RIS-Assisted Communications in Correlated Rayleigh Channels: Comparison of Training Overhead Reduction Schemes

Jue Wang ,Shuaifeng Lu ,Jing Wang ,Zhenyu Jiang ,Rui Tang ,Ruifeng Gao ,Yingdong Hu,Ye Li

1 School of Information Science and Technology,Nantong University,Nantong 226109,China

2 Department of Electronic Engineering,Tsinghua University,Beijing 100084,China

3 School of Transportation and Civil Engineering,Nantong University,Nantong 226109,China

4 Nantong Research Institute for Advanced Communication Technologies,Nantong 226109,China

Abstract: Channel training in reconfigurable intelligent surface (RIS)-assisted communications is usually conducted in an on-off manner,resulting in unaffordable training time overhead when the number of RIS elements is large.In this paper,for correlated Rayleigh channels,we compare three typical training overhead reduction schemes,namely RIS element selection (Scheme 1),element grouping (Scheme 2),and statistical CSI-based phase shifts design(Scheme 3).For Scheme 1 and Scheme 2,we propose two algorithms to select RIS elements (or form element groups) and determine the optimal number of activated elements(or formed groups),based on the channel correlation information only;for Scheme 3,we consider a semi-definite programming-based approach in the literature,and propose an alternative dominant eigenvector-based method for determining the RIS phase shifts vector.Via extensive simulations,we compare the achievable ergodic rates of these schemes versus the signal-to-noise ratio,the channel correlation level,and the element number-to-coherent time ratio,respectively,and discuss possible switching of the three schemes over these system parameters.At last,operation regions of the considered training overhead reduction schemes are shown in the plane characterized by the system parameters,which provides useful guidelines for practical scheme determination.

Keywords: reconfigurable intelligent surface;correlated Rayleigh channel;training overhead;ergodic achievable rate

I.INTRODUCTION

Reconfigurable intelligent surface (RIS) has been attracting increasing research interest in the pioneer studies towards beyond fifth-generation (5G) mobile communications[1—4].Although it might be realized in practice via various electromagnetic materials and techniques,RIS in general can be seen as a smart surface,comprising of a large number of passive reflection elements,while each element is able to dynamically adjust the phase(and amplitude in some cases)of its reflection wave.In this way,the signal strength at a target user can be enhanced through passive beamforming [5,6],the interference or information leakage towards certain directions can be alleviated [7—10],or from a more interesting perspective,the wireless propagation environment can be intelligently controlled where RIS can be viewed as controllable artificial scatterers[11,12].

Two major advantages are concluded for RISassisted wireless communications:Firstly,the size of a RIS element(and inter-element spacing)can be made much smaller than that of conventional antennas [3].This makes it possible to pack a large number of elements (correspondingly,there will be a large number of controllable paths for communication enhancement) within a finite array size.From this point of view,RIS can be seen as a promising supplement to future massive multiple-input multiple-output (MIMO)systems.Secondly and more importantly,RIS mainly works in a passive way and does not require radio frequency (RF) chains.Therefore,it is naturally beneficial for improving the energy efficiency and reducing the implementation cost (which are important to be concerned in the deployment of future massive communication networks),while improving the coverage and communication performance of the system[4].

The physical characteristics of RIS which offer these advantages also bring new challenges to the communication design.On the one hand,it is necessary to acquire precise channel state information(CSI) of the cascaded channel (i.e.,product of the transmitter-RIS and RIS-receiver channel links)for effective RIS phase shifts design.However,due to the passive nature of RIS elements,the channel training overhead,in terms of the training time duration,usually has to grow linearly with the number of RIS elements (N) [13].Though a largerNis preferable for better signal strength enhancement,it also results in longer training time duration,which subsequently reduces the effective data transmission time when the channel’s coherence time is finite.On the other hand,the closely-positioned RIS elements will lead to highly correlated spatial channel,and its impact on the system performance needs to be specifically discussed.

Research efforts have been devoted to reduce the training overhead for RIS-assisted communications.A straightforward idea is to activate only partial of the RIS elements for transmission,e.g.,selectMout ofNelements such that the training time duration can be reduced.1However,this comes at a cost that the RIS elements are not fully utilized.In[14,15],the authors proposed to group adjacent RIS elements in the transmission.Elements in the same group are linked together and employ the same phase shift parameter.With this approach,the training time duration can be reduced fromNtoL

For all these schemes,there still lacks of a comprehensive comparison among them to identify which one is preferable in practice.Intuitively,the performances of these schemes will depend on various system and environment parameters,such as the number of RIS elementsN,the channel coherence timeT,the signalto-noise ratio (SNR),and more importantly,the spatial correlation level of the channel.For example,with a high spatial correlation level,it is anticipated that the statistical CSI-based scheme might outperform the other two.Besides,spatial correlation will directly affect the grouping scheme,e.g.,more adjacent RIS elements with highly correlated channels can be arranged in the same group,while without too much performance degradation.

Aiming at revealing the impacts of the previously described parameters on the system performance,and providing a comprehensive comparison of these training overhead reduction schemes,we consider a correlated Rayleigh-product model for the cascaded RIS channel,and describe the implementation of three transmission schemes in detail.Namely,these are RIS element selection,element grouping,and statistical CSI-based phase shifts design.For the former two schemes,we propose two algorithms for element selection(and group formation),as well as best element number (and group number) determination,based on the correlation information of the channel only.For the statistical CSI-based scheme,we review existing method in the literature,where semi-definite programming (SDP) can be used to provide an effective solution,and also propose an alternative dominant eigenvector-based approach for comparison.After that,we conduct extensive simulations to demonstrate the performances of different schemes versus different system parameters,e.g.,the SNR,the RIS element number-to-coherence time ratio,and the spatial correlation level.Based on these results,the best operation regions of the three training overhead reduction schemes are discussed to provide useful guidelines for practical scheme selection.

The remainder of the paper is organized as follows:The system model is introduced in Section II,where we describe channel model and explain the trade-off between channel training overhead and achievable rate of the system.The three schemes for comparison are described in detail in Section III,where two algorithms for RIS element selection and element grouping are presented.Simulation results and discussion are provided in Section IV,where the performances of different schemes are compared versus various system parameters,and their best operation regions are discussed.Finally,Section V concludes this paper.

II.SYSTEM MODEL

We consider a RIS-assisted point-to-point wireless communication system shown in Figure 1,where the user attempts to transmit data to an AP while the direct user-AP link is blocked by obstacles.2Both the AP and user are equipped with single antenna.The RIS comprising ofNreflecting elements is connected to a controller,which determines appropriate reflection scheme (as will be discussed in Section III) and dynamically adjusts its phase shifts to enhance the achievable data rate of the system.Necessary information for phase shifts adjustment,e.g.,the CSI of the RIS-related channels,can be obtained at the AP via uplink training,and delivered to the RIS controller through a dedicated control link.

Figure 1.Considered system model.

Figure 2.Achievable ergodic rate vs.SNR at different spatial correlation levels.N=T=100.

Figure 3.Number of activated RIS elements (Scheme 1)and formed groups(Scheme 2)vs.SNR.Different line styles indicate different correlation levels.

2.1 Channel Model and Signal Model

Let hRU∈CN×1and hAR∈C1×Ndenote channels of the User-RIS link and the RIS-AP link,respectively.Since the RIS elements are usually closely positioned,we model hRUand hARas correlated Rayleigh fading channels[5],such that3

where RRU/AR∈CN×Nare the corresponding correlation matrices,and ?hRU/AR～CN(0,I) are i.i.d.complex Gaussian channel vectors,whose elements are normalized with zero mean and unit variance.

When a signalsis sent by the user with powerPt,it arrives at the AP via the cascaded channel through the RIS.Assume that then-th RIS element adjust its corresponding incident wave’s phase with?n,the received signal at the AP can be written as

and define the cascaded channel vector hC∈C1×N=(hC,1,...,hC,N).Written in terms of hRUand hAR,we have

Define the correlation matrix of hC,which describes the correlation coefficient between any two cascaded channel links,as

Via simple matrix manipulations of(5),we have

where⊙is the Hadamard product.

WhenhC,n,?ncan be known by the system designer,the optimal phase shift which maximizes the received signal power is given by[6]

where(·)?denotes conjugation of a complex variable,and ∠denotes its phase.

2.2 Channel Training and Achievable Rate

In this paper,we focus on discussing the time overhead required for channel training,while not analysing the performance of specific channel estimation techniques.Therefore,we assume that perfect CSI can be obtained via channel training for simplicity.4This allows us to concentrate more on the trade-off between training time consumption and RIS reflection gains,which is the main focus of this work.Taking into account practical channel estimation errors,and correspondingly optimizing the channel training parameter setting are beyond the scope of this paper,and therefore left for future research.

Assume the channel is block fading and stays constant in a time duration ofTtime slots.Here,a“slot”is defined as the time duration required for training and estimating the cascaded channel of one RIS element.Therefore,to estimate the cascaded channel for allNelements,in totalNtime slots are required according to the“on-off”machanism.The time left for data transmission isT ?Nand the ergodic achievable rate of the system,according to(3)and(8),is given by

where the expectation is taken over all fading channel realizations ofhC,n.

Note that in (9),whenTis finite and whenNis large,the system may not be able to benefit from increasingNdue to the fractional term.For this consideration,we investigate three different transmission schemes,aiming to reduce the training time overhead,as described in the following section.

III.TRANSMISSION SCHEMES

To reduce the training time overhead in (9),we consider the following three schemes: 1)RIS element selection,2) RIS element grouping,and 3) Statistical CSI-based reflection phase determination.

3.1 Scheme 1: RIS Element Selection

For Scheme 1,only a subset ofNRIS elements is selected for transmission,while the others are switched off.Denote the set of activated RIS elements asSact,we haveSact?SwhereS={1,2,...,N}.Moreover,|Sact|=M ≤Nis the cardinality of the set.In this case,(9)is rewritten as

We highlight the following aspects for Scheme 1:

? The RIS element selection is conducted in a longterm manner.That is,Sactin (10) stays fixed over all channel fading realizations.This is a reasonable choice to reduce practical implementation complexity.

? There will exist an optimalwhich maximizesRsch1.For exhaustive search,it requirestimes of calculations and comparisons.The complexity becomes unaffordable whenNis large,therefore,low-complexity element selection method is desired.

For the second aspect,we consider a heuristic approach which selectsMout ofNRIS elements,where the spatial correlation among the selected channel links is kept as small as possible.Intuitively,such a selection criterion might be beneficial for exploiting the diversity gain.The selection scheme only depends on RCdefined in (7),therefore it can be conducted conveniently with low complexity.A detailed greedy process for determiningSactis described as Algorithm 1,where in Step 4,the algorithm first identify the maximum correlation coefficient between RIS elementiand the current RIS elements inSact,i.e.,then selects the element which has the mini-mumand add it intoSact.In Steps 8—11,the algorithm determines the optimalMthat maximizes the achievable ergodic rate.

Algorithm 1.Correlation-based greedy RIS element selection.

Alternative scheme for element selection:Instead of selecting the RIS elements based on spatial correlation information,a lower-complexity method is to select the elements randomly.Intuitively,when the spatial correlation level is low,the random selection method will have similar performance as Algorithm 1.Comparison of these two schemes will be provided later in the simulations.

3.2 Scheme 2: RIS Element Grouping

The RIS element grouping scheme is inspired by[14],where a number of adjacent RIS elements are linked together to form a group.The channel training and phase adjustment are then conducted in a per-group manner to reduce the training time overhead,as described in detail in the following.

Assume that the overallNRIS elements are divided intoLdisjoint groups,Gl,l=1,...,L,and we have=S.The training time duration now consumesLslots;in slotl,only the RIS elements inGlis switched on,while the other groups are switched off.As a result,the AP is able to estimate the sum-channel of this group,

Accordingly,a common phase shift is applied for all RIS elements inGlduring transmission,such that

With(12),the signal model in(3)is rewritten as

and the achievable ergodic rate of Scheme 2 is

Similarly,we highlight the following aspects for Scheme 2:

? The RIS element grouping is also conducted in a long-term manner,for the same reason as that has been described for Scheme 1.

? There will also exist an optimal grouping that maximizesRsch2.However,without restriction on the group size,exhaustive search for the optimal group division will be infeasible due to the tremendous number of possible combinations.It is a reasonable and practical choice to let theLgroups to be equal-sized,i.e.,each group haselements in it.Without loss of generality,we assume thatis an integer in the following.

Once the total number of groups,L,is determined,how to select RIS elements to form a group needs to be investigated.Intuitively,the RIS elements in a same group should be guaranteed high inter-element correlation.This is because the common phase shift described in(12)is applied for all elements in the same group.WhenhC,n,?n ∈Glare highly correlated,applying(12)to the group will not cause too much performance degradation,as compared to the case that phase shift is adjusted individually for each element.For this consideration,we propose a correlation-based RIS element grouping algorithm in Algorithm 2.In Step 6,the algorithm selects the RIS element whichhas the largest minimum correlation coefficient with the current elements inGl.In Steps 11—14,the algorithm determines the optimalL ∈Lthat maximizes the achievable ergodic rate.

Algorithm 2.Correlation-based RIS element grouping.

3.3 Scheme 3:Statistical CSI-based RIS Phase Shift Design

Statistical CSI,such as the channel correlation matrices,is usually considered can be obtained with much less cost via long-term measurement[16].Using statistical CSI for transmission design can avoid the instantaneous channel training overhead,i.e.,eliminating the fractional term in (9).Different from the former two schemes,where the RIS phase shifts were designed to compensate the phases of the estimated instantaneous cascaded channels,now the RIS phase shifts will be designed to maximize the ergodic achievable rate,which is rewritten as follows:

where Φ=diag(ej?1,...,ej?N)∈CN×N.To optimize Φ for Scheme 3,analytical expression of(16)is required.

However,it is challenging to obtained a precise analytical expression for (16).Alternatively,we turn to maximize the average received power,i.e.,This is equivalent to maximize an upper bound of(16),which has been solved and shown to be effective in[5].For the reader’s convenience,we briefly review the derivation process in [5].First,it holds that

which can be solved with standard semi-definite program (SDP) techniques.Specifically,the rank 1 constraint is first relaxed to get the optimal,thenis obtained according to the dominant eigenvector ofDetails of the implementation are referred to[5].

We highlight the following aspect for Scheme 3:

? According to(20),the implementation of Scheme 3 requires knowledges of RRUand RAR.When the RIS elements are all passive,however,these knowledges cannot be known individually since only the cascade channel (and RCin (7)) can be obtained.In practice,the problem can be solved by adopting mixed active/passive RIS elements[21],or using empirical correlation models to predict RRUand RAR.

Alternative scheme for statistical CSI-based RIS phase shifts design:The objective in (20) can be rewritten as

where ? is a Hermitian matrix.Clearly,the maximum of(22)can be achieved with

where vdomis the dominant eigenvector of ?.However,the elements ofshould have unit amplitudes.For simplicity,we simply set then-th element ofas

This method,termed as dominant eigenvector-based approach hereafter,might not be optimal.However,it can be implemented with lower complexity,and outperforms the SDP-based approach in some cases as will be shown in the subsequent simulations.

3.4 Summary of this Section

We summarize the three considered schemes.Scheme 1 reduces the training time overhead fromwhile at a cost that the RIS elements are not fully utilized.For Scheme 2,the training time overhead is reduced tomeanwhile,via element grouping,all RIS elements are fully exploited to participate in the transmission.However,the CSI used for phase shift design in Scheme 2 is not ideal,since only the sum-channel information of a group can be acquired.For Scheme 3,the overhead for instantaneous channel training is totally avoided,but the information used for RIS phase adjustment is the most inaccurate:Only statistical CSI is used while the instantaneous CSI is unknown.

Considering the trade-off between training time overhead and RIS transmission efficiency(affected by both the number of activated RIS elements and the quality of available CSI),optimal selection among these three schemes exists.It might vary depending on a number of propagation and system parameters such as the channel correlation level,the total number of RIS elementsN,the length of the coherence timeT,and the SNR,etc.In the following,we compare the performance of these schemes with respect to different parameters via extensive simulations,trying to identify the switching boundary among these schemes,and provide useful information to guide practical RIS reflection scheme selection.

IV.SIMULATION AND DISCUSSION

4.1 Simulation Settings

4.2 Achievable Rate vs.SNR

According to the expressions for the achievable rates in (10),(15),and (16),the three schemes’ achievable rates have different slopes with increasing SNR.This indicates that there may exist cross-points between different rate curves,and therefore SNR might be an important parameter for optimal scheme determination.In Figure 2,we compare the achievable rate for the three schemes(as well as their corresponding alternative schemes described previously) versus increasing SNR.We consider three cases thatρ=0.1,0.5 and 0.9 as examples for the low,moderate and high spatial correlation levels.Several important observations are concluded from the figures,as discussed in detail in the following.

Firstly,the spatial correlation level barely has impact on the RIS element selection scheme (Scheme 1).Besides,as a kind of surprising observation,random RIS element selection almost has the same performance as the correlation-based element selection described in Algorithm 1.A possible explanation is as follows: As will be shown later in Figure 3,the number of activated RIS elements is in general much less than the total number of elements,N,in this simulation scenario.Since the spatial correlation decreases exponentially with the inter-element spacing,random selection can also be effective to guarantee a low correlation level among the selected elements.In a scenario where more RIS elements need to be activated and with higher spatial correlation,the proposed Algorithm 1 may show more advantage.

Secondly,it can be observed from Figure 2 that both the element grouping scheme (Scheme 2) and the statistical CSI-based design(Scheme 3)have better rate performance with increasing spatial correlation level.Specifically,the performance of Scheme 3 might be lower than the other schemes when the correlation level is low,while it will outperform the others when the spatial correlation becomes higher.Possible switching boundaries among these schemes in terms of the correlation level and the SNR exist,which will be discussed in later simulations.

At last,it is noted that for Scheme 3,both the SDPbased and dominant eigenvector-based approaches are not optimal,since they rely on certain approximations or relaxations.These two approaches mainly have very similar performances at low and moderate correlation levels,but the dominant eigenvector-based approach performs better and hence can be considered as an effective implementation method for Scheme 3 at high correlation levels.

To have a deeper look into the performances of Scheme 1 and Scheme 2 with increasing SNR,we further show the changing number of activated RIS elements(and formed groups)in Figure 3.For Scheme 1,it is shown that the number of activated elements decreases with the SNR.This can be explained: At high SNR,concerning the trade-off between training time overhead and signal power enhancement,the former plays a more important role in affecting the achievable data rate.Therefore,less RIS elements are activated at high SNR to enlarge the time for data transmission.Moreover,it is shown that the optimal number of activated RIS elements is barely affected by the channel’s correlation level,which conforms with the observation previously drawn from Figure 2.On the other hand,spatial correlation has more obvious impact on Scheme 2.Less RIS element groups will be formed at higher correlation levels.

4.3 Achievable Rate vs.Correlation Level

In order to better illustrate the changing of achievable rate with the spatial correlation level of the channel,we compare the rate vs.ρfor different schemes,at different SNR values in Figure 4.As shown in the figure,RIS element grouping (Scheme 2) in general has the best performance among all schemes,except for that when the spatial correlation level is high,the statistical CSI-based scheme may become a better choice.The RIS element selection scheme (Scheme 1) has a slightly decreasing rate curve with increasingρ,which indicates that although element selection prefers less correlated spatial channels,the channel correlation,however,does not play a critical role in affecting the rate performance.As being compared with the other two schemes,RIS element selection does not show advantage in most cases.A possible reason can be explained with the aid of Figure 3,where it was observed that only less thanRIS elements are activated for Scheme 1,while the other schemes can fully take advantage of all the available elements.With smallerN,it is anticipated that Scheme 1 might be able to perform better.This motivates our further simulations on the rate performance vs.as described in the following subsection.

Figure 4.Achievable ergodic rate vs.ρ at different SNRs.N=T=100.

4.4 Achievable Rate vs.

We compare the achievable rates of the considered schemes with increasingat different correlation levels and SNRs in Figure 5.As anticipated,the RIS element selection scheme starts to show its merit in the region thatis small,as highlighted by the dashed rectangle areas in Figure 5a and Figure 5b.This area shrinks when the SNR becomes higher or when the spatial correlation becomes larger.At low and moderate correlation levels,the RIS element grouping scheme dominate most of the operation regions;while with high correlation level,the statistical CSI-based scheme outperform the others over all theratios.

4.5 Operation Region Division for Different Schemes

From the previous simulations,it is clear that selection of the best training overhead reduction scheme depends on the system parameters,including the SNR,spatial correlation levelρ,and.In Figure 6,we further show the best operation region division for the three schemes in theplane.In the simulations,Algorithm 1 and Algorithm 2 are applied for Scheme 1 and Scheme 2,respectively.For Scheme 3,the dominant eigenvector-based approach is considered,since it in general can achieve a better performance than the SDP-based approach as shown by previous simulation results.

Figure 5.Achievable ergodic rate vs. at different spatial correlation levels and different SNRs.T=100.

Figure 6.Operation region division in the ρ-plane for different SNRs.N=36 and T is changing from 360 to 36 to get a high-resolution x-axis.

For every (ρ,) grid in the figures,we calculate the achievable ergodic rates for the three considered schemes,respectively,and mark the grids with different colors corresponding to the scheme that achieves the highest rate.The ergodic rate is obtained by averaging over 1000 random channel realizations.This causes some randomness in the region boundaries.Increasing the number of channel samples for Monte Carlo simulations would further smooth the boundaries but is also time consuming.Nevertheless,the changing trend of the three operation regions can be clearly shown with the current setting.

First,it is observed that the operation region of Scheme 1 i n general appears in the area when the values ofbothρandarelow .Thisisreasonable,as Scheme 1 prefers lesscorrelatedspatialchannel,and its drawback of not fully utilizing all the RIS elements would be less obvious atlowvalues.On the other hand,t heoperationregionof Scheme3 appears in the opposi tearea withlargeval uesofρand.The interme diate area between the operation regions of Scheme 1 and Scheme 3 is occupied by Scheme 2.Moreover,as the SNR increases,the operation region of Scheme 1 shrinks while that of Scheme 3 enlarges.This indicates that Scheme 3 has a deeper increasing slope in the rate-SNR curve,which can be confirmed with the simulation results previously shown in Figure 2.

We then provide more discussions for a fixed SNR,e.g.,see Figure 6a.Observing along the direction of theρ-axis,it is shown that the Scheme 1 region shrinks with increasingρ,while Scheme 3 region enlarges.This,again,is reasonable since Scheme 1 prefers less correlated channel while Scheme 3 prefers high spatial correlation.Note that a largerρis also beneficial for Scheme 2,however,the changing trend of Scheme 2 region,with respect toρ,is determined by the two boundaries of Scheme 1 and Scheme 3,respectively.Further observe the figure along the direction of the-axis,itis shownthatScheme 1 r egionshrinkswith i ncreasing,while theoperation regionsof theother two schemes enl arge in this direction.This indicates that RIS element selection can be a feasible choice when the channel coherence time is large;however,in channels with faster time domain variation (or whenNis very large),element grouping and statistical CSIbased design should be applied.By pre-identifying the region boundaries shown in Figure 6(This can be done via either offline simulations or possible mathematical analysis),practical RIS scheme selection can be conveniently conducted once the related system parameters are provided.

V.CONCLUSION AND FUTURE DIRECTIONS

We compared three typical training overhead reduction schemes,i.e.,RIS element selection,element grouping,and statistical CSI-based design,for RIS-assisted communications in correlated Rayleighproduct channels.Spatial correlation-based algorithms were proposed for practical implementation of the considered schemes.The ergodic rates achieved by these schemes were compared versus the SNR,the spatial correlation levelρ,and the element number-tocoherence time ratio.At last,best operation regions of these training-overhead reduction schemes were described in theplane at different SNRs,providing useful guidelines for the scheme selection in practical RIS-assisted communication systems.

Since we have put our focus on understanding the basic trade-off between training time overhead and RIS reflection gains,more practical and general models,such as the channel estimation error,multi-antenna and multi-user,are not considered in the current work.Analysing and comparing the actual performance of different RIS training overhead reduction schemes with these more comprehensive models could be an important research direction,where the training power and duration,precoding at the AP,pilot scheduling,etc.,should be jointly optimized.However,we note that the trade-off explained in this paper will still exist,and the comparison framework adopted herein can be extended to the new scenarios.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China under Grants 62171240,61771264,62001254,61971467,the Key Research and Development Program of Jiangsu Province of China under Grant BE2021013-1,and the Science and Technology Program of Nantong under Grants JC2021121,JC2021017.

NOTES

1According to[13,23,24],it is possible to“turn off”a RIS element by letting it work in the absorption mode.

2For the ease of exposition,we focus on the uplink.The downlink transmission can be similarly analyzed.

3As we are not focusing on the placement position of RIS,large-scale path loss is omitted in the channel modeling.Nevertheless,it can be conveniently added into the signal model when necessary.

4In practice,high estimation accuracy can be realized in many ways,e.g.,increasing the training power.As an important application scenario of RIS could be indoor coverage enhancement,where the transmission distance is relatively short,assuming perfect CSI acquisition could be a reasonable simplification in this case.