A kalman filter based joint hardware impairment and ris channel estimation method

Abstract

A kind of joint hardware damage and RIS channel estimation method based on Kalman filtering, construct system model, there is no direct link between base station and user in system;Channel model is constructed, including base station-intelligent super surface channel and intelligent super surface-user channel;Multi-user pilot transmission;State equation of cascaded channel is constructed, including channel state equation of intelligent super surface to user and state equation of cascaded channel;Measurement equation is constructed, in the presence of hardware damage, LS estimation is carried out to pilot signal received by base station, and vectorization processing is carried out;Phase shift state equation is constructed;Joint cascaded channel and phase shift state equation are constructed;State space equation is constructed;Nonlinear measurement function is linearized, then Kalman filtering is used to solve, realize channel estimation.Compared with prior art, the present application has the characteristics of stability, low complexity and good robustness to hardware damage.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and specifically relates to a joint hardware impairment and RIS channel estimation method based on Kalman filtering, which is used in wireless communication systems with device hardware impairments to improve channel estimation capabilities. Background Technology

[0002] In urban environments, direct communication links between users and base stations are often disrupted by buildings, trees, and other obstructions. As a low-power, passive, and low-cost device, smart metasurfaces can be flexibly deployed between base stations or users to establish connections and enable information transmission. By rationally configuring the phase shift of numerous passive reflective elements on the smart metasurface, the incident wave can be adjusted and reflected to the designated device. Since users are typically mobile, the channel between the smart metasurface and the user is time-varying. Kalman filtering, based on a state-space model, can effectively predict the channel, where prior channel information and real-time measurement information are used to improve the accuracy of channel estimation. However, in practical communication systems, there are non-negligible hardware impairments at the user, base station, and smart metasurface, such as phase noise, distortion noise, and phase shift. These hardware impairments significantly reduce the ability to estimate the channel; therefore, reducing the impact of hardware impairments on channel estimation is a crucial problem that urgently needs to be addressed.

[0003] A. Papazafeiropoulos et al., in their paper "Intelligent reflecting surface-assisted MU-MISO systems with imperfect hardware: Channel estimation and beamforming design" (IEEE Transactions on Wireless Communications, vol. 21, no. 3, pp. 2077-2092, Mar. 2022), proposed a channel estimation method based on the Least Minimum Mean Square Error (LMMSE). This method treats the sum of the direct link between the base station and the user, and the cascaded channel between the base station, smart metasurface, and the user as a whole, and uses the LMSE method to estimate this overall channel. This system simultaneously considers distortion noise at the base station and the user, as well as phase noise at the smart metasurface. The limitation of this method is that, because it estimates the channel sum of the direct link and the cascaded channel as a whole, it is only applicable to smart metasurface networks with fixed phase shifts.

[0004] Patent CN114785383A proposes a pilot pattern design method for a 1-bit ADC communication system assisted by a smart metasurface. The method's implementation steps are as follows: First, based on the minimum mean square error criterion, an optimization problem is constructed and solved numerically to obtain the optimal pilot pattern for the smart metasurface. Second, the smart metasurface switches its reflection coefficient matrix between different time slots according to the pre-calculated pilot pattern. The pilot sequence sent by the user side reaches the base station after reflection by the smart metasurface. Third, the base station jointly processes the quantized signals received in multiple time slots and obtains the estimated value of the cascaded channel through a linear estimator. The drawback of this method is that the pilot pattern optimization problem is a positive semi-definite relaxation problem with very high complexity and long numerical solution time, while the channel coherence time is typically in the millisecond range, making it difficult to re-optimize the algorithm in each time slot. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention aims to provide a joint hardware impairment and RIS channel estimation method based on Kalman filtering, which has the characteristics of stability, low complexity and good robustness to hardware impairment.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A joint hardware impairment and RIS channel estimation method based on Kalman filtering includes the following steps:

[0008] Step 1: Construct a system model where there is no direct link between the base station and the user.

[0009] Step 2: Construct the channel model, including the base station-smart metasurface channel and the smart metasurface-user channel;

[0010] Step 3, multi-user pilot transmission;

[0011] Step 4: Construct the state equations of the cascaded channels, including the channel state equations from the smart metasurface to the user and the state equations of the cascaded channels;

[0012] Step 5: Construct measurement equations, perform LS estimation on the pilot signals received by the base station in the presence of hardware impairment, and then perform vectorization processing.

[0013] Step 6: Construct the phase offset state equation;

[0014] Step 7: Construct the joint cascaded channel and phase offset state equations;

[0015] Step 8: Construct the state-space equations;

[0016] Step 9: Linearize the nonlinear measurement function, and then use Kalman filtering to solve for the channel estimation.

[0017] Compared with the prior art, the beneficial effects of the present invention are:

[0018] First, since this invention estimates cascaded channels that do not include smart metasurface phase shifts, it is not limited to fixed phase shifts, thus providing operability for subsequent further phase shift optimization and other processing. Furthermore, this paper employs the least squares (LS) channel estimation method, which is less complex, simpler to implement, and requires less channel information compared to the LMMSE method.

[0019] Second, the present invention uses random phase shifts in the intelligent metasurface during channel estimation, without requiring semi-definite relaxation optimization of the phase shift matrix, thus having very low implementation complexity.

[0020] Third, this invention takes into account comprehensive actual hardware impairments, including distortion noise and phase shift at the user and base station, as well as phase noise at the smart metasurface, making it a more realistic channel estimation method. Attached Figure Description

[0021] Figure 1 This is a scenario diagram of intelligent metasurface-assisted multi-user network communication according to the present invention.

[0022] Figure 2 This is a flowchart of the present invention.

[0023] Figure 3 This is the pilot transmission protocol of the present invention.

[0024] Figure 4 This is a flowchart illustrating the implementation of the present invention.

[0025] Figure 5 This is a simulation diagram of the normalized mean square error of the present invention. Detailed Implementation

[0026] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0027] As mentioned earlier, in practical communication systems, hardware impairments reduce channel estimation capabilities. Therefore, this invention provides a joint hardware impairment and RIS channel estimation method based on Kalman filtering, comprising the following steps:

[0028] Step 1: Build a system model.

[0029] Reference Figure 1 The method of the present invention is in Figure 1This system is implemented in the following scenario: It includes K single-antenna users, one base station, and one smart metasurface; the users are mobile with moderate movement speeds; the base station has M antennas, specifically a ULA array antenna in this embodiment; the smart metasurface has S reflecting elements, specifically a UPA array antenna in this embodiment. Control signals from the base station are transmitted to the smart metasurface via a wired connection, and a smart controller controls the phase shift and other configurations of the smart metasurface; a fixed random phase shift is set for the smart metasurface. in Let be the phase shift of the s-th reflecting unit of the intelligent metasurface during the j-th sub-stage of the n-th time slot. Randomly select from [0, 2π].

[0030] Step 2, construct the channel model.

[0031] The channels constructed in this invention include a base station-smart metasurface channel and a smart metasurface-user channel. Due to obstructions such as buildings, there is no direct link between the base station and the user; [the following is a separate section:] ... as well as Defined as the channels from the base station to the smart metasurface and from the smart metasurface to the k-th user in the nth time slot. Both channels are time-varying and remain constant within their respective coherence times. The base station-smart metasurface channel and the smart metasurface-user channel both follow a Ricean distribution, with a coherence time T... H Within this context, the base station-smart metasurface channel and the smart metasurface-user channel can be modeled as follows:

[0032]

[0033]

[0034] Where κ is the Rice factor, β BR and β Ru (k) represent the large-scale fading coefficients of the two channels, respectively. and Let represent the normalized non-direct rays, whose elements follow independent and identical distributions. and Let H1 and H2 represent the normalized direct radiation diameters. Since H1 remains constant during its coherence time, for simplicity, H1 is removed. The time slot index n. Furthermore, assume... At coherence time T H Since the internal structure remains unchanged, the time slot index n is also removed.

[0035] Step 3, refer to Figure 2 Design a multi-user pilot transmission protocol to transmit user pilots.

[0036] Reference Figure 3 T H and Representing channels respectively as well as The coherence time. Since the locations of the base station and the smart metasurface are fixed, it is assumed that the base station-smart metasurface channel changes more slowly than the smart metasurface-user channel, i.e. In this invention, it is assumed that Where N is an integer. For simplicity, assume... Channel from the smart metasurface to the k-th user coherence time The front T p The sequence is divided into a pilot transmission phase, and the remaining symbol length is used for the data transmission phase. The pilot transmission phase is further divided into J sub-phases, each sub-phase transmitting one pilot sequence of length τ. Therefore, each channel... coherence time A total of T were transmitted. p = Jτ pilot sequences; the time span consisting of J sub-stages is one time slot; orthogonal pilot sequences are allocated to all users.

[0037] Step 4: Construct the state equations of the cascaded channel

[0038] Step 4.1: Construct the channel state equation from the smart metasurface to the user.

[0039] Assuming different users have different movement speeds, based on a first-order autoregressive model, the channel from the smart metasurface to the k-th user... The state equation updated over time is:

[0040]

[0041] in The matrix represents the autoregressive coefficients of the k-th user. elements Indicates channel The time correlation coefficient, Indicates channel Modeling error. Due to For Rice channel, therefore The elements of follow a Gaussian distribution with a mean of . variance is Assuming that different reflecting units have similar time-dependent characteristics, i.e. Using Jake's model, the time correlation coefficient is determined by the symbol interval between adjacent time slots, i.e., Where J0(·) is the zeroth-order Bessel function. The maximum Doppler frequency shift for the k-th user is given; therefore, the time correlation coefficient is derived from... Sure, It can be simplified to A k =diag(a k ,a k ,…,a k ).

[0042] Step 4.2: Construct the state equations for the cascaded channel.

[0043] First, regarding the channel Diagonalize and multiply by matrix H1 to obtain

[0044]

[0045] Definition of the cascaded channel based on base station-smart metasurface-kth user The time-correlation characteristics of the cascaded channels can be obtained as follows:

[0046]

[0047] in

[0048] The state equations of the cascaded channel for different users are synthesized into the following expression, i.e., the state equations of the cascaded channel:

[0049] G n =AG n-1 +U n

[0050] Among them, G n Let A be the channel matrix of K user sets, and A be the autoregressive coefficient matrix of the K user sets, U n Modeling noise in the channel H1 from the base station to the smart metasurface and in different user state update equations. The set of products of , can be expressed by the following formulas:

[0051]

[0052]

[0053]

[0054] Step 5, construct the measurement equation

[0055] Step 5.1, the user transmits pilot signals.

[0056] Assumption For the pilot sequence of the k-th user in the n-th time slot, pilot sequence The τth symbol in the sequence. In this invention, orthogonal pilot sequences are used between users, that is, satisfying:

[0057]

[0058] Step 5.2, pilot signal received at the base station

[0059] When hardware damage exists, the pilot signal received at the base station is:

[0060]

[0061] Distortion noise at the user and base station can be modeled as a Gaussian distributed random variable, with average power proportional to the power of the transmitted and received signals. The distortion noise at the user's location has elements that follow a distribution. κ UE A proportionality coefficient characterizing the degree of impairment for each user. The distortion noise at the base station is... Its elements obey Distribution, among which and κ BS The extent of damage at the base station was depicted.

[0062] Phase noise at smart metasurfaces stems from the limited precision of the reflective element configuration. Assume the phase noise is uniformly distributed in [-k...]. r π,k r In π), where k r This represents the severity of hardware damage. The phase matrix with phase-shift noise at the smart metasurface is... in The phase of the s-th reflection unit in the j-th sub-stage of the n-th time slot. This represents the corresponding phase noise. p is the transmit power of the pilot sequence. This represents the noise in the j-th sub-stage of the n-th time slot.

[0063] Phase offset at the user and base station is typically caused by the local oscillator and can be modeled as a Wiener process. Phase offset is defined as... in For the phase offset of each user in the j-th sub-stage of the n-th time slot, This represents the phase offset of the m-th antenna of the base station in the j-th sub-stage of the n-th time slot. and It can be modeled as a discrete-time Wiener stochastic process:

[0064]

[0065]

[0066] in as well as These represent the random phase increments caused by the non-ideal local oscillators at the m-th antenna of the user and base station, respectively. The phase offsets of the transmitter and receiver are updated in each sub-stage.

[0067] Step 5.3, the base station uses the LS estimation method.

[0068] The base station uses the LS estimation method to obtain the received pilot signal.

[0069]

[0070] in

[0071]

[0072]

[0073] Step 5.4, Received signal vectorization processing

[0074] definition Where vec(·) is the vectorization operation. Using Can Rewritten as The above equation can then be rewritten as

[0075]

[0076] in

[0077] Signals from different sub-stages Combine them into a new vector, and obtain

[0078]

[0079] in,

[0080]

[0081]

[0082]

[0083]

[0084] Furthermore, by combining the received signals from different users into a new vector, the measurement equation is obtained.

[0085]

[0086] in, as well as

[0087] Step 6, Construct the phase offset state equation

[0088] Since the phase offset matrix is ​​part of the measurement matrix, and the base station does not possess phase offset information, channel estimation is challenging. Observations reveal that the phase offset matrix exhibits an update pattern similar to that of the concatenated channel. Therefore, this invention jointly estimates the phase offset and the concatenated channel. Because the phase offset is updated once per sub-stage, while the concatenated channel is updated once per time slot, to update the phase offset and the concatenated channel in a unified manner, the phase offset state equation is first recursively updated, resulting in the following formula:

[0089]

[0090]

[0091] in as well as

[0092] definition, as well as The above update formula can be rewritten in the following vector form:

[0093] ∈ n =∈ n-1 +Δ∈

[0094] ν n =ν n-1 +Δν

[0095] in, Δν×[Δv 1,1 ,…,Δv J,1 ,…,Δv 1,M ,…,Δv J,M ] T ; as well as

[0096] Step 7: Construct the joint cascaded channel and phase offset state equations

[0097] After vectorization, the concatenated channel vectors The state equation is

[0098]

[0099] in as well as rvec(·) represents the row vectorization operation on a matrix.

[0100] By combining the phase offset and channel variables into a new state vector, the complete state equation is obtained, i.e.

[0101]

[0102] in

[0103]

[0104]

[0105]

[0106] Step 8, construct the state-space equations

[0107] definition The final measurement equation is as follows: Combining the final measurement equation and the final state equation, the complete state-space equation is obtained as follows:

[0108]

[0109] in It is channel g n The product of the phase shift and the phase offset is a nonlinear measurement function. as well as

[0110] Step 9, Extended Kalman Filter

[0111] Step 9.1 Linearization Process

[0112] Because of the joint estimation of phase offset and concatenated channels For γ n The nonlinear function, whose nonlinearity mainly originates from the matrix. Specifically, the state vector γ n By channel g n And phase shift, and function It is channel g n The function is nonlinear, consisting of the product of phase shift and phase offset. For nonlinear measurement functions, an extended Kalman filter is needed to solve them. A first-order Taylor expansion can be used to transform the nonlinear function... Linearization, specifically, requires solving the nonlinear function with respect to the state variable γ. n The Jacobian matrix.

[0113]

[0114] Step 9.2 applies Kalman filtering to the linearized model, refer to... Figure 4 The specific steps are as follows:

[0115] Step 9.2.1, at the base station, the channel matrix g...n With the prior covariance matrix P n Perform initialization;

[0116] g 0 κ0 SMK×1

[0117] P 0 =I SMK+J+JM

[0118] Step 9.2.2: At the beginning of each channel coherence time, the base station utilizes the channel's time-related information. and the state noise covariance matrix Cascaded channel γ for the current time slot n|n-1 and the prior covariance matrix P n|n-1 Make predictions;

[0119]

[0120]

[0121] Step 9.2.3, using the prior covariance matrix P n|n-1 Measurement noise covariance matrix And the Jacobian matrix Ω of the nonlinear measurement function with respect to the channel matrix n Calculate the Kalman gain matrix K n ;

[0122]

[0123] K n =P n|n-1 (Ω n ) H (S n ) -1

[0124] Step 9.2.4: At the start of each channel coherence time, all users send pilot sequences to the base station. The pilot sequences are reflected by the smart metasurface and reach the base station. The base station then utilizes the received pilot sequences... and the Kalman gain matrix K n The predicted cascaded channel is corrected to obtain γ. n|n And obtain the posterior covariance matrix P n|n ;

[0125]

[0126] P n|n =P n|n-1 -K n Ω n P n|n-1

[0127] Let n = n+1, and repeat steps 9.2.2-9.2.4 until the complete channel estimation phase ends.

[0128] In this embodiment of the invention, the simulation results were obtained using MATLAB software, and the NMSE value was obtained by averaging 100 channel implementations. The total time slot length for channel estimation is N = 200. The base station and the smart metasurface are distributed on a two-dimensional plane with coordinates (-10, 0) and (0, 10) respectively. The number of base station antennas is M = 8, and the number of smart metasurface reflection units is S = 20. K = 2 single-antenna users are randomly distributed in a rectangular area of ​​20m × 10m. The path loss models from the base station to the smart metasurface and from the smart metasurface to the users are 30 + 22log 10 (d(m)), where d represents the distance. The Ricean factor is 10 dB. The channel coherence time from the base station to the smart metasurface is 10 times that from the smart metasurface to the user, i.e., T. H =10T h The Doppler frequency shift of different users follows a uniform distribution. Noise is σ 2 = -120dBm.

[0129] Figure 5 The method corresponding to this invention was compared with the channel estimation scheme proposed in paper 1, "Channel estimation and power scaling law of large reflecting surface with non-ideal hardware" (Y. Liu, E. Liu, R. Wang, and Y. Geng, 2020, arXiv: 2004.09761.). As shown in the figure, the NMSE achieved by both schemes increases with increasing pilot transmit power, reaching a performance plateau at a transmit power of p = 10 dB. Furthermore, as the severity of distortion noise increases, i.e., when κ... BS With κ UE As the value increases, NMSE performance gradually deteriorates, and the performance plateau reached also gradually worsens. However, at different κ values... BS With κ UE When the value is specified, the NMSE performance achieved by the method corresponding to this invention is superior to that achieved in Paper 1. This is because Paper 1 uses the ON / OFF method, meaning that only one reflecting unit is capable of signal reflection at any given time, thus failing to fully utilize the array gain of the smart metasurface.

Claims

1. A joint hardware impairment and RIS channel estimation method based on Kalman filtering, characterized in that, Includes the following steps: Step 1: Construct a system model where there is no direct link between the base station and the user. Step 2: Construct the channel model, including the base station-smart metasurface channel and the smart metasurface-user channel; Step 3, multi-user pilot transmission; Step 4: Construct the state equations of the cascaded channels, including the channel state equations from the smart metasurface to the user and the state equations of the cascaded channels; Step 5: Construct measurement equations, perform LS estimation on the pilot signals received by the base station in the presence of hardware impairment, and then perform vectorization processing. Step 6: Construct the phase offset state equation; Step 7: Construct the joint cascaded channel and phase offset state equations; Step 8: Construct the state-space equations; Step 9: Linearize the nonlinear measurement function, and then use Kalman filtering to solve for channel estimation. The solution process is as follows: Step 9.2.1: The base station initializes the channel matrix and the prior covariance matrix; Step 9.2.2: At the beginning of each channel coherence time, the base station uses the channel's time-related information and state noise covariance matrix to predict the concatenated channel and prior covariance matrix of the current time slot. Step 9.2.3: Calculate the Kalman gain matrix using the prior covariance matrix, the measurement noise covariance matrix, and the Jacobian matrix of the nonlinear measurement function with respect to the channel matrix; Step 9.2.4: At the start of the coherence time of each channel, all users send pilot sequences to the base station. The pilot sequences are reflected by the smart metasurface and reach the base station side. The base station uses the received pilot sequence and Kalman gain matrix to correct the predicted cascaded channel and obtain the posterior covariance matrix; repeat steps 9.2.2-9.2.4 until the complete channel estimation stage ends.

2. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 1, characterized in that, In step 1, the system includes One single-antenna user, one with A base station with a root antenna, and a base station with A smart metasurface with individual reflective units; the smart metasurface is configured with a fixed random phase shift. ,in For the first The first time slot The first sub-stage of the intelligent metasurface Phase shift of each reflecting unit, from Randomly selected from the list.

3. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 2, characterized in that, In step 2, the base station-smart metasurface channel and the smart metasurface-user channel are modeled as follows: in This represents the channel from the base station to the smart metasurface. Indicates the first The first time-slot smart metasurface to the [number]th k Channels for individual users; Rice factor, and These are the large-scale fading coefficients of the two channels, respectively. and They represent the normalized non-direct ranges, and These represent the normalized direct radius.

4. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 3, characterized in that, In step 3, coherence time The former The sequence is divided into a pilot transmission phase, and the remaining symbol length is for the data transmission phase; the pilot transmission phase is further divided into... Each sub-stage transmits a pilot sequence of length [length missing]. ,but Internal transmission One pilot sequence; Each sub-stage constitutes a time slot; orthogonal pilot sequences are allocated to all users.

5. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 3, characterized in that, Step 4, channel The state equation updated over time is: in Representing the Autoregressive coefficient matrix of individual users Indicates channel Modeling error, Indicates channel The time correlation coefficient; The state equation of the cascaded channel is: in For base stations - intelligent metasurfaces - the first cascaded channels for individual users To be K Channel matrix for a set of users for K The autoregressive coefficient matrix of a set of users, Channel from base station to smart metasurface Modeling noise in different user state update equations The set of products of, defined .

6. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 5, characterized in that, Step 5 includes: Step 5.1: Users use orthogonal pilot sequences; Step 5.2, when hardware damage exists, the pilot signal received at the base station is: For phase shift, ,in , For the first The first time slot Phase offset for each user in each sub-stage For the first The first time slot The first sub-stage base station Phase shift of the root antenna; The phase matrix at the smart metasurface exhibiting phase-shift noise. ,in For the first The first time slot In each sub-stage The phase of each reflecting unit, This corresponds to the phase noise; Distortion noise at the user's location. This refers to the distortion noise at the base station. The transmit power of the pilot sequence, For the first The first time slot Noise in each sub-stage, For the first The user in the first Pilot sequences for each time slot; Step 5.3: The base station performs LS estimation on the received pilot signal to obtain... in Step 5.4: Vectorize the received signal.

7. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 6, characterized in that, In step 6, and Modeled as a discrete-time Wiener stochastic process and recursively updated, the phase shift state equation is obtained as follows: in, , , , .

8. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 6, characterized in that, In step 7, after vectorization processing, the concatenated channel vectors are... The state equation is: in as well as , This indicates the row vectorization operation on the matrix; By combining the phase offset and channel variables into a new state vector, the complete state equation is obtained, i.e. in 。 9. The joint hardware impairment and RIS channel estimation method based on Kalman filtering according to claim 8, characterized in that, In step 8, the state-space equations are as follows: in It is a channel The product of the phase shift and the phase offset is a nonlinear measurement function. , , , , ,as well as .

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