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Intelligent Reflecting Surface Assisted WirelessCommunication: Modeling and Channel Estimation

Qurrat-Ul-Ain Nadeem, Member, IEEE, Abla Kammoun, Member, IEEE, Anas Chaaban, Member, IEEE,Merouane Debbah, Fellow, IEEE, and Mohamed-Slim Alouini, Fellow, IEEE

Abstract—The recently completed 5G new radio standard isa result of several cutting-edge technologies, including mas-sive multiple-input multiple-output (MIMO), millimeter (mm)-Wave communication and network densification. However, thesetechnologies face two main practical limitations 1) the lackof control over the wireless channel, and 2) the high powerconsumption of the wireless interface. To address the need forgreen and sustainable future cellular networks, the concept ofreconfiguring wireless propagation environments using IntelligentReflecting Surfaces (IRS)s has emerged. An IRS comprises ofa large number of low-cost passive antennas that can smartlyreflect the impinging electromagnetic waves for performanceenhancement. This paper looks at the evolution of the reflectiveradio concept towards IRSs, outlines the IRS-assisted multi-user multiple-input single-output (MISO) communication modeland discusses how it differentiates from the conventional multi-antenna communication models. We propose a minimum meansquared error (MMSE) based channel estimation protocol forthe design and analysis of IRS-assisted systems. Performanceevaluation results at 2.5 GHz operating frequency are providedto illustrate the efficiency of the proposed system.

I. INTRODUCTION

The Fifth Generation (5G) mobile communication standardpromises to provide enhanced mobile broadband, massiveconnectivity and ultra-low latency through various technologi-cal advances, including massive multiple-input multiple-output(MIMO), millimeter wave (mmWave) communications, andnetwork densification. However, these technologies consume alot of power and struggle to provide the users with guaranteedquality of service (QoS) in harsh propagation environments.For example: the network’s total energy consumption scaleslinearly with the numbers of base stations (BS)s and the activeantennas at each BS, while communication at mmWave bandssuffers from high path/penetration losses. These limitationshave resulted in the need for green and sustainable future cel-lular networks with control over the propagation environment.

An emerging concept that addresses this need is that of asmart radio environment (SRE), where the wireless propaga-tion environment is turned into an intelligent reconfigurablespace that plays an active role in transferring radio signalsfrom the transmitter to the receiver [1]. This concept can berealized by deploying arrays of low-cost antennas [2], smart

Q.-U.-A. Nadeem and A. Chaaban are with School of Engineering, TheUniversity of British Columbia, Kelowna, Canada (email: {qurrat.nadeem,anas.chaaban}@ubc.ca)

A. Kammoun and M.-S. Alouini are with the Computer, Electrical andMathematical Sciences and Engineering (CEMSE) Division, King AbdullahUniversity of Science and Technology (KAUST), Thuwal, Saudi Arabia23955-6900 (e-mail: {abla.kammoun,slim.alouini}@kaust.edu.sa)

M. Debbah is with CentraleSupelec, Gif-sur-Yvette, France (e-mail: mer-ouane.debbah@centralesupelec.fr).

reflect-arrays [3] and reconfigurable meta-surfaces [1] in theenvironment, to shape the impinging electromagnetic (EM)waves in desired ways in a passive manner, without generatingnew radio signals and thereby without incurring any additionalpower consumption. SRE is a recent but feasible conceptwith a lot of current research focusing on fabricating relevanthardware prototypes, implementing testbeds and doing system-level simulations [1], [4], [5].

Very recently, works approaching this subject from thewireless communication design perspective have appeared, inwhich the SRE is enabled by intelligent reflecting surfaces(IRSs). The IRS is viewed as a planar array of a large numberof passive reflecting antennas. Joint designs for precoding atthe BS and reflect beamforming at the IRS are proposed toachieve different communication goals, for example: improvethe network’s spectral or energy efficiency, increase the se-crecy capacity for physical layer security, assist in wirelesspower transfer [6]–[8]. Almost all existing works assume theIRS to have perfect channel state information (CSI), whichis highly unlikely in practice, given the IRS has no radioresources of its own to estimate the channels.

In this paper, we outline the IRS-assisted system modeland discuss how it differentiates from conventional multi-antenna communication systems. We first discuss the evolutionof the reflective radio concept towards IRSs along with itsimplementations and applications in wireless communicationsin Section II. The communication model for an IRS-assistedMISO system is introduced in Section III, and comparisons aremade with existing MISO communication models. We proposea novel minimum mean squared error (MMSE) based channelestimation protocol in Section IV by forming a control loopbetween the BS and IRS to serially estimate each IRS-assistedlink. Simulation results in Section V show the IRS-assistedsystem to be highly efficient but also sensitive to CSI errors.Some related research directions and concluding remarks arepresented in Section VI and VII respectively.

II. EVOLUTION TOWARDS IRSS

Reflective radio technology has emerged as an attractivesolution for designing energy and spectral efficient communi-cation systems [8]. In fact, the reflective devices (RDs), whichdo not use expensive and power-hungry active components,have become popular candidates to transmit signals to their re-ceivers or improve the transmission of primary communicationsystems, using EM scattering of the radio waves. The formeris known as backscatter communication (BSC) [9] while thelatter is referred to as reflective relay [8].

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Fig. 1: Typical implementation of an IRS system.

Traditional BSC is widely used to support low powerinternet-of-things (IoT) communication, where the RD exploitsits different reflection states to modulate its own messagesover a continuous wave signal generated by a dedicated radiofrequency (RF) emitter. A basic RD circuit varies the loadimpedance connected to its antenna through a switch to realizedifferent reflection states, e.g. different phase values. The morerecent ambient BSC exploits RF signals transmitted from anexisting primary source like the cellular BS or WiFi accesspoint and therefore no dedicated RF emitter is needed.

Reflective relays have been used to improve the QoS ofblocked or weak users in the primary system. Conventionally,a single antenna is deployed in the reflective relay, leadingto a weak reflective link, which can be improved by usingreflective arrays instead. The concept of reflective array wasfirst proposed in [10], when open-ended wave-guides wereused as antenna elements to change the phase of the reflectedsignal. Interest in reflective arrays increased in 1990s aftermicro-strip patch antennas were used to implement themand found applications in radar and satellite communication[11]. Although there have been conceptual discussions onreconfigurable reflective arrays, but hardware prototypes havebeen made available only recently [1]. This has led to theconcept of an IRS, which is a 2D structure of a large number ofpassive elements/antennas with the ability of reconfiguring theincident EM waves in real time. The first works that considerthe use of IRSs to re-program indoor and outdoor propagationenvironments appeared in 2012 [5] and 2018 [6] respectively.

We will now briefly discuss some current implementationsof IRSs. The authors in [2] present the implementation direc-tions for embedding arrays of low-cost antennas into the wallsof a building to passively reflect the incident wireless signals.The developed prototype uses three parabolic antennas loadedwith single-pole four-throw switches and is able to achieve64 different reflection configurations. In [3], a reflect-arraywith 224 reflecting units is fabricated, with each unit formedby loading a micro-strip patch element with an electronically-controlled relay switch. To continuously tune the phase re-sponses of the reflecting units, variable capacitors are inte-grated into the reflector panel. Alternate designs include usingpositive-intrinsic-negative (PIN) diodes, field-effect transistors(FETs), or micro-electromechanical system (MEMS) switcheswithin the reflecting panel. Current reflect-array designs allowthe configuration of the reflecting elements at the code-booklevel, such that the whole surface can be electronically shaped

to adaptively synthesize different beam shapes. Moreover,the design of reconfigurable meta-surfaces, composed of thinmeta-material layers of a large number of sub-wavelengthscattering particles (meta-atoms), has provided the capabilityof shaping the radio waves in fully customizable ways withproperties like negative refraction, anomalous reflection andperfect absorption [1]. The communication model in this workassumes the IRS to be realized using an array of antennas thatpassively reflect the incoming waves.

Fig. 1 shows a typical implementation of an IRS systemwhich consists of the IRS realized using patch antennas printedon a dielectric substrate, a copper back-plane to prevent signalleakage and a control circuit board that adjusts the reflectionamplitude and phases of the IRS elements, as triggered by asmall micro-controller. In practice, field-programmable gatearray (FPGA) can be implemented as the microcontroller,which also acts as a gateway to communicate/coordinate withthe BS (where all beam control is implemented) through aseparate wired or wireless backhaul link.

The most attractive application of IRS is to act as a reflectiverelay to improve the QoS of users suffering from unfavorablepropagation conditions. In this case, it resembles a full-duplex(FD) multi-antenna amplify-and-forward (AF) relay. However,the FD-AF relay needs active electronic components, suchas digital-to-analog convertors (DACs), analog-to-digital con-verters (ADCs), power amplifiers, as well as self-interferencecancellation circuits. In contrast, IRSs are meant to be realizedwith minimal hardware complexity and power requirements.Moreover, the received SNR through the IRS-assisted linkis shown to scale quadratically in the number of reflectingelements [8] as opposed to the classical beamforming methodsat the BS and AF relays, where the SNR scales linearly withthe number of antennas. With a large number of elements,IRS can be much more advantageous than AF relays and hasrecently found applications in physical layer security as well assimultaneous wireless information and power transfer systems.

Another recent application of IRSs is in mmWave communi-cation systems, where a BS comprising of few active antennasilluminates a nearby large IRS [12]. By scaling up the numberof passive elements at the IRS without increasing the numberof active antennas at the BS, massive MIMO beamforminggains are yielded. However, these work assume a loss-lessfixed connection between the BS and the IRS by placing thelatter very close to the BS. Different from this, we considerthe use of IRSs in the propagation environment to enhancecoverage and QoS, with the channel between the BS and IRSnot being loss-less and not necessarily being fixed. In the nextsection, we study the IRS-assisted system model along withhow it differentiates from conventional MISO, hybrid MISOas well as relay-assisted communication models.

III. COMMUNICATION MODEL

The proposed IRS-assisted multi-user MISO system is il-lustrated in Fig. 2a, which consists of a BS equipped withM antennas serving K single-antenna users. This communi-cation is assisted by an IRS, comprising of N nearly passiveantennas which introduce phase shifts onto the incoming signalwaves, attached to the facade of a building in the propagation

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(a) IRS-assisted multi-user MISO system. Red dashed lines repre-sent the estimated uplink channel vectors.

(b) Channel estimation protocol.

Fig. 2: Proposed IRS-assisted multi-user MISO communication model and channel estimation protocol.

environment. As discussed already in Fig. 1, the reflectionconfiguration of the IRS (i.e. the phase shifts applied byindividual IRS elements) is controlled by a micro-controller,which gets this information from the BS over a backhaul link.

The BS transmits the signal vector x =∑Kk=1

√pkgksk,

where pk, gk ∈ CM×1 and sk are the allocated power,digital precoding vector and data symbol of user k respectively.Given sk’s are i.i.d. CN (0, 1) variables, x has to satisfy thepower constraint E[||x||2] = tr(PGHG) = PT , where G =[g1, . . . ,gK ] ∈ CM×K and P = diag(p1, . . . , pK) ∈ CK×K .The received signal at user k is given as,

yk = (hHd,k + hH2,kΦHHH

1 )x + nk,

= (hHd,k + vHHH0,k)x + nk (1)

where HH1 ∈ CN×M is the channel from the BS to

the IRS, hH2,k ∈ C1×N is the channel from the IRSto user k, hHd,k ∈ C1×M the direct channel from theBS to user k and nk ∼ CN (0, σ2

n) is the noise at theuser. The IRS is represented by the diagonal matrix Φ =diag(β1 exp(jθ1), . . . , βN exp(jθN )), where θn ∈ [0, 2π] andβn ∈ [0, 1] represent the phase and the amplitude coeffi-cient for element n respectively. The uplink channel throughthe IRS H1Φh2,k can be equivalently expressed as H0,kv,where v = [β1 exp(jθ1), . . . , βN exp(jθN )]T ∈ CN×1 andH0,k = H1diag(hT2,k) ∈ CM×N . This formulation separatesthe response of the IRS in v from the cascaded channel outsidethe IRS control in H0,k, and will assist us in the design of thechannel estimation protocol in Section IV.

We will now discuss how this model is different and morechallenging to tackle in terms of beamforming design and CSIacquisition when compared to other multi-antenna models.

Conventional MISO Communication Model: Under thismodel, the received signal at user k is given as yk =hHd,kx + nk. Finding the optimal G and P that maximizethe optimization criteria of interest, like sum-rate, minimumrate, energy efficiency, subject to tr(PGHG) = PT , are well-studied problems in literature with optimal solutions, e.g. dirtypaper coding for sum-rate, optimal linear precoder in [7] forminimum rate. The channels are estimated at the BS eitherby exploiting channel reciprocity in time division duplexing

(TDD) systems or by explicit downlink training and CSIfeedback in frequency division duplexing (FDD) systems [13].

Relay-Assisted MISO Communication Model: The receivedsignal at user k is given as yk = hH2,kV

HyR + hHd,kx + nk,where yR = HH

1 x + nR, V ∈ CN×N is the diagonal AFmatrix of the relay and nR ∼ CN (0, σ2IN ), where N isthe number of antennas at the relay. The design goal is tofind the optimal P, G and V given tr(PGHG) = PT andE[tr(VHyRyHRV)] = PR, where PR is the Tx power at therelay. The BS estimates H1 using the pilot symbols sent bythe relay while h2,k is estimated at the relay based on the pilotsymbols sent by the users and the CSI is shared between therelay and BS. The joint design of G and V is challenging butseveral efficient algorithms exist in literature [14].

Hybrid Beamforming Model in mmWave Systems: Toreduce the number of RF chains needed for fully digitalprecoding in mmWave massive MISO systems, hybrid beam-forming architectures have been proposed where the overallbeamformer consists of a low-dimension digital beamformerfollowed by the analogue beamformer [12], [15]. The receivedsignal at user k is given as yk = hHd,kx + nk. The Tx signalx =

∑Kk=1

√pkVAgksk, where VA ∈ CM×MRF is the

analogue beamforming matrix with constraints |VA(i, j)| = 1,i = 1, . . . ,M , j = 1, . . . ,MRF and gk ∈ CMRF×1 is thedigital precoding vector, where MRF is the number of RFchains. The channels hd,ks are estimated at the BS under TDDand at the users (who then feedback this CSI to the BS) underFDD. Algorithms based on compressive sensing and channeldimension reduction, to reduce the huge CSI feedback over-head incurred in massive MISO systems, have been proposed[15]. The joint design of VA and G is challenging because ofthe unit-modulus constraints on VA. This non-convex problemcan not be be solved optimally using standard methods whichhas resulted in several suboptimal solutions.

In terms of precoding/beamforming design, the IRS-assistedsystem model is much more difficult to analyze as comparedto the first two models, due to the unit-modulus constraintson elements of the reflect beamforming matrix Φ. Althoughbeamforming optimization under unit-modulus constraints hasbeen studied in the context of hybrid digital/analog mmWave

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architectures [12], [15], such designs are mainly restricted tothe BS side, and are not directly applicable to the joint designof the precoding at the BS and reflect beamforming at theIRS. In terms of CSI acquisition, the IRS-assisted system isdifferent from all of the above models as IRS has no radioresources of its own to send pilot symbols to help the BSestimate H1 nor can it receive and process pilot symbolsfrom the users to estimate h2,ks. This is one of the biggestchallenges in the practical design of IRS-assisted systems [8].

The design of IRS-assisted systems also requires the correctmodeling of h2,k and H1. Existing works (e.g. [6]) utilizethe independent Rayleigh model, which is not practical unlessthe IRS elements are spaced far enough and the environmenthas rich scattering. Moreover, under this setting, the statisticsof the received signal do not change with the values of thephase shifts as N,M grow large so asymptotically there willbe no significant performance improvement due to IRS. It istherefore important to analyze the performance under the morepractical ray-tracing or correlated Rayleigh channel models.

The IRS is envisioned to be installed on a high rise buildingwhich will likely result in a LoS channel between the BS andthe IRS [7]. There are two ways to model this LoS channel.1) Rank-One Channel: Since the BS and the IRS have co-located elements, so the channel matrix H1 will have rank one,i.e. H1 = abH , where a ∈ CM×1 and b ∈ CN×1 describethe array responses at the BS and the IRS. The degrees offreedom offered by the IRS-assisted link will be one and theIRS will only yield performance gains when K = 1 [7].2) Full-rank Channel: To benefit from the IRS in the multi-user setting, we must have rank(H1) ≥ K. One way tointroduce this rank is to have scattering between the BS andthe IRS. Also using distributed IRSs, the LoS channel matrixbetween the BS and the IRSs can be made of high rank.

IV. CHANNEL ESTIMATION PROTOCOL

Channel estimation is necessary to compute the precoderG and the reflect beamforming matrix Φ. We focus on TDDsystems and exploit channel reciprocity in estimating thedownlink channels using the received uplink pilot signals fromthe users. The channel coherence period of τs is divided intoan uplink training phase of τcs and a downlink transmissionphase of τds. Throughout the training phase, the users transmitmutually orthogonal pilot symbols xp,k, where |xp,k|2 = pc.

The real difficulty is in the estimation of H1 and h2,ksas the IRS has no radio resources and signal processingcapability to send or receive pilot symbols. Therefore, theBS has to estimate all the channels and use them to computeG as well as Φ. The BS then provides information on therequired IRS reflection configuration (i.e. Φ or v in (1)) tothe micro-controller connected to the IRS. The informationcan be provided in the form of an index of a pre-definedquantized codebook shared by the BS and micro-controller,that contains the various reflection configurations possible atthe IRS. Wireless backhaul links in the mmWave and tera-hertzbands are suitable candidates to enable the BS to communicatewith the IRS controller under strict latency requirements [1].

To this end, note that H1 and h2,k have been cascaded asH0,k ∈ CM×N in (1), where H0,k = [h0,1,k, . . . ,h0,N,K ] is

a matrix of N column vectors. Each vector h0,n,k ∈ CM×1(shown in red curved arrows in Fig. 2a) can be interpreted asthe channel from the user to the BS through the IRS whenonly element n of the IRS is ON i.e. βn = 1, θn = 0 andβi = 0, i 6= n. We will focus on the MMSE estimation ofh0,n,k, n = 1, . . . , N and hd,k for k = 1, . . . ,K at the BS.

The total channel estimation time τc is divided into T +1 sub-phases, each of duration τs = τc

T+1 s, where T = N .During sub-phase 0, the BS requests the micro-controller tokeep all the IRS elements in the OFF state (i.e. βn = 0, n =1, . . . , N ) and the BS estimates the direct channel hd,k for allusers. During the tth sub-phase, where t = 1, . . . , T , the BSsends a signal to the micro-controller to switch element t of theIRS ON (i.e. βt = 1, θt = 0) while keeping all other elementsOFF so that the BS can estimate h0,t,k. The micro-controllertherefore triggers the control circuit board of the IRS in Fig. 1to implement the required v, e.g., v = [1, . . . , 0] in sub-phase1, v = [0, 1, 0, . . . , 0] in sub-phase 2 and so on.

The expressions of the MMSE estimates for all the channelvectors can be derived straightforwardly as follows. Let y0

represent the received training signal vector when all theelements of the IRS are OFF, given as,

y0 =

K∑k=1

hd,kxp,k + wB , (2)

where wB ∼ CN (0, σ2IM ) ∈ CM×1 is the noise vector at theBS. The BS uses y0 to estimate hd,k, ∀k. Similarly, yt, t =1, . . . , T , represents the received training signal vector whenelement t of the IRS is ON and is used to estimate h0,t,k forall the users. It can be expressed as,

yt =

K∑k=1

hd,kxp,k + h0,t,kxp,k + wB , t = 1, . . . , T. (3)

Note that each yi, i = 0, 1, . . . , T , contains the receivedsignals from all the K users. However since the users transmitmutually orthogonal pilot symbols, so the received trainingsignal vector yi is correlated one-by-one with the pilot symbolof each user to obtain the observation vector with respect toeach user as ri,k = yix

†p,k, where † represents the pseudo-

inverse. These independent observation vectors are then usedto obtain the estimates of the channel vector being estimated inthe ith sub-phase for all the users. The estimates are computedusing the MMSE estimation method [13]. This protocol is alsosummarized in Fig. 2b. The BS then uses the channel estimatesto compute the optimal beamforming vector v∗ in (1) andsends this information to the IRS microcontroller.

V. IRS DESIGN AND EVALUATION RESULTS

Assuming that the IRS elements have perfect reflectioncoefficient during downlink transmission, i.e. βn = 1, forn = 1, . . . , N , the IRS reflect beamforming matrix Φ mustsatisfy the unit-modulus constraints on its diagonal elements,i.e. |[Φ]n,n| = 1, for n = 1, . . . , N . For the single-user system,the vector v = [exp(jθ1), . . . , exp(jθN )]T is designed so asthe reflected signals from the IRS add constructively with theones received directly from the BS. Therefore the optimalΦ∗ = diag(v∗), where v∗ = exp(j HH

0 hd), where x returns

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(a) IRS-assisted single-user MISO system. The BS and IRS aremarked with their (x, y) coordinates.

20 40 60 80 100 120

0

10

20

30

40

Dashed lines: Without IRS

du

Rec

eive

dSN

R(d

B)

Perfect CSIImperfect CSI, σ2 = −180dBmImperfect CSI, σ2 = −170dBmPerfect CSI, N = 70

(b) Performance of an IRS-assisted single-user MISO system underperfect and imperfect CSI for M = 4, N = 35.

Fig. 3: Results for a single-user system.

the vector of phases of x. For the multi-user system, we focuson minimum user rate as the performance criteria and optimizethe IRS phases using an adaptation of Algorithm 1 from [7],which uses project gradient ascent to find Φ∗.

We utilize the parameter values described in Table I. Thepath loss values are computed for 2.5 GHz operating fre-quency using the 3GPP Urban Micro (UMi) parameters fromTR36.814 (detailed in Section V of [7]). We use the LoSversion to generate path loss for H1 and the non-LOS (NLOS)version to generate path losses for h2,k and hd,k. Moreover, 5dBi antennas are considered at the BS and IRS. Since IRS isdeployed much higher than the BS for the purpose of avoidingthe penetration losses that are caused by ground structures like

TABLE I: Simulation parameters.

Parameter ValueArray parameters:Carrier frequency 2.5 GHzBS, IRS configuration Uniform linear array (ULA),Tx power budget (pT ) 5 WNoise level −80dBmPath Loss:Model 10−C/10

dα

C (Fixed loss at d = 1m) 26dB (H1), 28dB (h2,k,hd)α (Path loss exponent) 2.2 (H1), 3.67 (h2,k,hd)Channel Estimation:τ , τc, τs .01s, .01τ , τc

N+1

pc 1 WChannel ModelsH1 in single-user case Rank-One: H1 = abH [7]H1 in multi-user case Full Rank [7]h2,k Correlated Rayleigh: R

1/2IRSk

zk

hd,k Correlated Rayleigh: R1/2BSk

zd,kRBSk ,RIRSk Generated using [[7] Sec. V]PrecodingSingle-user case Maximum ratio transmissionMulti-user case Optimal Linear Precoder [7]

buildings, we assume penetration losses of 10 dB for IRS-to-user link while that of 20 dB for BS-to-user link. We firstfocus on the single-user scenario shown in Fig. 3a and studythe received SNR in Fig. 3b by varying the value of du. Weobserve that in an IRS-assisted system, the user farther awayfrom the BS can still be closer to the IRS and receive strongerreflected signals from it resulting in an improvement in theperformance as observed for du > 30. Consequently, the IRS-assisted system is able to provide a higher QoS to a largerregion. For example, it will cover 110m with an SNR level ofat least 5dB, whereas the system without the IRS can coverabout 80m to achieve the same SNR level. Moreover, the usersplaced close to the IRS, e.g. located in 42 < du < 75 rangewill see gains ranging from 10 to 17 dB.

Doubling N at the IRS to 70, the received SNR scales byabout 6dB for users close to the IRS, which implies the scalingto be in the order of N2, corresponding to an array gain ofN and the reflect beamforming gain of N . However, the gainis negligible for 5 < du < 20 because the BS-to-user directchannel is much stronger than the channel through the IRS.Moreover, much higher coverage is possible with large numberof passive reflecting elements at the IRS.

The result also shows that the IRS-assisted system is moresensitive to channel estimation errors than the conventionalsystem. This is because for a constant channel estimation timeof τcs, the IRS-assisted system has to estimate N + 1 = 36channel vectors of dimension M whereas the direct systemonly needs to estimate one channel vector. Moreover, the errorbecomes more significant as the user moves away from the IRSbecause the channel vectors h0,n,k, n = 1, . . . , N , becomeweaker and more difficult to estimate.

Next we study the minimum user rate performance ofmulti-user system with the BS placed at (0, 0), IRS placedat (0, 100) and users distributed uniformly in the square(x, y) ∈ [−30, 30] × [70, 130] [6]. The net achievable rate ofuser k is given as

(1− τc

τ

)Rk where Rk = log2(1+SINRk),

accounting for the rate loss due to channel training. The chan-nel estimation time τc needs to be selected optimally to ensurea reasonable quality of channel estimates while minimizing the

6

10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−20

0.1

0.2

0.3

0.4

0.5

τc (s)

Min

imum

user

rate

(bps

/Hz)

M = 12, N = 54, τ = .01sM = 15, N = 23, τ = .01sNo IRS, M = 20, τ = .01sM = 12, N = 65, τ = .006sNo IRS, M = 20, τ = .006s

(a) Optimal value of τc for an IRS-assisted system to perform aswell as a conventional MISO system with 20 antennas.

10 20 30 40 50 60

0.4

0.6

0.8

1

N

Min

imum

user

rate

(bps

/Hz)

Perfect CSI, M = 12Imp. CSI, M = 12Perfect CSI, M = 15Imp. CSI, M = 15Perfect CSI, M = 20Imp. CSI, M = 20Perfect CSI, No IRS, M = 20Imp. CSI, No IRS, M = 20

(b) Performance of an IRS-assisted multi-user MISO system againstN under perfect and imperfect (imp.) CSI.

Fig. 4: Results for a multi-user system.

rate loss due to channel training. In Fig. 4a we plot the netachievable minimum rate against τc for a conventional MISOsystem (No IRS) with 20 active antennas at the BS servingK = 8 users, assuming a coherence interval of length 10ms.We also plot the net minimum rates for IRS-assisted systemswith a fewer number of active antennas at the BS. The value ofN for each M is chosen to ensure that the IRS-assisted systemperforms as well as the conventional system. The result showsthat the IRS-assisted MISO system with 54 passive reflectingelements at the IRS and only 12 active antennas at the BScan achieve the same performance as the considered largeMISO system. The same performance can also be achievedwith M = 15 antennas using N = 23 reflecting elements atthe IRS. Therefore, an IRS-assisted MISO system can be anenergy-efficient alternative to technologies like massive MISOand network densification.

At 2.5 GHz, the coherence interval τ ranges from 80ms foralmost stationary scenario (0.5 miles/h users’ movement) to6ms for dynamic scenario (6 miles/h running speed) [2]. Thesolid lines in Fig. 4a are plotted for τ = .01s and we observethat the net minimum rate is a unimodal function of τc. Forall considered IRS-assisted MISO systems τc = 5 × 10−4 sis optimal, whereas the conventional system could performas well with a smaller τc = 10−5s. When a more dynamicscenario (τ = .006s) is considered in the dotted lines inFig. 4a, the optimal channel estimation time is τc = 10−4s,resulting in poorer quality estimates. A higher value of N isthen needed to perform as well as the conventional large MISOsystem. Therefore, the IRS-assisted system is more sensitiveto the channel estimation process than the conventional systemsince a higher number of channels needs to be estimated. Thequality of estimates further deteriorates in dynamic scenarios,which results in rate loss. The IRS-assisted system should beable to adapt the channel training time as per the users’ speeds.In fact, an important future research direction is to make thechannel estimation protocol robust in high speed environments.

Fig. 4b corroborates the results of Fig. 4a for τ = .01s, byshowing the values of N needed to achieve the large MISO

gains (yielded by 20 BS antennas) by using a smaller numberof active antennas at the BS and relying on the IRS. We alsoshow the gains of introducing an IRS in a system being servedby a BS with 20 antennas (black curve). With 64 elements,the IRS can almost double the performance of the conventionalsystem.

The gains yielded by the IRS have been validated for a sub-6 GHz communication system in this section. However, futurenetworks will operate at the mmWave frequencies (30-100GHz), which are highly susceptible to severe signal attenuationfrom large structures like buildings, that can result in signalblockages. Introducing IRSs on these structures can enablecommunication to users with weak or blocked LoS paths byforming strong NLoS paths instead. Therefore, the IRSs willnot only yield performance gains similar to what we have seenin this section, but will actually enable communication to userswho do not have the direct channel hd,k in (1) available.

VI. FURTHER RESEARCH DIRECTIONS

As IRS-assisted wireless communication is a new paradigm,there exist a number of interesting research directions that canbe explored. We summarize them as follows.

A. Modeling Other IRS Implementations

This work has considered the use of antenna arrays to im-plement the IRS, where each antenna independently introducesa phase shift onto the impinging EM waves. Recent papers [1],[4], [8] envision the concept of SRE enabled by reconfigurablemeta-surfaces that have the ability to fully customize the inci-dent EM waves by providing many more functions in additionto the perfect reflection operation considered in this work[1]. The communication-theoretic performance analysis of theSREs enabled by reconfigurable metasurfaces is an importantresearch direction that should utilize accurate communicationmodels that describe the response of the metasurface as afunction of its EM properties. In fact, the response of ametasurface will depend on several factors, like its size, thespecific material it is made of, as well as on properties of

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the incident waves, like their angles and the polarization.EM compliant communication models for these surfaces areneeded to avoid studying too simplistic and unrealistic systemmodels. Experimentally-validated channel models that providepath-loss and fast-fading parameters for IRS-assisted linksunder different implementations are also needed.

B. CSI Estimation for Large IRSsIn the current works, the channel sensing limitations of the

IRS are ignored and perfect CSI is assumed to be available atthe IRS to design its parameters [6]–[8]. This paper proposeda channel estimation protocol where the channels through theIRS are estimated at the BS by training all the IRS elements,one-by-one. This can yield a large channel training overheadand require longer channel estimation times for large IRSs.

Alternate channel estimation protocols need to be developedthat do not require explicit channel estimation with respect toall the IRS elements. One way to do this is to use beam trainingto select the IRS phase matrix from quantized codebooks.Another solution is to embed a few low-power sensors inthe IRS, that sense the channels and report them to the BSthrough the IRS micro-controller. However, this solution willcompromise on the almost passive nature of the IRS.

Moreover, the channel estimation methods need to beadapted based on the technology being used to realize the IRS.For example: reflect-arrays do not require the phase introducedby each of its element to be tuned separately and thereforethe proposed protocol is not optimal. The capability of fullimpinging wavefront sensing provided by reconfigurable meta-surfaces also changes the way channel estimation needs to beperformed for this implementation of the IRS.

C. Theoretical Performance LimitsAlmost all existing works [6]–[8] consider the optimization

of the IRS’s induced phases by solving complicated, non-convex optimization problems. The optimal phases and theresulting performance are therefore computed numerically anddo not have any channel-dependent theoretical expressions(except for the single user, single IRS case in [8]) that yieldinsights into the impact of the channel as well as the radioparameters on the performance of the IRS-assisted commu-nication systems. Developing tractable analytical frameworksto study the performance of wireless networks enabled bymultiple IRSs is an important research direction.

D. Integration of IRSs with Existing/Emerging TechnologiesIRSs promise to improve the performance of wireless

communication systems by optimizing the environment ascompared to the existing solutions that optimize the communi-cation end-points. The integration of IRSs with other existingand emerging technologies, like massive MIMO, mmWaveand terahertz communication, small cells, relays, optical com-munication, vehicular communication etc., needs significantresearch attention. There are many important directions relatedto this integration, e.g. the judicious deployment of the IRSs inexisting systems, acquiring CSI at the pace of the highly time-varying channels that constitute the vehicular communicationsystems, optimal user-association schemes for systems withmany small cells, distributed IRSs and relays.

VII. CONCLUSION

In this paper, IRS-assisted wireless communication is en-visioned to be an important energy-efficient paradigm forbeyond 5G networks, achieving massive MISO like gainswith a much lower number of active antennas at the BS.The passive antennas constituting the IRS smartly re-configurethe signal propagation by introducing phase shifts onto theimpinging electromagnetic waves. This paper discussed theevolution of reflective arrays to the IRS concept, outlined thecommunication model of an IRS-assisted multi-user MISOsystem and explained how it differentiates from conventionalmulti-antenna communication models. Later we proposed anMMSE based channel estimation protocol to estimate the IRS-assisted links. We presented performance evaluation results at2.5 GHz operating frequency, which confirmed the superiorperformance of the proposed system while highlighting itshigh sensitivity to the quality of the channel estimates.

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