrm{LoS}}^{BS-RIS},{\theta }_{\mathrm{LoS}}^{BS-RIS}$ and ${\varphi }_{\mathrm{LoS}}^{BS},{\theta }_{\mathrm{LoS}}^{BS}$, respectively.

To determine the LoS probability $P\left(I_h=1\right)=\mu$, the 5G model in [25,61] can be used as follows:

$$\mu =\left\{\begin{array}{cc}1,\hfill & d_{BS-RIS}\le 1.2\hfill \\ exp\left(-{\displaystyle \frac{d_{BS-RIS}-1.2}{4.7}}\right),\hfill & 1.2<d_{BS-RIS}\le 6.5\hfill \\ 0.32exp\left(-{\displaystyle \frac{d_{BS-RIS}-6.5}{32.6}}\right),\hfill & d_{BS-RIS}>6.5\hfill \end{array}\right.$$

(19)

4.1.2. RIS-UE Channel

In this model for indoor communications, we can simplify the analyses by assuming that the RIS and the receiver are in close proximity, allowing for a direct LoS connection without any significant NLoS components present between them. The LoS-dominated RIS-UE channel $\mathit{g}$ is obtained by recalculating array response vectors for corresponding azimuth and elevation angles ${\varphi }_{UE}^{RIS-UE},{\theta }_{UE}^{RIS-UE}$, with the steps discussed in [25,26]. $L_{\mathrm{LoS}}^{RIS-UE}$ can be measured by replacing $d_{c,s}$ in (17) with $d_{RIS-UE}$.

The gain associated with RIS elements that reflect the signals to UE is calculated like in (13) by considering ${\theta }_{UE}^{RIS-UE}$ instead of ${\theta }_{c,s}^{BS-RIS}$. Finally, the vector $\mathit{g}$ can be formulated as follows:

$$\mathit{g}=\sqrt{G_e\left({\theta }_{UE}^{RIS-UE}\right)L_{\mathrm{LoS}}^{RIS-UE}}{e}^{j\eta }\mathbf{a}\left({\varphi }_{UE}^{RIS-UE},{\theta }_{UE}^{RIS-UE}\right)$$

(20)

4.2. Outdoor Physical Channel Model

This model considers UMi environments for frequencies of 28 and 73 GHz. The encompassing mmWave channel modeling outlined in Section 4.1 can be extended to outdoor environments by making appropriate adjustments to specific system parameters like n and $\sigma$, as per the outdoor environment. When adapting the indoor channel model for outdoor settings, the main difference lies in the channel connecting the RIS to the UE.

In the outdoor setting, this channel may experience small-scale fading, similar to indoor environments, but with the additional characteristic of having an arbitrary number of distinctive clusters. The LoS dominant channel, as described in (18), remains applicable when $d_{RIS-UE}$ is relatively short and has a high $\mu$. However, in the real world, when distance and environmental circumstances fluctuate, this LoS dominance assumption may not hold true. To effectively predict channel behavior, a more comprehensive technique is required.

The channel vector $\mathbf{g}$ for the outdoor scenario can be generally formulated as follows [25,61]:

$$\mathbf{g}=\tilde{\gamma }\sum _{c=1}^{\tilde{C}}\sum _{s=1}^{{\tilde{S}}_c}{\beta }_{c,s}\sqrt{G_e\left({\theta }_{c,s}^{RIS-UE}\right)L_{\mathrm{c},\mathrm{s}}^{RIS-UE}}\mathbf{a}\left({\varphi }_{c,s}^{RIS-UE},{\theta }_{c,s}^{RIS-UE}\right)+{\mathbf{g}}_{\mathrm{LoS}}$$

(21)

Here, $\tilde{C}$ and ${\tilde{S}}_c$ denote cluster count and sub-rays per cluster for the RIS-UE link, respectively. $\tilde{\gamma }=\sqrt{{\displaystyle \frac{1}{{\sum }_{c=1}^C{\tilde{S}}_c}}}$ is the normalization factor. $G_e\left({\theta }_{c,s}^{RIS-UE}\right)$ is the gain of RIS elements, and $L_{\mathrm{c},\mathrm{s}}^{RIS-UE}$ is the large-scale attenuation in the direction of the ${(c,s)}^{th}$ scatterer. $\mathbf{a}\left({\varphi }_{c,s}^{RIS-UE},{\theta }_{c,s}^{RIS-UE}\right)$ represents the array response vector for the associated azimuth and elevation angles. The channel parameters such as $n,z,\sigma$ for the outdoor propagation environment are tabulated in

Table 3. Path loss attributes for UMi [25,61].

Parameters	NLoS	LoS
n	3.19	1.98
$\sigma$ (dB)	$8.29$	$3.1$
z	0	0

[25,61].

5. Results and Validations

The ABER performance of the proposed RIS-assisted mmWave massive MIMO system is examined under 3GPP TR 38.901 V16.1.0 5G channel models using MATLAB R2023a. The channel matrices are generated for the desired number of realizations using the SimRIS channel simulator. The simulation setup is presented in

Table 4. Simulation Setup.

Parameters	Values
Carrier frequencies (GHz)	28 and 73
MIMO configurations	1 × 4, 1 × 16, 1 × 64
Size of RIS array	64, 256, 1024
Number of channel realizations	105
Modulation	BPSK
Target ABER	10−4

.

Figure 3 shows the ABER performance of 1 × 4 M-MIMO for the InH—indoor office environment at 28 GHz for varying $N$ values. To attain the desired ABER, $N=64$, $N=256$, and $N=1024$ systems demand an SNR of ∼78 dB, ∼74 dB, and ∼71 dB, respectively. It is noted that SNR gain increases with increases in N. For example, the $N=1024$ system has a ∼7 dB SNR gain compared to the $N=64$ system. Figure 4 depicts the ABER performance of 1 × 4 M-MIMO for an InH—indoor office environment at 73 GHz for varying $N$ values. To attain the desired ABER, the $N=64$, $N=256$, and $N=1024$ systems demand an SNR of ∼88 dB, ∼84 dB, and ∼78 dB, respectively. When the number of reflecting items is 1024, there is an SNR gain of ∼10 dB over the $N=64$ system and a ∼4 dB SNR gain over the $N=256$ system. SNR gain increases with N. In general, as frequency increases, so does path loss. By comparing Figure 3 and Figure 4, we notice that the $N=1024$ system requires an SNR of ∼71 dB for a frequency of 28 GHz, whereas the SNR required for 73 GHz is ∼78 dB, resulting in an additional ∼7 dB SNR to accomplish the same performance.

Figure 5 shows the ABER performance of the $N=256$ RIS-M-MIMO for an InH—indoor office environment at 28 GHz by varying the number of transmitting antennas, such as 4, 16, 64. To attain the desired ABER, $N_T=4$, $N_T=16$, and $N_T=64$ systems demand an SNR of ∼73 dB, ∼67 dB, and ∼63 dB, respectively. SNR gains rise together with an increase in the transmitter antenna count. The $N_T=64$ system has an SNR gain of ∼10 dB over the $N_T=4$ system. Figure 6 depicts the same settings as Figure 5, except the carrier frequency, which is set to 73 GHz. $N_T=4$, $N_T=16$, and $N_T=64$ systems demand an SNR of ∼84 dB, ∼77 dB, and ∼68 dB, respectively, to attain the desired ABER. SNR gains increase with $N_T$. The $N_T=64$ system has an SNR gain of ∼16 dB over the $N_T=4$ system. It is evident from Figure 5 and Figure 6 that increasing the frequency degrades performance due to path loss distortions.

Moving from 28 GHz to 73 GHz allows for larger bandwidth allocation to users, resulting in higher achievable data rates. Generally, interfering sources do not affect higher mmWave frequencies, resulting in lower interference and greater security. Additionally, smaller component sizes enable more extensive antenna arrays to be utilized. Figure 3, Figure 4, Figure 5 and Figure 6 show that moving from 28 GHz to 73 GHz increases the error rate for an indoor environment. However, the error rate performance can be improved by increasing $N_T$ and N. Increasing $N_T$ at the access point (AP) is not always feasible for indoor environments. As a lightweight architecture, RIS with several components can be easily mounted in indoor settings to overcome the impact of propagation losses.

Figure 7 shows the ABER performance of a 1 × 4 M-MIMO for an outdoor UMi—street canyon environment at 28 GHz by varying the N values. To attain the desired ABER, the $N=64$, $N=256$, and $N=1024$ systems demand an SNR of ∼83 dB, ∼75 dB, and ∼66 dB, respectively. It is observed that when $N$ increases, the SNR gain does as well. For example, the $N=1024$ system has an SNR gain of ∼17 dB compared to the $N=64$ system. According to Figure 3 and Figure 7, the SNR necessary for $N=1024$ is ∼66 dB for the outdoor environment and ∼71 dB for the indoor environment. When it comes to indoor environments, spatial correlation has a substantial impact on ABER performance.

Figure 8 depicts the ABER performance of the 1 × 4 M-MIMO for an outdoor UMi—street canyon environment at 73 GHz when $N$ is varied. To attain the desired ABER, $N=64$, the $N=256$, and $N=1024$ systems demand an SNR of ∼ 88 dB, ∼82 dB, and ∼72 dB, respectively. When the number of reflecting items is 1024, there is an SNR gain of ∼16 dB over the $N=64$ system and a ∼6 dB SNR gain over the $N=256$ system. For $N=1024$, the SNR necessary to attain the desired ABER is ∼66 dB for a frequency of 28 GHz and ∼72 dB for a frequency of 73 GHz. The performance suffers as a result of increased frequency. We can deduce from Figure 4 and Figure 8 that the ABER performance in an indoor environment is inferior to that in an outdoor environment. This is due to the influence of spatial correlation.

Figure 7 and Figure 8 show that the error rate increases when the operating frequency increases. However, to acquire the benefits of a higher frequency in the outdoor environment, we can provide the BS with a larger number of antennas and the passive RIS with a larger N. The RIS with more reflecting elements can be easily mounted outdoors. More transmitting antennas and reflecting elements in higher operating frequencies can form narrower beams, offering stable and reliable communication.

Figure 9 shows the ABER performance of $N=256$ RIS-M-MIMO for the UMi—street canyon outdoor environment at 28 GHz by varying the number of transmitting antennas, such as 4, 16, 64. To attain the desired ABER, the $N_T=4$, $N_T=16$, and $N_T=64$ systems demand an SNR of ∼75 dB, ∼68 dB, and ∼65 dB, respectively. SNR gains increase with $N_T$. The $N_T=64$ system has an SNR gain of ∼10 dB over the $N_T=4$ system. When $N_T=64$, the SNR necessary to attain the ABER demand is ∼63 dB for the indoor environment and ∼65 dB for the outdoor environment, as shown in Figure 5 and Figure 9.

Table 5. SNR required (in dB) in $1\times 4$ MIMO configuration system to achieve the target ABER for varying N values.

$\mathit{N}$	InH—Indoor Office		Umi—Street Canyon
	28 GHz	73 GHz	28 GHz	73 GHz
64	78	88	83	88
256	74	84	75	82
1024	71	78	66	72

and

Table 6. SNR required (in dB) to achieve the target ABER for varying $N_T$, fixed $N=256$ and $N_R=1$.

${\mathit{N}}_{\mathit{T}}$	InH-Indoor Office	Umi- Street Canyon
	28 GHz	28 GHz
4	73	75
16	67	68
64	63	65

show the effect of adjusting N and $N_T$ on SNR(dB) demands for various configurations.

Figure 10 depicts the ABER comparison of continuous infinite resolution and discrete reflection phase RIS under InH- indoor office environment at 28 GHz. To attain the desired ABER, the continuous phase RIS, 1-bit discrete phase RIS, and 2-bit discrete phase RIS demand an SNR of ∼78 dB, ∼90 dB, and ∼84 dB, respectively. The 2-bit discrete phase RIS has an SNR gain of ∼6 dB over the 1-bit discrete phase RIS. The 1-bit discrete phase RIS maps the phase shifts to 2 discrete phase levels, and the effect of the residual phase in (11) will be significant. Therefore, ${\epsilon }^{\prime }$ decreases. However, the 2-bit discrete phase RIS maps the phase shifts to 4 discrete phase levels, and the effect of the residual phase will be reduced; therefore, ${\epsilon }^{\prime }$ increases. Doubling P improves the SNR gain by ∼6 dB. By increasing P, the performance of the discrete phase RIS is approaching the ideal continuous phase RIS. A similar performance can also be observed in the outdoor environment, which is evident from Figure 11.

The proposed system can be adapted for scenarios involving multiple users, as illustrated in Figure 1 and Figure 2, it can be integrated with time division multiple access (TDMA). This setup divides the total time among the users (L). Each user receives a time slot of $1/L$ duration, during which all elements of the RIS are dedicated to that specific UE.

The rate attained by the l-th user in a continuous phase shifter RIS is given by

$$R_l={\displaystyle \frac{1}{L}}{log}_2\left(1+ϵ\right)$$

(22)

For the discrete reflection RIS, the rate attained by the l-th user can be obtained by replacing $ϵ$ in (22) by ${ϵ}^{\prime }$. The sum rate of the proposed system for multiple users can be obtained through ${\sum }_{l=1}^L{R}_l$. Figure 12, Figure 13 and Figure 14 present the sum rate performance under various conditions. The figures are plotted for $N_t=16$, two users with a single antenna ($N_r=1$) and 256 RIS elements. Figure 12 depicts the sum rate performance of two users in indoor and outdoor scenarios at varying mmWave frequencies. The figure shows that the increase in SNR enhances the sum rate performance. The figure clearly shows that the 28 GHz mmWave range outperforms the 73 GHz range. This is due to the higher dispersion and absorption properties of the mmWave band, which dominate at the higher mmWave frequencies. The figure indicates that the indoor scenario has better sum rate performance than the outdoor. An important observation is that even under an indoor environment, the higher mmWave frequency (73 GHz) transmission severely degrades compared to the outdoor scenario. This demonstrates how higher mmWave frequencies are sensitive to external objects.

Figure 13 and Figure 14 demonstrate the sum rate performance of two users in the InH—office and UMi—street canyon, respectively, at 28 GHz with continuous and discrete phase RIS. In this analysis, three distinct curves are presented, each representing different types of RIS: the continuous phase RIS, indicated by red squares; the 1-bit discrete phase RIS, represented by green circles; and the 2-bit discrete phase RIS, marked with blue triangles. The findings reveal a clear trend: the overall sum rate improves significantly as the SNR increases and b grows. Notably, the continuous phase RIS consistently outperforms the other configurations across the entire SNR range, achieving the highest sum rate. However, producing continuous or infinite resolution is impractical and increases hardware complexity. The discrete phase shift RIS, which operates with finite resolutions and thus reduces hardware complexity, does experience some performance degradation compared to the continuous phase shift RIS.

As illustrated in Figure 13 and Figure 14, the 1-bit discrete phase shift RIS can only achieve 2 levels, which leads to significant performance degradation. In contrast, the 2-bit discrete phase shift RIS, which provides four levels of resolution, shows improved performance. This demonstrates that increasing quantization bits results in a better sum rate. This observation highlights an essential trade-off in communication systems: while enhancing quantization resolution improves SE, it also introduces greater hardware complexity. Ultimately, finer phase resolution in RIS allows for better network performance, reflecting a crucial balance between efficiency and practicality in the design of advanced communication systems.

Table 7. Comparison of sum rate (bps/Hz) under continuous and discrete phase RIS at SNR of 90 dB and 28 GHz mmWave frequency.

Schemes	InH Office	UMi Streen Canyon
Continuous phase shift RIS	∼15.53	∼11.37
1-bit discrete phase shift RIS	∼1.8	∼0.537
2-bit discrete phase shift RIS	∼3.78	∼2.78
Difference (in bps/Hz) between continuous and 1-bit discrete phase shift RIS	∼13.73	∼10.84
Difference (in bps/Hz) between continuous and 2-bit discrete phase shift RIS	∼11.75	∼8.59

compares the sum rate (bps/Hz) under continuous and discrete phase RIS at 28 GHz mmWave frequency. It shows that the increase in quantization levels reaches the near-optimal solution.

6. Conclusions

This work introduces an RIS-assisted mmWave M-MIMO system to improve SE, EE, and reliability. The proposed approach involves having all transmit antennas convey the same information symbol to achieve additional diversity gain. The system’s performance is evaluated under 3GPP 5G indoor and outdoor channel models for 28 GHz and 73 GHz mmWave frequencies. The evaluation considers office and street canyon channel environments. The Monte Carlo simulation results show a significant decrease in the ABER performance of the RIS-assisted mmWave M-MIMO system in the investigated indoor and outdoor channels. Interestingly, the system’s ABER performance proves superior at 28 GHz compared to 73 GHz mmWave frequency, regardless of the indoor or outdoor scenario. Additionally, increasing N and $N_T$ significantly enhances the EE of the proposed system. In indoor environments, it is suggested to use 28 GHz for lower data rate requirements. For data-hungry applications, we recommend using 73 GHz by suitably increasing the number of reflecting components in RIS to compensate for the poor ABER performance. For outdoor environments with high data rate demands, we can use 73 GHz by appropriately selecting the number of antennas in the M-MIMO BS and the number of reflecting components in RIS.

Finally, the ideal continuous phase RIS in the proposed system is replaced with the practically implementable discrete resolution phase shifter RIS, and its ABER and sum rate performances are observed for indoor and outdoor environments. It has been observed that doubling the value of P results in a ∼6 dB increase in SNR gain. Due to the significant vulnerability to blockages and greater path loss at mmWave frequencies, these systems exhibit lower SE values than their sub-6 GHz counterparts. Nevertheless, the ample bandwidth in the mmWave spectrum allows for higher overall achievable sum rates. As the proposed work innovatively integrates RIS, mmWave, and M-MIMO and validates the performance under 3GPP standardized indoor and outdoor channels, it is a potential contender for physical layer technology in the upcoming landscape of B5G and 6G networks. Future work could focus on implementing an appropriate channel coding scheme to improve ABER performance. The proposed system model can be tested for blind and AP RIS configurations.