Channel Estimation for RIS Assisted Wireless Communications: Part I -- Fundamentals, Solutions, and Future Opportunities
aa r X i v : . [ c s . I T ] J a n Channel Estimation for RIS Assisted WirelessCommunications: Part I - Fundamentals, Solutions,and Future Opportunities (Invited Paper)
Xiuhong Wei, Decai Shen, and Linglong Dai
Abstract —The reconfigurable intelligent surface (RIS) with lowhardware cost and energy consumption has been recognized asa potential technique for future 6G communications to enhancecoverage and capacity. To achieve this goal, accurate channelstate information (CSI) in RIS assisted wireless communicationsystem is essential for the joint beamforming at the base station(BS) and the RIS. However, channel estimation is challenging,since a large number of passive RIS elements cannot transmit,receive, or process signals. In the first part of this invited paper,we provide an overview of the fundamentals, solutions, and futureopportunities of channel estimation in the RIS assisted wirelesscommunication system. It is noted that a new channel estimationscheme with low pilot overhead will be provided in the secondpart of this paper.
Index Terms —Reconfigurable intelligent surface (RIS), wire-less communication, channel estimation.
I. I
NTRODUCTION
Recently, reconfigurable intelligent surface (RIS) has beenproposed to enhance the coverage and capacity of the wirelesscommunication system with low hardware cost and energyconsumption [1]. In general, RIS consisting of massive passivelow-cost elements can be deployed to establish extra links be-tween the base station (BS) and users. By reconfiguring theseRIS elements according to the surrounding environment, RIScan provide high beamforming gain [2]. The reliable beam-forming requires accurate channel state information (CSI).Hence, it is essential to develop accurate channel estimationschemes for the RIS assisted wireless communication sys-tem [3].Although channel estimation has been widely studied inthe conventional wireless communication system, there aretwo main obstacles for conventional schemes to be directlyapplied in the RIS assisted system [4]. Firstly, all RIS elementsare passive, which cannot transmit, receive, or process anypilot signals to realize channel estimation. Secondly, since anRIS usually consists of hundreds of elements, the dimensionof channels to be estimated is much larger than that inconventional systems, which will result in a sharp increase of
All authors are with the Beijing National Research Center forInformation Science and Technology (BNRist) as well as the Departmentof Electronic Engineering, Tsinghua University, Beijing 100084, China(e-mails: [email protected], [email protected],[email protected]).This work was supported in part by the National Key Research andDevelopment Program of China (Grant No. 2020YFB1807201) and in partby the National Natural Science Foundation of China (Grant No. 62031019). Fig. 1. An example of RIS assisted wireless communication system. the pilot overhead for channel estimation. Therefore, channelestimation is a key challenge in the RIS assisted system, whichwill be investigated in this invited paper composed of twoparts.In the first part, we provide an overview of the fundamen-tals, solutions, and future opportunities of channel estimationin the RIS assisted wireless communication system. Firstly, thefundamentals of channel estimation are explained in SectionII. Then, in Section III, we discuss and compare three types ofoverhead-reduced channel estimation solutions that exploit thetwo-timescale channel property, the multi-user correlation, andthe channel sparsity, respectively. After that, we point out keychallenges and the corresponding future opportunities aboutchannel estimation in the RIS assisted system in Section IV.Finally, some conclusions are drawn in Section V.
Notation : Lower-case and upper-case boldface letters a and A denote a vector and a matrix, respectively; A T and A H denote the transpose and conjugate transpose of matrix A ,respectively; k a k denotes the l -norm of vector a ; diag ( x ) denotes the diagonal matrix with the vector x on its diagonal.II. F UNDAMENTALS OF C HANNEL E STIMATION IN T HE RIS A
SSISTED S YSTEM
In this section, we will first illustrate the system modelof an RIS assisted wireless communication system. Then,the channel estimation problem in this system will be pre-sented. Finally, we will introduce the basic channel estimationschemes.
A. System Model
For the uplink RIS assisted wireless communication systemas shown in Fig. 1, we consider one M -antenna BS and one N -element RIS to serve K single-antenna users. Let h d,k ∈ C M × denote the direct channel between the k th user and theBS, G ∈ C M × N be the channel between the RIS and the BS,and h r,k ∈ C N × be the channel between the k th user andthe RIS. The received signal y ∈ C M × at the BS can beexpressed by y = K X k =1 ( h d,k + G diag ( θ ) h r,k ) s k + w , (1)where s k is the symbol sent by the k th user, θ =[ θ , θ , · · · , θ N ] T is the reflecting vector at the RIS with θ n representing the reflecting coefficient for the n th RIS element,and w ∈ C M × is the received noise at the BS. Note that θ n can be further set as θ n = β n e jφ n , with β n ∈ [0 , and φ n ∈ [0 , π ] representing the amplitude and the phase for the n th RIS element, respectively.For the RIS assisted system, reliable beamforming requiresthe accurate CSI consisting of the direct link and the RISrelated reflecting link. We consider a time division duplex(TDD) RIS assisted system, where the downlink channel canbe obtained based on the estimated uplink channel because ofthe TDD channel reciprocity. B. Channel Estimation Problem
The channel estimation problem for the direct channel h d,k can be solved by the conventional schemes in the conventionalwireless communication system. Unfortunately, it is difficultto estimate the RIS related channels G and h r,k due to passiveRIS elements without signal processing capability.Let H k , G diag ( h r,k ) ∈ C M × N represent the cascadedchannel between the k th user and the BS via the RIS, and thereceived signal y in (1) can be also rewritten as y = K X k =1 ( h d,k + H k θ ) s k + w . (2)Note that many beamforming algorithms (i.e., how to de-sign the optimal RIS reflecting vector θ in (2)) aim tooptimize the power of the effective reflecting link, i.e., k G diag ( θ ) h r,k k = k G diag ( h r,k ) θ k = k H k θ k .Therefore, most of existing channel estimation schemes di-rectly estimate the cascaded channel H k instead of the indi-vidual channels G and h r,k .By adopting the orthogonal pilot transmission strategyamong users, the uplink channel estimation associated withdifferent users can be independent. Without loss of generality,the subscript k in h d,k , h r,k , and H k can be omitted torepresent the corresponding channels related to any users. C. Basic Channel Estimation Schemes
If all RIS elements are turned off, i.e., the incident electro-magnetic wave will be perfectly absorbed by the RIS insteadof reflected to the receiver , the RIS assisted communication Note that “turn off” is a widely used expression in the literature butinaccurate, since an RIS with all elements turned off is also a scatterer toreflect the incident electromagnetic wave. An implementation method with aspecial setting of RIS elements proposed in [5] can realize the perfect “turnoff” for the incident electromagnetic wave. system can be simplified as the conventional communicationsystem without the RIS. Hence, the direct channel h d can beestimated by some classical solutions such as the least square(LS) algorithm.As mentioned above, the channel estimation for the RISrelated channels G and h r is challenging. A straightforwardsolution is to estimate the cascaded channel H in (2) basedon the ON/OFF protocol proposed in [4]. The key idea is todivide the entire cascaded channel estimation process into N stages, where each stage only estimates one column vector of H ∈ C M × N associated with one RIS element. Specifically,the cascaded channel H ∈ C M × N can be represented by N columns as H = [ h , · · · , h n , · · · , h N ] , (3)where h n ∈ C M × is the cascaded channel correspondingto the n th RIS element. In the n th stage, only the n th RISelement is turned on, while the remained N − RIS elementsare turned off. Since the direct channel h d has been estimatedin advance, its impact can be removed from the received pilotsignal at the BS. Then, h n can be estimated based on the LSalgorithm. By following this similar procedure, h , · · · , h N can be estimated in turn by sequentially turning on the st, · · · , N th RIS element one by one, while the remained N − RISelements are turned off. After N stages, the cascaded channel H ∈ C M × N composed of N columns can be completelyestimated. However, since only one RIS element can reflectthe pilot signal to the BS based on the ON/OFF protocol, thechannel estimation accuracy may be degraded.In order to improve the channel estimation accuracy, [6]further proposed the discrete Fourier transform (DFT) protocolbased channel estimation scheme, where all RIS elements arealways turned on. In this scheme, the entire cascaded channelestimation process is still divided into N stages. However,in each stage, the reflecting vector θ at the RIS is speciallydesigned as one column vector of the DFT matrix. After N stages, based on the LS algorithm, the cascaded channel H can be directly estimated based on all received pilot signals in N stages at the BS. It is noted that the overall reflecting matrixfor N stages forms a DFT matrix of size N × N , which hasbeen proved to be the optimal choice to ensure the channelestimation accuracy [6].However, the required pilot overhead in [4], [6] is huge.This is mainly caused by the fact that the number of unknownchannel coefficients (e.g., × with 64 antennas at theBS, 256 elements at the RIS and single antenna at the user)in the RIS assisted communication system is much larger thanthat of unknown channel coefficients (e.g., × with 64antennas at the BS and a single antenna at the user) in the con-ventional communication system without the RIS. The hugepilot overhead will significantly decrease the effective capacityimprovement. Thus, it is essential to develop overhead-reducedchannel estimation schemes for the RIS assisted system. Inthe next Section III, we will introduce three typical types ofoverhead-reduced channel estimation solutions. Estimate the high-dimensional channel G Small timescaleLarge timescale time
Estimate the low-dimensional channels and Dual-link pilot transmission
Data transmissionUplink pilot transmission d h r h Fig. 2. The two-timescale channel estimation framework [7].
III. O
VERHEAD -R EDUCED C HANNEL E STIMATION S OLUTIONS
In this section, we will introduce three typical types ofchannel estimation solutions to reduce the pilot overhead,which exploit the two-timescale channel property, the multi-user correlation, and the channel sparsity, respectively.
A. Two-Timescale Based Channel Estimation
The first typical solution to reduce the pilot overhead forchannel estimation is to exploit the two-timescale channelproperty in the RIS assisted communication system [7]–[9].Specifically, the two-timescale channel property can beexplained as follows. On the one hand, since the BS andthe RIS are usually placed in fixed positions, the channel G between the RIS and the BS usually remains unchanged for along period of time, which shows the large timescale property.On the other hand, due to the mobility of the user, the channel h r between the user and the RIS and the direct channel h d between the user and the BS vary in a much smaller timescalethan that of the quasi-static channel G , which show the smalltimescale property.As shown in Fig. 2, based on this two-timescale chan-nel property, [7] proposed a two-timescale channel estima-tion framework, where the two different pilot transmissionstrategies are respectively designed for estimating the largetimescale channel G and the small timescale channels h d and h r . Firstly, the high-dimensional channel G is estimated oncein a large timescale by using the dual-link pilot transmissionstrategy proposed in [7]. Although the pilot overhead requiredfor estimating G is large due to its high dimension, suchoverhead is negligible from a long-time perspective. Then,based on the widely used uplink pilot transmission strategy,the low-dimensional channels h d and h r can be estimatedbefore data transmission in a small timescale. Although thesechannels have to be estimated more frequently, the requiredpilot overhead is small due to their low dimensions. As aresult, the average pilot overhead can be significantly reducedby exploiting the two-timescale channel property.The main difficulty of this scheme is how to estimate G ,since all RIS elements are passive without signal processingcapability. To achieve this goal, [7] proposed a dual-link pilottransmission strategy as mentioned before. The key idea isthat, the BS firstly transmits pilot signals to the RIS via thedownlink channel G T , and then the RIS reflects pilot signalsback to the BS via the uplink channel G . There are ( N + 1) sub-frames for the dual-link pilot transmission, where eachsub-frame consists of M time slots. In the m th time slot ( m = 1 , , · · · , M ) of the t th sub-frame ( t = 1 , , · · · , N +1 ), the m th antenna of the BS transmits the pilot signal s m ,t to the RIS and other ( M − antennas of the BS receive thepilot signal reflected by the RIS. The received pilot signal y m ,m ,t at the m th antennas of the BS can be representedas ( m = 1 , , · · · , M, m = m ) y m ,m ,t = (cid:2) g Tm diag( θ t ) g m + z m ,m (cid:3) s m ,t + w m ,m ,t = (cid:2) g Tm diag( g m ) θ t + z m ,m (cid:3) s m ,t + w m ,m ,t , (4)where g Tm ∈ C × N is the m th row vector of the uplinkchannel G , g m ∈ C N × is the m th row vector of thedownlink channel G T , θ t is the reflecting vector at the RISin the t th sub-frame, z m ,m is the self-interference aftermitigation from the m th antenna to the m th antenna of theBS, and w m ,m ,t is the received noise at the m th antennaof the BS. After N + 1 sub-frames, all received pilot signals { y m ,m ,t | ≤ m , m ≤ N, m = m , ≤ t ≤ N + 1 } can be obtained, which consist of M N unknown variables,i.e.,
M N elements of G . Then, based on all received pilots,each element of G can be alternately estimated in an iterativemanner by utilizing the coordinate descent algorithm [7].Some alternative schemes for estimating the channel G between the RIS and the BS were proposed [8], [9]. In [8],two users ( U and U ) are deployed near the RIS to assistits channel estimation. The uplink cascaded channels H foruser U , H for user U , and the U -RIS- U cascaded channelbetween the user U and the user U via the RIS are estimatedbased on the pilot symbols transmitted by the two users,respectively. After that, the entries for BS-RIS channel G can be calculated based on three estimated cascaded channelsmentioned above. By utilizing the long-term channel averagingprior information [9], the large timescale channel G can alsobe estimated based on the channel matrix calibration.After acquiring G , the low-dimensional channels h d and h r can be estimated based on the conventional uplink pilottransmission strategy. The user transmits the pilot signals to theBS via both the direct channel h d and the effective reflectingchannel GΦh r . Based on the received uplink pilot signalswith the known G and Φ , h d and h r can be directly estimatedat the BS by the conventional channel estimation algorithmssuch as the LS algorithm.Based on the two-timescale channel property, the largetimescale channel G and the small timescale channels h d and h r can be respectively estimated in different timescales, whichcan indeed significantly reduce the average pilot overhead.However, the channel estimation for G is still challenging.In [7], the BS should work in the full-duplex mode, wheredifferent antennas are required to transmit and receive pilotssimultaneously to estimate G . In [8], the complexity for userscheduling and the overhead for the U -RIS- U cascadedchannel feedback are not negligible. B. Multi-User Correlation Based Channel Estimation
Another solution to reduce the pilot overhead is to directlyestimate the corresponding cascaded channels by utilizingthe multi-user correlation. Since all users communicate withthe BS via the same RIS, the cascaded channels { H k } Kk =1 associated with different users have some correlations. Thus,this multi-user correlation can be exploited to reduce the pilotoverhead required by the cascaded channel estimation [10].Specifically, the multi-user correlation can be explained asfollows. For convenience, we take the n th column h k,n ∈ C M × of the cascaded channel H k = [ h k, , h k, · · · , h k,N ] ∈ C M × N as an example, which can expressed as h k,n = t k,n g n , (5)where t k,n denotes the channel between the k th user and the n th RIS element, which is also the n th element of h r , g n ∈ C M × denotes the user-independent channel between the n thRIS element and the BS, which is also the n th column vectorof G . Since different users enjoy the same channel G fromthe RIS to the BS, h k,n in (5) can be rewritten as h k,n = λ k,n h ,n , (6)where λ k,n = t k,n t ,n . (7)The key idea of the multi-user correlationbased cascaded channel estimation scheme can beexpressed as follows. Firstly, the cascaded channel H = [ h , , · · · , h ,n , · · · , h ,N ] for the first user (whichis also called as the typical user) can estimated by utilizingthe DFT protocol based channel estimation scheme discussedin Subsection II-C. Then, for the k th user with k ≥ , thecolumn vector h k,n ( n = 1 , , · · · , N ) of H k can be obtainedby only estimating the unknown scalar λ k,n in (7) with onlyone unknown coefficient instead of h k,n with M unknowncoefficients. Hence, there are only N scalars to be estimatedin total for obtaining the cascaded channel H k of size M × N .By exploiting the multi-user correlation, the pilot overheadcan be significantly decreased, since the number of channelcoefficients to be estimated becomes much smaller. However,this scheme proposed in [10] has assumed that there is noreceiving noise at the BS. In the typical scenario of lowSNR for channel estimation, the estimation accuracy will bedegraded. C. Sparsity Based Channel Estimation
The overhead-reduced channel estimation solutions in theprevious two subsections are mainly realized in the spatialdomain. By contrast, in this subsection, we will introducesome overhead-reduced based channel estimation solutions byexploiting the sparsity of channels in the angular domain [11],[12].In the conventional wireless communication system, sincethere are limited propagation paths, the channel h d is sparsein the angular domain. Thus, the channel estimation problemfor h d can be formulated as a sparse signal recovery problem,which can be solved by compressive sensing (CS) algorithmswith reduced pilot overhead. Similarly, the cascaded channel H ∈ C M × N in RIS assisted systems also shows the sparsitywhen transformed into the angular domain. Specially, byusing the virtual angular-domain representation, the cascadedchannel H can be decomposed as H = U M ˜ HU TN , (8) The angular channel (sparse)The spatial channel (non-sparse)
Fig. 3. The sparsity of the angular cascaded channel [11]. where ˜ H denotes the M × N angular cascaded channel, U M and U N are the M × M and N × N dictionary unitarymatrices at the BS and the RIS, respectively. The number ofnon-zero elements in ˜ H is determined by the product of thenumber of paths between the RIS and the BS and that betweenthe user and the RIS. Since there are the limited numberof scatters around the BS and the RIS, especially in high-frequency communications, ˜ H is usually sparse in nature [11],as shown in Fig. 3.Based on the sparsity of the angular cascaded channel, thecascaded channel estimation problem can be also formulatedas a sparse signal recovery problem [11]. Then, some classicalCS algorithms, such as orthogonal matching pursuit (OMP),can be directly used to estimate the angular cascaded channelwith reduced pilot overhead. However, these conventionalCS algorithms cannot achieve the satisfying estimation ac-curacy, especially in low SNR ranges. In order to improvethe estimation accuracy, a joint sparse matrix recovery basedchannel estimation scheme was proposed in [12]. In thisscheme, all angular channels associated with different userscan be projected to the same subspace by considering thefact that different users enjoy the same channel G from theRIS to the BS. However, for these sparsity based channelestimation schemes [11], [12], the required pilot overhead isstill high, since the sparsity of the angular cascaded channelbecomes less significant compared with the angular channelin conventional communications.Moreover, [13] proposed to divide the entire RIS into severalsub-surfaces, where all RIS elements on the same sub-surfaceare considered to have the same channel coefficients. There-fore, the number of the channel coefficients to be estimated canbe significantly decreased. By combining the typical overhead-reduced channel estimation schemes mentioned above withthis idea of dividing sub-surface, the pilot overhead can befurther reduced.For the sake of simplicity, the above discussions on channelestimation schemes take the narrow band as an example. Thesimilar idea can be extended to the wideband orthogonalfrequency division multiplexing (OFDM) channel estimation.Specifically, the channel on each sub-carrier can be estimatedseparately as in a narrow band system, such as [13]. It isnoted that the reflecting vector θ at the RIS are the same forall sub-carriers. Besides, by considering the common sparsityof angular domain channels among different sub-carriers, [14]proposed a joint overhead-reduced channel estimation schemefor all sub-carriers, where a denoising convolution neuralnetwork (DnCNN) is used to improve the estimation accuracy. IV. C
HALLENGES AND F UTURE O PPORTUNITIES FOR C HANNEL E STIMATION
In this section, we will point out key challenges for channelestimation in the RIS assisted wireless communication system,based on which the corresponding future research opportuni-ties will be discussed.
A. Ultra-Wideband Channel Estimation
In order to achieve ultra-high-speed wireless transmission,the RIS assisted ultra-wideband wireless communication willbe an important trend. However, the beam squint effect causedby the ultra-wideband communication brings a serious chal-lenge for the channel estimation, since the single physicalangle will be transformed to multiple spatial angles. [15] pro-posed a beam squint pattern matching based wideband channelestimation in the conventional wireless communication system.The similar idea may be applied in the wideband channel es-timation for the RIS assisted wireless communication system.
B. Spatial Non-Stationarity
To further exploit the potential beamforming gains andspatial resolutions of the RIS, the number of RIS elementsmay be hundreds of times larger than that of most scenariosdiscussed so far, which will result in a large size for the RISarray. With the significant increase of the array size, the RISrelated channels will present a new characteristic called as thespatial non-stationarity [16]. This channel characteristic meansthat the incident direction and power for the electromagneticwave at the RIS vary with different RIS elements. Under thiscondition, all existing channel estimation schemes based onthe spatial stationarity may not work. The estimation schemebased on the concept of visibility regions [16] may be used toaddress this challenge.
C. RIS Assisted Cell-Free Network
The cell-free network has been recently proposed to addressthe inter-cell interference of the conventional cellular network.In order to further improve the network capacity with lowpower consumption, the energy-efficient RISs can be investi-gated in the cell-free network. However, with the increase ofthe number of RIS, the number of channels to be estimatedincreases accordingly in the RIS assisted cell-free network.One possible solution is to exploit the multi-user correlationmentioned in [10] to reduce the number of channels to beestimated.
D. High Pilot Overhead
Since the RIS consists of a large number of elements, theRIS related channels have many coefficients to be estimated.Although some overhead-reduced channel estimation solutionshave been recently proposed, the required pilot overhead is stillhigh due to the passivity of RIS elements. By exploiting morechannel characteristics in the RIS, the pilot overhead can befurther reduced, which will be discussed in the second part ofthis invited paper composed of two parts. V. C
ONCLUSIONS
In the first part of this invited paper, we have investigated thechannel estimation in the RIS assisted wireless communicationsystem. Due to a large number of passive RIS elementswithout signal processing capability, the channel estimationin the RIS assisted system is more challenging than that inthe conventional system. We first explained the fundamentalsof channel estimation. Then, three typical types of overhead-reduced channel estimation solutions were introduced. Finally,we pointed out several challenges and the corresponding futureresearch opportunities for channel estimation. Note that afeasible solution to one of these key challenges, i.e., the highpilot overhead, will be proposed in the second part of thisinvited paper. R
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