A General Framework for RIS-Aided mmWave Communication Networks: Channel Estimation and Mobile User Tracking
11 A General Framework for RIS-Aided mmWaveCommunication Networks: Channel Estimation andMobile User Tracking
Salah Eddine Zegrar, Liza Afeef, and H¨useyin Arslan,
Fellow, IEEE
Abstract —Reconfigurable intelligent surface (RIS) has beenwidely discussed as new technology to improve wireless com-munication performance. Based on the unique design of RIS, itselements can reflect, refract, absorb, or focus the incoming wavestoward any desired direction. These functionalities turned out tobe a major solution to overcome millimeter-wave (mmWave)shigh propagation conditions including path attenuation andblockage. However, channel estimation in RIS-aided communi-cation is still a major concern due to the passive nature of RISelements, and estimation overhead that arises with multiple-inputmultiple-output (MIMO) system. As a consequence, user trackinghas not been analyzed yet. This paper is the first work thataddresses channel estimation, beamforming, and user trackingunder practical mmWave RIS-MIMO systems. By providing themathematical relation of RIS design with a MIMO system, athree-stage framework is presented. Starting with estimating thechannel between a base station (BS) and RIS using hierarchicalbeam searching, followed by estimating the channel between RISand user using an iterative resolution algorithm. Lastly, a populartracking algorithm is employed to track channel parametersbetween the RIS and the user. System analysis demonstrates therobustness and the effectiveness of the proposed framework inreal-time scenarios.
Index Terms —Reconfigurable intelligent surfaces, mmWave,channel estimation, beamforming, user tracking.
I. I
NTRODUCTION M ILLIMETER-WAVE (mmWave) communication hasbecome one of the key technologies of fifth-generation(5G) communication systems. Although mmWave achieveshigh data rate due to its wider signal bandwidth, it suffersfrom severe path loss [1]. Many solutions can be implementedto overcome these losses including high-dimensional multiple-input multiple-output (MIMO) operations, and reconfigurableintelligent surface (RIS) technology to mitigate the limitationconditions of high frequencies. Recently, RIS has attractedmuch attention as a highly promising technology that canmeet the requirements of the sixth-generation (6G) and beyondwireless networks. RISs capability arises from its ability tosupport MIMO systems in controlling and hardening thewireless channel, where a highly time-varying channel can
The authors are with the Department of Electrical and ElectronicsEngineering, Istanbul Medipol University, Istanbul, 34810, Turkey (e-mail: [email protected]; [email protected];[email protected]).H. Arslan is also with Department of Electrical Engineering, University ofSouth Florida, Tampa, FL, 33620, USA.This work has been submitted to the IEEE for possible publication.Copyright may be transferred without notice, after which this version mayno longer be accessible. behave as a deterministic one. The functionalities of RISincluding reflecting, diffracting, or scattering the transmittedsignal enhance the quality of the signal at the receiver side.These abilities come from its unique design where the ad-justable passive elements can individually steer the incidentelectromagnetic (EM) wave toward any specific direction bychanging their phases and gains only. Adjusting these elementsallows us to align all multipath of the reflected signal so thatthey are added constructively at the receiver [2]. This principleof the RIS elements fulfills the concepts of beamforming andsteering concepts [3], [4]. Therefore, with proper RIS size andreflection coefficients, the reflected signal is a beam, wherethe width of this beam is inversely proportional to the sizeof the RIS. Since these elements passively reflect the signal,they are easy to implement, have a low-cost deployment,and most importantly do not cause noise amplification [5].These features makes the RIS a strong candidate in upcomingwireless systems over conventional technologies.On the other side, RIS imposes a lot of challenges suchas channel estimation. Since the RIS is built of a large num-ber of passive elements, RIS-aided communication networkshave faced difficulties in estimating the channel reliably. Toovercome these difficulties, many channel estimation tech-niques have been proposed in the literature under differentapproaches.In single-user systems, [6] proposes a novel RIS architecturein which some of its elements are active by connecting themto a baseband processor. These active elements turned back tothe reflecting mode after estimating the channel. However, thissensor deployment, that activates the elements, increases theimplementation cost. Prior works [7]–[14] focused on intro-ducing channel estimation techniques with fully passive RISelements. A two-stage algorithm, in [7], for channel estimationis proposed. In the first stage, all RIS elements are turnedoff whereas the direct channel between the base station (BS)and user equipment (UE) is estimated. Then, in the secondstage, the elements are turned on one by one while the channelbetween each element and UE is being estimated. In spite ofthat, this strategy degrades the channel estimation accuracysince only a small portion of RIS elements are switched onat each time. This also requires using a separate amplitudecontrol and phase shifter for each element which increases thesystem cost, especially for a massive number of RIS elements.Therefore, the approach in [8] divides the RIS elements N into M sub-surfaces while keeping the elements on with maximumreflected amplitude during the channel estimation and data a r X i v : . [ ee ss . SP ] S e p transmission. Each sub-surface consists of N/M adjacentelements with a common reflection coefficient to reduce theimplementation complexity. Following the same approach, [9]proposes a discrete Fourier transform (DFT)-based channelestimation method where all the RIS elements are on at all timeslots and the DFT matrix is used to determine the reflectioncoefficients of these elements. In addition, minimum meansquared error (MMSE) algorithm is proposed in [10] to workwith DFT matrix to estimate the channel of both direct pathand the RIS-assisted path between the BS and UE in multiple-input single-output (MISO) system. For more realistic setting,[11] considers discrete-phase RIS reflecting elements that aregrouped into a relatively small number of sub-surfaces, andproposes a DFT-Hadamard-based reflection pattern strategyto minimize the channel estimation error in imperfect channelstate information (CSI). However, increasing the number ofsub-surfaces causes training overhead and degradation in thespectrum efficiency. Meanwhile, free-space path loss modelsfor the RIS-assisted wireless communication are proposed in[3], [15] using the EM and physical properties of a recon-figurable surface. In [3], a two-dimensional (2D) path lossmodel is derived and extended to three-dimensional (3D) onein [15] including far-field, near-field beamforming, and near-field broadcasting formulas are experimentally validated in theindoor environment.In a multiuser system, [12] investigates the MISO systemunder imperfect CSI, where it considers correlated Rayleighfading channel. The proposed protocol utilizes DFT-MMSEestimation and divides channel estimation into subphases,at each one, all users transmit orthogonal pilot symbols toestimate the RIS-assisted links. The work in [13] proposes athree-phase channel estimation framework for the RIS-assisteduplink MISO system to reduce the training duration. In phaseone, RIS elements are turned off and direct channels betweenUEs and BS are estimated. Then, in the next phase, among allUEs, only one UE transmitted pilots and the cascaded channelis estimated. In the last phase, the channel between all UEs andthe RIS is considered correlated, thus only the scaling factorsneed to be estimated. However, the training overhead, thenumber of supportable users, and the performance of channelestimation are the limits of this technique.In mmWave systems, channel estimation becomes morecritical with few works touching this problem [6], [14], [16],[17]. The work in [14] proposes a compressed-sensing-basedchannel estimation algorithm where the sparsity of the channelis exploited to implement channel estimation at a reducedpilot overhead in massive MIMO system. The sparsity of thechannel is capitalized using a distributed orthogonal matchingpursuit algorithm. It is assumed that there is prior knowledgeabout the channel between the BS and the RIS, and the pilotsare designed accordingly. However, considering the channelBS-RIS to be known and time-invariant are not practical sincemmWave channel is sensitive to small changes. Similarly, acompressed sensing algorithm is utilized in [18] to estimate thecascaded channel parameters in the RIS-assisted THz MIMOsystem in the indoor application scenarios, since it is assumedthat the estimation problem is equivalent to sparse recoveryproblem. Again, using the same method, [19] tries to find a sparse representation of the cascaded BS-RIS-UE channelin mmWave downlink system with the help of transposedKhari-Rao product and Kronecker product. The most recentwork for channel estimation in mmWave systems was in[20], where a two-stage cascaded channel estimation protocolis proposed by exploiting the sparsity of mmWave MIMOchannel of single BS, RIS, and UE. In the first stage, the beamsearching approach is introduced to have high angular domaininformation, then in a second stage, an adaptive grid matchingpursuit algorithm is proposed to estimate the high-resolutioncascaded channel. However, estimating a cascaded channel hasmany limitations as it will be explained and proved later inthis paper.Although the aforementioned channel estimation techniquesare theoretically effective with low mean square error (MSE)level, they depend on either cascaded channel concept or non-practical assumptions for estimating the channel BS-RIS-UE.Since RIS reflects the signal and focuses the energy intoa specific direction, UE’s location should be considered inthe estimation process. However, in [6]–[14], [16]–[19], thelocation is always ignored and only scenarios with stationaryBS, RIS and UE are considered. Furthermore, it is provenin [3], [15] that the path loss is a function of reflectioncoefficients of RIS which is always ignored in the channelestimation process when the phases are optimized for channelestimation.In this article, we develop a general three-stage frameworkfor the RIS-aided communication network, where practicalissues are considered in a realistic scenario. We summarizethe main contributions of this paper as follows • First, we derive the relation between RIS and MIMOsystem by providing an accurate configuration for the RISreflection coefficients array, noting that the resultant arrayis equivalent to the steering vector of the MIMO systemthat has uniform planner array (UPA) in its antennastructure. The derived model for the RIS is obtained fromthe free space far-field path loss model that is introducedin [15]. • Additionally, we optimize the reflected signal in anyspecific direction simply by controlling the phases, wherethe effect of channel BS-RIS is eliminated at the BSside, and the UE has the responsibility of estimating andcompensating channel RIS-UE. For the first time, thisoptimization proposes one channel control (BS-RIS) forthe RIS design instead of endeavoring the total cascadedchannel control. • Next, a novel channel estimation scheme for mmWaveRIS-MIMO system is proposed. This scheme is able toestimate both BS-RIS and RIS-UE channels separately,even though all RIS elements are passive. Starting withestimating the BS-RIS channel G using hierarchical beamsearching algorithm. Then, the RIS-UE channel H isestimated by adopting the iterative reweight algorithmthat is introduced in [21] to estimate the channel pathcoefficients only, exploiting the resultant angles from thebeam searching algorithm. • Then, the proposed scheme enables RIS-assisted com-munication to track mobile users. To the best of our knowledge, this has never been addressed in the literatureand it is considered one of the most challenging tasks tobe implemented by the RIS. The parameters of channel H are tracked using well-known algorithms such as theextended Kalman filter (EKF) algorithm. • Finally, the mmWave RIS-MIMO framework is stud-ied under practical and implementable assumptions. Theproposed design of the RIS reflection coefficients haslow computational complexity and applicable in real-timescenarios. Meanwhile, all channel effects are consideredin the design including path loss, fading, user’s loca-tion, incident and reflected angles. We analytically showthat our proposed design achieves better performancecompared to the conventional methods under the sameassumptions.The rest of this paper is organized as follows. Section IIdiscusses some assumptions available in the literature. SectionIII depicts the system model of the proposed RIS framework,and Section IV discusses how to control the RIS’s reflectioncoefficients to realize beamforming/steering functionalities.The novel channel estimation scheme is introduced is SectionV followed by channel tracking approaches. In Section VI, theperformance analysis is carried out, and Section VII concludesthe paper.
Notation: bold uppercase A , bold lowercase a , and unboldletters A, a are used to denote matrices, column vectors, andscale values, respectively. | a | and ∠ a are the magnitude andphase of a complex number. (cid:107) a (cid:107) F , (cid:107) a (cid:107) , and (cid:107) a (cid:107) are theFrobenius norm, (cid:96) pseudo-norm, and the (cid:96) norm. ( · ) H , ( · ) T , and ( · ) − denote the Hermitian transpose, transpose, andinverse. diag( a ) is the diagonal matrix with the vector a on itsdiagonal. C M × N denotes the space of M × N complex-valuedmatrices and vec( A ) is vectorizing the matrix A . A ⊗ B isthe Kronecker product of A and B and symbol j representsthe imaginary unit of complex numbers with j = − .II. I NVESTIGATION ABOUT
RISIn this section, three major concerns are discussed regardingpath loss, channel model, and user tracking in RIS-assistednetworks.
A. If multipath, path loss, and beamforming are to be op-timized at the same time, what should be the reflectioncoefficients of the RIS?
Prior works have investigated RIS phases matrix based ondifferent criteria. Some authors [3], [15], [22] specified the RISmatrix φ so that the path loss is minimized, while others [5],[8], [11], [13] used these phases to align all multipath and getrid of channel effects. And some other authors designed φ fordecreasing the error in channel estimation. Eventually, usingthe same parameters for multiple purposes at the same timewill create a conflict, and in this case, one general multi-goaldesign of the phases is required.Assuming that the RIS elements are placed in a uniformrectangular shape, then the reflection coefficients of these Fig. 1: RIS-aided communication system model.elements is reflected by φ = φ , φ , · · · φ ,N RIS ... . . . ... φ N RIS , φ N RIS , · · · φ N RIS ,N RIS , (1)where φ n,m = γ n,m e jα n,m is the ( n, m ) -th RIS element’sreflection coefficient, where α n,m ∈ [0 , π ) represents thephase shift induced by the ( n, m ) -th element in the RIS, and γ n,m ∈ [0 , stands for the reflection gain which will beconsidered unity throughout the paper i.e., γ n,m = 1 , ∀ ( n, m ) .Another convenient representation of φ in term of facilitatingcomputations is defined as Θ = diag { vec( φ ) } .Considering the system model that is shown in Fig. 1, thereflected signals from each element of the RIS are all alignedin phase to enhance the received signal power. It is assumedthat the direction of the radiation is toward the center ofthe RIS surface. For more simplification, let the dimensionsof the each element be d x × d x and the total number is M RIS = N RIS × N RIS elements. In this case, the free-space path loss is given as [15] β RIS = G t G r GN d x λ F ( θ t , ϕ t ) F ( θ r , ϕ r ) γ π d g d h × (cid:12)(cid:12)(cid:12)(cid:12) sinc (cid:0) πN RIS λ (sin θ t cos ϕ t + sin θ r cos ϕ r + δ ) d x (cid:1) sinc (cid:0) πλ (sin θ t cos ϕ t + sin θ r cos ϕ r + δ ) d x (cid:1) sinc (cid:0) πN RIS λ (sin θ t sin ϕ t + sin θ r sin ϕ r + δ ) d x (cid:1) sinc (cid:0) πλ (sin θ t sin ϕ t + sin θ r sin ϕ r + δ ) d x (cid:1) (cid:12)(cid:12)(cid:12)(cid:12) , (2)where δ (cid:0) m − (cid:1) d x + δ (cid:0) n − (cid:1) d y = λφ n,m π , G t , G r and G are the gains of the transmitter antenna, receiver antenna,and the RIS, respectively, λ is the wavelength, F ( θ, ϕ ) is thenormalized power radiation, ( θ t , ϕ t ) and ( θ r , ϕ r ) representthe elevation and the azimuth angles of the incidence waveand reflected wave, respectively, and d g and d h are thedistance from the BS to the RIS and from the RIS to theUE respectively. Let ( θ des , ϕ des ) be the angle from the RISto UE, if θ r = θ des and ϕ r = ϕ des , then (2) is maximized as β max ( d, θ, ϕ ) = G t G r GN d x λ F ( θ t , ϕ t ) F ( θ r , ϕ r ) γ π d g d h . (3) TABLE I: Impact of φ design on the received power Case Received signal’s power P r Ideal/desired case P r ∝ M RIS d g d h φ = φ P r ∝ Ad g d h , A ∈ [0 , M RIS ] φ = φ P r ∝ B M RIS d g d h , B ∈ [0 , φ = φ P r ∝ ABd g d h Infinite reflector P r ∝ B ( d g + d h ) [23] This corresponds to the phases of the RIS φ n,m being designedas follows ∠ φ n,m = mod (cid:18) − πλ d x (cid:20) (sin θ t cos ϕ t + sin θ des cos ϕ des )( m −
12 ) + (sin θ t sin ϕ t + sin θ des sin ϕ des ) ( n −
12 ) (cid:21) , π (cid:19) . (4)Fig. 2a shows the radiation pattern of the reflected signalwhen φ is set to reflect the received signal in a specificdirection ( θ des , ϕ des ) = (45 o , o ) , the power is focused inthe desired direction and diminishes elsewhere.RIS phases are optimized to obtain strongest channel im-pulse response φ n,m = max φ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) N (cid:88) n =1 M (cid:88) m =1 φ n,m G n,m H n,m (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (5)which implies φ n,m = − ∠ G n,m H n,m . In the same paper [8]however, in channel estimation, φ is chosen so that channelestimation error is minimized, for instance, the authors in [12]claim that for minimizing MSE, the reflection pattern of theRIS should be chosen to be N RIS × N RIS
DFT matrix φ n,m = DF T N RIS × N RIS . It is clearly seen that there is a contradictionof φ (cid:54) = φ (cid:54) = φ .“ In case of φ = DF T N RIS × N RIS , is it guaranteedthat all multipath are aligned, and the signal is reflectedtoward the direction of user with maximum power, i.e., P r ∝ M RIS × β max ? If not, up to what extent theestimated channel is reliable? And if some power is received,what ensures that the source of this power is the RIS and notother random reflectors? ”Table I summarizes all the above-mentioned cases of differ-ent RISs’ phases matrices compared to the ideal desired case.From this Table, it is concluded that for reliable channel esti-mation and communication using RIS, the RIS’s phases mustbe optimized taking into consideration beamforming/steeringdirection (UE’s location) and the impact of channels H and G . All the mentioned points here will be examined in detailin Section V. B. What is the impact of channel H and G on the RIS phases?Is it the same or different? Using what was discussed in Section II-A, and the basicproperties of RIS that are mentioned and proved in [3], [4],let it is assumed a scenario where a signal is going to bereflected toward the same location as shown in Fig. 2a with the assumption that G is an ideal channel i.e., it has unitarygain. The predefined values of the phases would be given by(3), and the resulted radiation will be exactly as in Fig. 2a.However, when G is assumed to be a sparse channel whereline-of-sight (LoS) path between BS and RIS is the dominantpath, it is observed that the beam is shifted toward a differentdirection than that of UE’s location as shown in Fig. 2b. Also,when channel G is very rich scattering, the UE will receivevery low power from RIS as shown in Fig. 2c, and in thiscase, the RIS may react worse than a normal reflector (metallicsurface, wall, etc.) [6]. Therefore, for a successful reflection , G should be individually estimated and then equalized at theRIS by simply reversing its effect.After reflecting the beam, the UE estimates and equalizes H to complete a successful communication . In a nutshell,RIS performs two operations separately1) Accumulation , where it collects all the energy receivedby each of its elements and then align them by can-celling the effects of channel G .2) Beamforming/Steering , the RIS acts like a virtual BS,and focuses or steers the incoming electromagneticwaves using (4) toward the UE’s location [22].
C. Assuming that our system has mobility, which part of thecascaded channel is considered varying; G , H , or both? Canthe UE be tracked if the varying source is unknown? The majority of the state-of-art considers the user to bestationary, and BS have always LoS with RIS. However,these assumptions are not realistic, and tend to limit the useof RIS. Besides, they are the consequence of utilizing thecascaded channel model that is given by H cascaded ∆ = GH .This representation makes channel tracking in time almostimpossible, since any change in H cascaded could be due tothe change in G , H or both. Also, in Section II-B, it wasshown that only G affects the phases of the RIS, not H .Furthermore, if G is estimated separately, estimating H isfeasible and tracking UEs becomes possible. Consequently, theassumption of having a mobile user is valid. For instance, theauthors in [14] claim that it is almost impossible to estimate G via conventional channel estimation schemes, since the RISelements are passive. This claim will be disproved during thiswork. III. S YSTEM MODEL
Consider a narrowband mmWave MIMO system, composedof one BS, one RIS and k UEs as depicted in Fig.1. Each,BS, RIS and UE, are equipped with equidistant UPAs asan antenna structure with half-wavelengthed distance betweenthe antenna elements in which they have M BS , M RIS , and M UE antenna elements, respectively. It is considered that theuplink and downlink transmissions are using a time-divisionduplexing (TDD) protocol that exploiting channel reciprocityfor the CSI acquisition at the RIS in both link directions.The BS is assumed to have M RF radio-frequency (RF) chainswhere the number of these chains is much smaller than the This is the reason why the gain is proportional to M RIS [3] (a) G is an ideal channel ( G = 1 ). (b) G is a sparse channel with LoS path isthe dominant. (c) G is a rich scattering channel. Fig. 2: The power pattern of the reflected beam from the RIS toward UE under three conditions of channel G antenna array elements and larger than the number of UEs( k ≤ M RF << M BS ) [24], while the UE consists of only oneRF chain. The RIS is placed near to the UE side and far fromthe BS to minimize the path loss effect [15]. In order to fullyutilize the functionality of the RIS, the channel path betweenthe BS and UE is assumed to be blocked by an obstacle. TheRIS structure is the same as the one proposed in Section II-A.Assuming that s training symbols are transmitted via or-thogonal precoding beams for each user, such that there is nointer-user interference. Under this assumption, we shall restrictthe analysis to one representative UE without loss of gener-ality. Under the assumption of flat-fading and perfect timingand frequency synchronization [25], the sparsity of the channelis exploited by using geometric channel modeling [26], [27],giving that G ∈ C M RIS × M BS and H ∈ C M UE × M RIS denotethe channel between BS-RIS and RIS-UE, respectively. The G model is given as G = (cid:80) L g l =1 z g,l a M RIS ( θ Rg,l , ϕ
Rg,l ) a HM BS ( θ Bg,l , ϕ
Bg,l ) , = A M RIS (Ω R ) diag( z g ) A HM BS (Ω B ) , (6)where L g is the number of channel paths received at theRIS, θ Rg,l , ϕ
Rg,l and θ Bg,l , ϕ
Bg,l are the elevation and azimuthangles of angle of arrival (AoA) and angle of departure (AoD)in each path, and z g,l is the complex channel coefficientbetween BS-RIS at l th path. z g = [ z g, , z g, , ..., z g,L g ] T , Ω R = [( θ Rg, , ϕ Rg, ) , ( θ Rg, , ϕ Rg, ) , ..., ( θ Rg,L g , ϕ Rg,L g )] T , and Ω B = [( θ Bg, , ϕ Bg, ) , ( θ Bg, , ϕ Bg, ) , ..., ( θ Bg,L g , ϕ Bg,L g )] . a M RIS isthe array response vector of the UPA [28] represented by a M i ( θ, ϕ ) = 1 √ M i (cid:18) q (cid:0) sin( θ ) cos( ϕ ) (cid:1) ⊗ p (cid:0) sin( θ ) sin( ϕ ) (cid:1)(cid:19) , (7)where q ( u ) = (cid:104) , e j πdλ u , ..., e j πdλ ( N x − u (cid:105) T and p ( v ) = (cid:104) , e j πdλ v , ..., e j πdλ ( N y − v (cid:105) T , for i ∈ { RIS, BS } . Goingthrough the same derivation, H is expressed as H = (cid:80) L h l =1 z h,l a M UE ( θ Uh,l , ϕ
Uh,l ) a HM RIS ( θ Rh,l , ϕ
Rh,l ) , = A M UE (Ψ U ) diag( z h ) A HM RIS (Ψ R ) , (8) where Ψ U = [( θ Uh, , ϕ Uh, ) , ( θ Uh, , ϕ Uh, ) , ..., ( θ Uh,L h , ϕ Uh,L h )] T , Ψ R = [( θ Rh, , ϕ Rh, ) , ( θ Rh, , ϕ Rh, ) , ..., ( θ Rh,L h , ϕ Rh,L h )] , and z h = [ z h, , z h, , ..., z h,L h ] T . The overall channel H eff ∈ C M UE × M BS between the BS-RIS-UE is written as H eff = β ( d g , d h , θ des , ϕ des ) HΘG , (9)where β ( d g , d h , θ des , ϕ des ) is the total path loss given by (3).IV. RIS CONTROL
This section describes how to control the reflecting co-efficients of the RIS so that all manipulation (beamform-ing/steering) can occur in real-time. The authors in [15] devel-oped a path loss model proved analytically and experimentally.The optimal phases to beamform/steer a reflected signal ina predefined direction is represented in (4), and it can beexpressed as vec( φ ) = Λ x ( θ t , ϕ t , θ des , ϕ des ) ⊗ Λ y ( θ t , ϕ t , θ des , ϕ des ) , (10)where Λ x ( . ) and Λ y ( . ) can be viewed as steering vectors onthe elevation and the azimuth direction, respectively, with Λ x = [ e j − N RIS2 2 πλ d x (Γ x ) , . . . , e j N RIS2 2 πλ d x (Γ x ) ] T , (11)and Λ y = [ e j − N RIS2 2 πλ dy (Γ y ) , . . . , e j N RIS2 2 πλ dy (Γ y ) ] T , (12)where Γ x = sin θ t cos ϕ t + sin θ des cos ϕ des and Γ y =sin θ t sin ϕ t + sin θ des sin ϕ des .For simplicity, we consider the case with maximum poweraccumulated i.e., θ t ≈ where the received beam is perpen-dicular to RIS surface, then (10) becomes a function of thedestination angles only. vec( φ ) = Λ x ( θ des , ϕ des ) ⊗ Λ y ( θ des , ϕ des ) . (13)As we can see, the reflection coefficients of RIS are equiva-lent to the steering vector of a UPA [29] in the MIMO model.To adjust the beam direction of the RIS, we just need to Fig. 3: Hierarchical beam searching algorithm procedures forchannel estimation.multiply φ with a weight vector which is designed to steer theRIS elements array toward the desired direction. According to(13), the array factor of an RIS is given as AF RIS = N RIS / (cid:88) n = − N RIS / N RIS / (cid:88) m = − N RIS / w m,n , (14)where w m,n = e j [ m πλ d x (Γ x )+ n πλ dy (Γ y )] denotes the weightvector. V. P ROPOSED C HANNEL E STIMATION
In order to apply the proposed estimation technique, theeffective channel in (9) can be rewritten as H eff = β ( d g , d h , θ des , ϕ des ) ˆ HΘ ˆ G , (15)where ˆ H = A M UE (Ψ U ) diag( z ) A HM RIS (Ψ R ) and ˆ G = A M RIS (Ω R ) diag( e j ∠ z g ) A HM BS (Ω B ) , and z is the gain of thecascaded channel G and H is considered. Since G is directlyresponsible of altering the RIS phases, it is more meaningfulto represent it only in terms of ∠ z g , and include the channelgain | z g | into H . Writing the channel in this form allows usto estimate ˆ H and ˆ G separately. A. Estimating BS-RIS channel
Since mmWave channel is sparse and the new representationof channel BS-RIS has unit amplitude, the problem of estimat-ing ˆ G becomes equivalent to the estimation of ( e j ∠ z g ) of eachpath. From Section II-B, ˆ G causes a shift in the reflected beam,and hence, estimating this shift leads to estimate ˆ G itself. Thiscould be done in three steps. First, estimating AoA and AoDfor the RIS reflected signal. Next, substituting these angles in(14) to get the reflection coefficients of RIS in the absence of ˆ G ’s effect. Then, these coefficients are compared to the lastcoefficient set by the BS, and subtracted from each other toget ˆ G .
1) Finding AoA and AoD:
An exhaustive beam search-ing algorithm can be used in this case, where all possibleangles are tested to find one optimal AoA/AoD. However,this approach requires a large amount of time due to itscomplexity [30]. Thus, we adopt a two-stage beam training method depicted in Fig. 3 consisting of primary and secondarybeam search [31]. For simplicity, the training procedure isdescribed in azimuth only in the latter part of this subsection,and by using the same analogy the procedure in elevation canbe deduced.The primary search will use hierarchical search to reducethe search time. As given in [31], two-way tree stage searchis used here at each layer. Let w ln denotes the codeword ofthe n th beam vector at the l th layer, at each layer only l antennas are activated. In total, there will be ℵ possible beamsand V = log ( ℵ ) layers, where each parent codeword w ln hastwo child codewords w l +1 n and w l +1 n +1 . It is aimed to obtain ( θ Uh,l , ϕ
Uh,l ) and ( θ Rh,l , ϕ
Rh,l ) through multiple steps. Starting bytesting four wide-beams in four successive time slots, wherethe RIS uses w r = [ w , w ] at reflecting mode and the UEuses w u = [ w , w ] at the receiving mode. The resulted signalfrom the l th stage can be written as y l = β ( d g , d h , θ des , ϕ des ) w Hu ˆ Hw r ˆs + w Hu n , (16)where ˆs = ˆ Gs , s = [ s , s , ..., s Z ] T is Z × vector oftransmitted symbols, and n is Z × complex Gaussian noisevector with zero-mean and variance σ o . At each stage wesearch for the pair ( ˜w lr , ˜w lu ) that satisfies the highest receivedsignal-to-noise ratio (SNR), i.e., max w r , w u (cid:18)(cid:12)(cid:12)(cid:12) w Hu ˆ Hw r ˆs (cid:12)(cid:12)(cid:12) (cid:19) = (cid:12)(cid:12)(cid:12) ( ˜w lu ) H ˆ H ˜w lr ˆs (cid:12)(cid:12)(cid:12) . (17)After V beam search, the optimum pair ( ˜w Vr , ˜w Vu ) is obtained.The elements of the primarily codebook matrix in azimuth of K beam patterns, τ discrete phase shift, and N RIS elementsis given by [31] w azn,k = exp (cid:18) − j πτ (cid:98) nkτK (cid:99) (cid:19) , (18)where n = 0 , ...N RIS − and k = 0 , ...K − . This code-book ensures that it has ℵ possible states, and it fully spans theazimuth range. Similarly, the primary beam codebook matrixin elevation is given by w eln,k = exp (cid:18) − j πτ (cid:98) nkτ K − (cid:99) (cid:19) . (19)Second stage starts after acquiring the primary codebook,where we make a secondary beam search by rotating theprimary beam to create higher-resolution secondary beams.These beams define the auxiliary codebook. Finally, ( ˜ w r , ˜ w u ) is considered the optimum codebook.Since the optimal transmission beam is represented by aweighting vector w = ˜ w el ⊗ ˜ w az , both AoA/AoD can beobtained. The AoA from RIS to UE can be found as ( θ Uh,l , ϕ
Uh,l ) = (cid:18) sin − (cid:0) − λτ (cid:98) kτK (cid:99) (cid:1) , sin − (cid:0) − λτ (cid:98) kτ K − (cid:99) (cid:1)(cid:19) . (20)In our model, since the RIS is located near to UE, weassume that the antenna arrays of the UE is always parallel tothe RIS, hence ( θ Rh,l , ϕ
Rh,l ) = ( θ Uh,l , ϕ
Uh,l ) [32]. Note that by setting the phases of the RIS according to equation (14),and setting the weighting vector to be any chosen codeword i.e., w =( w elr ⊗ w azr ) , beam searching could be implemented at the RIS.
2) Estimating ˆ G : If the RIS phases are set to directthe beam of the reflected signal toward the UE’s location ( θ Rh,l , ϕ
Rh,l ) , then the beam would be distorted and the radiationis shifted toward different direction due to the effect of channel ˆ G . Mathematically, this could expressed as ˆHΘ V (cid:48) ˆG = ˆHΘ ( θ Rh,l , ϕ
Rh,l ) G opt , (21)where G opt = G ( θ Bg, , ϕ Bg, , θ Rg, , ϕ Rg, ) , and Θ V (cid:48) is the lastconfigured set of phases by the BS at the V’-th stage of beamsearching process. By exploiting the angles obtained from (20)and by substituting them in (13), ˆ G can be estimated directlyas ˆ G = ( Θ V (cid:48) ) − Θ ( θ Rh,l , ϕ
Rh,l ) G opt . (22)By adopting this design, we assure that the effect of ˆ G isknown and its effects are cancelled by the RIS. Therefore,to set communication with any UE at direction ( θ des , ϕ des ) throughout the RIS, we simply set the phases by Θ = Θ ( θ des , ϕ des ) G opt ˆ G H ( ˆ G ˆ G H ) − . (23)Please refer to Appendix. A (cid:4) By substituting (23) in the total channel we obtain ˆHΘ ˆG = ˆHΘ ( θ des , ϕ des ) G opt , (24)where Θ ( θ des , ϕ des ) is set for any desired location, and thechannel estimation problem is reduced to estimate ˆH onlywhich will be explained in the next subsection. B. Estimating RIS-UE channel
Without loss of generality, assuming one RF chain is acti-vated at the BS side and Z symbols are transmitted, channelestimation model given in [21] is adopted here to estimatepath gains of all paths. For that, the system model is given as y = Q H H eff F s + Q H n , (25)where y ∈ C Z × is the received signal at UE, and Q ∈ C M UE × Z and F ∈ C M BS × Z are the hybrid combining andthe precoder matrices, respectively. The received signal at theUE can be explicitly expressed as y = β ( d g , d h , θ des , ϕ des ) Q H ˆ HΘ ˆ G F s + Q H n . (26)Assuming x = Θ ˆ G F s ∈ C M RIS × , where each element x i is the transmitted symbol. For channel estimation, wewill transmit known symbols at known indices, each receivedsignal corresponding to a transmitted pilot symbol at u timeslot is given as y p,u = β ( d g , d h , θ des , ϕ des ) q Hu ˆ H x p,u + q Hu n p,u . (27)Within U time slots, U p different pilot sequences are sentin each time slot, and y p = β ( d g , d h , θ des , ϕ des ) Q H ˆ Hx p + Q H n p , where y p = [ y p, , y p, , ..., y p,U ] T and Q =[ q , q , ..., q U ] T . By setting Y = [ y , y , .., y p , .., y U p ] T , X = [ x , x , .., x U P ] T and N = [ n , n , .., n U p ] T , we get Y = Q H ˆ HX + Q H N . (28) Note that the angles θ Bg, , ϕ Bg, , θ Rg, , ϕ Rg, are known from the fixedgeometry of the deployment of RIS and BS. Using the fact that the mmWave channel is sparse, the esti-mation of the channel ˆ H become equivalent to the estimationof z , Ψ U and Ψ R , and the problem is formulated as min z , Ψ U , Ψ R P ( z , Ψ U , Ψ R ) (cid:44) (cid:107) ˆ z (cid:107) , s.t. (cid:107) Y − Q H ˜ HX (cid:107) F (cid:54) (cid:15), (29)where (cid:107) ˆ z (cid:107) represents the number of non-zero elements, i.e.,the sparsest solution of the sparse channel ˜ H , ˜ H is theestimated channel matrix for ˆ H , and (cid:15) is the estimation errortolerance.Since the log-sum penalty is more sparsity encouraging, thelog-norm instead of (cid:107) ˆ z (cid:107) can be used here [33]. In addition,both Ψ U , Ψ R are already obtained in Section V-A using thebeam searching algorithm, thus the optimization is performedaccording to z only, and the problem P is given as min z P ( z ) (cid:44) L h (cid:88) l =1 log( | ˆ z | + δ ) , s.t, (cid:107) Y − Q H ˜ HX (cid:107) F (cid:54) (cid:15), (30)where δ ensures that the logarithmic function is always in itsdomain of definition. In addition to minimizing the numberof paths, minimizing the channel estimation error is needed.Hence, a regularization parameter ζ > is added, and P isreshaped to the following optimization problem min z P ( z ) (cid:44) L h (cid:88) l =1 log( | ˆ z | + δ ) + ζ (cid:107) Y − Q H ˜ HX (cid:107) F . (31)It turned out that the minimization of P is equivalent to theminimization of the iterative surrogate function [33] min z P ( i )4 ( z ) (cid:44) ζ − z H D ( i ) z + (cid:107) Y − Q H ˜ HX (cid:107) F , (32)where D ( i ) is expressed as D ( i ) = diag (cid:18) | ˆ z ( i )1 | + δ | ˆ z ( i )2 | + δ · · · | ˆ z ( i ) L h | + δ (cid:19) , (33)and ˆ z ( i ) is the estimate of z at the i th iteration. Then, theoptimization of (32) becomes as follows P ( i )4 ( z ) = ζ − z H D ( i ) z + U p (cid:88) p =1 (cid:107) y p − T p z (cid:107) , (34)where T p = Q H A M UE (Ψ U ) A HM RIS (Ψ R ) x p . P ( i )4 ( z ) = ζ − z H D ( i ) z + U p (cid:88) p =1 ( y p − T p z ) H ( y p − T p z )= z H (cid:18) ζ − D ( i ) + U p (cid:88) p =1 T Hp T p (cid:19) z − z H (cid:18) U p (cid:88) p =1 T Hp y p (cid:19) − (cid:18) U p (cid:88) p =1 y Hp T p (cid:19) z + (cid:18) U p (cid:88) p =1 y Hp y p (cid:19) . (35)For optimizing (35), the next step is obtained ∂P ( i )4 ( z ) ∂ z = z H (cid:18) ζ − D ( i ) + U p (cid:88) p =1 T Hp T p (cid:19) − (cid:18) U p (cid:88) p =1 y Hp T p (cid:19) = 0 . (36) Therefore, the optimal ˆ z that corresponds to the best estimationof ˜ H at the i th iteration is given by z ( i ) opt (cid:44) (cid:18) ζ − D ( i ) + U p (cid:88) p =1 T Hp T p (cid:19) − (cid:18) U p (cid:88) p =1 T Hp y p (cid:19) . (cid:44) (cid:18) ζ − D ( i ) + U p (cid:88) p =1 T Hp T p (cid:19)(cid:18) U p (cid:88) p =1 y Hp T p (cid:19) − . (37)In this iterative method, ζ is designed to be adaptive to fitboth a sparser estimation and a fast search. It is investigatedin details in [21], [33]. C. Channel Tracking
After estimating the channel parameters, i.e., channel coef-ficients, AoA, and AoD, and since the UE is under mobilityassumption, a channel tracking approach has been introducedhere to avoid often channel estimation by tracking the channelparameters. The channel tracking algorithms are significantlyfast, reliable, and robust which allow efficient data transfer be-tween transmitters and receivers in mmWave communications.Channel tracking in mmWave systems is firstly presented in[34], where an EKF based tracking algorithm is proposed to track AoA/AoD while the channel coefficient remains con-stant. However, the method has difficulties to track in a fast-changing channel environment since it requires pre-requisitesfor a full scan that causes long time measurement. To decreasethe measurement time and provide a more suitable trackingalgorithm, the authors in [35] proposed an alternative solutionthat requires only a single measurement with EKF estima-tion and a beam switching design. Additionally, least meansquare (LMS) and bi-directional LMS (BiLMS) algorithmsare introduced in [36] where advantages of both algorithmsare presented compared to EKF algorithm on imperfect CSIconditions while having faster convergence characteristics asSNR increases. However, both algorithms are not suitablefor higher nonlinearity systems. Therefore, the EKF trackingalgorithm is used in our RIS-assisted framework due to its lowcomplexity and good tracking performance.The tracking algorithm starts with setting a pair of trans-mitting and receive beams according to the estimated elevationand azimuth AoA/AoD from the channel estimator. One mainpoint that should be taken into consideration is that whiletracking, the predicted channel parameters should stay closeto the actual values so that the UE stays within half of thebeamwidth. Otherwise, if the tracking is no longer reliable orthe path of the beams does not exist anymore, the channelparameters should be re-estimated.The discrete-time model for the received signal symbolperiod at UE side is given in (26). Assuming that each vectorin F is given by f = a M BS ( θ, ϕ ) for the LoS path. In orderto start the tracking process, the measurement function shouldbe known. From (26), the measurement function is used totrack the observation signal and can be given as g measure = β ( d g , d h , θ des , ϕ des ) Q H ˆ HΘ ˆ G F , (38)where g measure depends on the channel parameters includingpath coefficients, elevation and azimuth AoD/AoA angles fromboth channels; BS-RIS and RIS-UE. EKF algorithm [35] isused to track these parameters. To evaluate the performance ofthe tracking process, a state evolution model is needed for thetracked parameters. A first-order Gaussian-Markov model isadopted for the path coefficient evolution over the time, whilea Gaussian process noise model is assumed for the elevationand azimuth AoD/AoA [32], [35], [36].The proposed three-stage RIS framework is summarized inAlgorithm 1. VI. S IMULATION RESULTS
In this section, simulation results are presented to evaluatethe performance of the proposed RIS-assisted framework. Thesimulation parameters are provided in Table II.
A. Channel Estimation Performance
At the first step of the proposed framework, we implementa two-stage beam search algorithm to determine the UE’slocation i.e., the AoD/AoA in elevation and azimuth domains.Fig. 4 illustrates the primary beam patterns reflected fromthe RIS, where N RIS = 8 elements, each elements canperform discrete phases shifts, and the resolution achieves
2 4 6 8 30210 60240 90270120 300150 330180 0 (a)
2 4 6 8 30210 60240 90270120 300150 330180 0 (b)
2 4 6 8 10 30210 60240 90270120 300150 330180 0 (c)
2 4 6 8 30210 60240 90270120 300150 330180 0 (d)
Fig. 4: Primary beam patterns N RIS = 8 , τ = 5 , K = 10 when channel G is ideal in (a) azimuth and (b) elevation domains,and when channel G is geometric model with L g = 5 paths in (c) azimuth and (d) elevation domains.TABLE II: Simulation Configuration Parameters ValueOperating frequency f c
28 GHzChannel paths L g L h M BS d λ/ Number of beam pattern in the codebook K (cid:15) K = 10 different patterns. Fig. 4a and Fig. 4b illustrate theten different patterns used at the final stage in elevation andazimuth , respectively. It should be mentioned that even thoughchannel G will shift the reflected beam corresponding to eachcodeword as discussed in Subsection II-B, still the resultedshifted beams will scan the whole space. This is shown byFig. 4c and Fig. 4d, where we can see that the channel G just caused a rotation in total beam patterns of the codebook.However, the UE will use the codebook normally and basedon the received optimal codeword, it can find the AoA by justcomparing this codeword to a predefined table, or from thepolar diagram illustrated in Fig. 4a and Fig. 4b.In the second step, channel H is estimated using the iterativeresolution algorithm and the performance of this algorithm isevaluated using normalized mean square error (NMSE) givenby NMSE = E (cid:34) || ˜H − ˆH || F || ˆH || F (cid:35) . (39)We consider narrowband mmWave channel with a MIMOsystem, number of antennas at the base station and at UE is N BS = 16 ×
16 = 256 and N UE = 2 × , respectively.The path gains are assumed to have Gaussian distribution. RISis assumed to have different geometries M RIS = 4 × , M RIS = 8 × and M RIS = 16 ×
16 = 256 ,for each case number of pilots is U p = 8 , U p = 32 and U p = 128 , respectively. We also assume one dominant LoSpath L h = 1 between RIS-UE. Conventional methods i.e.,cascaded channel estimation, were adopted in our system to becompared with the proposed algorithm, and most importantlyno prior knowledge of the UE’s location is assumed.Fig. 5 compares the NMSE performance against SNR. Theproposed scheme achieves very high performance comparedthe the conventional ones, where the NMSE keeps decreasing -5 0 5 10 15 SNR (dB) -2 -1 N M SE Fig. 5: NMSE performance comparison between the proposedframework and conventional approaches of channel H atdifferent RIS array sizes.with the SNR increasing, reaching almost . normalizederror at SNR = 15 dB and M RIS = 256 . The reasonis that in the proposed scheme, the power is focused onthe target UE before staring channel estimation protocol,this result is also reflected in the same figure at low SNRvalues, where NMSE is still relatively small even though thetransmit power is minimal. Also, increasing the number RISelements gives the better channel estimation, where the lowestNMSE corresponded to M RIS = 256 , then M RIS = 64 , andlastly to M RIS = 16 . However, the conventional algorithms,regardless of the number of RIS elements, have very badNMSE performance through all SNR values. The reason isthat the energy is not beamformed toward the UE most of thetime, and the received power from the beam sides is alwaysweak, and thus the channel cannot be estimated reliably. Theslight change at high SNR indicates that the UE in this caseis receiving slightly higher power, but still it is not enoughbecause it does not directly come from the main beam.
B. The Channel Tracking Performance
In this subsection, we assume that the channel between theBS and RIS is fixed and its parameters are constant during thetracking period. Also, it is assumed that the channel remainsstationary during this observation interval, and the channelsparsity in the mmWave makes the paths to be likely separated
20 25 30 35 40 45 50 55 60
Time index -2 -1 M SE ( R ad ) z hRhRhUhU Tracking duration
Fig. 6: MSE of the tracked parameters: complex path coeffi-cient, elevation and azimuth AoDs from the RIS, and elevationand azimuth AoAs at UE using EKF tracking algorithm.from each other under the assumption that the RIS is locatednear to UE location. Hence, only one single path falls into themain beam direction L h = 1 [35], giving that the state spacevector at each time index is x state = [ z (cid:60) z (cid:61) θ Rh ϕ Rh θ Uh ϕ Uh ] T , (40)where z = z (cid:60) + jz (cid:61) . By using the real and imaginary partof z , the state vector x state is a real vector which helps toavoid implementation issues when real and complex numbersare combined. Fig. 6 shows the MSE of the tracked channelparameters between RIS and UE using EKF algorithm withthe same filter setups as in [35] at SNR = 20 dB. It isclearly shown that the algorithm has the ability to reduce theestimation overhead for longer time since it can keep the errorbelow a certain threshold of half power beamwidth where itis given as (cid:52) θ dB ≈ λ √ M RIS d . [37].The overall performance of the proposed three-stage RISframework is illustrated in Fig. 7, where it is assumed thatboth proposed and conventional RIS-assisted communicationchannel estimation techniques know the location of the UEat the initial state, and that they are beamforming toward thisdirection at SNR = 20 dB. This assumption is favorable to theconventional scheme. The simulation consists of three states,in which the UE is stationary at first, then it starts movingand finally becomes stationary again. Fig. 7 shows that atthe initial state both methods perform well, achieving lownormalized error. However, the performance totally changesas the UE moves. In the proposed channel estimation scheme,as the UE starts moving, the channel is tracked until a certainthreshold and the beamforming is shifted based on the trackedparameters. After that, channel estimation is needed where theresult converges again to a minimum NMSE. In case of theconventional method, the error increases very fast which needsto be compensated by estimating the channel where the resultsettles to NMSE = 0 . , resulting in a huge performance gapbetween the two schemes.VII. C ONCLUSION
In this paper, we propose a three-stage framework for anRIS-aided mmWave MIMO communication system. In the
Time index -2 -1 N M SE ( R ad ) ConventionalProposed
Tracking levelTrackingKnown user location EstimationEstimation
Fig. 7: The overall system performance for the proposedthree-stage RIS framework compared to conventional cascadedchannel estimation methods.first and the second stages, the channel estimation problem isextensively studied and new approach is proposed to estimateBS-RIS channel (channel G ) and RIS-UE channel (channel H ) separately, by exploiting the shift in the direction of thebeams reflected from RIS due to G effect. The estimationof channel G is used to develop a low-complex, real-timeapplicable phase design. Then, the channel H is estimatedusing the iterative resolution method and the prior knowledgeof AoD/AoA that were estimated in the previous step. Inthe third stage, channel tracking algorithms are applied totrack the channel between RIS and UE, since estimatingchannels G and H are done separately which allows the userto have some level of mobility. The performance analysisshowed that the proposed framework can provide an accuratechannel estimation. The proposed framework for RIS-aidedcommunication was developed under very practical assump-tions which makes it very useful to be implemented withthe available RIS prototypes such MITs RFocus prototype [38], that beamforms and focuses the impinging radio wavestowards specified direction and location, respectively.A
CKNOWLEDGMENT
This work was supported by the Scientific and Technolog-ical Research Council of Turkey under Grant No. 5200030.A
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