Intelligent Surfaces for 6G Wireless Networks: A Survey of Optimization and Performance Analysis Techniques
Rawan Alghamdi, Reem Alhadrami, Dalia Alhothali, Heba Almorad, Alice Faisal, Sara Helal, Rahaf Shalabi, Rawan Asfour, Noofa Hammad, Asmaa Shams, Nasir Saeed, Hayssam Dahrouj, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini
11 Intelligent Surfaces for 6G Wireless Networks: ASurvey of Optimization and Performance AnalysisTechniques
Rawan Alghamdi, Reem Alhadrami, Dalia Alhothali, Heba Almorad, Alice Faisal, Sara Helal, Rahaf Shalabi,Rawan Asfour, Noofa Hammad, Asmaa Shams, Nasir Saeed, Hayssam Dahrouj, Tareq Y. Al-Naffouri, andMohamed-Slim Alouini
Abstract —This paper surveys the optimization frameworksand performance analysis methods for large intelligent surfaces(LIS), which have been emerging as strong candidates to supportnext generation wireless physical platforms (6G). Due to theirability to adjust the channels through intelligent manipulationsof the reflections phase shifts, LIS have shown promising meritsat improving the spectral efficiency of wireless networks. In thiscontext, researchers have been recently exploring LIS technologyin depth as a means to achieve programmable, virtualized,and distributed wireless network infrastructures. From a systemlevel perspective, LIS have also been proven to be a low cost,green, sustainable, and energy-efficient 6G solution. This paperprovides a unique blend that surveys the principles of operationof LIS, together with their optimization and performance analysisframeworks. The paper first introduces the LIS technologyand its physical working principle. Then, it presents variousoptimization frameworks that aim to optimize specific objectives,namely, maximizing energy efficiency, sum-rate, secrecy-rate,and coverage. The paper afterwards discusses various relevantperformance analysis works including capacity analysis, theimpact of hardware impairments on capacity, uplink/downlinkdata rate analysis, and outage probability. The paper furtherpresents the impact of adopting the LIS technology for po-sitioning applications. Finally, we identify numerous excitingopen challenges for LIS-aided 6G wireless networks, includingresource allocation problems, hybrid RF/VLC systems, healthconsiderations, and localization.
Index Terms —Large intelligent surfaces (LIS), 6G technology,wireless communication, massive MIMO, mmWave communica-tions
I. I
NTRODUCTION
The recent advent of large intelligent surfaces (LIS) empow-ers smart radio environments at overcoming the large powerconsumption and the probabilistic nature of electromagnetic(EM) wave transmission, thereby improving both the qualityof service (QoS) and radio connectivity [1]. Therefore, LISare envisioned to be one of the essential technology enablersof 6G and beyond wireless communications. By means ofcombating the uncontrollable and stochastic wireless propa-gation medium, LIS realize a controllable and smart radio
The first seven authors contributed equally to the manuscript, and sodid the eighth to tenth authors. R. Alghamdi, R. Alhadrami, D.Alhothali,H. Almorad, R. Asfour, A. Faisal, N. Hammad, S. Helal, R. Shalabi, A.Shams and H. Dahrouj are with the Department of Electrical Engineering,Effat University, Jeddah 22332, Saudi Arabia. N. Saeed, T. Y. Al-Naffouri,and M.-S. Alouini are with the Division of Computer, Electrical and Mathe-matical Sciences and Engineering, King Abdullah University of Science andTechnology, Thuwal 23955-6900, Saudi Arabia. environment in a software-controlled fashion, which booststhe communication capabilities. Software-defined or recon-figurable EM meta-surfaces are the fundamental technologybehind the LIS implementation that is capable of modulatingdata onto the received signals, customizing changes to the ra-dio waves, and intelligently sensing the environment. In otherwords, intelligent meta-surfaces are programmable frequency-selective surfaces that are composed of artificial thin meta-material films, that are adequate for energy-efficient and low-complexity wireless communications [2], [3]. The classicalutilization of LIS technology was initially restricted to satelliteand radar communication systems, and was not adopted byterrestrial wireless communications. The conventional wirelessradio transmission rather relies on traditional reflecting sur-faces, which only induce fixed phase shifts, and do not adapt tothe terrestrial time-varying wireless communication channels.Fortunately, the recent advances in metamaterials and micro-electro-mechanical systems (MEMS) lead to the advance ofreconfigurable reflecting surfaces. For instance, Kaina et al. first introduced the concept of LIS by using tunable surfacesto control the wireless propagation environment [4].Moreover, meta-surfaces are immune to noise in radio re-ceivers and do not require neither analog/digital converters, norpower amplifiers. Meta-surfaces can, therefore, manipulate andreflect the signals with extremely low-noise amplification. En-abling the LIS technology would also allow for reductions inpower consumption as compared to current wireless networks.Due to its relative high energy-efficiency, LIS technology isenvironmentally friendly, as its reduces the overall carbonfootprint [1], [5].From a spectrum deployment perspective, recent studiesshow that high-frequency transmission, such as millimeterwave (mmWave) and terahertz (THz) communications, canbe well realized using LIS [10]. Providentially, significantdisadvantages for the use of LIS are not known at the momentfor very high frequency deployments, especially at the rangeof 2.4 GHz to 60 GHz. This attractive attribute of LIS makesthem suitable for use in cutting edge communication andsensing technologies of 5G and beyond systems, which includeInternet of Things (IoT), Device-to-Device (D2D) communica-tions, Machine-to-Machine (M2M) communications, etc. [7],[11], [12].The above unique features of LIS make them suitablefor a variety of groundbreaking smart radio environments a r X i v : . [ ee ss . SP ] J un TABLE I: A list of LIS surveys.
Ref. Focus Comparison to our paper [1] Outlines different types of reconfigurable sur-faces and their theoretical performance limits Unlike these works, our paper surveys various criticaland technical aspects of LIS, including optimizationframeworks and performance analysis. The paperentails the physical working principle of LIS. It thenintroduces the optimization schemes for LIS-basedsystems, which include energy efficiency, sum-rate andsecrecy-rate. The paper afterwards surveys variousperformance analysis metrics including capacityanalysis, uplink/downlink data rate analysis, andoutage probability. Lastly, we suggest various openresearch issues on the LIS topic.[6] Explores the capabilities of reconfigurable reflec-tarrays for multi-band operation, amplification,and polarization manipulation[7] Motivates for using LIS in future wireless com-munication networks, especially for reducingpower consumption and improving connectivity[8] Summarizes studies on intelligent reflecting sur-faces, mainly their applications[9] Focuses on design and applications aspects ofintelligent reflecting surfacesapplications, both in indoor and in outdoor environments [13].For instance, in [14], the authors introduce the deployment ofa smart indoor environment using the concept of intelligentwalls empowered by machine-learning control algorithms forrealizing an indoor cognitive wireless network. In indoorenvironments, various objects including walls, furniture, andwindows, can influence the communication and coverage forwireless devices. As indoor scenarios (e.g., hospitals, hotels,security offices) require ultra-reliable high-speed communica-tions, the authors in [12] propose coating the indoor objectswith software-programmable hyper-surface tiles (a novel classof meta-surfaces), so as to improve both communicationand coverage aspects of indoor wireless systems. LIS haveindeed many other prospective applications, including indoorlocalization [15], health monitoring using smart T-shirts [7],imaging, quantum optics, and military purposes [12].Thanks to the converging breakthrough in developing smartsurfaces, boosting the operation of smart radio environmentswith intelligent and reconfigurable capabilities is more feasiblethan ever. Such emerging capabilities would indeed enable thenetwork operators to shape the radio waves propagation withcustomized functionalities. For example, the embedding ofmeta-surfaces into the outdoor and indoor objects would allowfor sensing the incoming signal response and feeding the sys-tem response back to the network controller [13]. Based on thesensed data, meta-surfaces can then configure and manipulatethe input signal wave through different EM behavior controlfunctions, e.g., wave reflection, refraction, polarization, orfull absorption. Moreover, reflection and refraction functionscan offer additional services, also known as wave steering ,that can override the conventional Snell’s law [12]. Throughextending the notion of network softwarization, a smart radioenvironment can facilitate programmatic commands, and canbe remotely configured and/or elastically optimized. Withoutgenerating new signals, which consume an additional extentof power, LIS are, therefore, able to meet the challengingrequirements of future wireless networks [11].It is worthy to note that LIS are complementary mediumsto support other emerging technologies, including backscat-ter communication, millimeter-wave communication, massivemultiple-input multiple-output (MIMO), and network densi- fication. For instance, LIS, albeit being distinct from mas-sive MIMO, can be viewed as an extension of conventionalMIMO systems. Reference [8] compares massive-MIMO withIntelligent Reflecting Surfaces (IRS) deployment in termsof information transfer capabilities. Although massive-MIMOboosts the energy and spectral efficiencies of the communi-cation links, it is not capable of tuning and controlling thewireless propagation environment. Moreover, unlike IRS thatis linearly proportional with the average transmit power [8],a logarithmic relationship exists between the capacity andaverage transmit power in massive-MIMO. Due to its arrayarchitecture, massive-MIMO further requires more significantpower consumption as compared to IRS.
A. Related Surveys
The topic of intelligent surfaces has rapidly attractedresearch interests with preliminary contributions tocommunication-theoretical modeling, optimization,deployment, and design of LIS-empowered networks.Hence, some recent surveys overview the revolutionarytechnology of LIS and their promising significance in futurewireless communication networks. In [1], the authors outlinedthe state-of-the-art reconfigurable surfaces solutions, 6Gapplications, and theoretical performance limits. Recently,Jun et al. provided a general overview of the data rate andreliability issues in LIS [8]. Reference [8] also discussed theuse of LIS in network security, channel estimation, and deeplearning-based paradigm for LIS-aided communications. Inthe context of practical implementation of LIS technology,Sean et al. surveyed the primary design architectures, such asthe reconfigurable-array lens and reflect-array antennas [6].Furthermore, the authors in [7] presented the recent researchefforts to deploy smart radio environments in practice, whichis a step forward towards redefining the current networkcommunication models. The authors in [9] then providedan overview of the performance analysis and optimizationin LIS-assisted networks, as a means to achieve differentwireless communications objectives. Reference [9] furtherdiscussed the diverse application scenarios that can exploitLIS, such as wireless power transfer, mobile edge computing,and unmanned aerial vehicle (UAV) based communication.
Table I provides an illustrative summary of the above recentLIS surveys.Unlike all existing works, the current survey is the first ofits kind which overviews the technical and critical aspectsof mathematical optimization and performance analysis ofLIS systems, and presents a handful of promising researchdirections towards the formulations of practical problemsin future beyond 5G systems. More specifically, our paperfirst entails the physical working principle of LIS. It thenintroduces the optimization schemes for LIS-based systems,which include energy efficiency, power optimization, sum-rate, secrecy-rate, and coverage. The paper afterwards surveysvarious performance analysis works including those whichtackle capacity analysis, the impact of hardware impairmentson capacity, uplink/downlink data rate analysis, and outageprobability. The paper also presents the localization errorperformance of centralized and distributed LIS systems. Lastly,we suggest various open research issues in the context of futureLIS-empowered systems.
B. Organization of the Survey
The rest of the paper is organized as follows. Section IIdiscusses the working principle of LIS, providing the associ-ated enabling technologies and models for the control of EMwave reflection. Section III covers the optimization techniquesfor LIS, while Section IV sheds light on the performanceanalysis of LIS. Section V discusses the error performanceand reliability analysis of LIS. In section VI, recent studieson the potential of positioning and coverage in LIS systemsare surveyed. Before concluding in section VIII, various futureresearch directions are discussed in section VII.II. W
ORKING P RINCIPLE
This section sheds light on the basic working principleof LIS from a physical layer perspective. We first note thatthere are several terminologies that are interchangeably usedto denote LIS in the literature, namely, intelligent reflectingsurfaces (IRS), reconfigurable intelligent surfaces (RIS), andsoftware-defined surfaces (SDS). Each of such terminologiesemphasizes one particular feature of the smart surface [8]. Forcompleteness, we refer to Table II for a comparison of suchvarious terms.LIS consist of a two-dimensional array made up of nu-merous low-cost passive reflecting EM elements, also knownas metamaterials [29]. Such metamaterials comprise eithervaractor diodes, or other MEMS technologies that have theability to intelligently adjust their induced phase shifts to attainthe desired communication objectives [30]. The metamaterialsconsist of repeated meta-atoms over a substrate with a specificEM behavior. The metamaterial’s EM behavior depends onthe meta-atom structure. Hence, some patterns of meta-atomsabsorb the entire incoming EM waves, while other modelsmay entirely reflect the incoming EM waves. The metasurfacesare dynamic, consisting of tunable elements that can switchtheir condition and EM behavior by applying an externalbias. These tunable elements may include CMOS switches orMEMS switches. In the metasurfaces, the switching elements
Element Bias PIN diodes
Fig. 1: Controlling the EM reflection using PIN diodes.
VaractorRefractor Unit Microcontroller
Fig. 2: Controlling the EM reflection using varactor-tunedresonators.control the meta-atoms that act as input and output antennas.Besides, the switching elements also connect the meta-atomsin custom topologies. That is, when incoming EM waves enterfrom an input antenna, they are routed based on the status ofthe switch, and exit via the output antenna, helping the LIS toachieve a customized reflection [12].There are various switching technologies to control theEM reflection from the smart surface, including PIN diodes,varactor-tuned resonators, liquid crystal, and MEMS tech-nologies. One way of controlling the reflection effect in ametasurface is by placing PIN diodes as switch elements. Anexternal bias switches the PIN diodes on and off, generatingtwo different states for the smart surface, as shown in Fig.1.When the PIN diode is turned off, the incoming energypenetrates the surface and is mostly absorbed. However, whenthe PIN diode is on, most of the incoming energy is reflected[1]. Additionally, varactor-tuned resonators are also used forcontrolling the signal’s propagation, as illustrated in Fig. 2.When the bias voltage is applied to the varactor, a tunablephase shift is attained. The liquid crystals can further tune thephase shift of the reflected signal, as suggested in [31]. Bydiffering the DC voltages on the patches of liquid crystal-loaded unit cells, the effective dielectric constant of anyindividual unit can be thus adjusted. As a result, the phaseshifts of the incoming signal can be controlled at variouslocations of the metasurface. Dynamic metasurfaces make up a
TABLE II: List of different LIS terms.
Ref. Surface Term Reason [2], [16], [17] Large Intelligent Surface (LIS) Considers limitless surface length or a massive numberof antennas.[8], [18], [19], [20] Intelligent Reflecting Surface (IRS) Emphasizes more on the reflecting property of the smartsurface.[1], [3] Reconfigurable Intelligent Surface(RIS) Highlights more the reconfigurability of the smart sur-face for the incident signal.[21], [22] Passive Intelligent Surface (PIS) Underlines the passive reflection with no power con-sumption.[23], [24] Reconfigurable Metasurface (RM) Emphasizes more on the metalic pattern through whichthe surface is engineered.[25] Software-Defined Surface (SDS) Considers the software-defined interaction between thesurface and incoming waves.[16] Software-Defined Metasurface(SDM) Emphasizes on both the metallic pattern and thesoftware-defined function.[26] Large Intelligent Metasurface(LIM) Assumes massive number of antennas for the asymptoticanalysis of metasurfaces.[27], [28] Smart Reflect-Arrays (SRA) Pinpoints the reflection function. dr s r d h s h d z point of re fl ection Fig. 3: Conventional two-ray propagation modeltile that consists of a gateway, to which the controller networkacquires a slave/master relationship. The controller networkrecords its running state and receives instructions to changethe current condition of the switching elements through thegateway [12].To get a better understanding of such working principle, wenext demonstrate a basic example of a controllable wirelesspropagation by means of inducing an intelligent surface. Theexample considers the conventional two-ray channel model fora free space environment and a reflecting surface deployed onthe ground plane [1]. The model postulates that the objects’size is considerably larger than the wavelength of the radiowave [32], and that the radio waves travel in straight lines,i.e., the energy is transported along individual curves. Moreconcisely, the model adheres to Fermat’s principle that statesthat the ray travels along the path between two points withminimum travelling time. The received signal is composedof the line-of-sight (LOS) ray and the reflected ray from theground, as depicted in Fig. 3. Then, according to Snell’s law of reflection, the point of reflection where the imaginary verticalline stands. The angle between the incident ray and this verticalline is equal to the angle between the reflected ray and theimaginary line. Based on this model, the destination power isrepresented as P d = P s (cid:18) λ π (cid:19) z + R × e − j ∆ φ r s + r d (1)where P s is the source power, λ is the wavelength, z is thedistance between the source and the destination antennas, r s is the distance between the source antenna and the point ofreflection on the LIS, r d is the distance between the pointof reflection and the destination antenna, R is the groundreflection coefficient, and ∆ φ = π ( r s + r d − z ) λ represents thephase difference between the two paths. If we assume that thedistance is very large, i.e., d >> h s + h d , then d ≈ z ≈ r s + r d and R = − . Now if we assume that there is no groundreflection, the expression (1) is simplified as P d = P s (cid:18) λ πd (cid:19) . (2)Both (1) and (2) show that the uncontrollable reflection fromthe ground surface degrades the received power of the signal.The literature on the topic includes other propagation modelsfor LIS, e.g., the two-ray system model with a single meta-surface, and the two-ray system model with an intelligent sur-face composed of many meta-surfaces. We refer the interestedreaders to reference [1], which discusses various propagationmodels for LIS. To best realize the full potential of LISsystems, our paper next focuses on ways of optimizing theperformance of LIS systems through surveying the major rele-vant optimization frameworks. The paper further addresses theperformance analysis of LIS systems, and illustrates severalopen issues in the context of LIS-aided wireless networks. Fig. 4: An IRS-aided wireless communication system from aBS. III. O
PTIMIZING
IRSIRS are proposed as intrinsic components of beyond-5Gwireless systems, as they have the potential of transmittingdata through multiple active elements, and intelligently adjust-ing the communication channel in the process [33]. The in-creasing demands for data rate requirements and higher-speedwireless communications for future networks have raised se-rious concerns on their power consumption, energy efficiency,secrecy rate, etc. As discussed earlier, IRS are considered ascontiguous surfaces of electromagnetically active materials.Thus, to realize the full potential of IRS systems, they have tobe well-designed, optimized and integrated. Hence, in this sec-tion, we survey the optimization frameworks of IRS, includingthe maximization of energy efficiency, sum-rate, secrecy-rateand coverage. Figure 4 illustrates the basic structure of IRSsystem, where N and M indicate the number of antennaelements at the IRS and BS, respectively. IRS are connectedto K single-antenna users, where h d,k , h r,k , and H denotethe channel links between the IRS to the k -th user, the BSto the k -th user, and the BS to the IRS, respectively. TableIII contains the list of symbols that are used in the followingsections. A. Energy Efficiency
With the rapid growth of wireless networks, the number ofconnected devices continues to increase exponentially, leadingto dense deployment of MIMO base-stations and access-points(APs). Since IRS comprise a massive number of reflectingelements, their deployments would enhance the efficiency offuture wireless networks, as high passive beamforming gainscan be collaboratively achieved via modifying the phase shiftsof the reflected signals [34].As maximizing the energy efficiency (EE) is a critical per-formance metric for balancing the throughput and the powerconsumption, the question of reaching an optimized strategyto reach a maximal EE performance is of high importancein IRS. To this end, the work in [3] proposes a significantsustainable energy-efficient approach. Since IRS are capableof amplifying and forwarding the signals without the need for TABLE III: List of Symbols
Symbol Definition Φ Phase shift vector Θ Diagonal matrix of the effective phase shifts P max Maximum transmit power h r Channel between AP-user h d Channel between IRS-user G Channel between AP-IRS H Channel between BS-IRS h r,k Channel between BS-user k h d,k Channel between IRS-user k w Beamforming vector p k Transmit power P BS BS’s total power consumption P UE Hardware static power P n ( b ) Phase shifter’s power consumption w i Precoding vectors for IDR v j Precoding vectors for EHR S The trace of a positive semi-definite matrix K Number of sub-carriers v IRS reflect beamforming vector W The transmit beamforming matrix at the BS x Transmit signal γ k The downlink SINR at the k th useradditional power amplifiers, IRS-based systems become morefavorable than conventional amplify-and-forward (AF) relaysystems [35]. In particular, reference [3] proposes an optimizedEE policy in IRS systems via optimizing the phase shifts andtransmit power, while satisfying specific power and Qualityof Service (QoS) constraints [3]. More precisely, reference[3] considers an IRS-based downlink multi-user multiple-input-single-output (MISO) system with K users, and one BSequipped with M antennas as shown in Fig.4. Reference [3]then addresses the following EE maximization problem: max Θ , P (cid:80) Kk =1 log (1 + p k σ − ) ξ (cid:80) Kk =1 p k + P BS + KP UE + N P n ( b ) (3a) s . t . log (1 + p k σ − ) ≥ R min ,k , ∀ k = 1 , , ..., K, (3b)tr (( H Θ H ) + P ( H Θ H ) + H ) ≤ P max , (3c) | Φ n | = 1 ∀ n = 1 , ..., N (3d)where ξ = η − , η denotes the efficiency of the power amplifierat the transmitter side, H is the channel matrix between theBS and the IRS, H is the compound channel matrix betweenthe IRS and all users, i.e., H = [ h Td, , h Td, , ..., h Td,K ] T , where h Td, denotes the channel vector between the IRS and user k ,and p k , P BS , P UE , P n ( b ) denote the transmit power of user k ,the total hardware power consumption at the BS, the hardwarestatic power, and the power consumption of each phase shifterfor b number of bits, respectively. Moreover, the total signalpower is denoted by P = diag ( p , ...., p k ) . The constraintin (3b) accounts for the individual QoS requirement, i.e., R min ,k of the k -th user. Constraint (3c) denotes the power Fig. 5: An IRS-aided wireless communication system from anAP. Fig. 6: An IRS-aided SWIPT system.budget, where H Θ H is the equivalent channel matrix, Θ is the diagonal matrix that accounts for the effective phaseshifts of the IRS elements, tr ( · ) is the trace operator, and P max is the maximum power transmitted by the BS. Notethat the superscript H indicates the Hermitian of a matrix.The constraint in (3d) discretizes the IRS phase shifts. Theabove formulated problem in (3) is a non-convex optimizationproblem. To this end, the work in [3] develops two efficientapproaches to solve problem (3). Firstly, an alternating op-timization technique is employed that iteratively solves forboth Θ and P . Secondly, both a gradient descent and asequential fractional programming (SFP) are adopted to solvethe problem. The results in [3] illustrate that an optimizedIRS-based system achieves an EE gain in the order of 300%as compared to the conventional AF-based systems. B. Power Optimization
In addition to EE, power optimization frameworks are pre-requisites for efficient utilization of future wireless networks.The majority of existing works on IRS assume continuousphase shifts for all reflecting elements, which is not practicaldue to physical hardware limitations [13], [22]. In [19], Wu et al. considered an IRS-assisted system which employs discretephase shifts at each element to support the communicationbetween the AP and the single antenna user. Configuringthe phase shifts results in adding the reflected and non-reflected signals together constructively by the IRS, therebyimproving the desired signal power and the wireless networkperformance. Note that the interference-free zone is created bythe IRS due to their spatial interference cancellation capability,which holds only by assuming an ideal case, i.e., where thephase shift at each reflecting element is continuous. Thisassumption, however, is not practical; therefore, the workin [19] considers a more practical approach with a limitednumber of discrete phase shifts, but with continuous transmitbeamforming vectors at the AP.The system model in [19] is a conventional MISO setup,consisting of N reflecting elements, a receiver with a singleantenna, and an AP equipped with M antennas as shown inFig. 5. This model is developed for downlink communicationassuming a quasi-static flat-fading channel. Moreover, [19]only accounts for the signals that are reflected by the IRSonce. Reference [19] objective is to minimize the transmittedpower at the AP by optimizing the transmit beamformingand passive reflect beamforming vectors at the AP and atthe IRS, respectively, while satisfying a signal-to-noise-ratio(SNR) threshold at the receiver side. The problem in [19] isformulated as follows: min w , Φ (cid:107) w (cid:107) (4a) s . t . | ( h Hr Θ G + h Hd ) w |≥ γσ , (4b) Φ n ∈ F , ∀ n (4c)where (cid:107) w (cid:107) denotes the total transmit power, Φ is the phaseshift vector Φ = [Φ , ..., Φ N ] , h Hr , h Hd , and G represent thechannel links between the AP to user, the IRS to user, andthe AP to IRS, respectively. The constraint (4b) assures thatthe SNR at the receiver side satisfies the user requirement γ .The second constraint (4c) restricts Φ n to be a discrete valuefrom the set F . Problem (4) is a non-convex optimizationproblem, and so the work in [19] tackles the problem usingan alternating optimization technique, where all N phase shiftsare optimized alternatively by tuning one phase shift at a time,while fixing the others. Reference [19] analytically proved thatIRS with discrete phase shifts can achieve the same asymptoticsquared power gain of the continuous phase shifts. It furtheremphasizes that utilizing discrete phase shifts accomplishes aconsiderable power saving.In [36], IRS are used to address the problem of simultaneouswireless information and power transfer (SWIPT). In a far-field, power transfer has low efficiency which limits the rate-energy trade-off performance of SWIPT systems. Furthermore,in SWIPT, energy harvesting receiver (EHR) demands highreceived power that is much higher than the informationdecoding receiver (IDR) power, which imposes practical effi-ciency issues. To overcome these challenges, the work in [36]proposes a novel SWIPT system aided by IRS technology. Thisapproach leverages the high beamforming gains achieved by the IRS to enhance the wireless power transfer efficiency andrate-energy trade-off performance of the SWIPT systems.The system model used in [36] is shown in Fig. 6, whichconsists of a MISO IRS-aided SWIPT system from the APto many receivers, i.e., IDRs and EHRs. The purpose ofutilizing IRS is to enhance the efficiency of EHRs that areplaced in the coverage area of the IRS. The IRS-assistednetwork has N reflecting elements to support SWIPT from M number of APs (with multiple antennas) to two typesof receivers (each with a single-antenna), which are IDRsand EHRs, expressed by K I and K E , respectively. Moreover,[36] considers a quasi-static flat fading channel model tocharacterize the optimal rate-energy performance. Note thatthe IRS can create an interference-free zone via passivebeamforming and active beamforming at the IRS and at theAP, respectively. For simplicity, the work in [36] assumes thatthe interference between the AP signals cannot be canceled bythe IDRs. To address the SWIPT system limitations, reference[36] aims at maximizing the EHRs’ received weighted sum-power, while achieving a certain signal-to-interference-plus-noise ratio (SINR) threshold at IDRs. This is achieved byoptimizing the transmit beamforming vectors and reflect phaseshifts at the AP and IRS, respectively. The SINR of the i -thIDR is given as follows (by taking into consideration that IDRscan not cancel the interference caused by the energy signals):SINR i = | h Hi w i | (cid:80) k (cid:54) = i,k ∈K I | h Hi w k | + (cid:80) j ∈K E | h Hi v j | + σ i (5)where h Hi = h Hr,i Θ G + h Hd,i given that h Hr,i , h Hd,i , and G represent the channel links between the AP and i -th IDR, IRSand i -th IDR, and AP-IRS, respectively. Note that w i and v j are the precoding vectors for IDR and EHR, respectively,where k, i ∈ K I and j ∈ K E . Here, let S be a positive semi-definite matrix that accounts for the energy weights of EHRs.The maximization problem can then be expressed as max w i , v j , Φ (cid:88) i ∈K I w Hi Sw i + (cid:88) j ∈K E v Hj Sv j (6a) s . t . SINR i ≥ γ i , ∀ i ∈ K I , (6b) (cid:88) i ∈K I (cid:107) w i (cid:107) + (cid:88) j ∈K E (cid:107) v j (cid:107) ≤ P max , (6c) ≤ Φ n ≤ π, ∀ n ∈ N (6d)where the received weighted sum-power by EHRs is given as (cid:88) j ∈K E α j E j = (cid:88) i ∈K I w Hi Sw i + (cid:88) j ∈K E v Hj Sv j , (7)and where constraint (6b) assures that the SINR at differentIDRs exceeds a certain threshold and (6c, 6d) express thepower budget and phase shift constraints, respectively. Theproblem (6) is a non-convex problem because of couplingthe transmit beamforming vectors and IRS phase shifts in theobjective function and in the SINR constraint. The optimiza-tion problem (6) is reformulated as an alternating optimizationproblem and then solved with semi-definite relaxation (SDR)by dropping the rank-one constraint, which is related tothe transmit pre-coders. Finally, the transmit pre-coders are recovered through eigenvalue decomposition over the attainedrank-one. The results in [36] show that the SWIPT systemwith IRS can radically increase rate-energy performance.In [13], the work proposes a new approach for point-to-pointMISO wireless networks using passive IRS. IRS are used toassess the information transmitted from the AP to the user asshown in Fig. 5. Hence, the user jointly gets both the signalsthat are transmitted from the AP and the one reflected by theIRS. The main objective is to maximize the total receivedpower at the receiver by optimizing the transmit beamformingand the phase shifts at the AP and at the IRS, respectively. Thenon-convex optimization problem is formulated as: max w , Φ | ( h Hr Θ G + h Hd ) w | (8a) s . t . || w || ≤ P max , (8b) ≤ Φ n ≤ π, ∀ n = 1 , ..., N , (8c)The diagonal matrix Θ = diag ( βe j Φ , ..., βe j Φ n , ..., βe j Φ N ) accounts for both the amplitude reflection coefficient β ∈ [0 , . The problem (8) is non-convex because of the cou-pled expression involving transmit beamforming w and phaseshifts Φ in the objective function. Therefore, problem (8) isreformulated using a centralized algorithm based on SDR torelax the rank-one constraint. The resultant problem is givenas: max V tr ( RV )s . t . V n,n = 1 , ∀ = 1 , ..., N + 1 , V (cid:23) , (9)where R = (cid:20) ( ΨΨ H ) ( Ψ h d ) h Hd Ψ H (cid:21) . (10) Ψ = diag ( h Hr ) G indicates the diagonal matrix of IRS-userlink. The authors in [13] obtained the eigenvalue decomposi-tion of V = U Σ U H , where U = [ e , ...e N +1 ] is a unitarymatrix, and Σ = diag ( λ , ..., λ N +1 ) is a diagonal matrix, bothwith a size of ( N +1) × ( N +1) . The resultant problem in (9) isa regular convex semi-definite program (SDP), and therefore,can be solved using CVX optimization solver [37]. Further-more, the work in [13] introduces a distributed algorithm withlow-complexity to solve (9), where the transmit beamformingand phase shifts are tuned by the AP and IRS alternatively.For the transmit beamforming vector w , the objective func-tion in (8) provides the resulting inequality: | ( h Hr Θ G + h Hd ) w |≤ | h Hr Θ Gw + h Hd w | . (11)Therefore, the equality in (11) holds if and only if arg( h Hr Θ Gw ) = arg( h Hd w ) = ϕ . Also, by utilizing thechange of variables, such as h Hr Θ Gw = v H a , where, v = [ e j Φ , ..., e j Φ N ] H , a = diag ( h Hr ) Gw , and neglectingthe constant term | h Hd w | , the problem (8) is reduced to (12)as follows: max v | v H a | s . t . V n = 1 , ∀ n = 1 , ..., N , arg( v H a ) = ϕ (12) The optimal solution of (12) is provided by v ∗ = e j ( ϕ − arg( a )) = e j ( ϕ − arg( diag ( h Hr ) Gw )) as in [13]. Therefore,the identical n -th phase shift is can be written as Φ ∗ n = ϕ − arg( h Hn,r g Hn w ) = ϕ − arg( h Hn,r ) − arg( g Hn w ) . Note that h Hn,r is the n -th element of h Hr (and g Hn repre-sents the n -th row vector of G ). g Hn w includes the transmitbeamforming and the channel link between the AP and theIRS. Furthermore, the phase of h Hd w is fixed as a constantfor all iterations to allow a distributed implementation. Notethat summation of the phase rotation and the beamformingvector is valid without adjusting the beamforming gain. Thenthe transmit beamforming can be written as w ∗ = √ ¯ p ( h Hr Θ G + h Hd ) H || h Hr Θ G + h Hd || e jα . (13)The AP adaptively chooses α in all the iterations such that h Hd ω ∗ is a real number. In conclusion, the solution of problem(12) can be achieved by applying the appropriate n -th phaseshift at the IRS. The distributed algorithm does not requirea feedback channel between the AP-IRS as compared to thecentralized algorithm. Also, it does not require utilizing SDPsolution since closed-form solutions exist. C. Sum-rate Maximization
Having discussed both EE and power consumption froman optimization perspective, we hereby review several op-timization formulations of maximizing the data rate gainsto fully exploit the IRS technology. In [38], all the IRS’elements are considered passive in the presence of a fewactive elements, which are controlled by the IRS controller.The IRS discover the best way to interact with the incomingsignal, provided the active elements, by using a deep learning-based solution. Furthermore, the main goal is to maximizethe received achievable rate, by designing the IRS reflectionbeamforming vector w . The achievable rate is expressed as R = 1 K K (cid:88) k =1 log (cid:0) SNR | ( h T,κ (cid:12) h R,κ ) w | (cid:1) , (14)where (cid:12) denote the Hadamard product, SNR = p T Kσ n repre-sents the total transmit power over the noise, h T,κ andh
R,κ represent the downlink channels, and K indicates the numberof sub-carriers. The reflection beamforming vector in the IRSis created by using the RF phase shifter. The beamformingvector is chosen from a predefined codebook Q where the goalis to find an optimal w ∗ that solves the following problem w ∗ = arg max w ∈ Q K (cid:88) k =1 log (cid:0) SNR | ( h T,k (cid:12) h R,k ) T w | (cid:1) . (15)Solving problem (15) yields the optimal rate as R ∗ = max w ∈ Q K K (cid:88) k =1 log (cid:0) SNR | ( h T,k (cid:12) h R,k ) T w | (cid:1) . (16)A comprehensive search is required to look for the opti-mal beamforming reflected vector w ∗ , which does not have a closed-form solution because of the quantized codebookconstraint and the time-domain exertion of the beamformingvector [38]. This extensive search increases the complexityof hardware implementation and power consumption signifi-cantly. For that reason, the objective is to design IRS-aidedsystems based on a deep learning solution to find the optimalachievable rate while satisfying a low-training overhead andlow hardware complexity. To this end, the work in [38]proposes a deep learning-based solution to predict the optimalreflection matrix while satisfying a low training overhead. Thework also suggests testing different deep learning models, oneof which is the reinforcement learning, that does not requirean initial dataset collection.Recently, the work in [39] considers the system model illus-trated in Fig. 5 and proposes maximizing spectral efficiency ofthe IRS-based system using two different algorithms, includingmanifold optimization and fixed-point iteration methods. Theproposed algorithms achieve higher spectral efficiency withlower computational complexity. The maximization problemis formulated as max Θ , w | ( h Hr Θ G + h d H ) w | s . t . Θ = diag ( e j Φ , e j Φ , ..., e j Φ M ) , || w || ≤ P max , (17)Note that the above optimization problem (17) is non-convexdue to the presence of phase shifts, and can be re-writtenas max v v H Rv s . t . | υ i | = 1 , i ∈ { , , ..., M + 1 } , (18)where v = [ x T , t ] T , x = [ e j Φ , ..., e j Φ M ] H , t ∈ R , and R = (cid:20) diag ( h Hr ) GG H diag ( h r ) diag ( h Hr ) Gh d h Hd G H diag ( h r ) 0 (cid:21) . (19)Note that (18) is a quadratically constrained quadratic program(QCQP) where the objective function is concave and canbe solved with an SDR method by discarding the rank-oneconstraint. This method provides an estimated solution, i.e., itdoes not guarantee an optimal solution. As mentioned before,the fixed point iteration method and manifold optimization canbe utilized to find a locally optimal solution for problem (17).Several other works on IRS assume fully reflective idealphase-shift models, where they assume a unified amplitudeat any phase shift. This implementation is not practical,due to hardware limitations. In contrast, [40] introduced afeasible phase shift model with a reflection coefficient whichapprehends the phase-dependent amplitude for a MISO wire-less system. The IRS controller is utilized to communicatewith the AP to control the IRS reflections, where the IRSreflecting elements are programmable by the controller. Recallthat Ψ = diag ( h Hr ) G . To design an IRS-assisted system, itis crucial to identify the relationship between the reflectionamplitude and phase shift. Let the incident signal be denotedas v n = β n (Φ n ) e j Φ , where Φ n , and β n denote the phase shiftand its amplitude, respectively. Based on these parameters,reference [40] considers the system model illustrated in Fig. 5 and formulates the optimization problem that maximizes theachievable rate by optimizing both the transmit beamformingvector w at the AP and the reflect beamforming vector v atthe IRS as follows max w , v , { Φ n } | ( v H Ψ + h Hr ) w | (20a) s . t . || w || ≤ P max , (20b) v n = β n (Φ n ) e j Φ n , ∀ n = 1 , ..., N, (20c) − π ≤ Φ n ≤ π, ∀ n = 1 , ..., N, (20d)where (20b) denotes the power constraint at the AP. Constraint(20c) denotes the reflection amplitude as a function of thephase shift, whereas (20d) accounts for the phase shift to bebetween - π and π . According to [41], the optimal transmitbeamforming for (20) is found using the maximum-ratio trans-mission, where w ∗ = √ P max (( v H Ψ + h Hr ) H ) || ( v H Ψ + h Hr ) || . By accountingfor w ∗ , the problem in (20) is reformulated as max v , Φ n || ( v H Ψ + h Hr ) || (21a) s . t . v n = β n (Φ n ) e j Φ n , ∀ n = 1 , ..., N, (21b) − π ≤ Φ n ≤ π, ∀ n = 1 , ..., N, (21c)Although problem (20) is simplified in (21), it remainsnon-convex and is complicated to be solved using classicaltechniques. Hence, the work in [40] utilizes an alternatingoptimization approach to tackle the problem, reaching a sub-optimal solution [41]. In [42], a weighted sum-rate (WSR) ismaximized instead, by jointly determining the active beam-forming at the BS and the passive beamforming at the IRS.Reference [42] considers a downlink multiuser MISO commu-nication system as shown in Fig. 4, containing M antennas atBS, IRS with N reflecting elements, and K end-users [42].The IRS are utilized to assist the BS in reducing the fadingand shadowing effects, where the decoding SINR is denotedas γ k = | ( h Hr,k + h Hd,k Θ H H ) w k | (cid:80) Ki =1 ,i (cid:54) = k | ( h Hr,k + h Hd,k Θ H H ) w i | + σ . (22)Here the k -th user treats signals that are transmitted fromother users as interference. Hence, the optimization problemis formulated as max W , Θ f ( W , Θ ) = K (cid:88) k =1 w k log (1 + γ k ) (23a) s . t . Φ n ∈ F , ∀ n = 1 , ..., N, (23b) K (cid:88) k =1 || w k || ≤ P max . (23c)The goal in (23) is to maximize the WSR as a function of W and Θ , where it represents the transmit beamformingmatrix at the BS and the reflection coefficient matrix at IRS,respectively. The term w k indicates the priority of the k -thuser. In (23b), F , F , F denote an ideal reflection coefficient,continuous, and discrete phase shifters, respectively, where F ∈ {F , F , F } . In addition, transmit power constraint Fig. 7: An IRS-aided wireless communication system subjectto interception.(23c) denotes the maximum feasible threshold power P max .Reference [42] tackled this non-convex optimization problemvia Lagrangian dual transform with a low computational com-plexity algorithm, by alternatively optimizing the active andpassive beamforming so as to attain a sub-optimal solution.The results suggest that beamforming optimization surpassesconventional models under given phase-shift models. D. Secrecy-rate Maximization
Besides improving the achievable rate and EE of wirelesscommunication systems, IRS can also achieve physical layersecurity. In fact, the IRS improve the secrecy data rate, i.e.,when the data rate at an eavesdropper decreases and the datarate at a legitimate receiver increases [8], [43]. Additionally,IRS focused transmissions from the smart meta-surfaces wouldboost communication network security. Therefore, given thatsignals might be subject to interception after transmission,optimizing secrecy rates becomes quite important. In [44],[45], the secrecy rate of the system is maximized by optimizingthe source transmit power and the IRS phase shift matrix.Since the formulated problem in (26) is not convex, thework in [44] proposes an alternating algorithm to acquire atractable solution. First, a closed-form solution for the sourcetransmit power is obtained and then a bisection search basedsemi-closed form solution is developed via tight bounding tooptimize the phase shift matrix.The system model in Fig. 7 consists of a source (Alice),IRS, receiver (Bob), and an eavesdropper (Eve). N indicatesthe number of antennas at Alice’s side, and L representsthe number of reflecting elements at the IRS. Also, reflectedsignals from the IRS are neglected due to their small power.Furthermore, to maximize the power matrix of the reflectedsignal, the work considers maximal reflection of the reflectedsignal matrix. Due to the fact that the IRS reflect Alice’s signal,the received signals at Bob’s side are the combination of both the signal from Alice and the IRS. The signal received at Bobis denoted by y b = h HIb Θ H aI x + h Hab x + n b , (24)where h HIb is the channel between Bob and the IRS. Φ i denotesthe phase shift obtained by the i -th reflecting element of theIRS, H aI is the channel between Alice and the IRS, and x represents the transmitted signal by Alice. The co-variancematrix W = E { xx H } of x satisfies ( tr ( W ) ≤ P max , where h Hab is the channel between Alice and Bob, and n b is theAWGN with variance σ n,b at Bob’s side. Similarly, the signalreceived by Eve is given as y e = h HIe Θ H aI x + h Hae x + n e , (25)where h HIe , h Hae are the channel between the IRS and Bob, andthe channel between Alice and Eve, respectively. The AWGNat Eve is denoted by n e with variance σ n,e . To improve thesecrecy rate for the above system setup, W and the phaseshift matrix Θ are jointly optimized. The achievable rate R s ( W , Θ ) needs to be maximized, i.e., max W ≥ , Θ R s ( W , Θ ) (26a) s . t . tr ( W ) ≤ P, | θ i | = 1 , i = 1 , · · · , L, (26b)where R s is given by R s ( W , Θ ) =log (cid:32) h HIb Θ H aI + h Hab ) W ( H HaI Θ H h Ib + h Hab ) σ n,b (cid:33) − log (cid:32) h HIe Θ H aI + h Hae ) W ( H HaI Θ H h Ie + h Hae ) σ n,e (cid:33) . (27) Note that the i -th diagonal element of Θ is denoted by Φ i . Due to the non-convexity caused by the unit modulusconstraints, the optimization problem (26) is hard to solve.Hence, to solve the secrecy rate maximization problem, analternating algorithm approach is used [44]. The algorithmoptimizes W with fixed Θ , and alternatively optimizes Θ fora given W . Optimization over W with a fixed Θ yields thefollowing problem max W ≥ h Hb W h b + σ n,b h He W h e + σ n,e (28a) s . t . tr ( W ) ≤ P max , (28b)where h B = H HaI Θ H h ab and h e = H HaI Θ H h ae . Similarly,the problem that maximizes Θ by fixing W , is given by max Θ | ( h HIb Θ H aI + h Hab ) w | + σ n,b | ( h HIe Θ H aI + h Hae ) w | + σ n,e (29a) s . t . | Φ i | = 1 , i = 1 , · · · , L. (29b)The optimization problem (29) is solved by using fractionalprogramming. The work in [44] developed a secrecy maxi-mization algorithm for multi-antenna communication systemswhere Eve has M ≥ antennas. E. Coverage Optimization
In the past, designing precoding and beamforming tech-niques for MIMO systems has received significant attention.This includes the minimization of transmit power and max-imization of the minimum SINR. Maximizing the minimumSINR has not been analyzed much by taking into considerationthe reflect beamforming design of the IRS. Therefore, thework in [30] proposes optimizing the IRS phase matrix thatmaximizes the minimum SINR. A projected gradient ascentalgorithm has been used to solve the optimization problem anddetermine the phases that maximize the minimum user SINRunder optimal linear precoder (OLP). The multi-user MISOcommunication system is shown in Fig. 4, which consistsof a BS with M antennas that communicate with K single-antenna users, and IRS that has N passive reflecting elements.The IRS are established on the surrounding building’s wallthat can adjust the phase shift of each reflecting componentto realize the desired communication objective. In [30], thework assumes that the BS-to-IRS channel satisfies the LoSconditions. Furthermore, it considers a complex scatteringenvironment, spatial correlation between the IRS elements, andcorrelated Rayleigh channels between the IRS and the usersdue to the user’s mobility. In [30], the transmitted signal x isdenoted by x = K (cid:88) k =1 (cid:114) p k K g k s k , (30)where g k ∈ C M is the precoding vector, p k is the signalpower, and s k is the data symbol for the k -th user, respectively.Moreover, the transmitted signal satisfies the constraint of theaverage transmission power per user. Hence, the downlinkSINR at a single user k is given by γ k = p k K | h Hk g k | (cid:80) i (cid:54) = k p i K | h Hk g i | + σ (31)here h k = √ β k H Θ R / IRS k h d,k denotes the overall channelbetween the BS and user k , where R IRS k denotes the spatialcorrelation matrix of the IRS with respect to user k . The max-min SINR problem is then defined as, max P,G min k γ k (32a) s . t . K TK P ≤ P max , (32b) (cid:107) g k (cid:107) = 1 , ∀ k. (32c)This optimization problem in (32) can be solved using theOLP to maximize the minimum SINR [46]. The aim is todesign the phase values of the IRS’ elements that appearin the diagonal of the reflect beamforming. To achieve thisgoal, an approach with infinite resolution phase shifters whereall channels are precisely known at the BS was assumed inreference [46], which employs the OLP to allocate the optimalpowers.To summarize, when the LoS channel between the BS andthe IRS is of rank-one, a closed-form solution with minimumSINR under the OLP is formulated [46]. As K increases,serving more than one user becomes more challenging due to TABLE IV: Comparison of optimization frameworks for LIS.
Ref. Assumptions & Limitations [3] Ignored the BS-user link due to unfavorable propagation conditions[19] Considered the reflected signals by the IRS for the first time only and ignored the rest. Also, the receivedsignal from AP-user for asymptotically large N is ignored[36] Assumed perfect channel state information (CSI) at the AP. Also, the work assigns each receiver withonly one dedicated energy beam[13] Neglected the power signal that is displayed by the IRS more than two times. Moreover, a flat-fadingchannel model is assumed, and perfect CSI at the IRS[38] Considered the presence of the global channel knowledge at the base station. However, getting thechannel knowledge needs huge training which is complicated[39] Assumed a flat-fading channel model and perfect CSI at the AP and the IRS. Also, the work considersthat all channels follows an independent Rayleigh fading[40] Assumed a quasi-static flat fading channel model, and considered reflected signals by the IRS for thefirst time only and ignored the rest[42] Assumed quasi-static flat-fading channels and known CSI[44] Considered maximal reflection without loss at the IRS[30] Assumed that the direct paths of the signal between the BS-users are blocked by obstacles and alsoperfect CSI is known at the BS.the SINR convergence. To solve this problem, the work [46]assumed that the LoS channel has a high rank and used thetools from random matrix theory developing a deterministicapproximation for the OLP parameters [30]. Lastly, the IRSphase matrix that maximizes the minimum SINR under theasymptotic OLP was designed using projected gradient ascent.This section explores relevant optimization frameworks soas to exploit the full capabilities of IRS-based systems. Asa summary, we also provide Table. IV which compares theoptimization frameworks for IRS and states the assumptionsconsidered in the literature. The next section focuses onanalyzing the performance of the IRS-based system fromseveral perspectives including capacity, hardware impairments,and data rate.IV. P ERFORMANCE A NALYSIS OF
LIS S
YSTEMS
LIS technology is expected to provide reliable wirelesscommunication when a LoS link is established, as previoussections discuss. The significance of this technology makes itvital to study the performance analysis of LIS-based systems.To this end, this section reviews the performance analysisof LIS systems from different aspects, such as asymptoticanalysis of uplink and downlink data rate, outage probability,and spectral efficiency. Because of their relatively large dimen-sions, it is often challenging to get closed-form solutions tomathematically describe LIS systems. This section, therefore,covers different methods of estimating and approximating LISsystems performance.
A. Capacity Analysis of LIS Systems
Due to LIS capabilities in empowering robust and high-speed 6G communication networks, it is evidently essentialto study the systems capacity, including hardware impairmenteffect, uplink/downlink transmission rate, and the impact ofphase shifts.
1) Data Transmission Capacity:
The authors in [2] studythe achieved unit-volume normalized capacity, where aninfinitely-sized LIS system and a fixed transmit power perunit volume P u are considered. As the wavelength λ goes tozero, the normalized capacity per unit-volume ˆ C approaches P u N , N is the AWGN, and P u = Pλ , where P refers to theterminal transmit power. The received signal in [2]’s system isoptimized and goes through a sinc-function-like match filteringprocess. As for the analysis, reference [2] also studies the LISsystem’s spatial degree of freedom (DoF) to be harvested (i.e.,the number of independent signal dimensions ρ ) [47], to alignwith Shannon’s capacity. The spatial DoF is measured as afunction of ˆ C for the high SNR slope, given as ρ = lim Pu N →∞ ˆ C log( P u N ) . (33)For a one-dimensional user-equipment (UE) deployment, thenormalized capacity is given by ˆ C = lim K →∞ C ∆ x , (34)where C, K , and ∆ x are the capacity, number of UEs,and the spacing between the neighboring UEs on the x -dimension, respectively. Similarly, the normalized capacity fortwo-dimensional UE deployment is given by ˆ C = lim K →∞ C ∆ s , (35)where ∆ s = ∆ x ∆ y is the spacing between the neighboringUEs. ∆ x and ∆ y represent the spacing between the neigh-boring UEs on the x - and y -dimension respectively. Solving(34) and (35) boils to having ∆ x = λ and ∆ s = λπ ,which tells that for infinitely-sized LIS of one-dimension, ˆ C is maximized when λ UEs are to be multiplexed per meter,whereas multiplexing πλ UEs spatially per meter maximizes ˆ C for two-dimensional UE deployment. Finally, [2] leverages LIS unit 1 LIS unit k Target LIS L L · · · · · ·· · ·· · · ... . . . ... · · ·· · ·· · · ... . . . ... M antennasDevice 1 Device k · · · Fig. 8: Single LIS system with K units serving up to K devices.the sampling theory to show that a hexagonal lattice is anoptimal sampling one, which minimizes the surface area of LISwhen every deployed antenna can earn only a single spatialdimension. Also, increasing K does not affect the capacityof the system, proving that it is a robust system with goodpotentials of data transmission interference suppression.
2) Hardware Impairments Analysis:
LIS systems are be-lieved to outperform the conventional communication systems;therefore, it is noteworthy to consider the analysis of LIS-systems in the presence of hardware impairments (HWI).Almost all communication systems encounter HWI, and LISsystems are no exceptions. That is, LIS systems have largesurface areas that would impact the HWI degradation over thesystem. The work in [48] studies the capacity degradation ofan LIS system in the presence of HWI, when serving one UE.The HWI is modeled as a Gaussian process, and its variancedepends on r , the distance of received signal power from thecenter of the LIS, which is turn is modeled as f ( r ) = αr β , (36)where α and β are two positive constants, and where α = 0 represents the case of no HWI. The capacity of an LIS systemtypically increases with a large surface area; however, anLIS system with HWI has the opposite performance. Thatis, increasing the surface area degrades the system capacityseverely, as shown in the numerical results of [48]. To over-come the significant impact of HWI on the LIS system, [48]proposes splitting the LIS system surface into K smaller units.This idea is yet to be discussed in section VI. B. Data Rate Analysis
One of the critical factors of analyzing communicationsystems is the achievable data rate. This section presents theliterature on the data rate expressions derived for LIS systems.
1) Uplink Rate for single-LIS Systems:
The work in [16]studies not only the uplink data rate of LIS systems, butalso shows the superiority of LIS systems’ performance overmassive MIMO systems. Also, [16] takes into considerationthe channel estimation error and channel hardening effects.In simple terms, [16] shows that the achieved capacity is correlated to the mutual information under the asymptoticanalysis on the number of antennas and connected UEs.The authors in [16] consider an LIS system shown inFig. 8. The system consists of a single large surface dividedinto a subarea of L × L denoted as units, each with M antennas spaced by ∆ L in a rectangular lattice. The LISsystem serves up to K devices, where each unit serves itscorresponding device. To avoid performance degradation thatmay occur due to the overlapping between the LIS unit andthe location of the device, [16] assumes deploying orthogonalresource management among devices. Therefore, all devicescommunicate to a non-overlapping unit.Using the above system, [16] analyzes the asymptoticperformance of the uplink data rate for boundless increasing M and K , where [16] approximates the system performanceby first defining the uplink data rate for one unit (i.e., unit k )as R k = log(1 + γ k ) , (37)where γ k is the received SINR of unit k , and is given by γ k = ρ k S k (1 − τ k ) I k . (38)In (38), ρ k is the uplink transmit SNR of device k , τ k ∈ [0 , represents the imperfection of the channel error estimation.The desired signal power is denoted as S k = | h kk | , h kk isthe channel between device k and the unit k of the LIS, and I k is the interference-plus-noise term for unit k .The authors in [16] approach the asymptotic performanceanalysis by first analyzing the moments of the random variable I k , then, obtaining its asymptotic moment, and finally derivingthe asymptotic moment of R k from I k . The study [16] showsthat S k converges to a constant that depends on the height ofthe device k and length of the LIS unit when M approachesinfinity. R k mean and variance can be approximately derivedbased on the mean and variance of γ k , denoted by µ γ k and σ γ k , respectively. Therefore, using Taylor expansion, the mean ¯ µ R k and variance ¯ σ R k of R k can be defined exclusivelyby the random variable I k , where the asymptotic mean andvariance of I k depend on the devices’ locations and the NLoSinterference correlation matrix: ¯ µ R k = log(1 + ¯ µ γ k ) − ¯ σ γ k µ γ k + 1) , (39)and ¯ σ R k = − ¯ σ γ k µ γ k + 1) + ¯ σ γ k (1 + ¯ µ γ k ) , (40)respectively, ¯ µ γ k and ¯ σ γ k are the asymptotic mean andvariance of γ k . Hence, the evaluation of the LIS systemperformance can be obtained with no need to run extensivesimulations.In large antenna-based systems, the system validity, latency,and diversity scheduling are controlled by the fluctuationsof mutual information. For this reason, the study of thechannel hardening effect is crucial for LIS-based systems.Hence, [16] studies the performance of mutual informationvariance as M increases. Given the asymptotic value of γ k and M = ( L ∆ L ) , the mean and variance of γ k can be · · · Target LISNeighboring LIS
LIS unit k ········· ... ... ...... Neighboring LIS
LIS unit 1 ········· ... ... ...
Fig. 9: The system model considered in [49], illustrating amulti-LIS system sharing the same frequency band.expressed as the asymptotic mean ¯ µ I k /M and the asymptoticvariance ¯ σ I k /M of the random variable I k . Using the scalinglaw, [16] shows that the asymptotic interference-plus-noise ¯ I k converges to a constant as M increases; hence, the asymptoticdata rate ¯ R k , its mean and variance converge to a constantvalue, proving that an LIS system indeed is influenced by thechannel hardening effect. Based on that, LIS lack schedulingdiversity and have better reliability and latency because of thedeterministic data rate. Finally, [16] compares the asymptoticperformance of the LIS system with massive MIMO in termsof data rate’s ergodic value and variance where the LISsystem has a higher ergodic rate. As M increases, however,the gap between the two starts shrinking, especially as thenumber of devices K grows. Although the two systems havesimilar performance for large values of M , this solution is notpractical for massive MIMO systems, as it requires a largephysical area, unlike the LIS systems. In terms of data ratevariance, a massive MIMO system shows a reduced channelhardening effect when the variance increases with M and thenconverges to a constant. As for the LIS system, the variancegoes to zero with an increase of M , which illustrates thechannel hardening effect and eventually shows LIS systemsperformance superiority in terms of reliability and latency.
2) Uplink Rate for Multi-LIS Systems:
Unlike prior worksthat only study the performance of a single LIS system, [49]studies the performance of a multi-LIS system (illustrated inFig. 9), by deriving an upper bound on the asymptotic systemspectral efficiency (SSE) and by investigating the impact ofpilot contamination. Based on the derivation of the upperbound, [49] attempts to optimize the length of pilot trainingand the number of served devices per an LIS system. Thesignificance of [49]’s study lies in the fact that acquiring thechannel state information (CSI) requires sending pilot signals;however, in multi-LIS systems, pilot contamination may occurdue to inter-LIS interference.The study in [49] considers a multi-LIS system consistingof N number of LIS, each with the same characteristics asin [16], where each surface of LIS has its signal processingmodule to receive signals, estimate CSI and detect uplinksignal from its corresponding device. The modeling of [49]’ssystem ensures not having an overlapping LIS unit (i.e., Uplink training interval Uplink data transmission interval t τ τ − t Fig. 10: The uplink frame structure showing the interval periodof a pilot signaling and data transmission [49].no intra-LIS interference) by having an orthogonal multipleaccess resource management schemes for devices with similarlocations. Considering an LIS system with a matched filter(MF), the MF requires an accurate CSI to suppress theinterference of a signal, where it gathers the CSI throughpilot signaling from a device to its corresponding LIS. Pilotsignaling of a device occurs during the coherent channel time τ within the uplink frame structure. In the uplink structure, pilotsignaling occurs in a period of t , while data transmission takesa period of τ − t , as shown in Fig.10. Given the orthogonalmultiple access scheme deployed, an orthogonal pilot sequenceof t ≥ K is allocated for each device for obtaining the requiredCSI at the LIS side. In the case of a multi-LIS system, the pilotsymbols used by two adjacent LIS lose their orthogonality,causing pilot contamination. For an uplink frame structure,the instantaneous SSE of the n -th LIS is given by R SSEn = (1 − tτ ) K (cid:88) k =1 R nk = (1 − tτ ) K (cid:88) k =1 log(1 + γ nk ) , (41)where R nk and γ nk are the data rate and SINR of unit k ,respectively. Next, [49] optimizes t , which maximizes theasymptotic SSE for the unboundedly growing M . As [2], [16]show, the signal power of unit k of LIS n (for N ≥ )converges to a deterministic value, with the increase of M .Following the investigation of [16], [49] shows that unlikemassive MIMO systems, as M increases, a multi-LIS sys-tem has negligible inter/intra-LIS-interference through NLOS.Also, the imperfect CSI of a multi-LIS system does not affectits SSE; the SSE of a multi-LIS system, regardless of its CSI,achieves the same performance of a single-LIS with perfectCSI. Also, [49] shows that the pilot contamination bounds amulti-LIS SSE performance due to the inter/intra-interferencecaused by LoS paths. Moreover, the authors in [50] analyze theperformance of LIS using orthogonal multiple access (OMA)and non-orthogonal multiple access (NOMA). The study in[50] reveals that NOMA may perform worse than OMA forthe users nearby LIS.Unlike massive MIMO systems where t is a factor affectingthe received SINR, [49] shows that when optimizing t for LISsystems, increasing t does not increase the SINR. Therefore,the optimal t ∗ which maximizes the SINR is the minimum t (i.e., t = K ). Finally, [49] asymptotically derives the optimalnumber of devices that maximizes SSE. Also, [49] verifies theanalytical derivations (approximation) with extensive simula-tions, where the study shows that the channel hardening effectof multi-LIS is closer to that of a single-LIS system, for ahigh number of K . The ergodic uplink rate of the single and multi-LIS system is shown, where the single-LIS system hasthe superior performance, and the gap between the two followthe analytical derivation that is a result of the generated pilotcontamination and inter-LIS interference. For the SSE, theincrease of inter-LIS interference causes K to increase, whichexplains the increase in the gap between the two performances.
3) Rate Impact on Phase Shifts :
As iteratively statedthroughout this manuscript, controlling phase shifts in LISsystems is a crucial factor for fine-tuning the communicationquality-of-service. According to [51], the practical implemen-tation of LIS relies on the limitations of phase shifts, whichdegrades the overall system performance. Therefore, [51]studies the uplink assisted communication system performanceand provides an approximated expression for the attainabledata rate. Also, the work in [51] shows the optimal number ofphase shifts needed for a particular data rate threshold.In an LIS assisted communication model that consists of a M × N planar array of electrically controlled elements, thenumber of phase shift patterns that can be generated by theLIS model is k , where k is the number of coding bits. Thephase shifts have a uniform interval expressed by ∆ θ = π k .One can obtain the phase shift value by multiplying the phaseshift interval by an integer s m,n that satisfies ≤ s m,n ≤ k − , i.e., the phase shift value is s m,n ∆ θ . The number ofphase shifts is limited in practice; thus, it is important to studythe effect of phase shifts limitations on the reliability of thesystem. The phase shift error can be expressed as a function ofthe optimal phase shift θ ∗ m,n and the closest phase shift ˆ θ m,n ,that is expressed as δ m,n = θ ∗ m,n − ˆ θ m,n , (42)where π k +1 ≤ δ m,n < π k +1 . (43)To evaluate the data rate degradation, (cid:15) must be defined, whichis the ratio of the error caused by the limited phase shifts to thecontinuous phase shifts. Therefore, for the system performanceto exceed a certain threshold, (cid:15) must be greater than (cid:15) , i.e., (cid:15) = log (1 + E [ˆ γ ])log (1 + E [ γ ]) ≥ (cid:15) , (44)where (cid:15) < , ˆ γ is the SNR expectation, and γ is the receivedSNR. The attainable data rate expression can be found in [51],where the final expression is bounded from both sides. Theupper bound is found when the Rician factor κ → ∞ , whilethe lower bound is calculated when κ → . The results in[51] show that the data rate increases with the increase of theLIS size. When the size of the LIS is sufficiently large, theSNR becomes proportional to the square of the number ofLIS elements. Most importantly, [51] finds that the requirednumber of bits to generate various phase-shifts depends on thesize of the LIS in the Rician channel conditions. The numericalresults indicate that three bits are needed for small-sized LIS,two bits for moderate size, and one bit for infinitely-sized LIS,which implies that two phase-shifts on average (i.e., = 2 phase-shifts) are enough for deploying extremely sizable LIS. V. R ELIABILITY A NALYSIS OF
LISWhile the above studies focus on the asymptotic analysis ofLIS systems, it is equally important to reflect on the reliabilityof the LIS system from an error analysis perspective. Thissection, therefore, presents some of the works which studythe error performance of LIS systems.
A. Rate Distribution and Outage Probability
Since the coverage and interference levels of indoor net-works depend on the location and properties of objects andobstacles, intelligent surfaces are competent enough to regulatethe smart propagation environment. Henceforth, LIS provide abetter quality of coverage, level of service, and improve systemperformance. The improvement of coverage can be based onusing frequency selective surfaces, and applying well-chosenmachine-learning control algorithms [52].In [53], the authors attempt to characterize the coverage interms of outage probability, which is a significant performancemeasure to estimate the reliability of the LIS systems. In[53], the asymptotic analysis of the sum-rate is used to obtainthe analytical expression of the outage probability. The studyin [53] claims that the approximation provides a preciseestimate of the probability of outage and reduces the necessityfor extensive simulations and extraneous computational time.Moreover, the simulation results prove that despite the fluctu-ating SNR, the probability of outage is unaffected when thenumber of antenna and devices is significantly large. Using thesame system model as in [16], [49], reference [53] formulatesthe sum-rate as follows: R = K (cid:88) k =1 R k . (45)Furthermore, [53] argues that because the individual rates R , R ...R K are not identical in distribution, the distributionof the sum-rate cannot be defined. The derivation of the outageprobability is, therefore, non-trivial. Instead of analyzing theindividual rate, each rate can be written as a function of arandom variable I k , i.e., R k = a k + b k I k , (46)where a k and b k are deterministic values that depend on thelength of the LIS units. The distribution of R can be foundusing the central limit theorem, such that for large values of M and K , the asymptotic distribution of R can be estimatedto follow a Gaussian distribution with mean and variance as: ¯ µ R = (cid:88) k log (1 + ρ k ¯ p k (1 − τ k )¯ µ I k ) (47)and ¯ σ R = (cid:88) k ¯ σ I k ρ k ¯ p k (1 − τ k ) ¯ µ I k (¯ µ I k + ρ k ¯ p k (1 − τ k )) (48)respectively. In (47) and (48), ¯ p k depends on the devicelocation and ρ k denotes the transmit SNR. Finally, the closed-form expression of the probability of outage is given as P o = P r [ R < R D ] = 1 − Q (cid:18) R D − ¯ µ R ¯ σ R (cid:19) , (49) where R D is the sum-rate threshold, and Q ( · ) represents the Q -function. B. Probability of Error for Intelligent and Blind Transmission
In [54], the authors provide a mathematical framework thatstudies the relationship between the reflecting elements, blindphases, and modulation errors in LIS systems. The work in[54] assumes having an LIS system with N reconfigurablereflecting elements and studies the error performance for twoscenarios. The first scenario considers an intelligent transmis-sion at the LIS (i.e., the channel phases are known), andthe second considers a blind transmission. By first derivingthe SNR, one can get the symbol-error-rate (SER) for M -arycommunication using phase-shift-keying (PSK). The authorsin [54] first compare the binary PSK with a pure AWGN signaland study the effect of increasing N .Using numerical evaluation, [54] shows that an LIS-basedsignal, which smartly adjusts the phases of the reflector(scenario-I), has low error-probability, even at low SNR val-ues. Also, [54] shows that doubling N improves the errorperformance with a dB gain. For the second scenario(scenario-II), where the channel phases are not known for theLIS, [54] shows that a gain of N × SNR can be obtainedusing the LIS system rather than point-to-point transmission.Finally, [54] suggests using LIS as an AP and compares theperformance of the system. Furthermore, [54] shows that theLIS-AP system can provide ultra-reliable communication withan improvement of dB in the case of intelligent transmission.Blind transmission in LIS-AP systems, however, yields thesame performance of conventional-LIS systems. C. Phase Shift Error Effect on Transmission
Adjusting the reflection phases, such that the signals atthe destination combine coherently, enhances the communi-cation performance. The calculation of accurate phase shifts,however, is not feasible in practice. Hence, [55] studies theperformance of the LIS in terms of signal transmission withphase error having a generic distribution. The authors in [55]analyze the LIS performance for a limited number of reflectorswith two types of errors, which are phase estimation error andquantization error. The signal at the receiver’s side is expressedas follows [55], Y = n √ γ HX + W, (50)where γ is the average SNR, X is the transmitted symbol, n isthe number of reflectors, and W ∼ N (0 , is the normalizedreceiver noise. The channel gain H is represented as H = 1 n n (cid:88) i =1 H i H i e j Ω i ∈ C, (51)where H i and H i are the complex fading coefficients be-tween source to reflector and reflector to destination, respec-tively.To maximize the SNR, the practical phase Φ i is set tocancel the summation of the phases H i and H i that denotesthe overall phases. Also, in (51), Ω refers to the phase noise which has a normal distribution between [ − π, π ] . Thework in [55] further assumes that θ i , i = 1 , . . . ., n areindependent and identically distributed having a common char-acteristic function, which is labeled as trigonometric/circularmoments. When n is large, H has a complex normal distri-bution with non-circular symmetry; however, [55] examinesthe performance when n is finite. When there is no phaseerror, which is the ideal case, the coefficient H is real and H ∼ N (cid:0) a , (1 − a ) /n ) (cid:1) , with a as the power parameter.When phase errors exist, H has a complex normal and circularsymmetric distribution ∼ (0 , n ) , which indicates that there isa lack of information about H i and H i phases.The study in [55] shows that the communication channelvian LIS with phase error is the same as a point-to-pointchannel with Nakagami fading, where the parameters of bothare influenced by phase uncertainty via the first two circularmoments. Moreover, the average SNR increases with n , andthe diversity order increases with n . Most importantly, whenthe number of reflectors is limited, the numerical analysis oferror rate verifies that the LIS performance is vigorous despitethe phase errors. D. Reflection Probability of LIS Systems
The work in [56] investigates the reflection probabilityof randomly distributed objects in the LIS-aided wirelessnetworks, where the reflection probability is a function of theLIS length and the locations of the transmitter, the receiver,and the targeted object. For an object to be a reflector, twoevents must hold. First, the transmitter and the receiver haveto be on one side of the reflector, lying on an infinite linethat intersects the infinite line of the object segment, whichwe refer to as Event 1. Second, a perpendicular bisector lineconnecting the transmitter and the receiver must intersect theobject segment itself, which we refer to as Event 2. Therefore,for LIS to reflect, the following probability must hold, P r ( LIS to reflect ) = P r { Event 1 ∩ Event 2 } . (52)This study indicates that the reflection probability of objectscoated with metasurfaces is independent of its length dueto its capability of adjusting the reflection angles, coveringmore than what is expected by Snell’s law [56] [57]. It isclear that for different length values, the reflection probabilityis almost constant, which indicates that small-sized objectscan attain a high likelihood of being a reflector when theyare placed appropriately. Therefore, it can reduce the costof manufacturing and deployment over large-sized reflectingsurfaces. Moreover, large-scale deployment of LIS improvesthe coverage area, reducing the blind-spots for terrestrialcellular BSs [58]. Nevertheless, the authors in [59] show thatcareful deployment and proper selection of phase shifts arenecessary to get the full potential of LIS systems. E. Impact of Size on Performance of LIS Systems
Recent theoretical works in [57] analyze the performanceof different-sized LIS systems by comparing them with relaystations in terms of the average SNR as a function of thenumber of elements and the end-to-end transmission distance. Furthermore, [57] states that for LIS to be large and act asanomalous mirrors, the geometric size of each component ofLIS has to be times greater than the radio wavelength ofthe impinging signal. Thus, whenever less than this thresholdvalue, the intelligent surfaces are considered small and actas diffusers. The study in [57] highlights how the averageSNR is scaled differently according to the type of connectivitywith either relay stations, large intelligent surfaces, or smallintelligent surfaces. For example, a relay station average SNRis scaled by a factor of M min (cid:0) d − SR , d − RD (cid:1) , (53)a large intelligent surfaces system average SNR is scaled bya factor of M ( d SR + d RD ) − , (54)and a small intelligent surfaces system average SNR is scaledby a factor of M (cid:0) d SR d RD (cid:1) − , (55)where d SR refers to the distance between the source andrelay/LIS, d RD refers to the distance between the relay/LISand destination, and M is the number of antenna elements atthe relay station or the LIS.In [60], the authors show that in relay stations, the averageend-to-end SNR grows linearly with M because the totalpower remains constant since the power is distributed amongall the antennas, as in (53). The average SNR, however,increases quadratically with M in large and small intelligentsurfaces systems, as in (54) and (55). The study in [61] claimsthat this is especially the case because each element behavesas a separate reflecting mirror that scales the power by thetransmittance before reflecting it.Moreover, in relay stations, the SNR scales with the smallestdistance between the two paths, as in (53). In LIS, the SNRscales with the total transmission distance, as in (54). Insmall intelligent surfaces, however, the signal from each meta-element may combine, resulting in the scaled SNR, as in(55). Hence, it is undeniable that the LIS outperform therelay stations and small intelligent surfaces since the SNRin the case of LIS has the most significant scaling law thatresults in having a better transmission rate. Furthermore, forspecific values of M at . GHz and GHz as examples,LIS significantly double the rate of transmission [57].VI. T HE P OTENTIAL OF P OSITIONING AND C OVERAGE IN
LIS S
YSTEMS
The next-generation wireless communication networks an-ticipate enabling accurate location-based services wheremmWaves and THz technologies will achieve a centimeterlevel of accuracy [62]. In this regard, LIS can be deployedboth for indoor and outdoor environments, making it one of theoptions for accurate positioning and localization. This section,therefore, surveys the recents works which study the potentialof positioning using LIS systems. Received signal strength(RSS) based positioning methods, in general, require high RSSvalues and coverage probability [63]. In particular, [64] derivesthe Cram´er-Rao Bound for UE localization and positioning, whereas [2] studies the performance of LIS for positioningand localization and comparing the accuracy of distributedand centralized LIS systems. On the other hand, [15] examinesthe potential of mmWave MIMO system positioning with andwithout the aid of an LIS system. Finally, [65] expands theLIS model from planar to spherical surfaces and assesses itsRSS and coverage.
A. Positioning in Centralized and Distributed LIS Systems
In [2], [64], the authors derive the Cram´er-Rao LowerBounds (CRLB) for UE navigation using the uplink signalof the LIS system. Notably, the analysis of [2] leveragesthe LIS system to provide robustness by subdividing a givensurface area into smaller units of intelligent surfaces (i.e.,distributed LIS system); however, the distributed LIS systemmay increase the complexity and feedback overheads. Thework [2] shows that the CRLB for a UE positioned at theperpendicular bisected line of the LIS decreases linearly asa function of the surface area. When a UE is not positionedas such, there is not a closed-form solution for the CRLB;however, [2] analytically approximates and shows that CRLBdecreases in a quadratic fashion.Also, the work [64] compares the centralized (Fig. 11) anddistributed (Fig. 12) deployment of LIS, in terms of the cov-erage probability. The centralized LIS system refers to havingeach surface in the system as a whole unit, whereas the dis-tributed LIS system refers to having each surface divided intoseveral smaller independent, intelligent units. The study [64]further shows that the distributed implementation has lowerCRLB for the x − and y − dimensions than the centralizedimplementation for the same total surface area. Also, the prob-ability of coverage for a distributed LIS system is significantlybetter than the centralized one, which eventually improvesthe positioning performance. The study [64] also verifies thatthe distributed implantation facilitates a flexible deployment,yet requires specialized hardware for phase calibration andcooperation between the LIS’ sub-units. Also, the distributedimplementation allows the units to be replaced when neededwithout affecting the whole system. Nevertheless, hardwareimpairments are minimized in distributed LIS [48], [2]. B. Positioning in mmWave Aided Systems
The quality of RSS values is a critical factor in determiningthe position of UEs. The study [15] investigates leveraging thephase and number of elements of the LIS system to aid themmWave systems in obtaining high accuracy of positioning.The authors in [15] study the difference in the positioningperformance of a conventional mmWave system and an LIS-assisted mmWave system. The study in [15] follows the sameprocedure of [64] to obtain the CRLB performance bound ofboth systems. Further, [15] controls the phase and amplitude ofthe propagated waves by using LIS, where the study ultimategoal is to use the LIS-aided system to minimize the error in theposition estimation. The results of [15] show that an LIS-aidedmmWave MIMO system has a better positioning performanceand smaller orientation error bound, when increasing thenumber of elements, even for as little as 40 elements. WH R
Fig. 11: Centralized deployment of LIS system. R WH Fig. 12: Distributed deployment of LIS system scaled byhalf.
C. Positioning Using Spherical LIS
The author in [65] expands the system of [2] to a sphericalLIS instead of a planar one. Using spherical surfaces insteadof planar has many advantages; for instance, it can act as areflecting surface as well as a relaying surface. One part ofthe spherical LIS can work as a reflecting surface, while theother part can act for relaying the signals to UEs. The latteris particularly useful when a UE is blocked from its servingBS. Also, unlike traditional planar LIS, a rotating user overspherical LIS would not impose changes in the information-theoretical properties, which yields an RSS gain for a mobileUE. Hence, [65] derives the CRLB for RSS based sphericalLIS systems in terms of the normalized distance given by ν = r/ cos θ , where r is the radius for the sphere and θ is theelevation angle of the UE. The study, then, compares the RSSand CRLB of a spherical LIS system with a planar LIS systemof the same surface area, i.e., the radius of the disk-shapedplanar LIS is r p = √ r . The CRLB of spherical LIS is derivedby evaluating the Fisher-information matrix and uses RSS tocompute CRLB in terms of the sphere radius. The CRLB ofspherical LIS, therefore, is given by [65]CRLB sph = 4 ν ( ν − , (56) while the CRLB of planar disk shaped LIS isCRLB pl = 4( ν + 1) . (57)It can be seen from (56) and (57) that the CRLB of sphericalLIS is smaller than the planar LIS, which makes it moreaccurate for positioning of the UEs. The results of [65] verifythe above findings, and show that especially when r increases,the spherical LIS outperforms the traditional planar one.VII. O PEN R ESEARCH I SSUES
Since the beginning of the recent active LIS research era,there has been a plethora of studies that focused on the jointbeamforming optimization problems, theoretical SNR andSEP derivations, channel estimation, and SINR maximization.Furthermore, many researchers investigated the application ofmachine learning tools and the evaluation of LIS potentialfor the mmWave/THz, free-space optics, and visible lightapplications [1]. For example, in [13], the authors explored theproblem of joint active and passive beamforming design thatminimizes the total transmit power at the BS. They employedoptimization techniques, such as semidefinite relaxation andalternating optimization, to solve the non-convex optimizationproblem. For SEP derivations, the author in [54] proposed aSEP mathematical framework for LIS systems by studying theability of using an LIS as an AP transmitter. However, in spiteof the timely studies mentioned above, there are open researchissues that should be tackled to guarantee a high level ofreliability in intelligent wireless networks. In the following, weexplore few of the promising upcoming research challenges.
A. Realistic Optimization Frameworks
Classical optimization problems need to be addressed andreformulated due to the fundamental challenges that IRSimplementation faces. Such issues are due to the fact themost of the current works are rather based on non-practicalassumptions, e.g., perfect channel estimation (i.e., perfect CSIassumptions), ignoring internal losses and far-field radiations,accurate beamforming and beamstearing, single-antenna UE,optimal precoding, etc. Hence, future works need to revisitsuch assumptions and examine the reliability of IRSs throughrealistic approaches.Moreover, while the majority of the studied optimizationproblems in LIS scenarios focus on maximizing the EE,throughput, and SINR, several objectives have not been ad-dressed in the literature yet. Firstly, the literature lacks under-taking LIS when it comes to ultra-reliable low latency com-munication. To this end, we propose minimizing the overallpower consumption of LIS users subject to transmit powerbudget and reliability constraints in terms of probabilisticqueuing delay. In particular, the reliability measure shouldaccount for events where users’ queue length exceeds a certainthreshold. For instance, after accounting for unknown CSI andnetworks dynamics, the problem can be solved using federatedlearning, i.e., through distributed approaches. Leveraging suchapproaches would enable multiple learners to define a set oflocal parameters from the existing training data where they Fig. 13: RF-VLC hybrid system for RISscan share their local models rather than sharing the trainingdata.Secondly, one can look into the energy harvesting (EH)aspect in LIS systems, whereby a possible source of energycan come from the ubiquitous radio transmitters. EH providesgreen and sustainable solutions to the power loss. Hence,EH-empowered LIS system can work as an energy harvester,where it converts the incident signal into electrical energy [66],[67]. Nonetheless, RF sources suffer from low incident powerlevels, mainly depending on the transmitted wave frequency,the antenna gain, and the communication range. Therefore,we propose maximizing the receiver incident power subjectto the transmitter power and the gap between the transmitterand the LIS. Adjusting the position angles of the antennas canmaximize the incident power of the received signal, where theoptimal position angles can be iteratively computed using theadaptive gradient ascent method.Finally, another approach that future studies must exploitis data-driven optimization. RIS systems are complex to ana-lyze and design compared to conventional wireless networks.Therefore, to reduce the complexity system, effective data-driven optimization techniques that depend on deep learning,transfer learning, and reinforcement learning should be con-sidered. In short, machine learning can prove to provide apowerful approach to improve the RIS-based communicationsystems performance.
B. Hybrid Systems: RF-VLC
RIS can empower the practical implementation of beyond5G (B5G) systems by means of controlling the randomness ofthe propagation environment. RIS provides other advantages,including EE and full-band response. Nevertheless, B5G net-works require significant enhancements in mobile broadband,enabling ultra-reliable low-latency communications [1]. To thisend, deploying hybrid systems can help in providing fast,efficient, and reliable communication networks. Specifically,visible light communication (VLC) has been a prominentresearch area in advanced communication systems [68], [69].VLC has the potential of providing ultra-high bandwidth, ro-bustness to electromagnetic interference, and inherent physicalsecurity. Both RIS-RF and VLC can be used in an outdoorenvironment as shown in Fig. 13, where mirrors reflect visible light (VL) signals to a photodetector in the users’ deviceswhile RISs are used to reflect RF signals from the BS.VL provides safe and health-friendly communication schemesthat can be exploited in health-constrained centers such ashospitals. Furthermore, RIS can be used to complement VLCwhenever line-of-sight conditions fail, thus, supporting futurewireless networks. Deploying this hybrid system model wouldprovide a reliable communication scheme that compensates forpotential failure of one of the connecting links. At the moment,most of the analysis in LIS exists only for RF and mmWavecommunications. Hence, future research can further investigatethe performance of hybrid technologies in the LIS realm.
C. Coating EM Materials
Recall from Sec. I that RIS consist of controllable EMmaterials, where the antennas are coated with reconfigurablethin layers of EM materials to control the propagation ofsignals. Therefore, tunable materials should be used to adjustthe signals’ phase shifts, thereby adapting the transmitted sig-nals according to the changes in the wireless environment [1].Meta-surfaces are the key enablers of such technologies [60].Moreover, a widely tunable bandgap material is suggested tosupport full-band response, where theoretically, it can operateat at any frequency band. To this end, to best realize theRIS systems, the usage of graphene is proposed as a futureresearch direction. The graphene bandgap ranges from eV to . eV. Consequently, it operates from the radio wave bandto the infrared band. Graphene reconfigurable meta-surfacescan further achieve beam steering, beam focusing, and wavevorticity control by means of local tuning. For instance, phasecontrol in graphene metasurfaces is achieved by changingits conductivity via electrostatic biasing. Due to such uniquecharacteristics, future research directions should exploit howto adjust the performance of graphene-based RIS systemsthrough optimizing the system conductivity via electrostaticbiasing. D. Health Issues
RF technologies are proliferating with the emergence of 6G.According to [70] and [71], a wide range of human healthconcerns are correlated with exposure to the RF radiations.The associated health issues with EM radiation exposure havebeen an open research topic for decades. However, the recentadvent of the LIS in indoor communication scenarios openedthe door for more concerns regarding the possible healthrisks. Mostly, indoor mmWave environments are studied forfuture applications as they offer large bandwidth for enablinghigh data rates. However, unlike cellular phone frequencies,mmWave radiations are high-frequency signals that have rela-tively deep penetration in the human body. Hence, the primaryconcern is the heating of the skin and eyes resulted from thebody absorption of mmWaves. In reality, recent studies showthat current estimating power density methods are not reliablefor determining the exposure compliance at close mmWaveinteraction [72]. Therefore, to maintain an efficient high-rateLIS system, we propose considering an optimization problemthat maximizes the data-rate, subject the health constraints, by means of adjusting the distance between several LISs,particularly in indoor environments. While increasing thedistance would decrease the RF exposure of users, it wouldaffect the system overall performance. Future research studiesmust, therefore, consider such trade-offs in performance versushealth issues by properly adjusting the networks differentparameters. E. Integration of 5G and 6G Technologies
LIS is one of the revolutionary and potential physical layertechnologies that generate a new communication paradigm thatmeets the requirements of future 6G networks [54], [73]. Also,smart radio environments may have a potential impact on theupcoming 6G technology markets, facilitating substantive im-provements in spectral efficiency with cost-effective solutions.One of the undiscovered research directions is the integrationof intelligent surfaces with emerging 5G technologies, suchas IoT [74], drones-aided communications [75], beamforming[76], and physical layer security [77]. For 6G technology,an LIS system has the potential to provide a pervasive andreliable wireless communication service, while suppressingadditional interference components such as noise and inter-user interface through both NLOS and LOS paths. Since theLISs decrease network interference level, they are expectedto improve the network capacity and user performance in 6Gnetworks, especially for high-density user environments suchas airports and stadiums. Even though the unique benefits ofLIS help creating a favorable wireless communication channel,its use-cases and application scenarios that meet new userrequirements and networking trends of 6G technology are stillin their exploratory phase. Furthermore, the economic impactand its sustainability of LIS-assisted smart radio environmenton B5G markets are key research questions that need to befurther studied [7], [54].
F. Localization Using LIS Systems
Positioning using LIS-aided mmWave systems can be an-alyzed and studied by jointly considering the design ofmmWave beamformer and LIS phase shifters. Also, the local-ization performance of distributed spherical LISs and central-ized spherical LIS systems can be investigated. Moreover, thestudy of the CRLB of LIS systems in the presence of NLoSchannels can be further pursued in future works. Also, theperformance regarding the positioning accuracy of LIS-aidedsystems highly depends on the placement of the reflectors andmetasurfaces. Therefore, it is important to find the optimallocations to place these reflectors and metasurfaces. Theplacement of these materials is a challenging task, which is aninverse problem of channel modeling. In channel modeling,being aware of the deployment, we can obtain the channelstate information using various channel modeling techniquessuch as ray tracing, etc. While based on the desired channelstate information, the optimal deployment of the materials inLIS is an inverse task, the solution of which remains an openproblem. VIII. C
ONCLUSION
Large intelligent surfaces (LIS) are a promising physicallayer technology for B5G systems. Such technology does notonly enhance wireless systems QoS, but also reduces the largepower consumption as compared to traditional networks. LISare made up of re-configurable EM meta-materials that arecapable of modulating data onto the received signals, cus-tomizing changes to the radio waves, and intelligently sensingthe environment. This paper provides a unique blend thatsurveys the principles of physical operation of LIS, togetherwith their optimization and performance analysis frameworks.The paper first introduces the LIS technology and its workingprinciple. Then, it presents various optimization techniquesthat aim to optimize specific objectives, namely, maximizingenergy efficiency, power, sum-rate, secrecy-rate, and coverage.The paper afterwards discusses various relevant performanceanalysis works including capacity analysis, the impact ofhardware impairments on capacity, uplink/downlink data rateanalysis, and outage probability. The paper further presentsthe impact of adopting the LIS technology for positioningapplications. Finally, we identify numerous exciting openchallenges for LIS-aided B5G wireless networks, includingnew resource allocation problems, hybrid RF/VLC systems,health considerations, and localization. To the best of theauthors’ knowledge, this survey is the first of its kind whichcombines the technical aspects of mathematical optimizationand performance analysis of LIS systems, and sheds lighton promising research directions towards the formulations ofpractical problems in future B5G systems.R
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