With the acceleration of 5G commercialization,re?search on 5G-advanced and 6G communication sys?tems is in full swing.The scarcity of wireless spec?trum resource has become severe
,and the increas?ing network coverage,cost and energy efficiency requirements become a pain point restricting the mobile communication indus?try.New expediting study for innovative solutions is in urgent need.The reconfigurable intelligent surface (RIS),a crossfusion of information metamaterials and mobile communica?tions
,is a new and revolutionary wireless communication enhancement technology.Its basic principle is to construct an intel?ligent and controllable environment by manipulating the electro?magnetic property of metamaterials through digital programming with low-cost hard ware architecture and tremendous flexibility.
It is necessary to obtain accurate channel state information(CSI) to support the promising capabilities of the RIS,such as expanding coverage,increasing transmission freedom,and conducting environmental perception and positioning.Differ?ent from the massive multiple input multiple output (MIMO),the RIS changes the electromagnetic wave propagation with segmented channels
.As RIS elements are passive and mas?sive,it becomes challenging to estimate the channel.
Many channel estimation algorithms have been designed for RIS-assisted communications.In Ref]4],a channel estima?tion method based on the ON-OFF approach is introduced,splitting the RIS into multiple elements and performing chan?nel estimation separately for each element.In Ref]5],the high-frequency scenario is considered,the low-rank property of the RIS channel is exploited,and a matrix filling problem is designed for channel estimation.The hybrid RIS architecture with sensing and signal processing ability is considered in Ref]6],and the sparseness is utilized to obtain highresolution channel parameters.To make full use of the col?lected data,a potential solution is to use the artificial intelli?gence (AI) method for channel estimation
.In addition,the position information is helpful for designing a low-complexity channel estimation method to obtain critical information such as the direction of arrival(DOA).
Moreover,as a RIS is usually large,new channel character?istics appear and affect channel estimation accuracy.New al?gorithms and protocols need to be designed to carry out practi?cal channel estimation and avoid complicated onboard signal processing operations.Most existing works are based on the channel model directly extended from the traditional MIMO channel model
,and the propagation delay is usually ne?glected.Different RIS elements receive signals with different path delays when a far-field signal impinges on the RIS.The delay between different elements can reach the same order of magnitude as the symbol interval,and different RIS elements will receive different amplitudes and phases of the identical symbol or even distinct symbols for the same sampling period.This phenomenon is called spatial-wideband effect.The frequency-wideband effect caused by multipath delay spread is considered in recent studies,while the spatial-wideband ef?fect is always ignored.As a result,the beam generated for dif?ferent frequencies cannot point toward the same direction,and reciprocally,the estimated incident angles are inaccurate if only the frequency-wideband effect is considered.
It was a cold, rainy, bleak1 afternoon when sixteen-year-old Diana, dressed in a borrowed parka() that was too large for her, boots, and blue jeans, crossed the field to meet the heir to the British throne.
She was no sooner at the fountain than she saw coming out of the wood a lady most gloriously dressed,28 who came up to her, and asked to drink. This was, you must know, the very fairy who appeared to her sister, but now had taken the air and dress of a princess, to see how far this girl s rudeness would go.
The youngest is the least experienced and perhaps most protected of the children in a family. The youngest is also the child least likely to receive a financial inheritance in the days when the eldest40 son received the bulk of a father s estate. The youngest would consequently find it necessary to know how to fend for themselves in the world by marrying well or choosing a career.Return to place in story.
In this paper,we analyze the frequency-dependent spatialwideband effect for RIS-assisted communications and present a high-resolution channel estimation algorithm based on offgrid sparse Bayesian learning (SBL) approach.Simulation re?sults are provided to verify the correctness of the spatialwideband effect and the effectiveness of the proposed com?pressive sensing (CS) algorithm.Moreover,the challenges and promising directions of RIS future research are discussed.
After calculation,we find that the marginal likelihood obeys Gaussian distribution as
where
is the antenna spacing,
is the angle of arrival and
is the wavelength.When the number of array elements is enor?mous and the transmission bandwidth is wide,for example,in a typical RIS-assisted communication,new affecting factors need to be considered.
Then the kids got to work. I watched, amazed, as a six-year-old gave up her $2.00 allowance so another little girl could have new mittens7. I saw a ten-year-old s eyes light up when he found the saber light-sword he d wanted, and then put it in the cart for a little boy he didn t even know. A warm, fuzzy blanket for the baby was my four-year-old nephew s choice.
In this paper,the millimeter frequency band is considered,the RIS is deployed in fixed locations such as building walls without mobility,and the BS is deployed at a high location with almost no obstacles around.The line-of-sight (LoS) path transmission between BS and RIS is usually stable and domi?nates the energy of the channel.In this way,the LoS assump?tion is adopted for the channel between BS and RIS.For RISassisted communications,the LoS channel can be obtained with prior knowledge of the location information and simple RIS signaling.The BS-RIS channel parameters can be con?veyed to user equipment (UE) through the control channel for RIS-UE channel estimation.Multiple RIS-UE channel estima?tions are performed within a single BS-RIS channel estimation period as the BS-RIS channel changes slowly.
The RIS-UE channel with spatial-wideband effect is ana?lyzed.For multipath propagation,the passband signal re?ceived by the(
,
)-th element of RIS is
where
is the path number,
f
is the carrier frequency,
β
is the
-th path gain,and
τ
is the delay of the
-th path re?ceived by the (
,
)-th RIS element.Since RIS is a twodimensional planar structure,we have
In Ref]9],the influence of the spatial-wideband effect on the massive MIMO channel is discussed,and the transceiver is redesigned for orthogonal frequency-division multiplexing(OFDM) systems.In Ref]10],the discrete-time channel for the hybrid mmWave massive MIMO system with the spatialwideband effect is modeled and the wideband channel is esti?mated through the Newtonized fully corrective forward greedy selection-cross validation-based algorithm.The authors of Ref]11] develop a spatial-wideband channel model for lens an?tenna arrays and design a fast angle estimation algorithm to es?tablish point-to-point mappings between the spatial-frequency patterns and the strongest discrete Fourier transform beam containing the incident angle.Nevertheless,few work has con?sidered the spatial-wideband channel model for RIS,and highresolution RIS channel estimation approach is lacking.
where
τ
denotes the delay of path
for the first RIS element,and
∈[0,2π)and
∈[0,π)are the azimuth and elevation angles.
As a result,the received baseband signal by the (
,
)-th RIS element in the time domain is
She turned around in a slow pirouette() and saw me standing6 in the doorway. Her song ended, and her beautiful movements with it, so abruptly7 that it felt like being shaken awake from a beautiful dream. The sudden silence rang in my ears. Grandma looked so much like a kid caught with her hand in a cookie jar that I couldn t help myself, and a slightly nervous laughter escaped. Grandma sighed and turned towards the kitchen. I followed her, not believing my eyes. She was walking with no difficulties in her beautiful shoes. We sat down by the table and cut ourselves big pieces of her delicious peach pie.
The frequency domain signals received on all RIS elements can be written in a matrix form as
Ah, dear godfather, said the horrified13 physician, light a new one for me, do it for love of me, that I may enjoy my life, be King, and the husband of the King s beautiful daughter
-point OFDM modulation is adopted to overcome fre?quency selective fading,and the received signal can be ar?ranged as
It can be observed that,for spatial-narrowband signals,a fixed beam can be generated with no frequency dependence.However,the generated beam has slight variations of the an?tenna radiation pattern correlated with the frequency for spatial-wideband signals.This is the main difference between spatial-wideband and spatial-narrowband channels.
“The bright warm sun shone on a little court, on the first warm day of spring. His bright beams rested on the white walls of the neighboring house; and close by bloomed the first yellow flower of the season, glittering like gold in the sun’s warm ray. An old woman sat in her arm chair at the house door, and her granddaughter, a poor and pretty servant-maid came to see her for a short visit. When she kissed her grandmother there was gold everywhere: the gold of the heart in that holy kiss; it was a golden morning; there was gold in the beaming sunlight, gold in the leaves of the lowly flower, and on the lips of the maiden. There, that is my story,” said the buttercup.
Through the above analysis,we have obtained the expres?sion of the RIS-UE channel considering the spatial-wideband effect.The spatial-wideband OFDM channel can be repre?sented by parameters including the angle,delay,and path gain.Once these parameters are obtained,the overall channel can be obtained easily.
For simplification,the received OFDM signal can be writ?ten as
Moreover,to estimate the RIS-UE channel from the received OFDM signal,a simple idea is to select part of the received signal to recover those parameters,avoiding the high dimen?sion disadvantage.
But, floating on the Shoes of Swiftness, the boy just managed to steal in, and waited till one of the sisters said to another, who had their one eye: Sister, what do you see? do you see old times coming back? No, sister
The Bayesian network of the RIS-UE channel model is shown in Fig.1.The prior distribution assumption for noise in?verse variance is gamma distribution.The channel gain obeys the two-layer prior model,where the first layer is the zeromean Gaussian distribution w.r.t.hyperparameter vector
and the second layer follows gamma distribution Γ(?|
,
)that connects
and
as
(
|
,
)=
(
,
),
(
α
)=Γ(
α
|
) and
=
(
).Moreover,those angle-related parameters and delay parameters are assumed to be uniformly distributed.
On-grid CS algorithms such as orthogonal matching pursuit(OMP)
are hard to achieve satisfying performance with low complexity as the number of channel parameters is enormous.The SBL algorithm is adopted to achieve super-resolution pa?rameter estimation performance.A parameterized dictionary with a varying grid is utilized to overcome the grid mismatch problem.According to Ref]13],uniform distribution is ad?opted as a priori distribution for angle and delay parameters.In this way,the channel estimation problem can be trans?formed into maximizing the posterior probability of multidimensional variables of angle,delay,and channel gain jointly.
The posterior probability distribution function (PDF) of the received spatial-wideband OFDM signal is
gation delay across the RIS can be neglected.The spatialnarrowband channel can be represented by
The array steering vector commonly used in MIMO is,
It can be inferred from Eq.(13) that
can be split into one part that is related to the
-th path and the other parts related to the other paths.An iterative approach can be utilized to find the desired solution for each path separately.The detail can be summarized as:
1) The noise variance is obtained by setting the partial de?rivative of
w.r.t.
to be zero.
2) For path
,the hyperparameter
α
can be obtained by choosing a value to make the partial derivative w.r.t.
α
to be zero.
3) The estimated
,
and
are obtained separately through the gradient descent or Newton method.
Although the globally optimal condition cannot be guaranteed,the proposed off-grid SBL algorithm can achieve a continuous convergence of the objective function and obtain a locally opti?mal solution.As the proposed algorithm processes continuous angle and delay directly,it can effectively overcome the grid mis?match problem and achieve super-resolution estimation accuracy.
” But the little mermaid had no occasion to do this, for the polypi sprang back in terror when they caught sight of the glittering draught, which shone in her hand like a twinkling star
I suspect my colleague Matt Pritchett might be with me on this. One of his cartoons this past week showed a father next to a television tuned13 to the World Cup, explaining to his children that at some point in the next few weeks, you are going to see me cry . And the day after the last survivor14 of the Great Escape died, he did a cartoon showing a gravestone with a mound15 of tunnelled earth trailing away from it. I seemed to have something in my eye when I saw that, and I expect he had the same something in his eye when he drew it.
In this section,the channel estimation performance is ana?lyzed.The RIS adopted is composed of 16×16 elements,and 4×4 elements are selected for channel estimation.The number of OFDM subcarriers is 64,and 8 or 16 subcarriers are se?lected for channel estimation.The central frequency is 60 GHz and the bandwidth is 1 GHz.
When a RIS is large enough and the signal bandwidth is wide enough,the physical propagation delay is non-negligible.The spatial-wideband effect brings challenging channel esti?mation difficulties and seriously affects system performance.Moreover,the inherent passive characteristics of the RIS pose the same phase shift for all frequencies.Thus,RIS elements cannot adapt to different received signal phases,and the spatial-wideband effect cannot be compensated.It is neces?sary to carefully design channel estimation and beamforming schemes for RIS with the spatial-wideband effect.
Most of the existing channel modeling methods follow the wireless channel models of 3GPP and ITU.However,the new challenges brought by the novel characteristics of RIS are ig?nored,and the lack of RIS wireless channel measurement be?comes a tremendous challenge for the current stage.It is ur?gent to develop a thoroughgoing RIS channel model consider?ing various fading factors.In addition,it is necessary to rea?sonably model hardware non-ideal factors such as the mutual coupling between sub-wavelength RIS elements and verify it through practical channel measurement.
The electromagnetic mutual coupling means that when mul?tiple antennas are close to each other,the electric field of one antenna will affect the current distribution of other antennas and generate a voltage at its terminals,thereby affecting the performance of the antenna array.To realize the intelligent control of the environment,a RIS is usually composed of tens of thousands of electromagnetic elements,with the element in?terval being less than half a wavelength.The mutual coupling within RIS is severe,and the radiation pattern is affected dra?matically.If no compensation is performed,the system perfor?mance will be decreased.The commonly used electromagnetic coupling analysis methods are the method of moment ap?proach
and the mutual coupling model based on S param?eters
.However,the hardware implementation of the RIS is diverse,including structures based on PIN tubes,varactor di?odes,liquid crystals,etc.How to reasonably model the imped?ance of RIS needs in-depth research.
In MIMO communications,it is assumed that the signals re?ceived by the antenna array are parallel.However,this ap?proximation only holds when the receiving array is in the farfield of the transmitting array.The case is different for a RIS as the near-field condition occurs more frequently.The trans?mission characteristics of spherical waves need to be consid?ered,and near-field research needs to be promoted urgently.
A significant feature of RIS is that the electromagnetic ele?ment can only produce a certain phase adjustment at a particu?lar moment
,and it is difficult for RIS to achieve ideal multibeams for multi-user transmission.One solution is maximizing a criterion and achieving a tradeoff by optimizing the RIS phase shift matrix.However,this solution is complicated and generally difficult to generate beams with precise directivity,restricting its value in actual products.Other solutions include RIS segmentation service for multi-users,matching BS-RIS and RIS-UE beam pairs to obtain suitable beams supporting multi-users,etc.However,the inherent performance loss due to the amplitude restriction of RIS element is difficult to com?pensate.Different subcarriers incident into the same RIS will cause different RIS electromagnetic responses,and different beams will be generated due to the spatial-wideband effect.Reasonable use of these properties may bring new inspiration to multi-user RIS-assisted transmission.
After the introduction of RIS,the communication system will face many challenges such as a more complex propagation environment,an increase in factors affecting channel capacity,etc.RIS needs to perform different functions according to dif?ferent requirements,such as beamforming,energy focusing and near-field broadcasting
.Studying the maximum capac?ity,energy efficiency,or optimization of other indicators under various schemes will be a hot spot for future research.
The Beast considered for a moment, and then he said, in a less furious tone: I will forgive you on one condition--that is, that you will give me one of your daughters
Standardization is an essential connection from technology to application.Although the research on RIS is still in the de?velopment stage,it is indispensable to study the impact of RIS standardization.At present,there are various channel estima?tion and beamforming approaches in academia,while the most basic question considered by the industry is how to standard?ize and apply them.
She ran forwards as quickly as she could, when a whole regiment13 of snow-flakes came round her; they did not, however, fall from the sky, which was quite clear and glittering with the northern lights
As a simple version of RIS is hoped to be deployed in 5Gadvanced network,the standardization of RIS is just around the corner.The points to be standardized for RIS include the use cases and requirements,RIS channel modeling,air inter?face design,and the RIS network architecture.The standard?ization mainly includes near-field and far-field channel model?ing,time slot structure design,channel and signaling design,channel measurement design,feedback design,and related protocol process design.The possible air interface designs in?clude reference signaling,channel feedback signaling,code?book,control signaling,etc.
The spatial-wideband effect is inevitable in the RIS chan?nel,and the communication quality will be affected seriously if the spatial-wideband effect is not handled well.To deal with this problem,we reanalyze the wideband RIS channel repre?sentation and design an off-grid SBL method to estimate the sparse channel parameters.The estimation of the channel pa?rameters through the activation of some RIS elements is real?ized and the complete channel is restored successfully.The simulation results prove the effectiveness of the off-grid SBL algorithm.Finally,the challenges to be dealt with for RISassisted communications are discussed.
[1]STRINATI E C,BARBAROSSA S,GONZALEZ-JIMENEZ J L,et al.6G:the next frontier:from holographic messaging to artificial intelligence using subtera?hertz and visible light communication [J].IEEE vehicular technology magazine,2019,14(3):42-50.DOI:10.1109/MVT.2019.2921162
[2]CUI T J.Information metamaterial and metasurface-from concept to system [C]//43rd International Conference on Infrared,Millimeter,and Terahertz Waves(IRMMW-THz).IEEE,2018:1-3.DOI:10.1109/IRMMW-THz.2018.8510031
[3]NGUYEN C L,GEORGIOUS O,GRADONI G,et al.Wireless fingerprinting lo?calization in smart environments using reconfigurable intelligent surfaces [J].IEEE access,2021,9:135526-135541.DOI:10.1109/ACCESS.2021.3115596
[4]MISHRA D,JOHANSSON H.Channel estimation and low-complexity beamform?ing design for passive intelligent surface assisted MISO wireless energy transfer[C]//IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP).IEEE,2019:4659-4663.DOI:10.1109/ICASSP.2019.8683663
[5]HE Z Q,YYAN X.Cascaded channel estimation for large intelligent metasur?face assisted massive MIMO [J].IEEE wireless communications letters,2019,9(2):210-214.DOI:10.1109/LWC.2019.2948632
[6]JIAN M,ZHAO Y.A modified off-grid SBL channel estimation and transmis?sion strategy for RIS-assisted wireless communication systems [C]//2020 Inter?national Wireless Communications and Mobile Computing (IWCMC).IEEE,2020:1848-1853.DOI:10.1109/IWCMC48107.2020.9148537
[7]LIU C,LIU X,NG D W K,et al.Deep residual learning for channel estimation in intelligent reflecting surface-assisted multi-user communications[J].IEEE trans?actions on wireless communications,2021.DOI:10.1109/TWC.2021.3100148
[8]TAHA A,ALRABEIAH M,ALKHATEEB A.Enabling large intelligent sur?faces with compressive sensing and deep learning [J].IEEE access,2021,9:44304-44321.DOI:10.1109/ACCESS.2021.3064073
[9]WANG B,JIAN M,GAO F,et al.Beam squint and channel estimation for wide?band mmWave massive MIMO-OFDM systems [J].IEEE transactions on signal processing,2019,67(23):5893-5908.DOI:10.1109/TSP.2019.2949502
[10]KIM I,CHOI J.Spatial wideband channel estimation for mmWave massive MIMO systems with hybrid architectures and low-resolution ADCs [J].IEEE transactions on wireless communications,2021,20(6):4016-4029.DOI:10.1109/TWC.2021.3054998
[11]WU K,NI W,SU T,et al.Exploiting spatial-wideband effect for fast AoA esti?mation at lens antenna array [J].IEEE journal of selected topics in signal pro?cessing,2019,13(5):902-917.DOI:10.1109/JSTSP.2019.2937691
[12]KULKARNI A,MOHSENIN T.Low overhead architectures for OMP compres?sive sensing reconstruction algorithm [J].IEEE transactions on circuits and systems I:regular papers,2017,64(6):1468 -1480.DOI:10.1109/TCSI.2017.2648854
[13]JIAN M,GAO F,TIAN Z,et al.Angle-domain aided UL/DL channel estima?tion for wideband mmWave massive MIMO systems with beam squint [J].IEEE transactions on wireless communications,2019,18(7):3515-3527.DOI:10.1109/TWC.2019.2915072
[14]GANESH M,SUBHASHINI K R,JAGAN B.A method of moments based algo?rithm to synthesize antenna arrays[C]//2017 International Conference on Wire?less Communications,Signal Processing and Networking (WiSPNET).IEEE,2017:1091-1095.DOI:10.1109/WiSPNET.2017.8299931
[15]AZHAR A A,ABD RASHIDN E,MAHMOOD M K A,et al.Effects of mutual coupling and array dissimilarity on angle estimation in MIMO radar [C]//2019 IEEE Asia-Pacific Conference on Applied Electromagnetics (APACE).IEEE,2019:1-6.DOI:10.1109/APACE47377.2019.9020903
[16]BJORMSON E,SANGUONETTI L.Power scaling laws and near-field behav?iors of massive MIMO and intelligent reflecting surfaces [J].IEEE open jour?nal of the communications society,2020,1:1306-1324.DOI:10.1109/OJCOMS.2020.3020925
[17]KAMMOUN A,CHAABAN A,DEBBAH M,et al.Asymptotic max-min SINR analysis of reconfigurable intelligent surface assisted MISO systems [J].IEEE transactions on wireless communications,2020,19(12):7748-7764.DOI:10.1109/TWC.2020.2986438
[18]PAN C,REN H,WANG K,et al.Reconfigurable intelligent surfaces for 6G systems:principles,applications,and research directions [J].IEEE communi?cations magazine,2021,59(6):14-20.DOI:10.1109/MCOM.001.2001076