Deep Learning based Channel Extrapolation for Large-Scale Antenna Systems: Opportunities, Challenges and Solutions
Shun Zhang, Yushan Liu, Feifei Gao, Chengwen Xing, Jianping An, Octavia A. Dobre
aa r X i v : . [ c s . I T ] F e b Deep Learning based Channel Extrapolationfor Large-Scale Antenna Systems:Opportunities, Challenges and Solutions
Shun Zhang,
Senior Member, IEEE,
Yushan Liu, Feifei Gao,
Fellow, IEEE,
Chengwen Xing,
Member, IEEE,
Jianping An,
Member, IEEE, and Octavia A.Dobre,
Fellow, IEEE
Abstract
With the depletion of spectrum, wireless communication systems turn to exploit large antenna arraysto achieve the degree of freedom in space domain, such as millimeter wave massive multi-input multi-output (MIMO), reconfigurable intelligent surface assisted communications and cell-free massive MIMO.In these systems, how to acquire accurate channel state information (CSI) is difficult and becomes abottleneck of the communication links. In this article, we introduce the concept of channel extrapolationthat relies on a small portion of channel parameters to infer the remaining channel parameters. Sincethe substance of channel extrapolation is a mapping from one parameter subspace to another, we canresort to deep learning (DL), a powerful learning architecture, to approximate such mapping function.Specifically, we first analyze the requirements, conditions and challenges for channel extrapolation.Then, we present three typical extrapolations over the antenna dimension, the frequency dimension,and the physical terminal, respectively. We also illustrate their respective principles, design challengesand DL strategies. It will be seen that channel extrapolation could greatly reduce the transmissionoverhead and subsequently enhance the performance gains compared with the traditional strategies. In
S. Zhang and Y. Liu are with the State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071,P. R. China (Email: [email protected]; ysliu [email protected]). F. Gao is with Department of Automation,Tsinghua University, State Key Lab of Intelligent Technologies and Systems, Tsinghua University, State Key for InformationScience and Technology (TNList) Beijing 100084, P. R. China (Email: [email protected]). C. Xing and J. An are with theSchool of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China (e-mail: [email protected];[email protected]). O. A. Dobre is with Faculty of Engineering and Applied Science, Memorial University, St. John’s NL AIC-5S7,Canada (e-mail: [email protected]). the end, we provide several potential research directions on channel extrapolation for future intelligentcommunications systems.
I. I
NTRODUCTION
With the rapid development of wireless technologies, we are entering the era of the fifthgeneration (5G) wireless communications and are heading towards the sixth generation (6G).Massive multi-input multi-output (MIMO) will continue to serve as one of the key technologiesfor 6G, as it can provide much more degrees of freedom than the conventional MIMO. Inparticular, massive MIMO combined with millimeter wave (mmWave) communications canachieve orders of magnitude enhancement in system throughput. For the cell-free massive MIMO,the distributed systems can potentially reduce the inter-cell interference through coherent cooper-ation between base stations (BSs) and provide higher coverage than co-located massive MIMO.Besides, the reconfigurable intelligent surface (RIS) with massive number of passive antennas caneffectively perform the desired beamforming and reconstruct the radio scattering environmentinto an intelligent environment. Unfortunately, as the number of antennas increases, all thesepromising wireless technologies require a large amount of training overhead in order to achieveaccurate channel state information (CSI).Traditionally, the channel reciprocity is utilized in time division duplex (TDD) massive MIMOsystems to reduce the cost of downlink channel estimation as long as the uplink CSI is obtained.For frequency division duplex (FDD) massive MIMO, the compressive algorithms that exploit thesparsity of channel in angle domain have been used to estimate CSI. However, the performanceof compressive sensing is restricted with the linear sparsity assumption that does not accuratelymatch the complex nonlinear sparse characteristics of the environment. Recently, Alkhateeb et al. revealed the deterministic relationship among different channels at different antennasand frequency bands, and introduced a new concept, namely the channel mapping in spaceand frequency domain [1]. With a similar principle, Esswie et al. proposed a spatial channelestimation scheme to reconstruct the downlink channel from uplink channel measurements forFDD MIMO systems [2]. In [3], Ali et al. constructed the channel covariance of the mmWavelink from the spatial characteristics of the sub-6 GHz band.
In fact, the essential principle of deterministic mapping among different channels is that usersat different spaces or different frequencies experience the same electromagnetic environment.Utilizing such deterministic mapping, the CSI at one space/frequency point can be used topredict the CSI at another space/frequency point, which is referred to as channel extrapolation .Clearly, channel extrapolation can be excitingly useful to reduce the training cost over massiveMIMO related systems. Inspired by the universal approximation capability of deep learning(DL) [4]–[6], it is possible to use DL to characterize the mapping among channels at differentspace/frequency locations.In this article, we introduce the mechanism for channel extrapolation and analyze its majorchallenges over three scenarios: antenna domain extrapolation, frequency domain extrapolationand physical terminal extrapolation. Specifically, for the antenna extrapolation, we propose touse the channel of a few uplink antennas to reconstruct the full downlink channel for an FDDsystem, and present the corresponding DL-based solution. For the frequency extrapolation, weconsider two cases: the channel mapping between two subcarrier sets within one frequency bandand the channel mapping across different frequency bands. For the terminal extrapolation, weconsider the channel mapping among different distributed users, where the sensors are appliedto provide additional information about the environment and DL is used to achieve the transferbetween neural networks (NNs) of distinct users. Finally, we discuss several potential researchdirections on channel extrapolation for future intelligent communications.II. P
ROBLEM F ORMULATION
A. The Concept of Channel Extrapolation
From the propagation characteristics of the electromagnetic wave, we know that when the userswitches the frequency or moves in a short time, its surrounding environment would not changemuch, which makes the channels at different spaces or different frequencies to have certainmapping relationship. Many efforts have been made to explore such mapping, and some effectivemapping models, e.g., the one between the uplink and downlink channels over the massive MIMOsystems, have been established. Nevertheless, channel mappings, like the one between the sub-6and mmWave bands or the one among different distributed antennas, are difficult to describe
The opportunities of DL-based channel extrapolation
MethodsFull spaceSelected subspace
Desired subspaceExtrapolate Imperfectlink conditions
Nonlinear mappingHardware impairment
High mobility
Hardware High
Mathematical interpolation
Deep learningDeterministic mapping
Target Method
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Fig. 1. The opportunities of DL-based channel extrapolation. mathematically. In [1], the authors proved that the large-scale antenna arrays are able to assurethe bijectiveness condition, which makes the channel mapping along the frequency and spacedimensions unique. Then, the authors utilized the DL approach to successively approximate suchchannel mapping. The key idea of DL-based channel extrapolation is illustrated in Fig. 1.
B. Challenges of DL-based Channel Extrapolation
In fact, channel extrapolation can be treated as a mapping from one parameter subspace toanother, which depends on three aspects: the acquisition of the original subspace information,the choice of the original subspace, and the mapping scheme from the original subspace tothe targeted one. Notice that the task of “the original subspace acquisition” is to estimate thesub-sampled channel of small size and can be easily implemented through the conventionalBayesian linear estimator, message passing algorithms, or DL-based algorithms. Therefore, inthe following, we will focus on the other two challenges:1)
Subspace selection : For the given full space, the raw input information is closely relatedwith the selection of subspace. Different selections would correspond to distinguished information compression rates and selection patterns , where the selected space is markedas ‘1’ while the others are marked as ‘0’. With the power, hardware, or performanceconstraints, it is possible to optimize the selection pattern and to provide a good startpoint for a specific extrapolation task. The sparser the selection pattern is, the less thetraining costs and hardware power consumption are, but the poorer the performance ofthe channel extrapolation will be. Thus, with the DL-based channel extrapolation, it isimportant to determine the selection pattern before starting the transmission. However, thecore operation of DL is the gradient descent algorithm that requires the mapping functionto be continuous and differentiable. Hence, the optimization of the subspace selection ischallenging for DL based channel extrapolation.2)
Mapping scheme : The DL-based channel extrapolation is similar to the super-resolution inthe field of image processing, in which it is important to properly exploit the correlationbetween data elements for information completion. In order to improve the performance ofthe NN, we can increase the number of data layers or modify the NN structure. However,more layers result in heavier calculation, and when the number of layers reaches a certainnumber, the degree of improvement becomes smaller. Sometimes, excessively deepening theNN will even cause the gradient explosion and disappearance. Thus, we aim to constructinga robust but simple NN structure to achieve better extrapolation performance and fasterconvergence, which is another challenge of the channel extrapolation.In the following, we present the channel extrapolation over the antenna dimension, the fre-quency dimension and the physical terminal separately, and show the effectiveness of each typeof extrapolation.III. C
HANNEL E XTRAPOLATION OVER A NTENNA D IMENSION
A practical way to implement large antenna arrays, e.g., massive MIMO, is to use the hybridanalog and digital architecture, where a small number of radio frequency (RF) chains areconnected to massive antennas through the fully connection or subarray connection structure.In this case, the limited number of RF chains have to connect the active antennas in turn forthe acquisition of downlink CSI, which consumes significant time resources, especially whenphysically switching the antennas costs non-ignorable time. Besides, over the RIS communication ........... . . .... Phase Shifters Base Station User ······
Antenna array
Co-located UserSelected antennas Other antennas
Extrapolation
Base Station UserRIS
Blocked RF ChainRF Chain RF
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Hybrid massive MIMORIS-assisted communicationAntenna extrapolation
Fig. 2. The channel extrapolation over antenna dimension for large-scale antenna systems. network, the channel size is in scale with the number of RIS elements, which is usually verylarge to achieve good electromagnetic reconfiguring performance. Thus, the channel estimationin RIS-aided network also requires significant time resources. With the new idea of channelextrapolation, we can explore the mapping relation between the partial antennas and the fullone in an offline manner, and accurately infer the CSI of full antennas from the partial antennasduring the online transmission. This type of channel extrapolation architecture is specificallyreferred to as antenna extrapolation and is illustrated in Fig. 2.Recently, there are some preliminary results on implementing the antenna extrapolation. In[7], the authors examined the antenna extrapolation for a massive MIMO system based on thedeep NN (DNN), which can capture the inherent relationship between the uplink and downlinkchannel data sets and extrapolate the downlink channels from a subset of the uplink CSI. In [ ? ],Zhang et al. realized the antenna extrapolation through a convolutional NN (CNN) in a RIS-aided communication system. Moreover, the authors proposed an antenna selection network thatutilizes the probabilistic sampling theory to select the optimal locations of those active antennas.In [9], we modify the NN structure by ordinary differential equation (ODE) which can describethe latent relations among different data layers and improve the performance gains of the antenna Epoch -35-30-25-20-15-10-50 N M SE [ d B ] r = 8 Traditional CNNr = 8 ODE-based CNNr = 16 Traditional CNNr = 16 ODE-based CNNr = 8r = 16 Fig. 3. The NMSE comparison of traditional CNN and ODE-based CNN against epochs for antenna extrapolation in a RIS-assisted communication system. Note that r denotes the number of active antennas at RIS. extrapolation.In Fig. 3, we provide evaluation results of the antenna extrapolation for the traditional CNNstructure and the ODE-based CNN structure in a RIS-aided system. The parameter settings are:a × uniform planar array (UPA) at BS, × UPA at RIS and single antenna at the user, wherethe antenna spacing is half wavelength. The carrier frequency is . GHz, the system bandwidthis MHz, and the number of subcarriers is . Moreover, the number of active antennas at RISis separately taken as and . The distribution of training and test users in the DeepMIMOdataset is the same as in [7]. It can be seen from Fig. 3 that with the increase of iteration time,the normalized mean square error (NMSE) curves decay fast first, and then slow down after epochs. As the number of active antennas increases, the NMSEs of the two structures decreaseand the performance gap between the two structures becomes larger. Hence, for a given numberof active antennas, the ODE-based CNN outperforms the traditional CNN and trains faster thanthe traditional CNN.In fact, the DL-based algorithms should adapt to the environmental changes and customizethe antenna extrapolation schemes according to the environmental information. Hence, oncethe environment changes, say when the users are moving, the corresponding NNs should be re- trained. Thus, how to achieve a good balance between the performance gains and the cost causedfrom retraining the DNN is another challenge for the antenna extrapolation. A possible solutioncould be the transfer and meta learning that has the ability to adapt to the new environmentquickly with a small amount of new training samples [10].IV. C HANNEL E XTRAPOLATION OVER F REQUENCY
Along the frequency dimension, the channel extrapolation can use one set of subcarriers toinfer another set of subcarriers, which is named frequency extrapolation . We present two typicalapplications for the frequency extrapolation in Fig. 4. One is to implement the channel extrap-olation between two subcarrier sets within a given frequency band. The other is to extrapolatechannels among different frequency bands, being suitable for the multi-band systems, say FDDmassive MIMO system. As seen later, the frequency extrapolation principle may even be feasiblewhen the gap between different frequency bands is large.
A. Frequency Extrapolation Within A Frequency Band
The orthogonal frequency division multiplexing (OFDM) technology with a large amount ofsubcarriers is usually adopted to capture the potential efficiency of large bandwidth and dealwith the frequency selective fading. Since the mathematical channel modeling among differentsubcarriers is available, one can sparsely place pilots at partial subcarriers, sound the incompletechannels and reconstruct the entire CSI over the full band via a signal processing approach.Although the performance of the signal processing approach is very good in a stable environment,its effectiveness degrades in more complicated scenarios. For example, in high mobility scenario,OFDM may encounter significant inter-carrier interference due to the Doppler spread. Moreover,when the length of the predefined cyclic prefix (CP) is smaller than that of the channel’s delayspread, the inter-symbol interference appears and destroys the signal modeling in the frequencydomain. In addition, the hardware impairments, such as the I/Q imbalance, phase noise andnonlinearity of the power amplifier, would cause nonlinear distortion in received signals.A possible solution is to utilizing the universal approximation capability of DL to characterizethe channel modeling in these complicated scenario and continue to reconstruct the channels ofall subcarriers from a small subset of subcarriers. Another key problem is that the traditionally
Sub-6 GHz
Transceiver (Fully-digital)mmWave
Transceiver (Analog-only) . . .... . . .... Sub-6 GHz Transceiver(Fully-digital)mmWave
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Extrapolation ···
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Multi-band MIMO (cid:708) including sub-6GHz and mmWave (cid:709)
Frequency extrapolation within one frequency band Frequency extrapolation between different frequency bands
User
Fig. 4. The channel extrapolation over frequency for multi-band MIMO systems, including sub-6 GHz and mmWave. adopted uniform pilot pattern cannot guarantee the optimal performance anymore and the designof the pilot pattern should be carefully addressed.In Fig. 5 (a), we offer the evaluation results of the frequency extrapolation in mmWave bandbased on the CNN and conventional interpolation scheme [5]. The antenna configuration is thesame as that in Fig. 3. The carrier frequency is GHz, and the subcarrier spacing is kHz.The number of subcarriers is , and the number of selected subcarriers for partial channelestimation is . The curves labeled by ‘InCP’ correspond to the case of insufficient CP, whilethe ones marked by ‘EnCP’ represent the case of enough CP. It can be seen from the Fig. 5(a) thatthe NMSE curves decay with the increase of the sample rate on the subcarrier. Meanwhile, theNMEs of CNN are always better than those of conventional interpolation, especially in the caseof insufficient CP. Moreover, in the case of enough CP, the gap between CNN and conventionalinterpolation becomes larger as the sample rate decreases. Sample rate -80-60-40-200 N M SE ( d B ) (a) Frequency extrapolation within one frequency band EnCP Interpolation [5]InCP Interpolation [5]EnCP CNNInCP CNN -10 -5 0 5 10 15 20
SNR of sub-6 GHz channel(dB) A cc t op [ ] (b) Frequency extrapolation between sub-6 GHz and mmWave bands
16 active antennas, FusionNet8 active antennas, FusionNet4 active antennas, FusionNet2 active antennas, FusionNetBaseline, DNN [14]
Interpolation FusionNetCNN Baseline
Fig. 5. The performance analysis of two frequency extrapolations in a multi-band system (including sub-6 GHz and mmWavebands).
B. Frequency Extrapolation Between Different Frequency Bands
DL-based frequency extrapolation can also be used to infer the downlink channel from theuplink one in FDD massive MIMO, which solves the problem resulted from the fact that thechannel is not reciprocal in the two different frequency bands. In fact, the technology of multiplebands transmission is a new trend, especially that recent communications systems are designedto work at both sub-6 GHz and mmWave bands, simultaneously [3], [11], [12]. In the dual bandsystem, the mmWave spectrum would provide a high speed link and offer gigabit-per-seconddata rates, but it would also face huge training overhead and high sensitivity to blockages. Sincethe mmWave and sub-6 GHz links experience the same scattering environment, it is possible tobuild a deterministic relationship between their channels and extrapolate the CSI of mmWaveband from that of the sub-6 GHz band.In [11], Li et al. used the sub-6 GHz spatial information to help beam selection in a mmWavesystem by exploiting the feature that the support set of the mmWave channels is a subset of thatfor the sub-6 GHz channels with the same grid quantization. In [12], Alrabeiah et al. performedbeam prediction at mmWave band from the CSI at sub-6 GHz band with the aid of a DNN.Moreover, the authors incorporated the materials’ dielectric coefficients at the sub-6 GHz andmmWave bands, which is critical information for the accurate mapping between the sub-6 GHz and mmWave signals.Although the effectiveness of the above work has been verified, the frequency extrapolationfrom sub-6 GHz to mmWave is practically inaccurate. This is mainly because the mmWave signalpropagation is highly sensitive to blockages, and the electromagnetic microwave impinging onthe arrays of two links have different angular spread (AS). Therefore, the mmWave channel isa sub-category of the sub-6 GHz channel [13], and the CSI of mmWave band could seriouslydeviate from that in sub-6 GHz. In order to calibrate the CSI deviation, we design a simple buttricky dual-input NN, referred to as FusionNet, to merge the features of sub-6 GHz channels and afew inherent pilots at mmWave band to improve the beam prediction [14]. It is worth mentioningthat the number of mmWave pilots is not enough to meet the channel estimation requirements;however, it can help refine the mmWave beam direction on top of the CSI information from thesub-6GHz band. Moreover, the balance between the auxiliary pilot overhead and the extrapolationperformance can be further optimized, and the pilot pattern along the frequency dimension canbe improved through the probabilistic sampling theory.In Fig. 5 (b) we display the evaluation results of the mmWave beam prediction based onDNN and FusionNet, respectively. The parameter configuration and the definition of top-1accuracy Acc top are the same as in [14]. The ‘baseline’ curve is the performance of theDNN, and the ‘active antennas’ represent the mmWave antennas that participate in the mmWavechannel estimation. The number of active antennas in the mmWave system is taken as , , , respectively, and the mmWave pilot signal-to-noise ratio (SNR) is dB. It can be seen fromthe Fig. 5(b) that the prediction accuracy of the FusionNet with any number of mmWave activeantennas is always better than that of the baseline method, especially at low SNR for the sub-6GHz channel estimation. Moreover, as the number of active mmWave antennas increases, thebeam prediction accuracy of FusionNet improves significantly but slows down after the numberof active mmWave antennas exceeds .V. C HANNEL E XTRAPOLATION OVER P HYSICAL T ERMINAL
Inspired by the channel-to-channel mapping, the authors of [1] verified that the channelextrapolation among different terminals at any position is possible, and then applied this map-ping concept to the distributed (cell-free) massive MIMO. With the key idea of [1], one can ExtrapolationExtrapolation ...... C P U AP APAPAP AP AP AP AP APAP AP AP C P U AP APAPAPAPAP
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APAPAPAPAPAPAP APAP APAPAPAPAPAPAP APAP xtrapolationxtrapolatioononnnnnxxExExEEEExtrapolationxtrapolation ......
Cell-free massive MIMOTerminal extrapolation
APAP
Fig. 6. The channel extrapolation over the physical terminal for a cell-free massive MIMO system. Note that the terminal canbe antenna array and user. employ a subset of terminals to infer the information for the other terminals, which is named terminal extrapolation ; this is illustrated in Fig. 6. If the terminals are close or are in a similarenvironment, then the terminal extrapolation is feasible and provides enough accuracy. However,with the increase of the distance between terminals, the number of common scattering objectsbecomes smaller and the latent relation becomes weaker, which deteriorates the performanceof the terminal extrapolation. In addition, this mapping would be closely related with the linkconditions, such as physical position of terminals and hardware states, which causes difficultiesfor terminal extrapolation. Hence, unlike the antenna and frequency extrapolations, the terminalextrapolation occurs among different parameter subspaces with large differences and it is difficultto realize satisfactory extrapolation performance only through NNs.Meanwhile, with the application of various types of sensors, the communication systems canavail of diverse information, such as users’ positions and mobility states. Hence, one can incor-porate the information from sensors to enhance the performance of terminal extrapolation [15].Explicitly, the terminals are equipped with sensors to detect the map of the static environment.Then, they can be divided into groups of terminals that share similar electromagnetic scatteringenvironments. Similar to the frequency extrapolation, we can resort to the FusionNet to mergea few pilots and sensing information to achieve a good extrapolation among terminals in onegroup. Nevertheless, the terminals’ channels in different groups are less correlated, and thus, these groups cannot share the common extrapolation NN. Separately designing and training theextrapolation NNs for different groups would yield a large computation burden.Inspired by the humans’ ability to transfer knowledge from previous experience, transferlearning has become a promising technology in the field of machine learning to solve similartasks with limited labeled data. This aims to improve the performance of target tasks by exploitingthe knowledge from source tasks. Recently, Yang et al. utilized a meta-learning scheme andeffectively adapted the CSI estimation NN to the new environment [10], which provides afeasible way to apply transfer learning or meta-learning to the terminal extrapolation. Giventhe constraints on the performance of the terminal extrapolation, one should also determinewhich group should be selected to infer the NNs of the other groups. Moreover, the size of thegroup should be carefully designed to balance the performance of terminal extrapolation andtraining cost. VI. F UTURE R ESEARCH D IRECTIONS
Although channel extrapolation has been established in theory and some preliminary resultshave been presented, there are still many open problems that need to be investigated over thelarge-scale antenna systems. We highlight several potential research directions as follows:
A. Joint Channel Extrapolation over Antenna, Frequency and Physical Terminal
The previously introduced three different channel extrapolation can be designed in a jointmanner. For example, one can apply the OFDM system with large bandwidth into RIS-assistedcommunications, i.e., the combination of antenna and frequency extrapolation. In such case, oneneeds to implement 2D sampling along the antenna-frequency domain, and then use the small2D subspace to construct the full 2D space over the antenna and frequency dimensions.
B. Optimization of NN and Resource Deployment
The existing works mainly demonstrated the effectiveness of DL-based channel extrapolations,while further effort is needed to optimize the parameters of the NN, e.g., the number of layers, aswell as to consider optimal resource deployment, e.g., location of auxiliary mmWave pilots overfrequency extrapolation, and distributed antennas/users scheduling over terminal extrapolation. C. Model-Driven Channel Extrapolation
The previously discussed channel extrapolation mainly works in a data-driven manner. If thelink conditions are good, the mapping function among different subspaces may be modeledmathematically, and a model-driven approach may be designed to enhance the performance ofchannel extrapolation. We may also design schemes that could intelligently switch between thedata-driven and model-driven manners according to the complexity requirement and the dynamicenvironment.
D. Vision-based Channel Extrapolation
In general, the communication environment information, such as building location, obstacleshape and material, dynamic pedestrian, and vehicle distribution, would determine the propa-gation of the electromagnetic waves at any location and any frequency band. Hence, one mayresort to sensors such as camera or radar to capture the 3D scene image of the environment andthen design the corresponding DL algorithm to assist all three types of channel extrapolation.VII. C
ONCLUSION
In this article, we have presented the channel extrapolation concept and analyzed its threemajor challenges, i.e., the acquisition of the original subspace information, the selection ofthe original subspace and the mapping scheme from the original subspace to the targeted one.We divided the channel extrapolation into three typical types: antenna extrapolation, frequencyextrapolation and terminal extrapolation. For antenna extrapolation, we found that the ODE-basedNN outperforms the traditional NN model. For frequency extrapolation, when the gap betweendifferent frequency bands is large, we need a small number of pilots to refine the extrapolation.For terminal extrapolation, due to subspaces with large difference, it is difficult to achieve a goodperformance only though NNs. Hence, the utilization of sensory data and transfer learning canimprove the extrapolation performance. Finally, we have introduced several potential researchdirections on channel extrapolation.In summary, channel extrapolation is a very promising and powerful tool to handle thecomplicated transmission scenarios when the mathematical modeling of the channel is inaccurateor even unavailable. This is especially applicable to mmWave massive MIMO, RIS-assisted communications and cell-free massive MIMO, and deserves a full investigation and exploitationfor such communications systems, which will incorporate intelligence in the future.R EFERENCES [1] M. Alrabeiah and A. Alkhateeb, “Deep learning for TDD and FDD massive MIMO: Mapping channels in space andfrequency,” in
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