Zhen Zhang, Jianhua Zhang, Yuxiang Zhang, Li Yu, Guangyi Liu
©SHUTTERSTOCK.COM/DEN RISE
The trend of using larger scale antenna arrays will continue toward 6G systems, where the number of antennas will be further scaled up to improve spectral efficiency. However, the increase in the number of antennas will bring new challenges to the physical layer, such as frequent feedback in high-speed mobile communications, multiband coexistence overhead from sub-6 (gigahertz) GHz to terahertz (THz), and energy consumption due to increased antenna components and circuits. In this article, we introduce artificial intelligence (AI)-based channel extrapolation to address these problems. Specifically, we divide the channel extrapolation into time, frequency, and space domains according to different application scenarios. The channel propagation characteristics that affect the extrapolation of each domain, such as the spatial consistency property (SCP), partial reciprocity, and spatial nonstationarity, are analyzed. The motivations for selecting various AI models in each domain are explained, and the performance of AI models is compared. Furthermore, we find the gain of cross-domain channel extrapolation based on transfer learning (TL). The simulation results show that the experience of the AI model cross different domains can be mutually reinforcing. Finally, we introduce several challenges for AI-based channel extrapolation, which can be regarded as potential research directions for realizing future AI-powered 6G systems.
6G mobile networks are expected to support further enhanced mobile broadband, ultramassive machine-type, enhanced ultrareliable and low-latency, long-distance, and high-mobility communications and other emerging scenarios for the 2030 intelligent information society, which requires instantaneous, extremely high-speed wireless connectivity [1]. Multiple antenna techniques will continue to play a vital role in 6G, such as ultramassive multiple-input, multiple-output (MIMO), reconfigurable intelligent surface, and cell-free massive MIMO. With the number of antennas further increasing, the pilot overhead, feedback delay, and energy consumption of channel estimation will become prohibitive. Therefore, a major challenge in 6G is the acquisition of accurate channel state information (CSI) while keeping the overhead low for channel estimation.
Various methods to reduce the channel estimation overhead have been proposed in massive MIMO systems. In time-division duplex systems, channel reciprocity is a feasible way to acquire downlink (DL) CSI through uplink (UL) CSI. In frequency-division duplex (FDD) systems, the compressed sensing (CS) technique is utilized to perform sparse channel estimation, which exploits the sparsity of wireless channels. Researchers have tried to extract multipath parameters and extrapolate the channel in the frequency domain to achieve FDD channel reciprocity [2]. However, for 6G systems, high-mobility scenarios become essential, and the CSI fluctuates dramatically within a short time period. Frequent CSI updates occupy system resources for useful signal transmission. Therefore, time-domain channel extrapolation based on previous CSI is crucial for reducing the channel estimation overhead. Moreover, with the development of ultramassive MIMO, the energy consumed by signal transmission and radio-frequency (RF) chains will become considerable. Space-domain extrapolation can utilize the partial CSI estimated at a few antennas to extrapolate the full ones.
In a word, channel extrapolation that utilizes selected CSI to extrapolate desired CSI is a powerful technique to reduce the overhead of channel estimation in future 6G systems. The fundamental principle of channel extrapolation is that users at different times, frequencies, and antennas have a similar physical environment. The propagation characteristics of electromagnetic waves are mainly affected by the physical environment. However, the real physical environment is complex. As shown in Figure 1, a wireless channel consists of various propagation paths, such as direct radiation, reflection, and diffraction of electromagnetic waves. The parameters of channel paths are usually influenced by the size, shape, and material of the scatterers around the base station (BS) and the user. Hence, the mapping relationships among channels at different times, frequencies, and antennas are often nonlinear. Conventional mathematical interpolation and CS-based methods have a hard time achieving a satisfactory performance because they are generally based on some linear assumptions. Moreover, the channel extrapolation strategy based on channel parameter extraction is challenging to apply to an existing system because of the high computational complexity of the high-resolution parameter estimation algorithms.
Figure 1 Concepts and challenges of channel extrapolation. OFDM: orthogonal frequency-division multiplexing; LOS: line of sight.
Recently, AI has been regarded as a major innovative technique for 6G. AI techniques have made tremendous progress in the problem of simulating intelligence, for example, in data fitting, clustering, inference, and optimization. Meanwhile, AI techniques have been applied to many problems in physical layer communications, such as channel estimation, signal detection, CSI feedback, and so on. Emerging AI strategies, such as generative adversarial networks (GANs), deep Q-networks (DQNs), and self-attention mechanisms, are extending the possible application of AI to more complicated problems in various scenarios. In conclusion, AI techniques can help solve the problem of nonlinear mapping and bring new opportunities for applications of channel extrapolation in 6G.
In this article, we propose to utilize the emerging AI technologies to perform wireless channel extrapolation in the time domain, frequency domain, and space domain. First, in Table 1, we summarize the similarities, causes, challenges, and methods of channel extrapolation in the three domains. Then, focusing on the electromagnetic wave propagation characteristics, opportunities for combining channel extrapolation with AI techniques in every domain are introduced. We also propose a strategy of cross-domain extrapolation based on TL for the first time. The parameters of the self-attention model are trained by the time-domain channel extrapolation data. Then, they can be used as initial parameters to train the space-domain extrapolation model. The cross-domain strategy can speed up the model training process of the space-domain extrapolation and achieve a low loss. Finally, we provide several key research issues for AI-based channel extrapolation for 6G systems.
Table 1 A summary of channel extrapolation in the time domain, frequency domain, and space domain.
High-mobility communications become a typical usage scenario for the 2030 intelligent information society [1]. In the scenario, frequent channel estimation consumes too many system resources because the CSI tends to be out of date in a short time period. The traditional channel estimations, such as the linear minimum mean-squared error (LMMSE), cannot adapt to the case of high-speed movement. The SCP provides a theoretical basis for time-domain channel tracking and extrapolation. The SCP characterizes the continuous and smooth evolution of channel multipath small-scale parameters in the time domain [3]. In Figure 2(a), we show the power delay profile (PDP) with different user locations. It can be seen that a mobile user experiences a similar scattering environment in a local area. Therefore, time-domain channel extrapolation can use previous CSI to infer the future CSI as the user moves. However, as the moving speed increases, the channel difference between adjacent time slots becomes more significant, and the challenge of time-domain channel extrapolation increases. Recently, AI-based time-domain channel extrapolation methods have shown promise and are worthy of attention.
Figure 2 (a) The PDP with different user locations from the 3D ray-tracing software Wireless InSite and (b) the model architecture of CPcGAN. PDP: power delay profile.
The authors of [4] combine a recurrent neural network (RNN) with the idea of a sliding window to design a sliding bidirectional gated recurrent unit (SBGRU) structure to track the time-varying fading channel. The simulation results show that the SBGRU approach outperforms both the least-square (LS) and LMMSE methods. In [5], the authors propose to utilize a convolutional neural network (CNN) and a boundary equilibrium GAN (BEGAN) to infer a future DL-CSI by the previous UL-CSI. The GAN as a generative model provides a solution to achieve data transformation among different subspaces. The GAN contains a generator model and a discriminator model. The generator model transforms input data from the original data distribution to the generated data distribution, and the discriminator model computes the distribution divergence between the generated data and desired data.
In fact, a wireless channel is composed of multiple propagation paths, and each path is described by amplitude, delay, angle, Doppler frequency shift, and so on. Therefore, a wireless channel has multidimensional features. It is difficult to define an accurate optimization direction by a loss function. Furthermore, from the CSI perspective, the extrapolation of the wireless channel should be a structured learning task. The values of the CSI do not exist independently, and they should be considered globally. As shown in Figure 2(b), the GAN can utilize the discriminator network to evaluate the extrapolation quality of the overall CSI. Hence, a GAN is a promising way to achieve channel extrapolation compared to a regular deep neural network (DNN) that uses the MSE as a loss function. In [6], the authors propose an architecture of channel extrapolation based on a conditional GAN (CPcGAN), which is displayed in Figure 2(b). Compared with the BEGAN architecture, the CPcGAN does not need to optimize network parameters in the extrapolation stage. Hence, it is more suitable for time-varying channel extrapolation.
In FDD massive MIMO systems, many system overheads are caused, such as DL pilots and UL feedback, because channel reciprocity cannot be utilized directly. Enabling FDD ultramassive MIMO based on the UL-CSI through channel extrapolation is one of the most promising methods. Many AI-based approaches have emerged. Moreover, both millimeter-wave (mmWave) and THz communications are key technologies of current research. Increasingly more frequency bands will be deployed and coexist in the future, ranging from sub-6 GHz to 10 THz. In multiband parallel communication systems, it is possible to use the channel information extracted from one frequency band to assist the link establishment of the other band. However, the frequency separation between bands under consideration is large, such as sub-6 GHz and mmWave, and many channel feature variations must be considered. Therefore, it isn’t easy to directly extrapolate the full CSI as in DL-CSI extrapolation. Still, it is possible to extrapolate the channel parameters. Considering the different system architectures, we divide frequency-domain channel extrapolation into two cases: UL-to-DL extrapolation for a standalone FDD system and low-to-high frequency extrapolation for a multiband parallel system.
In FDD massive MIMO systems, the UL and DL bands are separated, and the duplex spacing of bands is almost always much larger than the channel coherence bandwidth. In [2], the simulation results show that the extrapolation range of conventional LS and LMMSE is the order of only one coherence bandwidth. Hence, researchers are trying to find a breakthrough to realize the reciprocity of FDD UL and DL channels. In [7], the authors find that the delays and angles between the UL and DL channels are frequency independent in an FDD system; that is, they are almost equal. This means that the difference between the UL and DL channels mainly lies in the complex gain of each propagation path. The partial reciprocity creates an opportunity to extrapolate the DL-CSI using the UL-CSI, which only needs to be revised for each complex gain.
Some works have attempted to use advanced AI techniques to establish the mapping relationship between UL and DL channels, which achieves a satisfactory performance compared to traditional methods. The authors of [8] demonstrate that a CNN can extrapolate the DL-CSI by the UL-CSI from actual massive MIMO channel measurement data. UL-to-DL frequency extrapolation presents formal similarities to time-domain extrapolation. Hence, CPcGAN is suitable for time-domain or UL-to-DL frequency-domain extrapolation.
In Table 2, we provide the normalized MSE (NMSE) results of UL-to-DL channel extrapolation. The number of antennas is 64. The UL frequency is 3.4 GHz, and the frequency separations are 30 kHz, 120 kHz, 240 kHz, 10 MHz, 20 MHz, and 100 MHz, respectively. The UL-CSI is analyzed using eight convolutional layers with kernel sizes of 3 in the CNN. The output features are of sizes 16, 64, 128, 512, 128, 64, 16, and 2, respectively. All but the last layers are activated by leaky rectified linear unit (ReLU) activation functions. The network structure of CPcGAN is only modified from 36 × 7 in [6] to 64 × 1. When the frequency spacing between the UL and DL is more than 10 MHz, the LMMSE is invalid. AI-based UL-to-DL extrapolation can work effectively with bigger frequency gaps than the LMMSE. It is also tricky for AI-based approaches to achieve CSI extrapolation when the frequency spacing is 100 MHz. Hence, the extrapolation methods must be considered at the elaborate channel parameter level for large frequency separations.
Table 2 The NMSE comparison of LMMSE, CNN, and CPcGAN at various frequency separations for UL-to-DL channel extrapolation.
Multiband coexistence is an inevitable trend with mmWave and future THz system deployments, but the high-frequency signal will be more sensitive to blockages than the sub-6 GHz band. Besides, the channel estimation overhead of the sub-6 GHz band is also low because the number of antennas is few, and the system is fully digital. Unlike UL-to-DL channel extrapolation, the number of antennas often differs between low-frequency and high-frequency systems, resulting in different angular resolutions in beamforming. Partial reciprocity between low- and high-frequency channels does not necessarily exist, so utilizing sub-6 GHz CSI to extrapolate mmWave CSI directly is unrealistic. Therefore, two key questions need to be addressed: What useful information about an mmWave channel can be extrapolated from sub-6 GHz CSI, and how does one extrapolate it?
In [9], the authors propose a CS-based mmWave beam selection method, called the structured logit weighted-simultaneous orthogonal matching pursuit (SLW-SOMP). The sub-6 GHz CSI is used as the weighting of a logit weighted-orthogonal matching pursuit algorithm. The authors of [10] prove that the mapping functions between a sub-6 GHz channel and an optimal mmWave beam, and a sub-6 GHz channel and the mmWave blockage status are existent, respectively. DNN is demonstrated as an effective mathematical tool for learning mapping functions. We consider sub-6 GHz assisted mmWave blockage status and beam extrapolation from the channel propagation characteristics. In [11], we find an exciting diffraction phenomenon: the fluctuation range of the received power for a user terminal is frequency dependent, and the fluctuation will increase with amplitude before the blockage occurs. Accordingly, we propose a long-range blockage status extrapolation method for mmWave systems by utilizing the sub-6 GHz blockage feature. Simulation results show that the proposed method greatly increases the prediction range of the blockage.
To realize a mmWave beam extrapolation that can meet the performance requirements of 6G systems, the discrepancy between sub-6 GHz and mmWave channels must be considered. Analyzing the actual channel measurements of [12], two interesting phenomena can be found. (1) In the line-of-sight (LOS) scenario, the direction of the strongest beam is consistent between the sub-6 GHz and mmWave channels. Still, there is a slight deviation in the angle. (2) In the non-LOS scenario, the direction of the strongest beam is inconsistent between sub-6 GHz and mmWave channels, but the direction of the mmWave strongest beam is one of the residual path directions in the sub-6 GHz channel. In Figure 3, we give the power angular spectrum (PAS) at 3.5 and 28 GHz to further display the phenomenon. The optimal beam direction in the mmWave band is inconsistent with the sub-6 GHz band. Still, it appears in the sub-6 GHz suboptimal beam direction area, with only a small gap from the suboptimal direction. Inspired by this, we propose a feasible idea that allows AI algorithms to intuitively compare the differences between sub-6 GHz and mmWave channels and extrapolate a beam set for a mmWave beam sweep.
Figure 3 The basic idea of the DRL-DBS strategy and the PAS from Wireless InSite. PAS: power angular spectrum; DRL-DBS: deep reinforcement learning-based dynamic beam selection; QN: Q-network.
Figure 3 shows the flow of the deep reinforcement learning (DRL)-based dynamic beam selection (DRL-DBS) method. DRL techniques could interact with the wireless environment to analyze the changeable wireless channel, and the Q-network (QN) will be continuously updated as users move. Therefore, DRL, as an adaptive AI algorithm, will be better at dealing with the DBS problem than supervised learning techniques with fixed network parameters. We assume that the antennas in the sub-6 GHz and mmWave bands are colocated. First, we extract the angle information by multiplying the sub-6 GHz CSI with a discrete Fourier transform (DFT) matrix, where the angular direction of the DFT matrix is consistent with the mmWave beam codebook. We define the peak index on the extracted angle information. The index i is called the peak index, which needs to satisfy ${[}{\boldsymbol{p}}_{s}{]}_{i}\,{>}\,{[}{\boldsymbol{p}}_{s}{]}_{{i}{-}{1}}$ and ${[}{\boldsymbol{p}}_{s}{]}_{i}\,{≥}\,{[}{\boldsymbol{p}}_{s}{]}_{{i} + {1}}$, where ${\boldsymbol{p}}_{s}$ is the extracted angle information of the sub-6 GHz band. We set three beam sweep areas according to the peak indexes. The first two are located around the largest two peak indexes in power of the sub-6 GHz band. The third beam search area’s location can appear at any possible peak index. The size of each beam sweep area and the location of the third area need to be learned by multiple sets of DRL actions we preset. The angle information of the sub-6 GHz and mmWave channels is also the QN’s input, and the QN’s output is the Q-value of all actions. We select an action with the largest Q-value among all actions as the optimal action. The peak index of the sub-6 GHz channel determines the starting point of each index area, and the optimal action selects the size of each area. Therefore, three specific beam index areas are determined. Denote ${N}_{f}$ as the sum of the codewords’ number in all beam index areas. The union of three beam index areas is the final beam sweep set ${F}_{\text{bs}}$. After performing the mmWave beam sweep on the set, the BS selects the optimal beam index for downlink mmWave data transmission from the sweep results.
We define the reward function as the instantaneous achievable rate and consider the overhead of beam sweeping. Hence, the reward function in user location i is formulated as \begin{align*}{r}_{i} = & {\left\{{1}{-}\frac{\left[{{\left\vert{{F}_{\text{bs}}}\right\vert}_{i} + {\xi}\left({{N}_{{f},{i}}{-}{\left\vert{{F}_{\text{bs}}}\right\vert}_{i}}\right)}\right]{T}_{b}}{{T}_{m}}\right\}} \\ & {\times}\,\frac{1}{{K}_{m}} \mathop{\sum}\limits_{{k} = {1}}\limits^{{K}_{m}}{{\log}_{2}}\left({{1} + \frac{{\left\vert{{\bf{h}}_{{m},{i}}^{H}\left[{k}\right]{\bf{f}}_{i}}\right\vert}^{2}{P}_{{m},{i}}}{{\sigma}_{{m},{i}}^{2}}}\right) \tag{1} \end{align*} where ${K}_{m}$ is the number of subcarriers. The penalty factor ${\xi}$ is utilized to avoid overlapping among multiple subareas. Denote ${T}_{m}$ as the duration of one time slot (coherence block) and ${T}_{b}$ as the overhead of a single beam sweep. Moreover, ${\bf{h}}_{m}$ and ${\bf{f}}$ represent the mmWave channel and selected codeword vector, respectively. Denote ${P}_{m}$ and ${\sigma}_{m}^{2}$ as the power of the transmitted signal and additive noise, respectively.
In Figure 4, we fix the signal-to-noise ratio (SNR) of the sub-6 GHz channel as 30 dB and evaluate the average achievable rate (AAR) at different SNRs of the mmWave channel. The AAR is defined as \begin{align*}{\text{AAR}} = & \frac{1}{{N}_{u}}\mathop{\sum}\limits_{{i} = {1}}\limits^{{N}_{u}}{\frac{1}{{K}_{m}}}\left({{1}{-}\frac{{N}_{{b},{i}}{T}_{b}}{{T}_{m}}}\right) \\ & {\times}\,\mathop{\sum}\limits_{{k} = {1}}\limits^{{K}_{m}}{{\log}_{2}}{\left({1} + \frac{{\left\vert{{\bf{h}}_{{m},{i}}^{H}\left[{k}\right]{\bf{f}}_{i}}\right\vert}^{2}{P}_{{m},{i}}}{{\sigma}_{{m},{i}}^{2}}\right)} \tag{2} \end{align*}
Figure 4 The AARs of various mmWave beam extrapolation methods at different SNRs of the mmWave channel. AAR: average achievable rate; SNR: signal-to-noise ratio; ExS: exhaustive search.
where ${N}_{u}$ is the number of users. Denote ${N}_{b}$ as the number of beam sweeps. The mmWave and sub-6 GHz systems have 64 and eight antennas, respectively. The results of the exhaustive search (ExS) approach, the SOMP algorithm [9], the SLW-SOMP algorithm [9], and the DNN-based beam prediction approach [10] are also offered for comparison. The upper bound of the AAR is calculated utilizing the optimal beamforming vector in the mmWave beam codebook. The performance of the DRL-DBS method is superior to the other approaches and is closest to the upper bound. This demonstrates the superiority of DRL-based dynamic beam extrapolation.
For time-domain extrapolation, the AI algorithm uses the CSI of time slot t − 1 to infer the CSI of time slot t. For frequency-domain extrapolation, the CSI of frequency ${f}_{u}$ is utilized to infer the CSI of frequency ${f}_{d}$. In massive MIMO systems, the RF chains are connected to the antennas through a fully or partially connected structure. The number of RF chains is much smaller than the number of antennas. The limited number of RF chains has to connect to the active antennas in turn for achieving complete channel estimation. Even without considering energy consumption, the resulting overhead for pilot and feedback increases with the number of antennas. Hence, the channel estimation of an ultramassive antenna array will cause a huge overhead in future 6G systems, which means that obtaining the CSI for time slot t − 1 or frequency ${f}_{u}$ will also bring a significant burden to the system. If the antennas of a massive antenna array are divided into two sets—the selected antenna set and the desired antenna set—space-domain channel extrapolation aims to utilize the CSI on the selected antenna set to infer the CSI on the desired antenna set. Therefore, only the CSI corresponding to the antennas in the selected antenna set needs to be estimated by pilots, which can significantly reduce the pilot and feedback overhead in various multiantenna technologies.
The authors of [13] try to perform space-domain channel extrapolation by linear regression and support vector regression in machine learning. The numerical results demonstrate the capacity of the AI algorithm in space-domain channel extrapolation. However, many existing channel measurements for massive MIMO have shown that the spatial nonstationarity of the channel is significant [14]. The spatial nonstationarity means that some propagation paths are only visible to parts of the antennas of a massive antenna array. In other words, the larger the separation between antenna locations, the greater the disagreement among channels, such as the number and angle of multipaths. Therefore, the positional relationship between the antennas needs to be considered to improve the space-domain extrapolation performance for 6G systems.
For a CNN, a convolution kernel with a fixed size has a tough time fitting changeable visibility regions of the spatial nonstationarity channel. For an RNN, it is challenging to memorize the CSI information of distant antennas in ultramassive MIMO systems. Self-attention can correlate different positions of the CSI sequence and enable further parallelization. Meanwhile, the position embedding can keep the positional relationship between the antennas. Hence, we propose a space-domain channel extrapolation based on self-attention for the first time, called a channel transformer (CT). The self-attention mechanism is shown in Figure 5. The input features are converted into three vectors of query ${\bf{q}}$, key ${\bf{k}}$, and value ${\bf{v}}$ through three learnable matrices: Wq, Wk and Wv. The output is computed as a weighted sum of all values ${\bf{v}}$, where the weight ${a}_{{m},{n}}$ assigned to each value vn is calculated by a dot product of the query qm with the corresponding key kn. Considering vn as the high-level feature of the CSI on the nth antenna, self-attention can learn the relevance between each antenna CSI.
Figure 5 Spatial nonstationarity, the self-attention mechanism, and the CT.
In fact, the CSI of the desired antennas is unknown for space-domain channel extrapolation. Hence, it is hard to learn the real relevance between the CSI of the desired antennas and the selected antennas. The time-domain extrapolation utilizes the CSI of the N antennas at time slot t −1 to infer the CSI at time slot t. If the self-attention model is used for time-domain extrapolation, the relevance between various antennas can also be learned. To keep the consistency of the data in the training and testing stage, we first learn the relevance between various antenna CSIs through time-domain channel extrapolation. Then, the model parameters learned by the time-domain extrapolation are used as the initial model parameters of the space-domain extrapolation. Finally, these parameters will be fine-tuned by the space-domain extrapolation data. In the fine-tuning stage, the initial CSI of the desired antennas is computed by linear interpolation.
Figure 6(a) shows the NMSE of test data versus epoch. The x-axis values are the number of training epochs. In our simulation, a uniform linear array with 64 antennas is adopted, i.e., N = 64. The antennas for channel estimation are 8, 16, and 32, uniformly selected from all antennas. With the increase in selected antennas, the NMSE has steadily dropped. TL brings two benefits to space-domain extrapolation. 1) At the beginning of fine-tuning, the NMSE of the CT with TL is much lower than that of the CT without TL, which means that TL can speed up the training process of space-domain extrapolation. 2) After the fine-tuning results are stable, the CT with TL can achieve a lower NMSE than the CT without TL. Figure 6(b) shows the NMSE of the LMMSE, fully connected (FC) network, CNN, and CT methods. The FC layers have 128, 256, 256, 512, 256, 256, 128, and 128 nodes, respectively. All but the last layers are activated by leaky ReLU activation functions. The structure of the CNN is consistent with that used in UL-to-DL frequency extrapolation. The CT outperforms the other strategies, so the self-attention mechanism with TL is very suitable for channel extrapolation of ultramassive antenna arrays in future 6G systems.
Figure 6 The NMSE performance analysis of space-domain channel extrapolation. (a) The NMSE of test data versus epoch with 8, 16, and 32 selected antennas. “NTL” means that each layer of the model is initialized by default, without TL. (b) The NMSE comparison of LMMSE, FC, CNN, CT-NTL, and CT with 8, 16, and 32 antennas for space-domain channel extrapolation. FC: fully connected.
The current channel extrapolation achievements have shown that AI-assisted channel extrapolation is very advantageous. To release the full potential of AI-based channel extrapolation, the following challenges and open issues deserve further research.
For future 6G systems, higher mobile speeds, wider frequency bands, and larger antenna arrays have become a predictable evolutionary trend. With the emergence of various complex application scenarios, multidomain joint channel extrapolation will become an effective scheme to reduce channel estimation overhead. For example, the DL-CSI of all antennas is inferred from the UL-CSI of partial antennas, which utilizes both frequency-domain and space-domain channel extrapolation. When considering the high-speed mobile scenario, even time–frequency–space three-domain joint channel extrapolation is required to reduce the necessary multidimensional channel resources.
The application of AI algorithms in wireless communication is generally faced with the problem of poor algorithm robustness. However, there are many model knowledge-based approaches in the wireless communication field that are often robust. How to efficiently combine model- and data-driven methods is the focus of future channel extrapolation research. For example, for channel extrapolation based on parameter extraction, the iterative estimation algorithm is unfolded in the form of a DNN, and the model’s parameter space is expanded by adding learnable parameters. Data knowledge can optimize the learnable parameters to improve the estimation efficiency.
A wireless channel is determined by the physical environment because the propagation of electromagnetic waves is mainly affected by scatterers in the environment. As many mobile terminals, such as those in vehicles, are equipped with various sensors, different forms of environmental information can be obtained, for example, location coordinates by GPS, radar echoes, visual images by cameras, and point clouds by lidar. It is a potential solution to extract specific higher level environmental features for specific-domain channel extrapolation by AI algorithms, such as graph neural networks.
Although AI-based channel extrapolations are excellent solutions, there is little research on their expressive power of function representation. Most of the current research still relies on hand-crafted AI models. It is necessary to conduct a theoretical analysis to study the relationship between the expressive power of AI models and the model architecture, which can help design AI-based channel extrapolation models and achieve a compromise between fitting error and generalization error.
The strategy of the cross-domain training provides a possibility of meta-learning in channel extrapolation, which can train adaptive AI models at different propagation conditions for 6G intelligent BSs. Furthermore, unsupervised learning is worth considering for channel extrapolation in future work as it does not need to collect data labels. The authors of [15] design a flexible loss function through achieved rate, enabling an unsupervised training method. This can motivate the development of channel parameter extrapolation techniques. Also, various resource overheads need to be optimized. For example, dynamically adjusting the numbers and positions of the selected antennas will reduce feedback and improve performance in space-domain extrapolation. Meanwhile, by exploiting a dynamic neural network with various dynamic strategies, different channels can be processed by different network components, achieving a balance between model optimization and computing resource overhead.
AI-based channel extrapolations improve the environmental adaptability of the physical layer and achieve a high degree of embedded AI in the next generation of communications networks. In this article, we summarize the recent development of AI-based channel extrapolation and describe several novel and efficient AI-based extrapolation architectures. Specifically, for time-domain channel extrapolation, a conditional GAN is suitable for a high-speed dynamic time-varying channel. For frequency-domain extrapolation from low frequency to high frequency, DRL can adjust the policy according to the changes in the wireless channel environment. For space-domain channel extrapolation, self-attention can learn the relevance between various channels on different antennas. The cross-domain extrapolation strategy based on TL can accelerate the training process of the AI model and improve the extrapolation accuracy. However, we admit that the applications of emerging AI techniques in channel extrapolation are in their infancy with various open research issues. Therefore, we have introduced several potential research issues on channel extrapolation. Combined with model and environmental knowledge in the wireless channel field, more multidomain joint channel extrapolation methods that benefit from state-of-the-art AI technologies deserve further research.
The work is supported by the National Science Fund for Distinguished Young Scholars (61925102), the National Natural Science Foundation of China (92167202), the National Natural Science Foundation of China (62101069 and 62031019), the National Natural Science Foundation of China (62201087), and the Beijing University of Posts and Telecommunications-China Mobile Communications Group Co., Ltd. Joint Innovation Center. The corresponding author of this article is Jianhua Zhang.
Zhen Zhang (zhenzhang@bupt.edu.cn) received his B.S. degree in communication engineering from the China University of Petroleum (East China), in 2017, where he is currently pursuing his Ph.D. degree in information and communication engineering with the Beijing University of Posts and Telecommunications, Beijing 100876, China. His current research interests include channel modeling, over-the-air testing, and deep learning.
Jianhua Zhang (jhzhang@bupt.edu.cn; www.zjhlab.net) received her Ph.D. degree in circuits and systems from the Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China, where she is now a professor. She has published more than 200 articles in referred journals and conferences. Her current research interests include 5G and 6G, artificial intelligence, and massive multiple-input, multiple-output and millimeter-wave channel modeling.
Yuxiang Zhang (zhangyx@bupt.edu.cn) received his B.S. degree in electronic information engineering from Dalian University of Technology in 2014 and his Ph.D. degree from the Beijing University of Posts and Telecommunications (BUPT) in 2020. From 2018 to 2019, he was a visiting scholar with the University of Waterloo. He is now a postdoctoral researcher at BUPT, Beijing 100876, China. His current research interests include channel modeling, massive multiple-input, multiple-output, beamforming, and over-the-air testing.
Li Yu (li.yu@bupt.edu.cn) received his B.S. degree from Tianjin University in 2011 and his M.S. degree from the Beijing University of Posts and Telecommunications (BUPT) in 2014. Since 2018, he has been pursuing his Ph.D. degree at BUPT, Beijing 100876, China. His current research interests include channel modeling, channel prediction, massive multiple-input, multiple-output, and machine learning.
Guangyi Liu (liuguangyi@chinamobile.com) received his Ph.D. degree from the Beijing University of Posts and Telecommunications. He is currently a fellow and 6G lead specialist at China Mobile Research Institute, Beijing 100053, China, where he is in charge of wireless technology research and development, including 5G and 6G.
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Digital Object Identifier 10.1109/MVT.2023.3234169