Technological Evolution from RIS to Holographic MIMO

*Jiguang He, Chongwen Huang, Li Wei, Yuan Xu, Ahmed Al Hammadi and Merouane Debbah*

### **Abstract**

Multiple-input multiple-output (MIMO) techniques have been widely applied in current cellular networks. To meet the ever-increasing demands on spectral efficiency and network throughput, more and more antennas are equipped at the base station, forming the well-known concept of massive MIMO. However, traditional design with fully digital precoding architecture brings high power consumption and capital expenditure. Cost- and power-efficient solutions are being intensively investigated to address these issues. Among them, both reconfigurable intelligent surface (RIS) and holographic MIMO (HMIMO) stand out. In this chapter, we will focus on the ongoing paradigm shift from RIS to HMIMO, covering both topics in detail. A wide range of closely related topics, e.g., use cases, hardware architectures, channel modeling and estimation, RIS beamforming, HMIMO beamforming, performance analyses of spectral- and energy-efficiency, and challenges and outlook, will be covered to show their potential to be applied in the next-generation wireless networks as well as the rationales for the technological evolution from RIS to holographic MIMO.

**Keywords:** reconfigurable intelligent surface, holographic MIMO, energy efficiency, channel estimation, hybrid precoding

### **1. Introduction**

In order to fully achieve 5G/6G enhanced mobile broadband communications, it is an inevitable trend to move from microwave frequency band, e.g., sub-6 GHz to millimeter wave (mmWave) or even terahertz (THz) frequency bands [1]. However, various challenges are introduced accordingly, such as severe path loss, high power consumption, serious hardware impairment, and frequent blockage. At the early stage, researchers devoted to addressing these aforementioned challenges through hybrid analog-digital precoding along with large-sized antenna arrays at both transmitter and receiver sides, which was verified to offer nearly the same performance in terms of achievable rate compared to its pure digital precoding counterpart under full channel state information (CSI) assumption [2]. However, the energy efficiency (EE) of mmWave or THz system needs to be further enhanced, since the power consumption from digital-to-analog/analog-to-digital converter and up/down converter in the radio frequency (RF) chains is still high. Various novel massive MIMO architectures

are analyzed and compared in [3], where reflect/transmit array-based architectures are verified to obtain the best trade-off.

There are two promising candidate technologies, aiming for not only enhancing EE but also spectrum efficiency (SE). One is the reconfigurable intelligent surface (RIS), and the other is holographic multiple-input multiple-output (HMIMO). At the early stage, much more effort were made on RIS-assisted networks compared to HMIMO. Recently, the emphasis of the research community has been shifted toward HMIMO. RIS and HMIMO share some similarities, e.g., made of a large number of cost-efficient low power consumption elements. However, they differ in various aspects. The RIS is usually a passive, tunable, and intelligent metasurface. Unlike the traditional active relays, which can perform either amplify-and-forward (AF), decode-and-forward (DF), or compute-and-forward (CF), RIS does not possess any baseband processing capability. Thus, it can not receive and post-process any incident signals from other network nodes, e.g., base station (BS) or mobile station (MS). Because of this, RIS brings difficulty in efficient yet effective channel estimation for the system. For instance, the BS has to estimate two large dimensional channel coefficient matrices (i.e., MS-RIS and RIS-BS channels) simultaneously via uplink pilot signal transmission. In addition, during the sounding process, coordination and strict synchronization among the MS, RIS, and BS are required. Nevertheless, by deploying an RIS between the BS and the MS, it enables virtual line-of-sight (LoS) transmission especially when the direct LoS between the BS and the MS is temporally blocked. The RIS can also enhance radio localization thanks to the following reasons: (i) The RIS is a natural anchor upon its deployment; (ii) The RIS offers high-resolution angle of departure (AoD) and/or angle of arrival (AoA) estimation; (iii) The RIS can further extend the localization range. Studies show that RIS can also benefit integrated sensing and communication (ISAC) [4].

The full potential of RIS can not be realized unless the CSI acquisition is performed efficiently and effectively. However, there is still a large room for improvement. Meanwhile, an obvious trend has been seen for a paradigm shift from RIS to HMIMO. Under the framework of HMIMO, the tunable metasurface acts as an active transceiver, which is a greener way to implement the massive (mmWave/THz) MIMO systems without the need of a massive number of RF chains. The HMIMO transceiver is made of densely packed meta-atoms, usually with sub-wavelength inter-element spacing (unlike half-wavelength inter-element spacing for RIS), enabling super directivity. However, HMIMO has more severe mutual coupling effect compared to RIS. The large-sized HMIMO aperture pushes the far field further away. Therefore, most studies focus on radiative near-field propagation when modeling the HMIMO channels. An interesting finding that extra degrees of freedom (DoFs) exist even when the MS is located at the LoS path of the BS has been discovered recently [5]. HMIMO surfaces are powerful in transferring the orbital angular momentum (OAM) property, yielding enhance system capacity within a few Rayleigh distances. A comprehensive comparison between RIS and HMIMO can be found in **Table 1**. The foreseeable key performance indicator (KPI) enhancement by the introduction of RIS and/or HMIMO generally includes: (i) Gbps or even Terabit/s level average or peak data rate, (ii) seven 9's reliability, (iii) sub-ms air interface latency, and (iv) cm-level localization accuracy.

From the industrial perspective, ETSI lauched an Industry Specification group on RIS, covering various research aspects. RIS Tech Alliance (RISTA) focuses on bringing together industrial and academic partners, pushing the RIS techniques from theory into practice. The RIS technology white paper was released by RISTA on March 2023.


#### **Table 1.**

*Comprehensive comparison between RIS and HMIMO.*

Also, 3GPP listed RIS as one of the additional RAN1/2/3 candidate topics. In this sense, it will probably receive a high chance to be studied and included in Release 19. HMIMO techniques have not been studied and included in any global or regional standard development organization (SDO) bodies yet. However, it is highly probable that it will gain tremendous attraction and momentum in the near future as a technique beyond massive MIMO.

### **2. RIS vs. HMIMO hardware architectures**

Both RIS and HMIMO are metasurfaces equipped with integrated electronic circuits that can intelligently control the incoming waves, resulting in a programmable electromagnetic field. They are both composed of feeding, substrate, and unit cells. Precisely, the feed can excite the RIS or HMIMO to generate the desired electromagnetic waves, and the substrate support the structure. In addition to the feeding line and substrate, the radiation elements play an important role, which is mounted on the substrate and form uniform/non-uniform radiation patterns, transforming the reference waves into radiated waves. There are some differences in the fabrications or configurations between the RIS and HMIMO.

Specifically, in RIS systems, the feeds are set outside the meta-surface while the feeds are attached to the HMIMO surface in a more flexible behavior [6]. In such way, the electromagnetic waves propagate along the HMIMO surface, and the elements are excited one by one, enabling HMIMO to serve as a transceiver. However, RIS requires additional configuration of external feeding lines to excite unit cells, as shown in **Figure 1**. In addition, since the long feeding line is adopted in RIS, the layout in the implementation is much more complex than the series feeding in HMIMO systems. Thus, HMIMO is more suitable to be implemented in various scenarios compared with RIS. Then we will discuss the details in fabrication from the perspective of feed, substrate, and unit cells for RIS and HMIMO.

In RIS, the spatial feeding techniques are adopted, such as a horn antenna or microstrip antenna array are placed very close to RIS to feed such structures. The feed is adopted to generate a reference wave to excite unit cells in RIS. A single- or a

**Figure 1.** *A schematic view of RIS hardware structures.*

multi-layer stack of planar structure are fabricated using lithography and nanoprinting methods [6]. Each RIS element situated on a ground plane adopts varactor diodes or other electrical materials to reflect incoming waves electronically by providing phase modulation. Since no amplifier is employed, RIS consumes less energy and is easily deployed into building facades, room, up to being integrated into human devices. The input voltage to varactor diodes can be controlled to provide variable capacitance, which is an important characteristic of the materials that constitute RIS units. The unit cell in RIS can be fabricated using various varactor types, including metal plate with vias, D-shaped patch, split-ring, and conductive patch separated by the annular slot [7]. In addition to varactor diodes, positive intrinsic-negative (PIN) diodes can also be utilized to tune the impedance in RIS unit cells, i.e., the on/offstate of PIN diodes exhibits the magnitude and phase difference of the reflection.

Compared with RIS, the fabrication in HMIMO is much more diverse due to development in metamaterials, as shown in **Figure 2**. In HMIMO systems, the feed is integrated into the HMIMO or located externally. The reference wave generated by the feed propagates along the HMIMO surface, then the designed wave is excited from the interference wave of the reference wave and the reflected wave from the object. Clearly, the location of the feed generates a specific propagation mode, for example, a transverse electric propagation mode of the reference wave is supported if the feed is located on the HMIMO surface, while a transverse magnetic propagation mode is supported if the feed is placed on the bottom of HMIMO surface [9]. In addition to the location of feed, the feed material also affects the propagation mode. For example,

**Figure 2.**

*The two operation modes of HMIMOS systems along with their implementation and hardware structures [8].*

#### *Technological Evolution from RIS to Holographic MIMO DOI: http://dx.doi.org/10.5772/intechopen.112039*

dipoles, planar Vivaldi feed, antipodal Vivaldi feed, and dipole-based Yagi-Uda-feed are capable of exciting transverse electric propagation mode [9].

The substrate enables the reference wave to propagate along the HMIMO surface. The substrate can be in a plate shape that supports the surface wave mode or in a microstrip line shape that supports the waveguide mode [9]. Surface wave mode refers to the propagation of electromagnetic waves along the surface of the HMIMO transceiver. By controlling the states and properties of elements on the surface, HMIMO can guide and manipulate surface waves to achieve specific functions such as wavefront shaping or beamforming. Waveguide mode refers to the guided propagation of electromagnetic waves within internal or integrated waveguides, which can be within the system or attached to it. These waveguides may serve as feeds or interconnections within the HMIMO system. In addition, the substrate materials are also different, i.e., the dielectric substrate and semiconductor substrate [9]. For example, the dielectric substrate is commonly adopted in HMIMO systems, such as printed circuit board, laminates substrate, silicon dioxide substrates, and anisotropic artificial substrates. The silicon dioxide substrate also possesses a low dielectric loss, such as the graphene patches transferred silicon dioxide substrate adopted in tunable THz HMIMO systems. In addition to the above dielectric substrate, the semiconductor substrate is also employed in HMIMO systems for the low cost and excellent conductivity [9].

The radiation elements can be manufactured by metal, dielectric, and graphene materials [9]. Specifically, metal radiation elements exhibit high conductivity and are applicable to low frequencies with insignificant losses. The dielectric radiation elements are more suitable for a wider range of bandwidth. The graphene radiation elements are also the perfect choice for THz HMIMO systems or optical communications.

The HMIMO surface can be divided into contiguous and discrete modes [8]. In contiguous HMIMO systems, a virtually uncountably infinite number of radiation elements are incorporated in a limited area, generating spatially continuous aperture. Such a scheme provides a theoretically infinite number of elements that can approach the inherent capacity and spatial resolution limit. However, the contiguous mode is impractical, thus a discrete HMIMO mode is proposed, which is composed of countable radiation elements. This mode has higher feasibility and lower power consumption while achieving lower spatial resolution and undesired side lobes. Some studies have compared the contiguous mode and discrete mode to investigate the optimal discretization bits. Hu et al. [10] showed that 2 bits quantization is able to approximate the sum rate with contiguous HMIMO systems for multi-user scenario, while 1 bit quantization is enough in the single-user scenario.

In order to achieve both contiguous and discrete apertures, fabrication methods are important. Typically, programmable metamaterials are adopted to approximate the contiguous HMIMO surfaces, where the varactor loading technique is adopted in continuous monolayer metallic structures incorporating a large number of metaparticles [8]. Each meta-particle consists of two metallic trapezoid patches, varactor diodes, and a continuous strip. Specifically, whether the element radiates the energy of the reference wave into free space depends on the state of the diodes [11]. The bias voltage is input to varactor diodes to manipulate the phase and amplitude of each radiation element, resulting in a controlled electromagnetic environment. Different from the contiguous HMIMO systems, the discrete HMIMO systems involve a number of meta-particles, which are composed of a metamaterial layer (graphene material), sensing and actuation layers, shielding layer, computing layer, and interface and communication layer [8].

### **3. RIS vs. HMIMO channel modeling and estimation**

Channel modeling plays an essential role in understanding the fundamentals of the channel characteristics, developing cutting-edge signal processing algorithms, and optimizing network resources. The authors in ref. [12] focused on the free-space path loss models for RIS-assisted wireless communications and established a rigorous relationship between them and system parameter setups, e.g., the distances between the transmitter/receiver and the RIS, the RIS aperture, the radiation patterns of antennas, etc. The power scaling laws were studied in ref. [13] for asymptotically large RISs. The work in ref. [14] divided the RIS into multiple RIS tiles and derived the corresponding tile response functions with arbitrary transmission mode, and incident and reflection directions. Based on these, a physics-based end-to-end channel model was developed for the RIS-assisted wireless systems, taking into account the effect of transmission mode, incident angle, and reflection angle of all RIS tiles.

RIS channel estimation can be classified into three major categories, including model-based, data-driven, and the mixture of the former two. For the model-based RIS CE, various approaches are considered to estimate the individual channels, cascaded channel, or channel parameters. Under the assumption of passive RIS, the pilot signals received at the BS (over uplink transmissions) or MS (over downlink transmissions) include the information of channel coefficient matrices for both hops, i.e., BS-RIS and RIS-MS links, which in turn brings more difficulties on CSI acquisition. In the literature, such kind of RIS CE can be done by leveraging the bilinear generalized approximate message passing (BiG-AMP) for sparse matrix factorization and the Riemannian manifold gradient-based algorithm for matrix completion [15]. The framework of two-stage RIS-aided channel estimation (TRICE) was proposed in ref. [16] to estimate the cascaded channel matrix, followed by parallel factor (PARAFAC) tensor decomposition [17] to obtain the two individual channels. Compressive sensing (CS) techniques, e.g., orthogonal matching pursuit (OMP) and generalized approximate message passing (GAMP), were also applied in the RIS-assisted networks [18] to estimate the cascaded channel. Different from the previous works, the authors in ref. [19] focus on estimating the channel parameters in two stages, by adopting off-grid CS technique, i.e., atomic norm minimization (AMN). The availability of channel sparsity is essential in the aforementioned approaches. Extension from single-user scenario to multi-user scenario, the different properties of the channels, i.e., BS-RIS and RIS-MS channels, are leveraged in the design of the CE algorithm [20]. The properties include the changing rate and channel sparsity. The former determines the frequency of CE, and the latter determines the training overhead of channel estimation. Note that all the MSs share the same BS-RIS channel, which can be considered to reduce the training overhead. In terms of datadriven approaches, the authors in ref. [21] designed a twin convolutional neural network (CNN) architecture to estimate both direct and cascaded channels from received pilot signals. By leveraging the advantages of both model-based and data-driven approaches, deep unfolding-based RIS channel estimation exhibits excellent performance [22]. **Figure 3** depicts the RIS channel estimation results from different approaches, where three training overhead values, i.e., *K* ¼ 24,28,32, are considered. The numbers of transmit antennas and RIS elements are 16 and 32, respectively, while the MS is assumed to have a single antenna. Deep unfolding outperforms the ANM thanks to its mixture nature of data-driven and model-based approaches [22].

The HMIMO channel modeling focuses on the radiative near-field propagation due to the electromagnetically large antenna arrays employed at the transmitter and/or the receiver. The model incorporating arbitrary scattering propagation conditions was

*Technological Evolution from RIS to Holographic MIMO DOI: http://dx.doi.org/10.5772/intechopen.112039*

**Figure 3.** *Comparison of RIS CE with different schemes.*

proposed by adopting the first principles of wave propagation and Fourier plane-wave series expansion of the channel response [23]. The equivalent wavenumber domain channel from the spatial domain was obtained via transformation. Meanwhile, the Fourier plane-wave series expansion of the channel response was studied in ref. [23]. The equivalent wavenumber domain channel from the spatial domain was obtained via transformation. Meanwhile, the physically-meaningful stochastic channel model of non-isotropic radio waves propagation was also obtained for the far-field case [24]. The mathematically tractable HMIMO channel model is essential for algorithm development, such as holographic beamforming, detailed in the next section.

The holographic MIMO channel estimation was investigated in ref. [25], where the authors proposed a subspace-based channel estimation approach for the far-field propagation condition. Such an approach only requires the information of the subspace of the spatial correlation matrix while attaining the performance of minimum mean square error (MMSE) estimator in the high SNR regime. It is well known that the MMSE estimator requires complicated matrix inverse operation and full knowledge of the spatial correlation matrix. An extension to near-field channel estimation can be found in ref. [26], where the polar domain sparsity other than angular domain sparsity along with off-grid CS technique, i.e., polar-domain simultaneous iterative gridless weighted (P-SIGW) scheme, were considered.

### **4. RIS beamforming vs. HMIMO beamforming**

The RIS can perform beam focusing and offer beamforming gain in order to compensate for the severe path loss. For the SISO system, the optimal RIS beamforming vector can be found based on the CSI of the BS-RIS and RIS-MS channels. For more complicated scenarios, e.g., MIMO systems, finding the optimal RIS

design is not straightforward because of the strict RIS hardware constraints. In the literature, researchers focused on the design of RIS beamforming and TX beamforming/precoding simultaneously, termed as joint active and passive beamforming. References [6, 27] are among the first ones dealing with such a challenging problem. In these works, perfect or imperfect CSI information was assumed. In other words, the joint design is considered after the CE phase, detailed in Section 3. Another alternative way to do this is to create a beam codebook and conduct beam scanning to find the optimal beam pair, one used at the BS and the other used at the RIS. There are several challenges raised in the codebook design. The large-sized RIS requires huge computation for the beam codebook design, aiming at the collection of beams having full coverage of the space. Second, the beam may have many sidelobes, resulting from the RIS hardware constraints. Third, the beam scanning process is supposed to be time inefficient when both nodes adopt large-sized codebooks.

Unlike RIS beamforming, HMIMO beamforming is much more tricky due to the closely packed patch antennas. Even the simple linear precoding schemes, such as zero-forcing (ZF), with continuous-aperture surfaces are impractical due to a large number of patch antennas, not to mention MMSE beamforming, which can be accounted for expensive matrix inversion operation. To solve this, ref. [28] leveraged a novel low-hardware complexity ZF precoding scheme that is based on a Neumann series (NS) expansion, which replaces the expensive matrix inversion operation while being similar in terms of achievable sum rate with conventional ZF, as shown in **Figure 4**. For the holographic beamforming, the authors in refs. [10, 29] also studied discrete amplitude-controlled holographic beamforming and analyzed the effect of radiation amplitude discretization on the sum rate for the downlink multi-user communication system. In order to realize holographic beamforming, the holographic interference principle that the holographic transceivers record the interference between the reference wave and arbitrary desired object waves, known as an interference pattern, is considered. By coupling the reference wave with the interference

#### **Figure 4.**

*Comparison of ZF precoding schemes and NS-based ZF precoding for HMIMO systems with 729 transmit patch antennas and 144 receive patch antennas (spacing is λ=*3*) [28].*

pattern, the holographic transceivers are capable of performing beamforming toward the desired direction by radiation amplitude control of the reference wave propagating along the metasurface. Di [30] studied joint hybrid digital beamforming and holographic beamforming for wideband OFDM transmissions while compensating for the beam squint loss via linear additivity of holographic interference patterns.

The above work mainly dealt with beamforming in the spatial domain, however, the polarization domain should not be ignored in RIS and HMIMO systems as well. The adoption of the dual-polarization (DP) or tri-polarization (TP) feature is expected to further improve the performance without enlarging antenna array size, enabling multiple independent information to be sent in two or three polarization directions, thus offering polarization diversity in addition to spatial diversity to improve spectral efficiency. However, the cross-polarization in polarization systems also brings new interference and degrades system performance, thus, the beamforming in polarization domain is required. To exploit polarization diversity, a few recent works discussed the deployment of DP RIS systems [31–33]. The work in ref. [33] proposed a RIS-based wireless communication structure to control the reflected beam and polarization state to maximize the received signal power. de Sena et al. [31] also designed a transmission scheme in RIS-assisted systems. Although HMIMO can also integrate polarization techniques, there is still a little difference between RIS and HMIMO. Specifically, due to the large size of HMIMO and higher frequencies, the communication range shifts from the traditional far-field region to the near-field zone [13], and the achievable polarization diversity also increases from two to three, i.e., TP HMIMO is available. The difficulty of polarization interference increases in TP HMIMO since the number of cross-polarization components is one in DP RIS and two in TP HMIMO. To fully exploit polarization diversity and remove both spatial and polarization interference, a two-layer precoding design was investigated for multi-user TP HMIMO systems, which is compared with the user-cluster-based scheme, i.e., different users are assigned to different polarizations [34], as shown in **Figure 5**. A complete list of works on holographic beamforming can be found in ref. [9].

**Figure 5.** *Spectral efficiency of the user-cluster-based and two-layer beamforming schemes.*

To be specific, the beamforming in the spatial domain mainly removes interference resulting from the mutual coupling or inter-users, while the beamforming in the polarization domain is designed to remove polarization interference caused by crosspolarization components.

### **5. Performance analyses**

The phase shift and power allocation schemes are designed in RIS-assisted systems for higher energy efficiency and lower transmit power. Huang et al. [6] developed energy-efficient designs based on alternating maximization, gradient descent search, and sequential fractional programming methods, and these RIS-based resource allocation methods could provide up to 300% higher EE in comparison with the use of regular multi-antenna amplify-and-forward relaying, as shown in **Figure 6**. In addition, Yang et al. [35] adopted a dual method to solve the problem of resource allocation for multiuser communication networks with a RIS-assisted wireless transmitter. In this network, the sum transmit power of the network is minimized by controlling the phase beamforming of the RIS and transmit power of the base station, which could reduce up to 94% and 27% sum transmit power compared to the maximum ratio transmission (MRT) beamforming and ZF beamforming techniques, respectively.

Beamforming design is important in enlarging coverage, enhancing capacity, and removing inter-user interference. For example, Huang et al. [36] proposed a joint design of digital beamforming matrix at the BS and analog beamforming matrices at the RISs for the multi-hop RIS-assisted communication network to improve the coverage range at THz-band frequencies, leveraging deep reinforcement learning (DRL)

**Figure 6.**

*Average EE using either RIS or AF relay versus the maximum transmit power constraint P*max *a) M* ¼ 32 *BS antennas, K* ¼ 16 *users, N* ¼ 16 *RIS elements; and b) M* ¼ 16 *BS antennas, K* ¼ 8 *users, N* ¼ 8 *RIS elements [6].*

#### *Technological Evolution from RIS to Holographic MIMO DOI: http://dx.doi.org/10.5772/intechopen.112039*

to combat the propagation loss. Simulation results showed that the two-hop scheme is able to improve 50% more coverage range of THz communications compared with the zero-forcing beamforming without RIS and 14% more transmission distances than that of the single-hop scheme. The authors in ref. [37] jointly optimized the active beamforming of the power station and the passive beamforming of the RIS in an iterative behavior using Lagrange dual theory to improve system EE, simulation results showed that a higher EE is achieved compared to the throughput-based maximization algorithm. The study in ref. [38] investigated the approximations of the average rate of user equipment and a RIS configuration algorithm to improve the average sum rate with low complexity in RIS-assisted multiple-input single-output (MISO) systems. The study in ref. [39] leveraged DRL to jointly design of transmit beamforming matrix at the base station and the phase shift matrix at the RIS, and the result showed its comparable sum-rate performance with the classic weighted minimum mean square error algorithm.

The above methods require the full knowledge of instantaneous CSI, which requires burdensome overhead. Therefore, some works designed beamforming schemes with imperfect CSI. For example, Gao et al. [40] studied the robust beamforming design for RIS-assisted communication systems from a multi-antenna access point to a single-antenna user under imperfect CSI. By decoupling the nonconvex optimization problem into two subproblems, the transmit beamforming at the access point is optimized and discrete phase shifts of RIS is designed to minimize the transmission power of access point (AP), subject to a signal-to-noise ratio constraint at the user. Simulation results showed that the proposed scheme can approach the performance of the perfect CSI counterpart and substantially outperform traditional non-robust methods. Gan et al. [41] investigated the ergodic capacity using the alternating direction method of multipliers, fractional programming, and alternating optimization methods, in RIS-assisted multi-user MISO wireless systems, considering statistical CSI instead of instantaneous CSI. Simulation results showed that such statistical CSI design achieved decent performance compared with the instantaneous CSI-based design, especially in the low and moderate SNR regimes. Gan et al. [42] proposed a low-complexity algorithm via the two-timescale transmission protocol in cell-free systems through statistical CSI at RISs and instantaneous CSI at BSs, where the joint beamforming at BSs and RISs is facilitated via alternating optimization framework to maximize the average weighted sum-rate. A power gain on the order of Oð Þ *M* is achieved without LoS components, with *M* being the BS antenna's number.

The DoF is also an important performance indicator. In addition to the inherent DoF limit of the RIS, rotating the RIS rather than moving it over a wide area can also obtain a considerable improvement. For example, Cheng et al. [43] considered the extra DoF offered by the rotation of the RIS plane and investigated its potential in improving the performance of RIS-assisted wireless communication systems by considering the radiation pattern. The results showed that the maximum capacities are obtained by rotating RIS, as shown in **Figure 7**. Compared with RIS systems, the strong mutual coupling generated from the sub-wavelength spacing between adjacent antennas is inevitable in HMIMO communications, resulting in distorted radiation patterns and low radiation efficiencies. However, ignoring the mutual coupling would not seriously affect the DoF of the HMIMO, i.e., the DoF reaches its limit when the antenna number is larger than 2*Lx=λ*<sup>0</sup> þ 1, where *Lx* is the array size, and *λ*<sup>0</sup> is the wavelength [44]. For an antenna number larger than 2*Lx=λ*<sup>0</sup> þ 1, the DoF ceases to increase while the radiation efficiencies keep decreasing, resulting in a reduced capacity.

**Figure 7.** *Impact of RIS rotation angle θ*<sup>0</sup> *on the ergodic capacity [43].*

### **6. Challenges and outlook**

In this chapter, we cover various aspects of RIS and HMIMO, such as channel modeling, estimation, beamforming control, etc. Both of the techniques share some common challenges before their implementations and applications to future wireless systems. For instance, the difficulty of channel estimation increases as the number of meta-atoms increases. It might be even more difficult to estimate RIS channels due to the inherent passive nature of the RIS. The HMIMO channel estimation requires a larger training overhead compared to the current massive MIMO CE due to a further increase in the number of elements. The fundamental study of the performance limits needs a full understanding of the electromagnetic (EM) theory and physics, which also applies to channel modeling.

#### **6.1 CE for multi-hop RIS-empowered systems**

RIS plays an important role in transmitting signals for unfavorable scenarios, especially when the direct links are blocked due to walls or obstacles. Most of the current works mainly focus on single-hop RIS-assisted systems, however, in practical scenarios where the receiver is quite far away from the transmitter, employing multihop RIS for signal relaying becomes imperative. In such a case, the desired signal will pass through more than one RIS, thus a high-order cascaded channel is generated. Unfortunately, the current channel acquisition methods, including model-free based schemes and model-based approaches, are only applicable to single-hop RIS-assisted wireless communications, and CE in multi-hop RIS is complex due to the involvement of higher-order channels. Plus the incapability of signal processing at the RIS part, the CE for multi-hop channels at the receiver/transmitter is much more challenging. Some existing works may enlighten the possible solutions to this challenge, for instance, the involved channels can be represented as variables in a factor graph, the relationship among these channels is denoted as factors, then the effective message-passing algorithms in multi-layers can be derived for the posterior probability of unknown

channels. Nevertheless, the inherent ambiguities in such a factor graph should be carefully addressed.

In addition, most of the current works design beamforming for RIS-assisted wireless communications with perfect CSI, however, CE techniques may not perfectly estimate all involved channels, and imperfect CSI has negative impacts on beamforming design. Specifically, the estimation error in cascaded channels in RISaided communications may be larger due to error propagation. Consequently, taking estimation errors in beamforming design is necessary, i.e., a more robust beamforming scheme should be designed.

#### **6.2 CE-implicit schemes for RIS-assisted communications**

The training overhead in the CE process is normally large, therefore, designing RIS-assisted systems in the absence of explicit channel information could save temporal and spatial resources greatly. Fortunately, it is feasible to design such beamforming schemes without explicit CE for various RIS-empowered wireless communications. This approach optimizes system parameters without relying on the traditional explicit CE paradigm, saving training overhead and avoiding power allocation to the training part as well. For example, the explicit CE can be bypassed using machine learning methods to achieve a superior transmission rate or facilitate the phase matrix design using statistical parameters instead of instantaneous CSI.

#### **6.3 Low-complexity beamforming for HMIMO systems**

The large number of closely packed patch antennas increases the complexity of the beamforming design for HMIMO systems. For instance, the traditional ZF and MMSE beamforming schemes are impractical to be directly applied in hardware design. Therefore, low-complexity beamforming is imperative in practical applications. One beamforming approach is to replace matrix inversion with polynomial functions, as introduced in this chapter. However, such methods rely on the specific channel structure and may diverge under some parameter settings. Consequently, an effective and robust beamforming technique is expected for HMIMO systems, in order to eliminate both spatial and polarization interference or enhance signal strength in the desired direction.

#### **6.4 Optimal design for HMIMO**

Although the continuous HMIMO can achieve the spatially continuous aperture, it is infeasible to construct such a continuous structure in practical applications. Therefore, the discrete HMIMO that incorporates a large number of patch antennas is the most viable approach. Although increasing the number of patch antennas would bring performance benefits, this improvement reaches the plateau for the specific number of patch antennas, i.e., the optimal number of patch antennas, which can be accounted for by mutual coupling effects. For instance, the more patch antennas placed in a fixed area, the stronger mutual coupling generated, resulting deformed radiation pattern and reduced antenna efficiency. Consequently, the performance gain brought by the larger number of antennas ceases eventually. Based upon this observation, the optimal configuration to achieve the best performance of HMIMO systems is required to be investigated.

Albeit the aforementioned challenges for both RIS and HMIMO techniques, HMIMO other than RIS will be widely recognized as a beyond massive MIMO technique. We will witness the growing trend of paradigm shift from RIS to HMIMO in the near future.
