Channel estimation for very large scale multiple-input multiple-output in terahertz frequency band

Abstract

The embodiment of the invention discloses equipment, a method, a device and a computer readable storage medium for channel estimation of ultra-large scale multiple-input multiple-output (UM-MIMO) in a terahertz (THz) frequency band. The method includes obtaining a first codebook matrix associated with a first antenna arrangement at a first device and a second codebook matrix associated with a second antenna arrangement at a second device, where a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and wherein the second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; and characterizing a channel between the first device and the second device at least based on the first codebook matrix and the second codebook matrix.

Description

Technical Field

[0001] Various example embodiments of the present disclosure generally relate to the field of telecommunications, and in particular, to methods, devices, apparatuses, and computer-readable storage media for channel estimation for ultra-massive multiple-input multiple-output (UM-MIMO) in the terahertz (THz) band. Background Art

[0002] In recent years, with rich bandwidths from multi-GHz to even THz, the THz spectrum in the range from 0.1 to 10 THz has attracted a surge of attention in academia and industry. THz wireless communication has the ability to support high data rates of terabits per second and is regarded as a candidate pillar for the sixth-generation (6G) wireless network. Summary of the Invention

[0003] Generally, example embodiments of the present disclosure provide a solution for channel estimation for UM-MIMO in the THz band.

[0004] In a first aspect of the present disclosure, a first device is provided. The first device includes: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the first device to at least: obtain a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at a second device, where a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other at a predetermined distance, and where a second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other at a predetermined distance; and characterize a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

[0005] In a second aspect of the present disclosure, a method is provided. The method includes: obtaining a first codebook matrix associated with a first antenna arrangement at a first device and a second codebook matrix associated with a second antenna arrangement at a second device, where a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other at a predetermined distance, and where a second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other at a predetermined distance; and characterizing a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

[0006] In a third aspect of the present disclosure, an apparatus is provided. The apparatus includes: means for obtaining a first codebook matrix associated with a first antenna arrangement at a first device and a second codebook matrix associated with a second antenna arrangement at a second device, wherein a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and wherein a second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; and means for characterizing a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

[0007] In a fourth aspect of the present disclosure, a computer-readable medium is provided. The computer-readable medium includes instructions stored thereon for causing an apparatus to at least perform the method according to the second aspect.

[0008] It should be understood that the present invention content section is not intended to identify key or essential features of embodiments of the present disclosure, nor is it intended to be used to limit the scope of the present disclosure. Through the following description, other features of the present disclosure will become readily understood. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Embodiments of the present disclosure are presented in the sense of examples, and their advantages are explained in more detail below with reference to the accompanying drawings.

[0010] Figure 1 An example communication environment is shown in which example embodiments of the present disclosure can be implemented;

[0011] Figure 2 An example diagram of an antenna arrangement according to some example embodiments of the present disclosure is shown;

[0012] Figure 3 Example results of channel estimation by using different algorithms according to some example embodiments of the present disclosure are shown;

[0013] Figure 4 A flowchart of a method implemented at a first device according to some example embodiments of the present disclosure is shown;

[0014] Figure 5 A simplified block diagram of a device suitable for implementing example embodiments of the present disclosure is shown; and

[0015] Figure 6 A block diagram of an example computer-readable medium according to some example embodiments of the present disclosure is shown.

[0016] Throughout the drawings, the same or similar reference numerals may denote the same or similar elements. DETAILED DESCRIPTION

[0017] The principles of the present disclosure will now be described with reference to some example embodiments. It should be understood that these embodiments are described for illustrative purposes only and help those skilled in the art understand and implement the present disclosure, without implying any limitation on the scope of the present disclosure. The embodiments described herein can be implemented in various ways other than the ways described below.

[0018] In the following description and claims, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0019] References in the present disclosure to "one embodiment", "an embodiment", "example embodiment", etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but not every embodiment necessarily includes that particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is considered within the knowledge of those skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

[0020] It should be understood that although the terms "first", "second", etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, without departing from the scope of the example embodiments, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element. As used herein, the term "and / or" includes any and all combinations of one or more of the listed terms.

[0021] As used herein, "at least one of the following: <list of two or more elements>" and "at least one of <list of two or more elements>" and similar phrases, where the list of two or more elements is joined by "and" or "or", means at least any one of the elements, or at least any two or more of the elements, or at least all of the elements.

[0022] As used herein, unless expressly stated otherwise, performing a step "in response to A" does not mean that the step is performed immediately after A occurs, but may include one or more intermediate steps.

[0023] The terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the example embodiments. As used herein, unless the context clearly dictates otherwise, the singular forms "a", "an" and "the" are also intended to include the plural forms. It will be further understood that the terms "comprise", "comprising", "have", "has", "include" and / or "including", when used herein, specify the presence of the stated features, elements and / or components, etc., but do not preclude the presence or addition of one or more other features, elements, components and / or combinations thereof.

[0024] As used in this application, the term "circuit" may refer to one or more or all of the following: (a) Only hardware circuit implementations (such as implementations only in analog and / or digital circuits); and (b) Combinations of hardware circuits and software, for example (if applicable): (i) Combinations of analog and / or digital hardware circuits and software / firmware; and (ii) Any portions of (a plurality of) hardware processors (including (a plurality of) digital signal processors), software, and (a plurality of) memories that work together to cause a device such as a mobile phone or a server to perform various functions; and (c) (A plurality of) hardware circuits and / or (a plurality of) processors, such as (a plurality of) microprocessors or a part of (a plurality of) microprocessors, which require software (e.g., firmware) for operation, but the software may not be present when not required for operation.

[0025] This definition of circuit applies to all uses of the term in this application (including any claims). As another example, as used in this application, the term circuit also covers implementations of only hardware circuits, or processors (or a plurality of processors), or a part of a hardware circuit or a processor and its (or their) additional software and / or firmware. For example and if applicable to a particular claim element, the term circuit also covers a baseband integrated circuit or a processor integrated circuit for a mobile device or a similar integrated circuit in a server, a cellular network device, or other computing or network devices.

[0026] As used herein, the term "communication network" refers to a network that complies with any suitable communication standard, such as New Radio (NR), Long Term Evolution (LTE), LTE-Advanced (LTE-A), Wideband Code Division Multiple Access (WCDMA), High Speed Packet Access (HSPA), NarrowBand Internet of Things (NB-IoT), etc. In addition, the communication between the terminal device and the network device in the communication network can be performed according to any suitable generation of communication protocol, including but not limited to the first generation (1G), second generation (2G), 2.5G, 2.75G, third generation (3G), fourth generation (4G), 4.5G, fifth generation (5G) communication protocol and / or any other protocol currently known or to be developed in the future. Embodiments of the present disclosure can be applied in various communication systems. Given the rapid development of communication, there will of course also be future types of communication technologies and systems in which the present disclosure can be implemented. The scope of the present disclosure should not be regarded as limited to the foregoing systems.

[0027] As used herein, the term "network device" refers to a node in a communication network through which a terminal device accesses the network and receives services therefrom. The network device may refer to a base station (BS) or an access point (AP), for example, Node B (NodeB or NB), evolved Node B (eNodeB or eNB), NR NB (also known as gNB), Remote Radio Unit (RRU), Radio Head (RH), Remote Radio Head (RRH), relay, Integrated Access and Backhaul (IAB) node, low power node (such as femto, pico), Non-Terrestrial Network (NTN) or non-terrestrial network device (such as satellite network device, Low Earth Orbit (LEO) satellite and Geostationary Earth Orbit (GEO) satellite, aircraft network device, etc.), depending on the terminology and technology applied. In some example embodiments, the Radio Access Network (RAN) split architecture includes a Centralized Unit (CU) and a Distributed Unit (DU) at the IAB donor node. The IAB node includes a Mobile Terminal (IAB-MT) part, which behaves similar to a UE towards the parent node, while the DU part of the IAB node behaves similar to a base station towards the next-hop IAB node.

[0028] The term "terminal device" refers to any terminal device capable of wireless communication. By way of example and not limitation, a terminal device may also be referred to as a communication device, user equipment (UE), subscriber station (SS), portable subscriber station, mobile station (MS), or access terminal (AT). Terminal devices may include, but are not limited to, mobile phones, cellular phones, smart phones, IP voice (VoIP) phones, wireless local loop phones, tablet computers, wearable terminal devices, personal digital assistants (PDAs), portable computers, desktop computers, image capture terminal devices such as digital cameras, game terminal devices, music storage and playback appliances, in-vehicle wireless terminal devices, wireless endpoints, mobile stations, laptop embedded devices (LEEs), laptop mounted devices (LMEs), USB dongles, smart devices, wireless customer premise equipment (CPEs), Internet of Things (IoT) devices, watches or other wearable devices, head-mounted displays (HMDs), vehicles, drones, medical devices and applications (e.g., remote surgery), industrial devices and applications (e.g., robots and / or other wireless devices operating in an industrial and / or automated processing chain environment), consumer electronic devices, devices operating on commercial and / or industrial wireless networks, etc. A terminal device may also correspond to the mobile terminal (MT) part of an IAB node (e.g., a relay node). In the following description, the terms "terminal device", "communication device", "terminal", "user equipment", and "UE" may be used interchangeably.

[0029] As described above, in recent years, the THz spectrum in the range from 0.1 to 10 THz has attracted a surge of attention from academia and industry. The ultra-wide bandwidth of THz wireless communication still comes at the cost of severe atmospheric attenuation, which brings high propagation losses and constraints on communication distance. However, the sub-millimeter wavelength of the THz band enables the deployment of UM-MIMO. By employing up to thousands of antennas, the sharp beams with strong beamforming gain generated can overcome the distance limitation problem.

[0030] Due to large reflection, scattering, and diffraction losses, the THz channel is sparse and consists of line-of-sight (LoS) paths and only a few non-line-of-sight (NLoS) paths. The THz multi-antenna channel suffers from limited multiplexing imposed by the number of multipaths rather than the number of antennas as in microwaves.

[0031] To enhance multiplexing, a wide-spacing multi-subarray (WSMS) antenna array arrangement is proposed. Hereinafter, the WSMS antenna array arrangement may also be referred to as a WSMS system or a WSMS architecture. Compared with a compact antenna array arrangement, the subarray spacing in the WSMS system is enlarged. In this way, additional propagation paths are created between the subarrays, which enables an additional multiplexing gain to be associated with the number of subarrays for both the UE side and the gNB side. For example, benefiting from the multiplexing gain due to the enlarged subarray spacing, the spectral efficiency of the WSMS architecture is much higher than that in the compact antenna array arrangement, e.g., 402% higher when the transmit power is equal to 15 dBm.

[0032] However, the benefits of the WSMS structure rely on accurate antenna-level channel state information (CSI). Since the enlarged subarray spacing in the WSMS structure extends the near-field propagation region, in the WSMS structure, channel estimation based on the plane wave assumption is no longer valid, and thus the spherical wave propagation between the subarrays needs to be considered. That is, due to the differences in channel propagation characteristics, current channel estimation methods may not be properly applied to the WSMS structure.

[0033] Therefore, in the case of applying the WSMS antenna array arrangement, a mechanism for channel estimation for UM-MIMO in the THz band is proposed in the present disclosure. The first device obtains a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at the second device, and characterizes the channel between the first device and the second device based at least on the first and second codebook matrices. The first antenna arrangement includes a first plurality of subarrays spaced apart from each other at a predetermined distance, and the second antenna arrangement includes a second plurality of subarrays spaced apart from each other at a predetermined distance.

[0034] On the one hand, the proposed solution presents a subarray-based sparse channel representation codebook for channel estimation applicable to the WSMS structure. On the other hand, two recovery algorithms are proposed to reduce the complexity of channel estimation and simultaneously improve the estimation accuracy.

[0035] Example embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0036] Figure 1 An example communication environment 100 in which example embodiments of the present disclosure may be implemented is shown. In the communication environment 100, a plurality of communication devices including a first device 110 and a second device 120 may communicate with each other.

[0037] In Figure 1In the examples, in some scenarios, the first device 110 may include a terminal device, and the second device 120 may include a network device that serves the terminal device. In other scenarios, the first device 110 may include a network device that serves the terminal device, while the second device 120 may include a terminal device.

[0038] It should be understood that Figure 1 the number of devices and their connections shown in are for illustrative purposes only and do not imply any limitation. The communication environment 100 may include any suitable number of devices configured to implement the example embodiments of the present disclosure.

[0039] In the following, for illustrative purposes, some example embodiments are described in the case where the first device 110 operates as a network device and the second device 120 operates as a terminal device. However, in some example embodiments, the operations described in connection with the network device may be implemented at the terminal device or other devices, and the operations described in connection with the terminal device may be implemented at the network device or other devices.

[0040] In some example embodiments, if the first device 110 is a network device and the second device 120 is a terminal device, the link from the second device 120 to the first device 110 is referred to as an uplink (UL), and the link from the first device 110 to the second device 120 is referred to as a downlink (DL). In the DL, the first device 110 is a transmitting (TX) device (or transmitter), and the second device 120 is a receiving (RX) device (or receiver). In the UL, the second device 120 is a TX device (or transmitter), and the first device 110 is an RX device (or receiver).

[0041] The communication in the communication environment 100 may be implemented according to any suitable communication protocol(s), including but not limited to cellular communication protocols of the first generation (1G), second generation (2G), third generation (3G), fourth generation (4G), fifth generation (5G), sixth generation (6G), etc., wireless local area network communication protocols such as Institute of Electrical and Electronics Engineers (IEEE) 802.11, and / or any other protocol known currently or to be developed in the future. In addition, the communication may utilize any suitable wireless communication technology, including but not limited to: code division multiple access (CDMA), frequency division multiple access (FDMA), time division multiple access (TDMA), frequency division duplexing (FDD), time division duplexing (TDD), multiple input multiple output (MIMO), orthogonal frequency division multiple access (OFDM), discrete Fourier transform spread OFDM (DFT-s-OFDM), and / or any other technology known currently or to be developed in the future.

[0042] Figure 2FIG. shows an example diagram of an antenna array arrangement 200 in accordance with some example embodiments of the present disclosure. For purposes of discussion, reference will be made to Figure 1 For example, the legend 200 will be discussed by using a first device 110 and a second device 120.

[0043] In some example embodiments, a first antenna arrangement on the Rx side (e.g., hereinafter, Rx may be referred to as the first device 110) may have a first plurality of sub-arrays spaced from each other at a predetermined distance. A second antenna arrangement on the Tx side (e.g., hereinafter, Tx may be referred to as the second device 120) may have a second plurality of sub-arrays spaced from each other at a predetermined distance. That is, both the Rx side and the Tx side may be arranged with WSMS antenna array arrangements.

[0044] It should be understood that the first antenna arrangement and the second antenna arrangement may have the same number or different numbers of sub-arrays. The predetermined distance between two adjacent sub-arrays in the first antenna arrangement may be the same as or different from the predetermined distance between two adjacent sub-arrays in the second antenna arrangement.

[0045] It should be understood that the predetermined distance may be set to any suitable value. For example, the predetermined distance may be 256λ, where λ is the wavelength.

[0046] As Figure 2 shown, the WSMS antenna array arrangement 200 may have four sub-arrays, namely sub-arrays 201 to 204, which are spaced from each other at a distance D. Each sub-array may be arranged with a plurality of antennas.

[0047] Channel estimation in a UM-MIMO system operating in millimeter-wave and THz frequencies may employ a compressed-sensing (CS)-based channel estimation method, which may utilize the channel sparsity in the spatial angular domain of the millimeter-wave and THz bands and reduce the overhead of beam training. The key point for determining the sparse channel representation may focus on finding the channel representation codebook.

[0048] In some example embodiments of the present disclosure, the first device 110 obtains a first codebook matrix associated with the first antenna arrangement at Rx and a second codebook matrix associated with the second antenna arrangement at TX.

[0049] For the WSMS antenna array arrangement, a sub-array-based codebook may be employed, which may be in units of each sub-array. The sub-array-based codebook may maintain a block-diagonal form, and a grid-of-beams (GoB) codebook may be deployed based on the sub-arrays in each block. It should be understood that single polarization is considered for the WSMS antenna array arrangement in the present disclosure, where two polarizations are not excluded.

[0050] Specifically, the first codebook matrix can be determined by associating a set of beam grid codebooks with each subarray from a first plurality of subarrays, and wherein the second codebook matrix can be determined by associating the set of beam grid codebooks with each subarray from a second plurality of subarrays.

[0051] In some embodiments, the diagonal blocks in the first codebook matrix correspond to respective sets of beam grid codebooks associated with each subarray from the first plurality of subarrays, and the diagonal blocks in the second codebook matrix correspond to respective sets of beam grid codebooks associated with each subarray from the second plurality of subarrays.

[0052] For example, at the Rx, the codebook can take virtual angles for each subarray from a fixed number N ar of sampling points, where N ar = N arx N arz represents the number of antennas on one subarray, where N arx and N arz represent the number of antennas on the x-axis and z-axis respectively.

[0053] The GoB codebook for the subarray on the Rx side can be expressed as: where each vector can have the form of For example, and

[0054] Defining the channel representation codebook matrix at the Rx (i.e., the first codebook matrix) is denoted as U Sr , with K r U GoB deployed on its diagonal to form a block-diagonal matrix for K r subarrays at the Rx, the first codebook matrix can be expressed as: U Sr = diag[U GoB ,..., U GoB , with dimensions of N r × N r , where N r = N ar × K r (2)

[0055] The channel representation codebook matrix at the Tx (i.e., the second codebook matrix) is denoted as U St , which can have a form similar to equation (2). That is, the first device 110 obtains the first codebook matrix U Sr and the second codebook matrix USt .

[0056] The subarray-based codebook can be more suitable for WSMS structures with non-uniformly distributed antennas and has much higher accuracy than the current GoB codebook.

[0057] Based at least on the above codebook matrix, the channel between the first device 110 and the second device 120 can be characterized as: H HSPM ≈U Sr ΛU St H (3) Where H HSPM represents the channel matrix with a hybrid spherical and plane wave (HSPM) channel model, which can enhance propagation modeling in the case of applying a WSMS antenna array arrangement, U Sr and U St represent the first codebook matrix and the second codebook matrix respectively, and Λ is the on-grid sparse channel matrix by taking each pair of columns between U Sr and U St as grid points, that is, each element of the on-grid matrix Λ can indicate the channel gain of the grid points. Hereinafter, the on-grid sparse channel matrix Λ can also be referred to as the channel gain matrix.

[0058] Then, the first device 110 can determine the on-grid matrix Λ to recover the channel.

[0059] In some example embodiments, two sparse recovery algorithms can be applied to channel recovery, namely, low-complexity split Tx and Rx estimation (STRE) and spatially correlated grid reduction estimation (GRE).

[0060] The STRE algorithm can separately divide the estimation of non-zero grid points into the Tx side and the Rx side. Through this algorithm, the search complexity is reduced from to approximately while the GRE algorithm further reduces the complexity of STRE based on the fact that non-zero grid points (or virtual angles) located on different subarrays may be close in the spatial domain.

[0061] For example, when the subarray spacing is equal to 256λ, the elevation angle difference of the LoS path between subarrays at a typical communication distance in the THz band of 10 m is approximately 1.5 degrees. The search complexity of the GRE algorithm is further reduced to approximately where K represents the number of subarrays.

[0062] In the case of applying the STRE recovery algorithm, the first device 110 can determine the non-zero grid points on the channel gain matrix Λ based at least on the channel representation codebook matrix and the received signal.

[0063] For the purpose of channel estimation, a beam training process is required to obtain channel observations. During training, both the Tx and Rx generate beams and transmit or receive pilot signals respectively. Each beam is generated from a pre-stored beam codebook and is constructed by tuning the phase shift values in the analog transmit beamforming and receive combining matrices. Due to the configuration of the WSMS structure, both the transmit beamforming and receive combining matrices can maintain a block-diagonal structure. After the Tx and Rx scan all beam combinations, the received signals can be collected and constructed for channel estimation. The received signal after the beam training process can be expressed as: Y = W H H HSPM F + N (4) where W and F represent the receive combining matrix and transmit beamforming matrix of the beam training respectively. W and F are aggregated at different time instances, and N refers to the received noise. Hereinafter, the receive combining matrix W can also be referred to as the first beamforming matrix, and the transmit beamforming matrix F can also be referred to as the second beamforming matrix.

[0064] It should be understood that the receive combining matrix W and transmit beamforming matrix F for the beam training process, as well as the block-diagonal codebook for sparse channel representation, can be specified in the RRC signaling to meet the requirements of channel estimation.

[0065] The process of the STRE recovery algorithm can be shown as follows: Table 1: Process of the STRE recovery algorithm

[0066] The input of the STRE algorithm (hereinafter also referred to as Algorithm 1) in Table 1 includes the received signal Y, the collected combining matrix W and transmit matrix F of the beam training (i.e., the first beamforming matrix and the second beamforming matrix), and the channel representation codebook matrix U Sr and U St (i.e., the first codebook matrix and the second codebook matrix). The non-zero grid points at the Rx and Tx are stored in Π r and Π t respectively, and Π r and Π r are initialized as empty sets.

[0067] In step 1, define B r = W H U Sr and B t = F H U St, the row positions of Λ are estimated for non - zero grid points. Specifically, y sumr can be calculated in row 2 of Table 1 as where "YB t " can also be referred to as the first weighted representation of the received signal. Due to the sparsity of Λ, s sumr = B r H y sumr is a sparse vector, and the non - zero positions in s sumr are related to the non - zero rows of Λ. Therefore, the positions of the non - zero rows of Λ can be determined by estimating the non - zero positions of s sumr .

[0068] Specifically, by setting y = y sumr , B = B r and the number of iterations I ∝ K r K t N p in row 4 of Table 1, an algorithm for estimating non - zero positions (shown in Table 2 below and also referred to as Algorithm 2 in the following text) can be used to complete the estimation of the non - zero rows of Λ collected in the set Π r .

[0069] Similarly, in step 2, the column positions of Λ are estimated for non - zero grid points. As shown in row 6 of Table 1, since the positions of the non - zero rows of Λ have been determined in the previous stage, using these rows is sufficient to determine the non - zero columns of Λ collected in Π t . Alternatively, without the constraint of the summation operation in row 6 of Table 1, the determination of the column positions of Λ can be independent of the row positions of Λ. Then, in step 3, the estimated A r and A t are first obtained in row 10 as and Then the channel gain matrix on the sparse grid is estimated in row 11 of Table 1 as Based on these estimated matrices, the channel matrix is finally recovered as Completing the STRE algorithm in Table 1.

[0070] For example, the process of estimating the non - zero positions of y sumr (Algorithm 2) can be shown as follows: Table 2: Process of Estimating Non - zero Positions

[0071] Based on the process shown in Table 2, the details of estimating the positions of non-zero grids using the received signal y and the measurement matrix B can be further illustrated. The correlation between the measurement matrix B and the residual vector r can be calculated first. The most correlated column index is denoted as n, which is regarded as the newly found grid index and is added to the grid set Π. The estimated signal on the grid specified by Π is calculated.

[0072] Then, the residual vector is updated by removing the influence of the non-zero grid points on the Rx side or the Tx side that have been estimated in the previous steps. By repeating these processes, the T index is selected as the estimated non-zero grid points on the Rx side or the Tx side.

[0073] Although the example in Table 1 shows the case of first determining the non-zero rows and then determining a set of non-zero columns based on the non-zero rows. It should be understood that a set of non-zero columns can also be determined before the non-zero rows or simultaneously with the determination of the non-zero rows. The example shown in Table 1 should not limit the scope of the present disclosure.

[0074] By using the STRE algorithm, the estimation of the Tx and Rx non-zero grid points can be split, which can reduce the search complexity. For example, the search complexity is reduced from to approximately

[0075] Regarding the GRE algorithm (which can also be referred to as Algorithm 3 hereinafter), the computational complexity can also be reduced by considering the spatial correlation between subarrays. As described above, when the subarray spacing is equal to 256λ, the elevation angle difference for the LoS path between two subarrays at a typical communication distance in the THz band of 10m is only about 1.5 degrees. Therefore, for the signals on the Rx side, the spatial angles for different subarrays are close in the WSMS channel. If the codebooks for each subarray can be considered separately, the positions of the non-zero grid points will be close across subarrays.

[0076] Therefore, the GRE algorithm can first calculate the positions of the non-zero grid points located in one subarray, which are saved as the reference grid. For the remaining subarrays, the grid search space is reduced by restricting the potential grids in the neighborhood of the reference grid to reduce the complexity. The value of the neighboring grids depends on the correlation between subarrays. More specifically, the value of the neighboring grids can expand with a larger subarray spacing and a smaller communication distance.

[0077] The process of the GRE algorithm can be as follows: Table 3: Process of the GRE algorithm

[0078] The grid reduction of the GRE algorithm operates in Steps 1 and 2 of Algorithm 1, which is detailed in Algorithm 3 and shown in Table 3. The input to the GRE algorithm includes the summed channel observations y sum , the sensing matrix Φ, the codebook U for the subarrays sub , the number of iterations I, the number of subarrays K, and the number of beams b for the subarrays. In Step 1 of Algorithm 1, these parameters are computed for the non-zero grid search in the row indices of Λ, where y sum = y sumr , Φ = W, U sub = U DFT , T = N p , K = K r and b = b r , where b r represents the number of beams for the subarrays at Rx. In Step 2 of Algorithm 1, these parameters are computed for the non-zero grid search in the column indices of Λ, where y sum = y sumt , Φ = F, U sub = U DFT , T = N p , K = K t and b = b t , where b t represents the number of beams for the subarrays at Tx.

[0079] For the k-th subarray, the GRE algorithm first obtains its sensing matrix Q in rows 2 and 3 of Table 3 respectively, where Q = Φ((k - 1)*N a + 1:kN a , (k - 1)*b + 1:kb) and the observation vector y sumk = y sum ((k - 1)*b + 1:kb). For the first subarray, when k = 1, the non-zero grid points associated with U sub are directly estimated and recorded as the reference grid in Π1. Specifically, B = Q H U sub is computed and Algorithm 2 is deployed to obtain the estimated grid in Π1. If k > 1, then can be constructed by selecting the neighboring q grids for each point in row 8 of Table 3 as the potential search grid. Thus, the potential search grid for each subarray is dynamically updated according to the estimated grid points in the previous subarray. Alternatively, the potential search grid can be a fixed set determined according to the reference grid Then, is computed and Algorithm 2 is deployed to obtain the estimated grid in Π1. Finally, in row 12 of Table 3, according to the index of the subarray, in Π kThe positions in can be transformed into grid positions for the entire array and saved in Π. Specifically, by numbering the sub-arrays and the grid positions of each sub-array, the positions in Π k are one-to-one related to the points in Π.

[0080] In this way, compared with the STRE algorithm, the search complexity can be further reduced by using the GRE algorithm. For example, the search complexity can be reduced to about where K represents the number of sub-arrays.

[0081] Since the positions of the non-zero grid points are determined, the first device 110 can further determine the channel gain at each non-zero grid point and thus recover the channel based on the characterized channel (shown in Equation 3).

[0082] With the scheme of the present disclosure, the inaccuracy of the GoB codebook for the WSMS structure can be avoided. In addition, due to the STRE and GRE recovery algorithms, the search overhead associated with the amplified dimensions of UM-MIMO in the THz band can be reduced.

[0083] According to an embodiment of the present disclosure, some evaluations are performed based on the proposed mechanism to verify the performance of channel estimation. The carrier frequency is 0.3 THz, the bandwidth for the sub-THz system is 5 GHz, and the number of antennas of the sub-arrays at Tx and Rx is set to 64, and the number of sub-arrays is 4. The estimation accuracy is revealed according to the normalized mean square error (NMSE), which is defined as where represents the estimated channel matrix and H HSPM is the ideal channel matrix.

[0084] The evaluation of the NMSE performance with respect to the signal-to-noise ratio (SNR) can be shown in Figure 3 . During the training process, the random phase shift coefficients of the training codebook for WSMS can be considered. During our simulation, the number of neighboring grids in GRE is fixed at 5.

[0085] As Figure 3 shown, the proposed STRE and GRE methods based on the sub-array-based codebook perform much better than the traditional OMP and CoSaMP based on the full-array-based GoB codebook. Specifically, when SNR = 0 dB, the estimated NMSE of OMP and AMP remains close to 0 dB, while the NMSE of the STRE and GRE algorithms is reduced by -2.1 dB and -2.5 dB compared with the traditional solutions and continues to decrease as the SNR increases. This result verifies the accuracy and effectiveness of the proposed sub-array-based codebook in sub-THz or THz systems.

[0086] In addition, it can be observed that the performance of the low-complexity GRE algorithm is close to that of the STRE algorithm at low SNRs from -20 to 0 dB. However, the NMSE difference increases with increasing SNR. This is because, in GRE, especially under noisy conditions, potential grid errors can be avoided by determining the potential search grid based on the reference grid. However, since the optimal grid for the entire array cannot be completely mapped to the first subarray, the performance of GRE becomes worse than that of STRE as the SNR increases. For this reason, we can infer that the GRE algorithm is more attractive in the low SNR region.

[0087] The comparison results of the computational complexity of the proposed STRE and GRE algorithms with the traditional OMP and CoSaMP algorithms can be summarized as follows. Table 4: Comparison of computational complexity

[0088] As shown in Table 4, the number of antennas and subarrays at Tx and Rx are denoted as N, respectively. r =N t =N and K r =K t =K.N p is the number of paths. The complexity of OMP and CoSaMP algorithms mainly comes from the joint Rx and Rx grid search, which are approximately Benefiting from separate Tx and Rx searches, the complexity of STRE is reduced to approximately Moreover, with the complexity of Compared with STRE, spatial correlation further reduces the complexity of the GRE algorithm. When N becomes large in UM-MIMO, the relative values ​​of the complexity of these algorithms can be approximated as and

[0089] Figure 4 4 shows a flow chart of a method implemented at a first device according to some example embodiments of the present disclosure. Figure 1 For the purpose of discussion, reference will be made to Figure 1 Method 400 is described.

[0090] At 410, the first device 110 obtains a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at the second device. A first plurality of subarrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and a second plurality of subarrays in the second antenna arrangement are spaced apart from each other by a predetermined distance.

[0091] In some example embodiments, a first codebook matrix is determined by associating a set of beam grid codebooks with each subarray from a first plurality of subarrays, and wherein a second codebook matrix is determined by associating the set of beam grid codebooks with each subarray from a second plurality of subarrays.

[0092] In some example embodiments, diagonal blocks in the first codebook matrix correspond to respective sets of beam grid codebooks associated with each subarray from the first plurality of subarrays, and diagonal blocks in the second codebook matrix correspond to respective sets of beam grid codebooks associated with each subarray from the second plurality of subarrays.

[0093] At 420, the first device 110 characterizes the channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

[0094] In some example embodiments, the first device 110 may obtain received information, determine a plurality of non-zero grid points based at least on the first codebook matrix, the second codebook matrix, and the received signal, with the grid points correspondingly associated with a pair of vectors selected from the first codebook matrix and the second codebook matrix; and characterize the channel based on the channel gains associated with the plurality of non-zero grid points and the first codebook matrix and the second codebook matrix.

[0095] In some example embodiments, the first device 110 may obtain a first beamforming matrix and a second beamforming matrix, determine a first weighted representation of the received signal based on the second beamforming matrix and the second codebook matrix, and determine a second weighted representation of the received signal based on the first beamforming matrix and the first codebook matrix. The first device 110 may also determine a set of non-zero rows based at least on the first weighted representation of the received signal, and determine a set of non-zero columns based at least on the second weighted representation of the received signal; and determine the determined non-zero grid points based on the determined set of non-zero rows and the determined set of non-zero columns.

[0096] In some example embodiments, if a set of non-zero rows is determined, the first device 110 may determine a set of non-zero columns based on the second weighted representation of the received signal and the determined set of non-zero rows.

[0097] In some example embodiments, if a set of non-zero columns is determined, the first device 110 may determine a set of non-zero rows based on the first weighted representation of the received signal and the determined set of non-zero columns.

[0098] In some example embodiments, the first device 110 may select a reference subarray from a first plurality of subarrays or a second plurality of subarrays, and determine a first plurality of non-zero rows or a first plurality of non-zero columns on the reference subarray. The first device 110 may also determine a second plurality of non-zero rows or a second plurality of non-zero columns on another subarray from the first plurality of subarrays or the second plurality of subarrays based on a grid search space associated with the determined first plurality of non-zero rows or the first plurality of non-zero columns on the reference subarray; and determine a plurality of non-zero grid points based at least on the first plurality of non-zero rows or the first plurality of non-zero columns and the second plurality of non-zero rows or the second plurality of non-zero columns.

[0099] In some example embodiments, the grid search space includes at least one of the following: the determined first plurality of non-zero rows or the first plurality of non-zero columns, rows adjacent to the determined first plurality of non-zero rows within a predetermined range, or columns adjacent to the determined first plurality of non-zero columns within a predetermined range.

[0100] Optionally, the first device includes a terminal device and the second device includes a network device; or the first device includes a network device and the second device includes a terminal device.

[0101] In some example embodiments, the apparatus (e.g., implemented at the first device 110) capable of performing method 400 may include components for performing the corresponding steps of method 400. The components may be implemented in any suitable form. For example, the components may be implemented in a circuit or a software module.

[0102] In some example embodiments, the apparatus includes: components for determining a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at the second device, where the first plurality of subarrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and where the second plurality of subarrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; and components for characterizing a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

[0103] In some example embodiments, the first codebook matrix is determined by associating a set of beam grid codebooks with each subarray from the first plurality of subarrays, and where the second codebook matrix is determined by associating the set of beam grid codebooks with each subarray from the second plurality of subarrays.

[0104] In some example embodiments, the diagonal blocks in the first codebook matrix correspond to the respective sets of beam grid codebooks associated with each subarray from the first plurality of subarrays, and the diagonal blocks in the second codebook matrix correspond to the respective sets of beam grid codebooks associated with each subarray from the second plurality of subarrays.

[0105] In some example embodiments, the components for characterizing a channel further include: a component for obtaining a received signal; a component for determining a plurality of non-zero grid points based at least on a first codebook matrix, a second codebook matrix, and the received signal, the grid points being correspondingly associated with a pair of vectors selected from the first codebook matrix and the second codebook matrix; and a component for characterizing the channel based on the channel gains associated with the plurality of non-zero grid points and the first codebook matrix and the second codebook matrix.

[0106] In some example embodiments, the component for determining non-zero grid points includes: a component for obtaining a first beamforming matrix and a second beamforming matrix; a component for determining a first weighted representation of the received signal based on the second beamforming matrix and the second codebook matrix, and a second weighted representation of the received signal based on the first beamforming matrix and the first codebook matrix; a component for determining a set of non-zero rows based at least on the first weighted representation of the received signal and determining a set of non-zero columns based at least on the second weighted representation of the received signal; and a component for determining non-zero grid points based on the determined set of non-zero rows and the determined set of non-zero columns.

[0107] In some example embodiments, the component for determining a set of non-zero columns: if a set of non-zero rows is determined, a component for determining a set of non-zero columns based on the second weighted representation of the received signal and the determined set of non-zero rows.

[0108] In some example embodiments, the component for determining a set of non-zero rows includes: if a set of non-zero columns is determined, a component for determining a set of non-zero rows based on the first weighted representation of the received signal and the determined set of non-zero columns.

[0109] In some example embodiments, the component for determining non-zero grid points includes: a component for selecting a reference subarray from a first plurality of subarrays or a second plurality of subarrays; a component for determining a first plurality of non-zero rows or a first plurality of non-zero columns on the reference subarray; a component for determining a second plurality of non-zero rows or a second plurality of non-zero columns on another subarray from the first plurality of subarrays or the second plurality of subarrays based on a grid search space associated with the determined first plurality of non-zero rows or the first plurality of non-zero columns on the reference subarray; and a component for determining a plurality of non-zero grid points based at least on the first plurality of non-zero rows or the first plurality of non-zero columns and the second plurality of non-zero rows or the second plurality of non-zero columns.

[0110] In some example embodiments, the grid search space includes at least one of the following: a determined first plurality of non-zero rows or a first plurality of non-zero columns, rows adjacent to the determined first plurality of non-zero rows within a predetermined range, or columns adjacent to the determined first plurality of non-zero columns within a predetermined range.

[0111] Optionally, the first device includes a terminal device and the second device includes a network device; or the first device includes a network device and the second device includes a terminal device.

[0112] Figure 5 is a simplified block diagram of a device 500 suitable for implementing example embodiments of the present disclosure. The device 500 may be provided to implement a communication device, for example, as Figure 1 shown in the first device 110. As shown, the device 500 includes one or more processors 510, one or more memories 520 coupled to the processors 510, and one or more communication modules 540 coupled to the processors 510.

[0113] The communication module 540 is used for two-way communication. The communication module 540 has one or more communication interfaces to facilitate communication with one or more other modules or devices. The communication interface may represent any interface necessary for communicating with other network elements. In some example embodiments, the communication module 540 may include at least one antenna.

[0114] As a non-limiting example, the processor 510 may be of any type suitable for a local technology network and may include one or more of the following: a general-purpose computer, a special-purpose computer, a microprocessor, a digital signal processor (DSP), and a processor based on a multi-core processor architecture. The device 500 may have multiple processors, such as application integrated circuit chips that are subordinate in time to a clock synchronized with a main processor.

[0115] The memory 520 may include one or more non-volatile memories and one or more volatile memories. Examples of non-volatile memories include, but are not limited to, read-only memory (ROM) 524, electrically programmable read-only memory (EPROM), flash memory, hard disks, compact discs (CDs), digital versatile discs (DVDs), optical discs, laserdiscs, and other magnetic and / or optical storage. Examples of volatile memories include, but are not limited to, random access memory (RAM) 522 and other volatile memories that do not persist during a power outage duration.

[0116] The computer program 530 includes computer-executable instructions executed by an associated processor 510. The instructions of program 530 may include instructions for performing the operations / actions of some example embodiments of the present disclosure. Program 530 may be stored in a memory, such as ROM 524. The processor 510 may execute any suitable actions and processing by loading program 530 into RAM 522.

[0117] Example embodiments of the present disclosure may be implemented by means of program 530, enabling device 500 to execute any process of the present disclosure as discussed with reference to Figures 2 to 4 the present disclosure. Example embodiments of the present disclosure may also be implemented by hardware or by a combination of software and hardware.

[0118] In some example embodiments, program 530 may be tangibly embodied in a computer-readable medium, which may be included in device 500 (such as in memory 520) or in other storage devices accessible by device 500. Device 500 may load program 530 from the computer-readable medium into RAM 522 for execution. In some example embodiments, the computer-readable medium may include any type of non-transitory storage medium, such as ROM, EPROM, flash memory, hard disk, CD, DVD, etc. As used herein, the term "non-transitory" is a limitation of the medium itself (i.e., tangible, rather than a signal), rather than a limitation on the persistence of data storage (e.g., RAM versus ROM).

[0119] Figure 6 An example of a computer-readable medium 600 is shown, which may be in the form of a CD, DVD, or other optical storage disk. Program 530 is stored thereon.

[0120] Generally, the various embodiments of the present disclosure may be implemented in hardware or dedicated circuits, software, logic, or any combination thereof. Some aspects may be implemented in hardware, while other aspects may be implemented in firmware or software, which may be executed by a controller, a microprocessor, or other computing devices. Although the various aspects of the embodiments of the present disclosure are shown and described as block diagrams, flowcharts, or using some other graphical representation, it should be understood that, by way of non-limiting example, the blocks, devices, systems, techniques, or methods described herein may be implemented in, for example, hardware, software, firmware, dedicated circuits or logic, general-purpose hardware or controllers, or other computing devices, or some combination thereof.

[0121] Some example embodiments of the present disclosure also provide at least one computer program product tangibly stored on a computer-readable medium, such as a non-transitory computer-readable medium. The computer program product includes computer-executable instructions, such as those included in program modules and executed in a device on a target physical or virtual processor, to perform any of the methods as described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform particular tasks or implement particular abstract data types. In various embodiments, the functions of program modules may be combined or split among program modules as needed. The machine-executable instructions for program modules may be executed within a local or distributed device. In a distributed device, program modules may be located in both local and remote storage media.

[0122] The program code for performing the methods of the present disclosure may be written in any combination of one or more programming languages. The program code may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, such that the program code, when executed by the processor or controller, causes the functions / operations specified in the flowchart and / or block diagram to be implemented. The program code may execute entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0123] In the context of the present disclosure, the computer program code or related data may be carried by any suitable carrier such that a device, apparatus, or processor can perform the various processes and operations as described above. Examples of carriers include signals, computer-readable media, etc.

[0124] The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any suitable combination of the foregoing. More specific examples of the computer-readable storage medium will include an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0125] Moreover, although the operations are depicted in a particular order, this should not be construed as requiring that the operations be performed in the particular order shown or in a sequential order, or that all of the illustrated operations be performed, to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the foregoing discussion, these should not be construed as limitations on the scope of the present disclosure, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in the context of separate embodiments may also be implemented in combination in a single embodiment, unless expressly stated otherwise. Conversely, various features that are described in the context of a single embodiment may also be implemented separately or in any suitable sub-combination in multiple embodiments, unless expressly stated otherwise.

[0126] Although the present disclosure has been described in language specific to structural features and / or methodological acts, it is to be understood that the disclosure defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the above specific features and acts are disclosed as example forms of implementing the claims.

Claims

1. A first device, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the first device to at least: obtain a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at a second device, wherein a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and wherein a second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; and characterize a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

2. The first device according to claim 1, wherein the first codebook matrix is determined by associating a set of beam grid codebooks with each sub-array from the first plurality of sub-arrays, and wherein the second codebook matrix is determined by associating the set of beam grid codebooks with each sub-array from the second plurality of sub-arrays.

3. The first device according to claim 1 or 2, wherein diagonal blocks in the first codebook matrix correspond to respective sets of beam grid codebooks associated with each sub-array from the first plurality of sub-arrays, and diagonal blocks in the second codebook matrix correspond to respective sets of beam grid codebooks associated with each sub-array from the second plurality of sub-arrays.

4. The first device according to any one of claims 1 to 3, wherein the first device is further caused to: obtain a received signal; determine a plurality of non-zero grid points based at least on the first codebook matrix, the second codebook matrix, and the received signal, the grid points being correspondingly associated with a pair of vectors selected from the first codebook matrix and the second codebook matrix; and characterize the channel based on channel gains associated with the plurality of non-zero grid points and the first codebook matrix and the second codebook matrix.

5. The first device according to claim 4, wherein the first device is further caused to: obtain a first beamforming matrix and a second beamforming matrix; determine a first weighted representation of the received signal based on the second beamforming matrix and the second codebook matrix, and determine a second weighted representation of the received signal based on the first beamforming matrix and the first codebook matrix; determine a set of non-zero rows based at least on the first weighted representation of the received signal, and determine a set of non-zero columns based at least on the second weighted representation of the received signal; and determine the non-zero grid points based on the determined set of non-zero rows and the determined set of non-zero columns.

6. The first device according to claim 5, wherein the first device is further caused to: if the set of non-zero rows is determined, determine the set of non-zero columns based on the second weighted representation of the received signal and the determined set of non-zero rows.

7. The first device according to claim 5, wherein the first device is further caused to: If it is determined that the set of non-zero columns is determined, determine the set of non-zero rows based on the first weighted representation of the received signal and the determined set of non-zero columns.

8. The first device according to claim 4, wherein the first device is further caused to: select a reference subarray from the first plurality of subarrays or the second plurality of subarrays; determine a first plurality of non-zero rows or a first plurality of non-zero columns on the reference subarray; determine a second plurality of non-zero rows or a second plurality of non-zero columns on another subarray from the first plurality of subarrays or the second plurality of subarrays based on a grid search space associated with the determined first plurality of non-zero rows or the first plurality of non-zero columns on the reference subarray; and determine the plurality of non-zero grid points based at least on the first plurality of non-zero rows or the first plurality of non-zero columns and the second plurality of non-zero rows or the second plurality of non-zero columns.

9. The first device according to claim 8, wherein the grid search space includes at least one of the following: the determined first plurality of non-zero rows or the first plurality of non-zero columns; rows adjacent to the determined first plurality of non-zero rows within a predetermined range; or columns adjacent to the determined first plurality of non-zero columns within a predetermined range.

10. The second device according to any one of claims 1 to 9, wherein the first device includes a terminal device, and the second device includes a network device; or the first device includes a network device, and the second device includes a terminal device.

11. A method, comprising: at a first device, determine a first codebook matrix associated with a first antenna arrangement at the first device and a second codebook matrix associated with a second antenna arrangement at a second device, wherein the first plurality of subarrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and wherein the second plurality of subarrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; and characterize a channel between the first device and the second device based at least on the first codebook matrix and the second codebook matrix.

12. The method according to claim 11, wherein the first codebook matrix is determined by associating a set of beam grid codebooks with each of the first plurality of subarrays, and wherein the second codebook matrix is determined by associating the set of beam grid codebooks with each of the second plurality of subarrays.

13. The method according to claim 11 or 12, wherein diagonal blocks in the first codebook matrix correspond to respective sets of beam grid codebooks associated with each of the first plurality of subarrays, and diagonal blocks in the second codebook matrix correspond to respective sets of beam grid codebooks associated with each of the second plurality of subarrays.

14. The method according to any one of claims 11 to 13, wherein characterizing the channel includes: acquiring a received signal; Determine a plurality of non-zero grid points based at least on the first codebook matrix, the second codebook matrix, and the received signal, where the grid points are correspondingly associated with a pair of vectors selected from the first codebook matrix and the second codebook matrix; And Characterize the channel based on the channel gains associated with the plurality of non-zero grid points, the first codebook matrix, and the second codebook matrix.

15. The method according to claim 14, wherein determining the non-zero grid points includes: Obtain a first beamforming matrix and a second beamforming matrix; Determine a first weighted representation of the received signal based on the second beamforming matrix and the second codebook matrix, and determine a second weighted representation of the received signal based on the first beamforming matrix and the first codebook matrix; Determine a set of non-zero rows based at least on the first weighted representation of the received signal, and determine a set of non-zero columns based at least on the second weighted representation of the received signal; And Determine the non-zero grid points based on the determined set of non-zero rows and the determined set of non-zero columns.

16. The method according to claim 15, wherein determining the set of non-zero columns includes: If it is determined that the set of non-zero rows is determined, determine the set of non-zero columns based on the second weighted representation of the received signal and the determined set of non-zero rows.

17. The method according to claim 15, wherein determining the set of non-zero rows includes: If it is determined that the set of non-zero columns is determined, determine the set of non-zero rows based on the first weighted representation of the received signal and the determined set of non-zero columns.

18. The method according to claim 14, wherein determining the non-zero grid points includes: Select a reference subarray from the first plurality of subarrays or the second plurality of subarrays; Determine a first plurality of non-zero rows or a first plurality of non-zero columns on the reference subarray; Based on the grid search space associated with the determined first plurality of non-zero rows or the first plurality of non-zero columns on the reference subarray, determine a second plurality of non-zero rows or a second plurality of non-zero columns on another subarray from the first plurality of subarrays or the second plurality of subarrays; And Determine the plurality of non-zero grid points based at least on the first plurality of non-zero rows or the first plurality of non-zero columns and the second plurality of non-zero rows or the second plurality of non-zero columns.

19. The method according to claim 18, wherein the grid search space includes at least one of the following: The determined first plurality of non-zero rows or the first plurality of non-zero columns; Rows adjacent to the determined first plurality of non-zero rows within a pre-determined range; or Columns adjacent to the determined first plurality of non-zero columns within a pre-determined range.

20. The method according to any one of claims 11 to 19, wherein The first device includes a terminal device, and the second device includes a network device; or The first device includes a network device, and the second device includes a terminal device.

21. An apparatus, comprising: A component for obtaining a first codebook matrix associated with a first antenna arrangement at a first device and a second codebook matrix associated with a second antenna arrangement at a second device, wherein a first plurality of sub-arrays in the first antenna arrangement are spaced apart from each other by a predetermined distance, and wherein a second plurality of sub-arrays in the second antenna arrangement are spaced apart from each other by a predetermined distance; And A component for characterizing a channel between the first device and the second device at least based on the first codebook matrix and the second codebook matrix.

22. A non-transitory computer-readable medium comprising program instructions for causing a device to at least perform the method according to any one of claims 11 to 20.

Images