A channel estimation method for XL-MIMO system under hybrid ADC architecture

Abstract

The present invention discloses a channel estimation method for an XL-MIMO system under a hybrid ADC architecture, belonging to the field of channel estimation technology. The method comprises: establishing a channel model comprising a base station near-field spherical wave model and a user far-field plane wave model, receiving a pilot signal sent by the user, and quantizing the received signal using the hybrid ADC architecture to obtain a quantized signal; modeling the channel estimation problem as an amplitude recovery optimization problem based on the quantized signal, wherein the constraints of the objective function include the Hadamard product constraint of the quantized signal and the amplitude matrix, a channel sparsity constraint, and a low-rank constraint; decomposing the amplitude recovery optimization problem into subproblems based on the alternating direction multiplier method; and iteratively solving each subproblem until an iteration termination condition is met to obtain a channel estimation matrix. This method can avoid the limitations of traditional phase recovery methods and improve the accuracy of channel estimation.

Description

Technical Field

[0001] The present invention relates to an XL-MIMO system channel estimation method under a hybrid ADC architecture, belonging to the technical field of channel estimation. Background Art

[0002] Massive Multiple-Input Multiple-Output (MASSIVE MIMO) is one of the most critical technologies in current 5G communications. By deploying massive antenna arrays at base stations (BSs), Massive MIMO technology can achieve orders of magnitude improvements in spectral efficiency through beamforming or multiplexing. For future 6G communication systems, ultra-large-scale multiple-input multiple-output (XL-MIMO) technology will expand the antenna scale to levels far exceeding existing Massive MIMO, effectively achieving a tenfold increase in spectral efficiency. Furthermore, thanks to the abundant spectrum resources in the millimeter wave (mmWave) and terahertz (THz) bands, high-frequency band communications can provide massive available bandwidth. Furthermore, the extremely small physical size of high-frequency antennas creates favorable conditions for the deployment of ultra-large-scale antenna arrays. Therefore, the integration of high-frequency bands and ultra-large-scale MIMO is widely considered a key enabling technology for future 6G communication systems.

[0003] Similar to current 5G mmWave massive MIMO, hybrid precoding architectures are widely considered a key enabler for high-band XL-MIMO, primarily due to the extremely high power consumption of high-frequency radio frequency (RF) chains. Efficient hybrid precoding requires accurate channel state information at the base station. However, because the number of RF chains in a hybrid precoding architecture is far smaller than the number of antennas, the base station cannot simultaneously observe the signals from all antennas. This results in unacceptable pilot overhead, a particularly significant issue in XL-MIMO systems with a very large number of antennas.

[0004] To meet the high-density connectivity and ultra-high speed requirements of 6G networks, recent research has proposed deploying XL-MIMO systems with ultra-large array apertures at base stations as a key candidate technology for 6G. Compared to traditional massive MIMO, new XL-MIMO systems significantly extend the near-field region of electromagnetic waves, placing access devices in a near-field electromagnetic propagation environment. In this scenario, a spherical wavefront model is required to accurately model the near-field channel, rather than the traditional far-field plane wave assumption. This places new demands on signal processing methods. To address this issue, some studies have investigated XL-MIMO near-field channel estimation using a grant-based multiple access mechanism, but such methods only support limited user scales. Current state-of-the-art massive access Joint Active Device Detection and Channel Estimation (JADCE) schemes are based on the far-field plane wave assumption, significantly degrading their performance in near-field MIMO channels. Furthermore, deploying high-resolution analog-to-digital converters (ADCs) on all antennas in an XL-MIMO system poses practical challenges. To reduce system cost and power consumption, some studies have proposed MIMO receivers that utilize low-resolution ADCs. However, the quantization noise introduced by low-resolution ADCs can severely degrade received signal accuracy, limiting detection performance. In practical applications, receiver architectures that combine high-speed, high-resolution ADCs with large antenna arrays are prohibitively expensive and power-hungry. Using only high-speed, high-resolution ADCs or only 1-bit ADCs is impractical. The former is prohibitively expensive and power-hungry, while the latter presents practical challenges, including lower bounds on data detection error, capacity limitations, complex time / frequency synchronization, and challenging channel estimation. Summary of the Invention

[0005] The purpose of the present invention is to provide a channel estimation method for an XL-MIMO system under a hybrid ADC architecture, which can avoid the limitations of traditional phase recovery methods and improve the accuracy of channel estimation.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] In a first aspect, the present invention provides a channel estimation method for an XL-MIMO system under a hybrid ADC architecture, comprising:

[0008] A channel model is established that includes a near-field spherical wave model for the base station and a far-field plane wave model for the user. The pilot signal sent by the user is received and quantized using a hybrid ADC architecture to obtain a quantized signal.

[0009] Based on the quantized signal, the channel estimation problem is modeled as an amplitude recovery optimization problem. The constraints of the objective function include the Hadamard product constraint of the quantized signal and the amplitude matrix, the channel sparsity constraint, and the low-rank constraint.

[0010] Based on the alternating direction multiplier method, the amplitude recovery optimization problem is decomposed into:

[0011] Amplitude matrix update subproblem: restore the amplitude information of the quantized signal;

[0012] Auxiliary variable update subproblem: balancing channel estimation residuals;

[0013] Channel parameter update subproblem: jointly handle channel sparsity constraints and low-rank constraints;

[0014] Lagrange multiplier update subproblem: adjust constraints;

[0015] Iteratively solve each sub-problem until the iteration termination condition is reached to obtain the channel estimation matrix.

[0016] In combination with the first aspect, further, the base station's received signal matrix for:

[0017] ;

[0018] in, 、…、 Respectively represent the 1st, ..., The received signal of the base station in time slots, represents the pilot signal matrix sent by the user, ,in, 、…、 Respectively represent the 1st, ..., The pilot signal sent by the user in the time slot is represents the additive white Gaussian noise matrix of the channel, ,in, 、…、 Respectively represent the 1st, ..., Additive white Gaussian noise of the time slot channel;

[0019] Channel matrix from user to base station for:

[0020] ;

[0021] in, Indicates the total number of antennas equipped with the base station, Indicates the total number of antennas equipped by the user, represents the total number of paths from the user to the base station, Indicates the first The complex gain of each path, 、 They represent the first The arrival angle and departure angle of each path, Indicates the first The propagation distance of each path, represents the far-field steering vector, , represents the near-field steering vector, ,in, represents the imaginary unit, represents the wavelength of the near-field spherical wave, 、…、 、…、 Respectively represent the 1st, ..., 、…、 The root antenna is relative to the The distance of the path, ,in, represents the antenna index, represents the antenna spacing, represents the base station near-field codebook, represents the user far-field codebook, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents transpose, represents the conjugate transpose.

[0022] In combination with the first aspect, further, quantizing the received signal through the hybrid ADC architecture to obtain the quantized signal includes:

[0023] Quantize the received signal in the digital domain using a high-resolution ADC or a 1-bit ADC to obtain a quantized signal;

[0024] The quantized signal is:

[0025] ;

[0026] in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the channel matrix from user to base station, represents the pilot signal matrix sent by the user, represents the additive white Gaussian noise matrix of the channel, Represents a quantized operation.

[0027] Combined with the first aspect, further, the quantization process of the high-resolution ADC is equivalent to the identity transformation, and the quantization process of the 1-bit ADC satisfies ,in, represents the symbolic function, represents the real part, represents the imaginary part, represents an imaginary unit;

[0028] Will Rewritten as:

[0029] ;

[0030] in, Indicates the base station Received signal matrix of the root antenna The corresponding quantized signal matrix, Represents the RF chain index set of the high-resolution ADC, Indicates the RF chain index set of the 1-bit ADC.

[0031] In combination with the first aspect, further modeling the channel estimation problem as an amplitude recovery optimization problem based on the quantized signal includes:

[0032] Based on the amplitude recovery algorithm, the channel estimation problem is modeled as an amplitude recovery optimization problem. The objective function of the amplitude recovery optimization problem is:

[0033] ;

[0034] in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the amplitude matrix, represents the mixed magnitude-sign product, ,in, represents the real part, represents the imaginary part, represents the Hadamard product, represents the imaginary unit, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, represents the conjugate transpose, represents the Frobenius norm, represents the L1 norm, represents the regularization coefficient, represents matrix vectorization, represents the matrix rank operation, Indicates the total number of paths from the user to the base station;

[0035] Introducing auxiliary variable matrix based on alternating direction multiplication method , the objective function of the amplitude recovery optimization problem is rewritten as:

[0036] ;

[0037] in, Indicates the indicator function, used to force The non-negativity of

[0038] Augmented Lagrangian function for amplitude recovery optimization problem for:

[0039] ;

[0040] in, represents the Lagrange multiplier matrix, represents the residual matrix, , represents the matrix trace operation, Represents the penalty parameter of the alternating direction multiplier method.

[0041] Combined with the first aspect, the objective function of the amplitude matrix update subproblem is further:

[0042] ;

[0043] in, represents the Lagrange multiplier matrix, represents the residual matrix, represents the matrix trace operation, represents the penalty parameter of the alternating direction multiplier method, represents the Frobenius norm, represents the amplitude matrix, represents the real part, represents the imaginary part, represents the conjugate transpose;

[0044] The objective function of the auxiliary variable update subproblem is:

[0045] ;

[0046] in, It is an auxiliary variable matrix introduced based on the alternating direction multiplication method;

[0047] The objective function of the channel parameter update subproblem is:

[0048] ;

[0049] in, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents matrix vectorization, represents the L1 norm, represents the regularization coefficient, represents the matrix rank, Indicates the total number of paths from the user to the base station;

[0050] The update formula of the Lagrange multiplier update subproblem is:

[0051] ;

[0052] in, 、 Respectively represent 、 The Lagrange multiplier matrix of the iteration, Represents the received signal matrix of the base station The corresponding quantized signal matrix, Indicates the The magnitude matrix of the iteration, represents the mixed magnitude-sign product, ,in, represents the Hadamard product, represents the imaginary unit, Indicates the The sparse matrix of the iteration, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, It is Auxiliary variable matrix for iterations.

[0053] In combination with the first aspect, further, when iteratively solving each subproblem, the amplitude matrix update subproblem, the auxiliary variable update subproblem, the channel parameter update subproblem, and the Lagrange multiplier update subproblem are solved in sequence, completing one iteration, and iterating repeatedly until the iteration termination condition is met to obtain the channel estimation matrix;

[0054] Solving the amplitude matrix update subproblem involves:

[0055] The linear and quadratic terms in the objective function of the amplitude matrix update subproblem are combined into a single Frobenius norm term by the matching method:

[0056] ;

[0057] Ignore constant terms , the objective function of the amplitude matrix update subproblem is simplified to:

[0058] ;

[0059] in, ;

[0060] Will Expand to element-by-element calculation and decompose the objective function of the amplitude matrix update subproblem into independent optimization of the real and imaginary parts:

[0061] ;

[0062] in, represents the first intermediate variable matrix, ;

[0063] right Perform closed-form non-negative projection on each element of :

[0064] ;

[0065] in, Indicates the The first intermediate variable matrix of the iteration, ;

[0066] Solving the auxiliary variable update subproblem includes:

[0067] merge 、 Two items are about The quadratic function , the objective function of the auxiliary variable update subproblem is simplified to:

[0068] ;

[0069] in, represents the second intermediate variable matrix, ;

[0070] right Take the derivative and set it to zero:

[0071] ;

[0072] get:

[0073] ;

[0074] Substitution The expression of is:

[0075] ;

[0076] Solving the channel parameter update subproblem includes:

[0077] Let the third intermediate variable matrix , the objective function of the channel parameter update subproblem is simplified to:

[0078] ;

[0079] Solve the channel parameter update subproblem through sparsity processing and low-rank projection;

[0080] The iteration termination condition is:

[0081] ;

[0082] in, Indicates the convergence threshold.

[0083] In combination with the first aspect, further sparsity processing includes:

[0084] Let the temporary matrix of the current iteration be ,initialization And update it:

[0085] ;

[0086] right Apply a soft thresholding operation to each element of :

[0087] ;

[0088] in, Represents the sparse matrix obtained by the soft threshold operation No. Rank Column elements, express No. Rank Column elements;

[0089] Low-rank projections include:

[0090] right Perform singular value decomposition:

[0091] ;

[0092] in, represents the left singular vector matrix, represents a diagonal matrix of singular values, represents the right singular vector matrix;

[0093] Before Retention principal components, and obtain a low-rank approximate matrix for:

[0094] ;

[0095] in, express Before column vector, express upper left corner The sub-matrix of express Before column vector;

[0096] It is the optimal estimate after sparsity processing and low-rank projection, and satisfies:

[0097] .

[0098] In a second aspect, the present invention provides a computer device, comprising:

[0099] Storage medium for storing computer programs;

[0100] A processor is configured to execute the computer program to implement the XL-MIMO system channel estimation method under the hybrid ADC architecture according to the first aspect.

[0101] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the XL-MIMO system channel estimation method under the hybrid ADC architecture described in the first aspect.

[0102] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the XL-MIMO system channel estimation method under the hybrid ADC architecture described in the first aspect.

[0103] Compared with the prior art, the present invention has the following beneficial effects:

[0104] Compared with traditional channel estimation methods, the XL-MIMO system channel estimation method under the hybrid ADC architecture provided by the present invention adopts the hybrid ADC architecture to quantize the received signal, models the channel estimation problem as an amplitude recovery optimization problem based on the quantized signal, and decomposes the amplitude recovery optimization problem into four subproblems based on the alternating direction multiplier method. By iteratively solving each subproblem, a channel estimation matrix is ​​obtained. This method can avoid the limitations of traditional phase recovery methods and improve the accuracy of channel estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 is a schematic diagram of a channel model provided by an embodiment of the present invention;

[0106] Figure 2 2. It is a schematic diagram comparing the performance of the channel estimation method provided by an embodiment of the present invention and other channel estimation methods for different numbers of pilot signals;

[0107] Figure 3 This is a schematic diagram comparing the performance of the channel estimation method provided by an embodiment of the present invention and other channel estimation methods under different signal-to-noise ratio environments. DETAILED DESCRIPTION

[0108] The technical solution of the present invention will be further described in detail below in conjunction with specific implementation methods.

[0109] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and are not to be construed as limiting the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0110] An embodiment of the present invention provides a channel estimation method for an XL-MIMO system under a hybrid ADC architecture, comprising:

[0111] A channel model is established that includes a near-field spherical wave model for the base station and a far-field plane wave model for the user. The pilot signal sent by the user is received and quantized using a hybrid ADC architecture to obtain a quantized signal.

[0112] Based on the quantized signal, the channel estimation problem is modeled as an amplitude recovery optimization problem. The constraints of the objective function include the Hadamard product constraint of the quantized signal and the amplitude matrix, the channel sparsity constraint, and the low-rank constraint.

[0113] Based on the alternating direction multiplier method, the amplitude recovery optimization problem is decomposed into:

[0114] Amplitude matrix update subproblem: restore the amplitude information of the quantized signal;

[0115] Auxiliary variable update subproblem: balancing channel estimation residuals;

[0116] Channel parameter update subproblem: jointly handle channel sparsity constraints and low-rank constraints;

[0117] Lagrange multiplier update subproblem: adjust constraints;

[0118] Iteratively solve each sub-problem until the iteration termination condition is reached to obtain the channel estimation matrix.

[0119] The XL-MIMO system channel estimation method under the hybrid ADC architecture provided by the embodiment of the present invention is applied to an uplink multi-user millimeter wave XL-MIMO system, wherein a uniform planar array is deployed at both the base station and the user, wherein the base station is equipped with a very large-scale antenna array and the user is equipped with a uniform planar array. A base station with one antenna serves a Antenna users.

[0120] This embodiment considers an uplink narrowband communication system from a user to a base station, where the user sends a message of length pilot sequence.

[0121] Communications in the millimeter-wave band are subject to high attenuation, necessitating the use of large antenna arrays to concentrate power at the receiver. The large bandwidth also increases the power consumption and hardware requirements of the analog-to-digital converter (ADC). In practical applications, receiver architectures that combine high-speed, high-resolution ADCs with large antenna arrays are too expensive and power-hungry. Using only high-speed, high-resolution ADCs or only 1-bit ADCs is impractical. The former is too expensive and power-hungry, while the latter also presents practical challenges, including lower bounds on data detection error, limited capacity, complex time / frequency synchronization, and challenging channel estimation.

[0122] This embodiment provides a channel estimation method under a hybrid ADC architecture, in which most antennas are equipped with 1-bit resolution ADCs and a few antennas are equipped with high-resolution ADCs. This method can jointly utilize the amplitude information of the high-resolution ADC and the sign information of the 1-bit ADC to recover the amplitude information lost by quantization through non-negative amplitude constraints, avoiding the limitations of traditional phase recovery methods. At the same time, the optimization process has dual constraints of sparseness and low rank, which can improve the robustness of channel estimation and suppress noise and interference. In addition, this embodiment supports the near-field spherical wave model for high-frequency band XL-MIMO systems, rather than the traditional far-field plane wave assumption.

[0123] In a possible embodiment, the received signal of the base station is:

[0124] ;

[0125] in, Indicates the The received signal of the base station in time slots, represents the channel matrix from user to base station, Indicates the The pilot signal sent by the user in the time slot is Indicates the The mean of the time slot channel is zero and the variance is Additive white Gaussian noise.

[0126] Base station receiving signal matrix for:

[0127] ;

[0128] in, 、…、 Respectively represent the 1st, ..., The received signal of the base station in time slots, represents the pilot signal matrix sent by the user, ,in, 、…、 Respectively represent the 1st, ..., The pilot signal sent by the user in the time slot is represents the additive white Gaussian noise matrix of the channel, ,in, 、…、 Respectively represent the 1st, ..., The mean of the time slot channel is zero and the variance is Additive white Gaussian noise.

[0129] Channel matrix from user to base station for:

[0130] ;

[0131] in, Indicates the total number of antennas equipped with the base station, Indicates the total number of antennas equipped by the user, represents the total number of paths from the user to the base station, Indicates the first The complex gain of each path, 、 They represent the first The arrival angle and departure angle of each path, Indicates the first The propagation distance of each path, represents the far-field steering vector, , represents the near-field steering vector, ,in, represents the imaginary unit, represents the wavelength of the near-field spherical wave, 、…、 、…、 Respectively represent the 1st, ..., 、…、 The root antenna is relative to the The distance of the path, ,in, represents the antenna index, represents the antenna spacing, represents the base station near-field codebook, represents the user far-field codebook, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents transpose, represents the conjugate transpose.

[0132] In a possible embodiment, quantizing the received signal by using a hybrid ADC architecture to obtain the quantized signal includes: quantizing the received signal in a digital domain by using a high-resolution ADC or a 1-bit ADC to obtain the quantized signal.

[0133] In this embodiment, the quantized signal is:

[0134] ;

[0135] in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the channel matrix from user to base station, represents the pilot signal matrix sent by the user, represents the additive white Gaussian noise matrix of the channel, Represents a quantized operation.

[0136] In this embodiment, a mixed precision ADC (including high-resolution ADC and 1-bit ADC) is deployed in the base station. During the pilot symbol transmission phase, each user sends a signal with a length of pilot sequence.

[0137] Base station receiving signal matrix It can be expressed as:

[0138] .

[0139] For mixed-precision ADCs, Different forms of high-resolution ADC and 1-bit ADC are available. Under the mixed-precision ADC architecture, There are different mathematical representations for high-resolution ADCs and 1-bit ADCs.

[0140] Specifically, for the high-resolution ADC channel connected to the RF link, its quantization process is equivalent to the identity transformation, while the quantization process of the 1-bit ADC satisfies ,in, represents the symbolic function, represents the real part, represents the imaginary part, Represents an imaginary unit.

[0141] Therefore, it can be Rewritten as:

[0142] ;

[0143] in, Indicates the base station Received signal matrix of the root antenna The corresponding quantized signal matrix, Represents the RF chain index set of the high-resolution ADC, Indicates the RF chain index set of the 1-bit ADC.

[0144] In a possible embodiment, modeling the channel estimation problem as an amplitude recovery optimization problem based on the quantized signal specifically includes the following steps:

[0145] Step 1: Based on the amplitude recovery algorithm, the channel estimation problem is modeled as an amplitude recovery optimization problem;

[0146] Since the base station's receiving signal matrix Only the sign information of the real and imaginary parts is retained, while the corresponding amplitude information is completely lost. This problem can be viewed as the dual form of the classic phase recovery problem: in traditional phase recovery, the phase information of the received signal is lost, but the target signal can be effectively recovered through phase completion technology.

[0147] This embodiment proposes an amplitude recovery (AR) algorithm, assuming that the base station's received signal matrix The amplitude matrix Known, in the absence of noise we can get:

[0148] .

[0149] Compared to using only Perform channel estimation based on The channel matrix estimation can significantly reduce complexity. Based on this theoretical motivation, this embodiment proposes a new channel estimation framework: the Amplitude Retrieval (AR) algorithm. Its core idea is to achieve synchronous estimation of amplitude information and channel parameters through joint optimization.

[0150] In this embodiment, the objective function of the amplitude restoration optimization problem is:

[0151] ;

[0152] in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the amplitude matrix, represents the mixed magnitude-sign product, ,in, represents the real part, represents the imaginary part, represents the Hadamard product, represents the imaginary unit, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, represents the conjugate transpose, represents the Frobenius norm, represents the L1 norm, represents the regularization coefficient, represents matrix vectorization, represents the matrix rank operation, represents the total number of paths from the user to the base station, The number of sparse paths in the channel is , 、 Ensure the amplitude matrix Non-negativity. Through hybrid quantization and 𝜞, recovering 𝑿 while leveraging its sparsity and low-rank properties to improve the estimation accuracy.

[0153] Step ②: Introduce auxiliary variable matrix based on alternating direction multiplication method , the objective function of the amplitude recovery optimization problem is rewritten;

[0154] In this embodiment, the objective function of the amplitude restoration optimization problem is rewritten as:

[0155] ;

[0156] in, Indicates the indicator function, used to force The non-negativity of .

[0157] In this embodiment, the augmented Lagrangian function of the amplitude recovery optimization problem is for:

[0158] ;

[0159] in, represents the Lagrange multiplier matrix, represents the residual matrix, , represents the matrix trace operation, Represents the penalty parameter of the alternating direction multiplier method.

[0160] In one possible embodiment, the objective function of the amplitude matrix update subproblem is:

[0161] ;

[0162] in, represents the Lagrange multiplier matrix, represents the residual matrix, represents the matrix trace operation, represents the penalty parameter of the alternating direction multiplier method, represents the Frobenius norm, represents the amplitude matrix, represents the real part, represents the imaginary part, represents the conjugate transpose.

[0163] The objective function of the auxiliary variable update subproblem is:

[0164] ;

[0165] in, It is an auxiliary variable matrix introduced based on the alternating direction multiplier method.

[0166] The objective function of the channel parameter update subproblem is:

[0167] ;

[0168] in, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents matrix vectorization, represents the L1 norm, represents the regularization coefficient, represents the matrix rank, Indicates the total number of paths from the user to the base station.

[0169] The update formula of the Lagrange multiplier update subproblem is:

[0170] ;

[0171] in, 、 Respectively represent 、 The Lagrange multiplier matrix of the iteration, Represents the received signal matrix of the base station The corresponding quantized signal matrix, Indicates the The magnitude matrix of the iteration, represents the mixed magnitude-sign product, ,in, represents the Hadamard product, represents the imaginary unit, Indicates the The sparse matrix of the iteration, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, It is Auxiliary variable matrix for iterations.

[0172] In this embodiment, the function of updating the Lagrange multiplier is to adjust the multiplier through the residual term and gradually tighten the constraint condition.

[0173] In one possible embodiment, when iteratively solving each subproblem, the amplitude matrix update subproblem, the auxiliary variable update subproblem, the channel parameter update subproblem, and the Lagrange multiplier update subproblem are solved in sequence to complete one iteration, and the iteration is repeated until the iteration termination condition is reached to obtain the channel estimation matrix.

[0174] Specifically, the iterative solution of each sub-problem includes the following steps:

[0175] Step 1: Solve the amplitude matrix update subproblem;

[0176] In this embodiment, solving the amplitude matrix update subproblem specifically includes:

[0177] The linear and quadratic terms in the objective function of the amplitude matrix update subproblem are combined into a single Frobenius norm term by the matching method:

[0178] ;

[0179] Ignore constant terms , the objective function of the amplitude matrix update subproblem is simplified to:

[0180] ;

[0181] in, ;

[0182] Will Expand to element-by-element calculation:

[0183] ;

[0184] in, express No. Rank Column elements, express No. Rank Column elements, Represents mixed quantization and The element-wise product of ;

[0185] Due to the constraints The real and imaginary parts are non-negative, and the objective function of the amplitude matrix update subproblem is decomposed into independent optimization of the real and imaginary parts:

[0186] ;

[0187] in, represents the first intermediate variable matrix, ;

[0188] right Perform closed-form non-negative projection on each element of :

[0189] ;

[0190] in, Indicates the The first intermediate variable matrix of the iteration, .

[0191] For high-resolution ADC channels, , so the amplitude is directly given by and Recovery, for 1-bit ADC channel, , at this time, only the sign information is used to constrain the amplitude direction, and the non-negative projection ensures the physical rationality of the amplitude. express No. Rank Column elements, express No. Rank Column element.

[0192] Step 2: Solve the auxiliary variable update subproblem;

[0193] In this embodiment, solving the auxiliary variable update subproblem specifically includes:

[0194] merge 、 Two items are about The quadratic function , the objective function of the auxiliary variable update subproblem is simplified to:

[0195] ;

[0196] in, represents the second intermediate variable matrix, ;

[0197] right Take the derivative and set it to zero:

[0198] ;

[0199] get:

[0200] ;

[0201] Substitution The expression of is:

[0202] ;

[0203] in, As an auxiliary variable, it balances the residual of the current channel estimation and the penalty term of the Lagrange multiplier, ensuring the convergence of the alternating direction multiplier method ADMM framework.

[0204] In addition, the residual of the channel estimate is:

[0205] .

[0206] Step 3: Solve the channel parameter update subproblem;

[0207] In this embodiment, solving the channel parameter update sub-problem specifically includes:

[0208] Let the third intermediate variable matrix , the objective function of the channel parameter update subproblem is simplified to:

[0209] ;

[0210] The channel parameter update subproblem is solved through sparsity processing and low-rank projection.

[0211] Sparsity handling includes:

[0212] Let the temporary matrix of the current iteration be ,initialization And update it:

[0213] ;

[0214] right Apply a soft thresholding operation to each element of :

[0215] ;

[0216] in, Represents the sparse matrix obtained by the soft threshold operation No. Rank Column elements, express No. Rank Column element.

[0217] The purpose of the soft threshold operation is to set small values ​​to zero, retain the coefficients of significant paths, and suppress false paths caused by noise.

[0218] Low-rank projections include:

[0219] right Perform singular value decomposition:

[0220] ;

[0221] in, represents the left singular vector matrix, represents a diagonal matrix of singular values, represents the right singular vector matrix;

[0222] Before Retention principal components, and obtain a low-rank approximate matrix for:

[0223] ;

[0224] in, express Before Column vector with dimension , express upper left corner The sub-matrix of , express Before Column vector with dimension .

[0225] It is the optimal estimate after sparsity processing and low-rank projection, and satisfies:

[0226] .

[0227] Step 4: Solve the Lagrange multiplier update subproblem;

[0228] In this embodiment, solving the Lagrange multiplier update subproblem is to update the Lagrange multiplier according to the update formula of the Lagrange multiplier update subproblem.

[0229] Update Lagrange multipliers After that, order , return to step 1 and recalculate ,followed by 、 , and update it again , loop in sequence until the termination condition is reached, and output the channel matrix obtained by the last update As the channel estimation matrix, and output the amplitude matrix obtained by the last update , sparse matrix .

[0230] In this embodiment, the iteration termination condition is:

[0231] ;

[0232] in, Indicates the convergence threshold.

[0233] To verify the effectiveness of the XL-MIMO system channel estimation method under the hybrid ADC architecture provided by the embodiment of the present invention, the XL-MIMO system channel estimation method under the hybrid ADC architecture provided by the embodiment of the present invention was applied to an uplink multi-user millimeter wave XL-MIMO system for simulation experiments.

[0234] This example considers an uplink multi-user millimeter wave XL-MIMO system with 64 antennas and served by a base station (BS). The BS is equipped with an ultra-large uniform linear array (ULA) with 512 antenna elements. The channel model is as follows: Figure 1 As shown in FIG. 1 , the performance comparison of the channel estimation method provided by the embodiment of the present invention and other channel estimation methods for different numbers of pilot signals is shown in FIG. Figure 2 As shown in FIG. 1 , the performance comparison of the channel estimation method provided by the embodiment of the present invention and other channel estimation methods under different signal-to-noise ratio environments is shown in FIG. Figure 3 shown.

[0235] The simulation results verify the superiority of the channel estimation method (ADMM-AR algorithm) provided by the embodiment of the present invention over the traditional channel estimation methods (least squares method (LS algorithm) and orthogonal matching pursuit method (OMP algorithm)). The channel estimation accuracy is evaluated based on the normalized mean square error (NMSE), that is, ,in, express The estimated value of Represents the expected operation.

[0236] The present invention takes into account the sparse characteristics of the channel and adopts a sparse channel estimation method based on hybrid ADC channel amplitude recovery for the near-field spherical wave model of the XL-MIMO system, thereby achieving higher channel estimation accuracy than traditional channel estimation methods.

[0237] An embodiment of the present invention provides a computer device, including:

[0238] Storage medium for storing computer programs;

[0239] A processor is configured to execute a computer program to implement the XL-MIMO system channel estimation method under the hybrid ADC architecture provided by any embodiment of the present invention.

[0240] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the channel estimation method for an XL-MIMO system under a hybrid ADC architecture provided by any embodiment of the present invention is implemented.

[0241] An embodiment of the present invention provides a computer program product, including a computer program. When the computer program is executed by a processor, the channel estimation method for an XL-MIMO system under a hybrid ADC architecture provided by any embodiment of the present invention is implemented.

[0242] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code.

[0243] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0244] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0245] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0246] The above are only preferred embodiments of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A channel estimation method for an XL-MIMO system under a hybrid ADC architecture, characterized in that: include: A channel model is established that includes a near-field spherical wave model for the base station and a far-field plane wave model for the user. The pilot signal sent by the user is received and quantized using a hybrid ADC architecture to obtain a quantized signal. Based on the quantized signal, the channel estimation problem is modeled as an amplitude recovery optimization problem. The constraints of the objective function include the Hadamard product constraint of the quantized signal and the amplitude matrix, the channel sparsity constraint, and the low-rank constraint. Based on the alternating direction multiplier method, the amplitude recovery optimization problem is decomposed into: Amplitude matrix update subproblem: restore the amplitude information of the quantized signal; Auxiliary variable update subproblem: balancing channel estimation residuals; Channel parameter update subproblem: jointly handle channel sparsity constraints and low-rank constraints; Lagrange multiplier update subproblem: adjust constraints; Iteratively solve each sub-problem until the iteration termination condition is reached to obtain the channel estimation matrix; Modeling the channel estimation problem as an amplitude recovery optimization problem based on the quantized signal includes: Based on the amplitude recovery algorithm, the channel estimation problem is modeled as an amplitude recovery optimization problem. The objective function of the amplitude recovery optimization problem is: ； in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the amplitude matrix, represents the mixed magnitude-sign product, ,in, represents the real part, represents the imaginary part, represents the Hadamard product, represents the imaginary unit, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, represents the conjugate transpose, represents the Frobenius norm, represents the L1 norm, represents the regularization coefficient, represents matrix vectorization, represents the matrix rank operation, Indicates the total number of paths from the user to the base station; Introducing auxiliary variable matrix based on alternating direction multiplication method , the objective function of the amplitude recovery optimization problem is rewritten as: ； in, Indicates the indicator function, used to force The non-negativity of Augmented Lagrangian function for amplitude recovery optimization problem for: ； in, represents the Lagrange multiplier matrix, represents the residual matrix, , represents the matrix trace operation, Represents the penalty parameter of the alternating direction multiplier method.

2. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 1, characterized in that Base station receiving signal matrix for: ； in, 、…、 Respectively represent the 1st, ..., The received signal of the base station in time slots, represents the pilot signal matrix sent by the user, ,in, 、…、 Respectively represent the 1st, ..., The pilot signal sent by the user in the time slot is represents the additive white Gaussian noise matrix of the channel, ,in, 、…、 Respectively represent the 1st, ..., Additive white Gaussian noise of the time slot channel; Channel matrix from user to base station for: ； in, Indicates the total number of antennas equipped with the base station, Indicates the total number of antennas equipped by the user, represents the total number of paths from the user to the base station, Indicates the first The complex gain of each path, 、 They represent the first The arrival angle and departure angle of each path, Indicates the first The propagation distance of each path, represents the far-field steering vector, , represents the near-field steering vector, ,in, represents the imaginary unit, represents the wavelength of the near-field spherical wave, 、…、 、…、 Respectively represent the 1st, ..., 、…、 The root antenna is relative to the The distance of the path, ,in, represents the antenna index, represents the antenna spacing, represents the base station near-field codebook, represents the user far-field codebook, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents transpose, represents the conjugate transpose.

3. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 1, characterized in that The received signal is quantized through a hybrid ADC architecture. The quantized signal is obtained by: Quantize the received signal in the digital domain using a high-resolution ADC or a 1-bit ADC to obtain a quantized signal; The quantized signal is: ； in, Represents the received signal matrix of the base station The corresponding quantized signal matrix, represents the channel matrix from user to base station, represents the pilot signal matrix sent by the user, represents the additive white Gaussian noise matrix of the channel, Represents a quantized operation.

4. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 3, characterized in that The quantization process of high-resolution ADC is equivalent to the identity transformation, and the quantization process of 1-bit ADC satisfies ,in, represents the symbolic function, represents the real part, represents the imaginary part, represents an imaginary unit; Will Rewritten as: ； in, Indicates the base station Received signal matrix of the root antenna The corresponding quantized signal matrix, Represents the RF chain index set of the high-resolution ADC, Indicates the RF chain index set of the 1-bit ADC.

5. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 1, characterized in that The objective function of the amplitude matrix update subproblem is: ； in, represents the Lagrange multiplier matrix, represents the residual matrix, represents the matrix trace operation, represents the penalty parameter of the alternating direction multiplier method, represents the Frobenius norm, represents the amplitude matrix, represents the real part, represents the imaginary part, represents the conjugate transpose; The objective function of the auxiliary variable update subproblem is: ； in, It is an auxiliary variable matrix introduced based on the alternating direction multiplication method; The objective function of the channel parameter update subproblem is: ； in, is the sparse representation of the channel under the codebook, that is, a sparse matrix, represents matrix vectorization, represents the L1 norm, represents the regularization coefficient, represents the matrix rank, Indicates the total number of paths from the user to the base station; The update formula of the Lagrange multiplier update subproblem is: ； in, 、 Respectively represent 、 The Lagrange multiplier matrix of the iteration, Represents the received signal matrix of the base station The corresponding quantized signal matrix, Indicates the The magnitude matrix of the iteration, represents the mixed magnitude-sign product, ,in, represents the Hadamard product, represents the imaginary unit, Indicates the The sparse matrix of the iteration, represents the pilot signal matrix sent by the user, represents the base station near-field codebook, represents the user far-field codebook, It is Auxiliary variable matrix for iterations.

6. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 5, characterized in that: When iteratively solving each subproblem, the amplitude matrix update subproblem, auxiliary variable update subproblem, channel parameter update subproblem, and Lagrange multiplier update subproblem are solved in sequence to complete one iteration. The iteration is repeated until the iteration termination condition is reached to obtain the channel estimation matrix. Solving the amplitude matrix update subproblem involves: The linear and quadratic terms in the objective function of the amplitude matrix update subproblem are combined into a single Frobenius norm term by the matching method: ； Ignore constant terms , the objective function of the amplitude matrix update subproblem is simplified to: ； in, ; Will Expand to element-by-element calculation and decompose the objective function of the amplitude matrix update subproblem into independent optimization of the real and imaginary parts: ； in, represents the first intermediate variable matrix, ; right Perform closed-form non-negative projection on each element of : ； in, Indicates the The first intermediate variable matrix of the iteration, ; Solving the auxiliary variable update subproblem includes: merge 、 Two items are about The quadratic function , the objective function of the auxiliary variable update subproblem is simplified to: ； in, represents the second intermediate variable matrix, ; right Take the derivative and set it to zero: ； get: ； Substitution The expression of is: ； Solving the channel parameter update subproblem includes: Let the third intermediate variable matrix , the objective function of the channel parameter update subproblem is simplified to: ； Solve the channel parameter update subproblem through sparsity processing and low-rank projection; The iteration termination condition is: ； in, Indicates the convergence threshold.

7. The XL-MIMO system channel estimation method under the hybrid ADC architecture according to claim 6, characterized in that: Sparsity handling includes: Let the temporary matrix of the current iteration be ,initialization And update it: ； right Apply a soft thresholding operation to each element of : ； in, Represents the sparse matrix obtained by the soft threshold operation No. Rank Column elements, express No. Rank Column elements; Low-rank projections include: right Perform singular value decomposition: ； in, represents the left singular vector matrix, represents a diagonal matrix of singular values, represents the right singular vector matrix; Before Retention principal components, and obtain a low-rank approximate matrix for: ； in, express Before column vector, express upper left corner The sub-matrix of express Before column vector; It is the optimal estimate after sparsity processing and low-rank projection, and satisfies: 。 8. A computer device, characterized in that: include: Storage medium for storing computer programs; A processor, configured to execute the computer program to implement the XL-MIMO system channel estimation method under the hybrid ADC architecture according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the channel estimation method for the XL-MIMO system under the hybrid ADC architecture according to any one of claims 1 to 7 is implemented.

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