Robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system

Abstract

The invention discloses a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system. The method comprises the following steps: establishing a receiving signal model of a transceiver under the condition of considering that a channel estimation error exists in a multi-carrier MIMO SWIPT system; based on a receiving signal model of the transceiver, establishing an optimization problem of a pre-coding matrix, an equalization matrix, a feedback matrix and a power division proportion of a joint subcarrier by taking the minimization of a total mean square error of a receiving signal as a target; and converting the optimization problem, and solving the converted optimization problem by using a preset algorithm to obtain an optimal precoding matrix, an optimal equilibrium matrix, an optimal feedback matrix and an optimal power division proportion of the corresponding subcarrier when the total mean square error of the received signal is minimum. The method can implement the design of a nonlinear transceiver adapted to a multicarrier MIMO SWIPT system.

Description

Technical Field

[0001] The present invention relates to the field of nonlinear transceivers, and more specifically, to a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system. Background Art

[0002] In the 6G era, wireless power communication technology (simultaneous wireless information and power transfer, SWIPT) is a technology with great development potential. It can provide wireless power to a large number of IoT devices and effectively extend the working cycle of energy-constrained IoT networks. The transceiver is responsible for the signal transmission and reception of wireless power communication technology and is an important part of wireless power communication technology.

[0003] Traditional transceivers are mainly linear transceivers. For the case of perfect channel state information (CSI), the prior art has studied multi-carrier MIMO SWIPT systems based on power splitting (PS), and minimized different mean square error (MSE) functions and maximized energy efficiency under different constraints. For the case of imperfect channel state information, the prior art proposed a robust beamforming scheme based on PS MIMO SWIPT networks, and maximized the data confidentiality rate under the constraints of signal-to-interference-plus-noise ratio (SINR), EH and transmit power. The prior art work is extended to PS-based MIMO SWIPT IoT networks, and maximizes the minimum energy collection power among all users under the premise of satisfying the data confidentiality rate and total transmit power constraints. The prior art studies TS-based amplification and forwarding and decoding and forwarding MIMO SWIPT relay systems, and maximizes mutual information under the constraints of source node transmit power and relay node transmit power. The prior art studies a full-duplex MIMO SWIPT IoT network and maximizes the worst-case secure energy efficiency of the system under the conditions of EH constraints and transmit power constraints. For traditional wireless information transmission systems, nonlinear transceivers can improve the communication performance of MIMO systems. Considering the design complexity of energy-constrained terminals, Tomlinson-Harashima precoding (THP) technology is more suitable for MIMO SWIPT IoT networks because the transmitter can afford the computational overhead required for nonlinear signal processing. So far, the prior art has proposed a robust design scheme for a single-carrier MIMO SWIPT system based on THP, and minimized the average MSE of the received signal under the premise of meeting the EH and transmit power constraints. However, the separate receiver scheme in the prior art is not suitable for IoT terminal devices, because in actual application, equipping the terminal with a dedicated EH receiver will increase the cost. In addition, the single-carrier transmission scheme of the prior art is also not suitable for frequency-selective fading channel scenarios, because the matrix optimization-based algorithm in the prior art has a high complexity, which makes it difficult to expand to multi-carrier MIMO scenarios.

[0004] The prior art discloses a robust multi-carrier MIMO wireless power system design method under non-ideal channel information, including the following steps: S1: considering the channel error, establishing a channel estimation error model; S2: establishing a receiving signal model of the transceiver of the wireless power communication system according to the channel estimation error model; S3: establishing a transceiver signal optimization problem, the goal of which is to minimize the MSE of the transceiver information decoder equalization signal under the premise of satisfying a given transmission power constraint and an average collection power constraint; S4: solving the transceiver signal optimization problem using an alternating optimization algorithm to obtain an optimal transceiver design solution. This method is mainly aimed at linear transceivers, but not at nonlinear transceivers. Summary of the invention

[0005] Aiming at the technical gap that nonlinear transceivers have not been applied to multi-carrier MIMO SWIPT systems, the present invention proposes a robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT systems to achieve the design of nonlinear transceivers adapted to multi-carrier MIMO SWIPT systems.

[0006] The primary purpose of the present invention is to solve the above technical problems. The technical solution of the present invention is as follows:

[0007] Robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system, including:

[0008] S1: Considering the presence of channel estimation errors in a multi-carrier MIMO SWIPT system, a transceiver receiving signal model is established;

[0009] S2: Based on the received signal model of the transceiver, with the goal of minimizing the total mean square error of the received signal, an optimization problem of the precoding matrix, the equalization matrix, the feedback matrix and the power division ratio of the joint subcarrier is established;

[0010] S3: transform the optimization problem, solve the transformed optimization problem using a preset algorithm, and obtain the optimal precoding matrix, optimal equalization matrix, optimal feedback matrix and optimal power division ratio of the corresponding subcarrier when the total mean square error of the received signal is minimized.

[0011] Furthermore, the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier is as follows:

[0012]

[0013] C3: 0≤β≤1

[0014] Tr represents the trace in linear algebra, M krepresents the MSE matrix of the kth subcarrier, k represents the subcarrier number, N represents the total number of subcarriers, P k represents the precoding matrix of the kth subcarrier, β represents the power division ratio, C k represents the feedback matrix of the kth subcarrier, G k represents the equalization matrix of the kth subcarrier, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, Represents the input power requirement of the energy harvester with respect to the system design.

[0015] Furthermore, the step S3 comprises:

[0016] S30101: converting the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint optimization problem of the precoding matrix and the power division ratio;

[0017] S30102: Solving the joint optimization problem of the precoding matrix and the power split ratio to obtain an optimized precoding matrix and an optimized power split ratio;

[0018] S30103: updating an equalization matrix and a feedback matrix according to the optimized precoding matrix and the optimized power division ratio;

[0019] S30104: Repeat steps S30102 to S30103 until the joint optimization problem of the precoding matrix and the power split ratio converges to a preset accuracy, and obtains the optimal precoding matrix, the optimal power split ratio, the optimal equalization matrix and the optimal feedback matrix.

[0020] Furthermore, in step S30103, the optimal expression of the equalization matrix is ​​as follows:

[0021]

[0022] represents the optimized equalization matrix of the kth subcarrier, P k represents the precoding matrix of the kth subcarrier, represents the estimated channel matrix of the kth subcarrier, C k represents the feedback matrix of the kth subcarrier, R yk Indicates calculation of intermediate quantities;

[0023] The optimal expression of the feedback matrix is ​​as follows:

[0024]

[0025] Q k represents the lower triangular matrix of the kth subcarrier, L k represents the number of symbols carried by the kth subcarrier, [Q k ] i,j Represents the data of the i-th row and j-th column of the k-th subcarrier, where k represents the subcarrier number.

[0026] Furthermore, the joint optimization problem of the precoding matrix and the power split ratio is as follows:

[0027]

[0028] C3: 0≤β≤1

[0029]

[0030] represents the second MSE expression of the kth subcarrier, Tr represents the trace in linear algebra, k represents the subcarrier number, N represents the total number of subcarriers, P k represents the precoding matrix of the kth subcarrier, β represents the power division ratio, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, represents the input power requirement of the energy harvester for system design, Q k represents the unit lower triangular matrix of the k-th subcarrier.

[0031] Furthermore, the step S3 comprises:

[0032] S30201: Convert the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint scalar optimization problem of power allocation and power division ratio;

[0033] S30202: fix the power split ratio, solve the joint scalar optimization problem about power allocation and power split ratio, and obtain a power allocation scheme and an optimal precoding matrix;

[0034] S30203: searching for an optimal power split ratio according to the power allocation scheme and the joint scalar optimization problem regarding power allocation and power split ratio;

[0035] S30204: Calculate an optimal equalization matrix and an optimal feedback matrix based on the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power split ratio of the joint subcarrier, the optimal precoding matrix and the optimal power split ratio.

[0036] Furthermore, the expression of the joint scalar optimization problem of power allocation and power split ratio is as follows:

[0037]

[0038] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F0 represents a function, μ k,i 、v k,i Indicates the calculation of intermediate quantities.

[0039] Furthermore, in step S30202, the joint scalar optimization problem regarding power allocation and power split ratio is solved as follows:

[0040]

[0041] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F1 represents a function, Indicates the calculation of intermediate quantities.

[0042] Furthermore, in step S30202, the joint scalar optimization problem regarding power allocation and power split ratio is solved as follows:

[0043]

[0044] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, t k represents the relaxation variable of the kth subcarrier, g k 、hk Indicates the calculation of intermediate quantities.

[0045] Furthermore, in step S30203, the optimization problem of searching for the optimal power split ratio is as follows:

[0046]

[0047] G represents a unimodal function about β, represents the power allocation scheme, F represents the power split ratio optimization problem, and β represents the power split ratio.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention establishes a receiving signal model of a transceiver in the presence of a channel estimation error in a multi-carrier MIMO SWIPT system; based on the receiving signal model of the transceiver, an optimization problem of a precoding matrix, an equalization matrix, a feedback matrix and a power division ratio of a joint subcarrier is established with the goal of minimizing a total mean square error of the received signal; the optimization problem is transformed, and the transformed optimization problem is solved using a preset algorithm to obtain an optimal precoding matrix, an optimal equalization matrix, an optimal feedback matrix and an optimal power division ratio of the corresponding subcarrier when the total mean square error of the received signal is minimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system provided in Example 1.

[0051] Figure 2 This is a structural diagram of the receiving signal model of the transceiver provided in Example 1.

[0052] Figure 3 A flow chart for converting and solving the optimization problem provided in Example 1.

[0053] Figure 4 A flow chart for converting and solving the optimization problem provided in Example 1.

[0054] Figure 5 This is a single-peak characteristic curve diagram of the power division ratio provided in Example 1.

[0055] Figure 6 This is a comparison chart of the complexity analysis of each algorithm provided in Example 1.

[0056] Figure 7 This is a simulation parameter diagram provided for Example 1.

[0057] Figure 8 This is a comparison chart of the average total mean square error and transmission power provided in Example 1.

[0058] Fig. 9 This is a comparison chart of bit error rate and transmission power provided in Example 1.

[0059] Fig.10 This is a comparison chart of the average total mean square error and transmission power provided in Example 1. DETAILED DESCRIPTION

[0060] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0061] In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

[0062] It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0063] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0064] Example 1

[0065] like Figure 1 As shown, a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system includes:

[0066] S1: Considering the presence of channel estimation errors in a multi-carrier MIMO SWIPT system, a transceiver receiving signal model is established;

[0067] S2: Based on the received signal model of the transceiver, with the goal of minimizing the total mean square error of the received signal, an optimization problem of the precoding matrix, the equalization matrix, the feedback matrix and the power division ratio of the joint subcarrier is established;

[0068] S3: transform the optimization problem, solve the transformed optimization problem using a preset algorithm, and obtain the optimal precoding matrix, optimal equalization matrix, optimal feedback matrix and optimal power division ratio of the corresponding subcarrier when the total mean square error of the received signal is minimized.

[0069] like Figure 2 As shown, a t Transmitting antennas and N r In a multi-carrier MIMO SWIPT system with 10 receiving antennas, the total bandwidth W of the system is evenly distributed to N subcarriers. Due to the time-varying characteristics of the wireless channel and the limited length of the pilot symbol, channel estimation errors are inevitable. The model can be described as:

[0070]

[0071] k=1,...,N, is the estimated channel matrix of the kth subcarrier, is a random matrix and each element is independently and identically distributed CN(0,1), σ e,k It represents the channel estimation error variance. This technique assumes that both the transmitter and receiver have the same imperfect CSI.

[0072] Assume that the information symbol vector carried by the kth subcarrier is expressed as L k ≤min{N t ,N r},s k All elements of are modulated by M-QAM, with a mean of 0 and a variance of 1. Before transmission, s k First, it is sent to the THP unit for processing. The THP unit consists of a modulo operation and a strict lower triangular feedback matrix The specific operation process of the modulo operation is: in represents the largest integer not exceeding z. Then, the THP unit outputs the signal vector Its nth element can be expressed as and and is to v k The elements are restricted to The complex vector in the region. According to the above analysis, we can get:

[0073]

[0074] in Lower triangular matrix with unit diagonal elements, u k =s k +i k is a valid signal vector. If M is large enough, then Next, a frequency domain precoding matrix Used to process v k , and get the transmitted signal. After the transmitted signal propagates through the wireless channel, the received signal can be expressed as

[0075]

[0076] in is the additive white Gaussian noise vector.

[0077] For power splitting, this technique assumes that all antennas use the same PS ratio β∈(0,1). Part β of the received signal power is used for energy collection, and the remaining (1-β) is used for information decoding. Therefore, the frequency domain signals used for EH and ID can be expressed as:

[0078]

[0079] in, It represents the AWGN vector introduced by the ID circuit during signal processing.

[0080] For energy harvesting, the total input power to the energy harvester is According to Parsval's theorem, we can further get:

[0081]

[0082] The derivation in (1.6) applies: If the elements of X obey CN(0,σ 2 ), E[XMX H ]=σ 2 Tr(M)I. This technology adopts a nonlinear EH model, that is, the energy collection power γ(E in ) is about E in The nonlinear function can be expressed as:

[0083]

[0084] in, E m and E0 represent the input power of the energy harvester and the activation power of the energy harvester, respectively. The parameters τ and ν determine the function γ(E in ) curve characteristics. Let E th represents the EH requirement of the system design, so the EH constraint of the system design can be obtained as γ(E in )≥E th , the equivalent constraints are derived:

[0085]

[0086] in

[0087] For information decoding, after the equalization matrix The processed signal is:

[0088]

[0089] in, is an automatic gain control factor used to simplify the derivation. The MSE matrix of the kth subcarrier, It can be further deduced as:

[0090]

[0091] in,

[0092] Furthermore, the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier is as follows:

[0093]

[0094] C3: 0≤β≤1

[0095] Tr represents the trace in linear algebra, M k represents the MSE matrix of the kth subcarrier, k represents the subcarrier number, N represents the total number of subcarriers, P k represents the precoding matrix of the kth subcarrier, β represents the power division ratio, C k represents the feedback matrix of the kth subcarrier, G k represents the equalization matrix of the kth subcarrier, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, Represents the input power requirement of the energy harvester with respect to the system design.

[0096] It should be noted that {P k ,X k C k} indicates that the same k corresponds to P k ,X k C k .

[0097] Furthermore, if Figure 3 As shown, the step S3 includes:

[0098] S30101: converting the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint optimization problem of the precoding matrix and the power division ratio;

[0099] S30102: Solving the joint optimization problem of the precoding matrix and the power split ratio to obtain an optimized precoding matrix and an optimized power split ratio;

[0100] S30103: updating an equalization matrix and a feedback matrix according to the optimized precoding matrix and the optimized power division ratio;

[0101] S30104: Repeat steps S30102 to S30103 until the joint optimization problem of the precoding matrix and the power split ratio converges to a preset accuracy, and obtains the optimal precoding matrix, the optimal power split ratio, the optimal equalization matrix and the optimal feedback matrix.

[0102] In order to minimize the total mean square error of the received signal, we need to About G k The first-order derivative of is zero, and the optimal expression of the equilibrium matrix can be obtained:

[0103]

[0104] represents the optimized equalization matrix of the kth subcarrier, P k represents the precoding matrix of the kth subcarrier, represents the estimated channel matrix of the kth subcarrier, C k represents the feedback matrix of the kth subcarrier, R yk Indicates calculation of intermediate quantities;

[0105] Equation (1.11) is the famous Wiener filter. Substituting it into (1.10) and using the matrix inversion lemma, we can get:

[0106]

[0107] in,

[0108] According to equation (1.12), the mean square error of the i-th symbol in the k-th subcarrier can be written as:

[0109]

[0110] in, yes From formula (1.13), we can see that different [M k ] i,i The minimization of can be performed independently. Let T k The Cholesky decomposition of Where Q k is a lower triangular matrix, so we can get:

[0111]

[0112] in, is a lower triangular matrix, and has From formula (1.14), we can see that if we want to minimize the MSE value, the sum of formula (1.14) must be zero. The optimal expression of the feedback matrix is ​​as follows:

[0113]

[0114] Q k represents the lower triangular matrix of the kth subcarrier, L k represents the number of symbols carried by the kth subcarrier, [Q k ] i,j Represents the data of the i-th row and j-th column of the k-th subcarrier, where k represents the subcarrier number.

[0115] It should be noted that and are feedback matrices, and in, The diagonal of the matrix is ​​all zeros. The diagonal of the matrix is ​​all 1.

[0116] Substituting equation (1.15) into equation (1.12) we can obtain:

[0117]

[0118] For a given {G k ,C k}, the optimization problem P1 degenerates into a joint optimization problem of the precoding matrix and the PS ratio:

[0119]

[0120] In order to transform P 2 into a convex SDP problem, slack variables need to be introduced: and Therefore, P2 can be equivalent to the following formula:

[0121]

[0122] stC3: 0≤β≤1

[0123]

[0124] P k represents the precoding matrix of the kth subcarrier, represents the estimated channel matrix of the kth subcarrier, C k represents the feedback matrix of the kth subcarrier, G k represents the equalization matrix of the kth subcarrier, X k represents the slack variable, β represents the power split ratio, Tr represents the trace in linear algebra, The third MSE expression for the k-th subcarrier is: Indicates the calculation of intermediate quantities. represents the identity matrix, L k represents the number of symbols carried by the kth subcarrier, δ k,sp represents the standard deviation of the signal processing noise, represents the input power requirement of the energy harvester for system design, E * (X k ) represents the received signal power.

[0125]

[0126] It should be noted that this problem is a convex SDP problem, so it can be solved using convex optimization solvers such as CVX.

[0127] Furthermore, if Figure 4 As shown, the step S3 includes:

[0128] S30201: Convert the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint scalar optimization problem of power allocation and power division ratio;

[0129] S30202: fix the power split ratio, solve the joint scalar optimization problem about power allocation and power split ratio, and obtain a power allocation scheme and an optimal precoding matrix;

[0130] S30203: searching for an optimal power split ratio according to the power allocation scheme and the joint scalar optimization problem regarding power allocation and power split ratio;

[0131] S30204: Calculate an optimal equalization matrix and an optimal feedback matrix based on the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power split ratio of the joint subcarrier, the optimal precoding matrix and the optimal power split ratio.

[0132] Furthermore, the joint optimization problem of the precoding matrix and the power split ratio is as follows:

[0133]

[0134] C3: 0≤β≤1

[0135]

[0136] represents the second MSE expression of the kth subcarrier, Tr represents the trace in linear algebra, k represents the subcarrier number, N represents the total number of subcarriers, P krepresents the precoding matrix of the kth subcarrier, β represents the power division ratio, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, represents the input power requirement of the energy harvester for system design, Q k represents the lower triangular matrix of the k-th subcarrier.

[0137] It can be seen that P 4 is still a k} and β. To solve this non-convex problem, this technology proposes a two-layer optimization algorithm. Specifically, in the inner optimization, β is fixed, and then the precoding matrix {P k} optimization; in the outer layer optimization, the GSS algorithm is used to search for the optimal PS ratio.

[0138] For a fixed β, P 4 can be rewritten as k}Optimization problem:

[0139]

[0140] P5 is a precoding matrix optimization problem, which can be further simplified using the following proposition.

[0141] Proposition 1: For problem P 5, the optimal precoding matrix It has the following structure:

[0142]

[0143] in, Depend on Front L k The eigenvectors corresponding to the large eigenvalues ​​are composed of is a diagonal matrix, z k,i is the power allocated to the i-th symbol of the k-th subcarrier, is a unitary matrix obtained by geometric mean decomposition (GMD) such that All diagonal elements of are equal to

[0144]

[0145] Among them, λ k,i yes The i-th largest eigenvalue of .

[0146] Proof: For a fixed β, if constraint C2 can be satisfied, then P5 degenerates into minimizing the total mean square error under a given transmit power constraint.

[0147] Substituting equations (1.18) and (1.19) into P5, the precoding matrix optimization problem is simplified to a scalar power allocation optimization problem P6:

[0148]

[0149] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F0 represents a function, μ k,i 、v k,i Indicates the calculation of intermediate quantities.

[0150] in,

[0151] Obviously, P 6 is still a non-convex optimization problem. Therefore, this technology proposes two power allocation schemes to transform it into an approximate convex form, namely: APA (average power allocation) method and SCA (successive convex approximation) method.

[0152] For the APA approach, it can be observed that represents the power allocated to the kth subcarrier. In order to obtain an approximate convex form of P 6, it is necessary to make While keeping the constraints unchanged, P 6 can be transformed into P7:

[0153]

[0154] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F1 represents a function, Indicates the calculation of intermediate quantities.

[0155]

[0156] Since all constraints of problem P7 are affine, it can be verified that P7 is a convex optimization problem by proving that the Hessian matrix of the objective function is semi-positive definite, and then the Lagrangian dual algorithm can be used to solve it. According to the Karush-Kuhn-Tucker (KKT) condition, the expression of the joint scalar optimization problem of power allocation and power split ratio can be obtained as follows:

[0157]

[0158] Indicates the calculation of intermediate quantities, i, j, k indicate serial numbers, L k Indicates the number of symbols carried by the kth subcarrier, N r represents the number of receiving antennas, represents the variance of the channel estimation error, λ k,i express The i-th largest eigenvalue of represents the average power allocated to the kth subcarrier, represents the calculated intermediate quantity of the kth subcarrier, u and v represent non-negative dual variables, and δ k,i represents the i-th calculated intermediate quantity of the k-th subcarrier, φ k,i represents the i-th calculated intermediate quantity of the k-th subcarrier, η k,i represents the i-th calculated intermediate quantity of the k-th subcarrier.

[0159] For the SCA method, in order to obtain an approximate convex form of P6, it is necessary to introduce a slack variable {t k}, and then we get an equivalent photogenic form of P 6:

[0160]

[0161] It can be seen that the only non-convex item in P 8 is C 10 , using logarithmic transformation, C 10 Transforms into:

[0162]

[0163] in, To obtain C 11 An approximate convex form of , which can be expanded using a first-order Taylor expansion to convert f k Convert to affine approximation form:

[0164]

[0165] in, is the optimal solution of the SCA method at the mth iteration. Therefore, the approximate convex form of P 8 at the (n+1)th iteration can be obtained, that is, the expression for solving the joint scalar optimization problem of power allocation and power split ratio is as follows:

[0166]

[0167] E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, t k represents the relaxation variable of the kth subcarrier, g k 、h k Indicates the calculation of intermediate quantities.

[0168] It can be proved that P9 is a convex optimization problem, which can be solved efficiently using the Lagrange dual algorithm. According to the KKT condition, the optimal and They are:

[0169]

[0170] in, u, v and w k They are respectively about the constraints C8, C9 and C 12 The non-negative dual variable of .

[0171] Furthermore, in step S30203, the optimization problem of searching for the optimal power split ratio is as follows:

[0172]

[0173] G represents a unimodal function about β, represents the power allocation scheme, F represents the power split ratio optimization problem, and β represents the power split ratio.

[0174] It should be noted that, in general, β can be obtained by exhaustive search, but the corresponding complexity will be relatively high. Because it is a unimodal function, it is more efficient to use the GSS (Golden-section-search) algorithm to solve it.

[0175] The simulation parameters are set as follows: t =N r=2,P th =27dBm, E th =-5dBm, When β∈{0.01,0.02,...,1}, the single-peak characteristic curve of G is as follows: Figure 5 as shown in .

[0176] It should be noted that, because G represents a unimodal function about β, the GSS algorithm can be used to calculate the optimal power division ratio β, and the optimal power division ratio β minimizes the mean square error.

[0177] Here is the proof that G is a unimodal function with respect to β:

[0178] G(θβ1+(1-θ)β2)≤max{G(β1),G(β2)},

[0179] β1 and β2 are any feasible power split ratios, θ∈[0,1]. It can be shown that F({z k,i},β) is a monotonically increasing function of β, so we can get:

[0180]

[0181] Assume β1≤β2, represents the power allocation result of the inner layer optimization in step S30202 when β2 is fixed. The above formula can be deduced as follows:

[0182]

[0183] It represents the power allocation result of the inner layer optimization in step S30202 when β1 is fixed.

[0184] if If established, then

[0185]

[0186] Otherwise, we can get:

[0187]

[0188] Combining the above formulas, we can finally deduce:

[0189]

[0190] This means that G(β) is quasi-convex. According to the properties of quasi-convex functions, G(β) is a unimodal function.

[0191] The algorithm complexity of the above solutions is as follows Figure 6 As shown:

[0192] AO (alternating optimization) stands for alternating optimization algorithm, which is the algorithm shown in steps S30101 to S30104.

[0193] SS (structural solution) represents a structured algorithm, which is the algorithm shown in steps S30201 to S30204.

[0194] Regardless of whether it is the AO algorithm or the SS algorithm, according to formula (1.11), {G k} involves matrix inversion and matrix multiplication operations, and the total number of arithmetic operations required is According to formula (1.15), update once {C k}Involves Cholesky decomposition, matrix inversion, and matrix multiplication operations. The total number of arithmetic operations required is

[0195] For {P k ,β}, the alternating optimization algorithm solves the SDP problem P3 once, and the computational complexity is Where ∈ is the solution accuracy. For the SS algorithm, optimize {P k The complexity of ,β} mainly comes from matrix operations and Lagrange dual algorithm to solve P 7 or P 9. Specifically, matrix operations involve eigenvalue decomposition, GMD decomposition, and calculation according to formula (1.18) The required computational complexity is once: as well as Therefore, the total computational complexity of matrix operations is: In addition, the complexity of solving P 7 and P 9 using the Lagrange dual algorithm is and This is proportional to the number of optimization variables.

[0196] The computational complexity of all algorithms is summarized in Table 1, where N1, N2, and N3 represent the number of iterations required for the AO algorithm, the GSS algorithm, and the SCA algorithm to converge, respectively. During the simulation, it can be observed that the typical values ​​are: N1≈300, N2≈10, and N3≈5, which further verifies that the SS algorithm has a lower complexity than the AO algorithm.

[0197] according to Figure 7 The parameters shown in the figure are simulated for 3000 independent channel implementations, and the results are as follows:

[0198] like Figure 8 As shown, with the transmission power P thAs the total mean square error of all design schemes continues to increase, it continues to decrease. For the same algorithm, THP (Tomlinson-Harashima precoding), that is, the total mean square error of the nonlinear transceiver is always better than that of the linear transceiver. Regardless of whether it is a nonlinear transceiver or a linear transceiver, the performance of the robust design is always better than that of the non-robust design. In addition, the nonlinear transceiver performance of the GSS+SCA algorithm is almost the same as that of the alternating optimization algorithm; however, in the lower transmission power area, there is a performance "gap" between the GSS+APA algorithm and the alternating optimization algorithm. This is because: for a given power split ratio (PS ratio), the SCA algorithm can always reach the local optimal point of the objective function.

[0199] Fig. 9 It is shown that for the same algorithm, the bit error rate of the nonlinear transceiver is always better than that of the linear transceiver. This is because the nonlinear transceiver has the ability to suppress inter-symbol interference. In addition, it can be observed that for the nonlinear transceiver, in the medium and high transmission power region, the bit error rate of the robust design is much better than that of the non-robust design. However, this conclusion does not hold for the linear transceiver, which means that minimizing the total mean square error is more conducive to reducing the bit error rate of the nonlinear transceiver. In addition, it is worth noting that for nonlinear transceivers, the bit error rate of the alternating optimization algorithm is not always the best among all robust algorithms. For example, when P th =31dBm, this is because the design goal of this technology is to minimize the total mean square error rather than the bit error rate.

[0200] like Fig.10 As shown, when E th =-5dBm, as the channel estimation error σ e,k As σ increases from 0.001 to 0.0032, the performance gap between the robust design and the non-robust design is also increasing. e,k =0.0032, as E th From -10dBm to -5dBm, the total mean square error performance of all robust algorithms in the low transmit power area also deteriorates. This is because in this case, the receiver needs to use more receiving power for the energy collection branch, which leads to a decrease in the performance of the information decoding branch. Therefore, in actual application, it is necessary to balance the energy collection performance and information decoding performance.

[0201] The same or similar reference numerals correspond to the same or similar components;

[0202] The terms used in the drawings to describe positional relationships are only used for illustrative purposes and should not be construed as limiting this patent;

[0203] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system, characterized in that: include: S1: Considering the presence of channel estimation errors in a multi-carrier MIMO SWIPT system, a transceiver receiving signal model is established; S2: Based on the received signal model of the transceiver, with the goal of minimizing the total mean square error of the received signal, an optimization problem of the precoding matrix, the equalization matrix, the feedback matrix and the power division ratio of the joint subcarrier is established; S3: transform the optimization problem, solve the transformed optimization problem using a preset algorithm, and obtain the optimal precoding matrix, optimal equalization matrix, optimal feedback matrix and optimal power division ratio of the corresponding subcarrier when the total mean square error of the received signal is minimized.

2. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 1, characterized in that: The optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier is as follows: C3：0≤β≤1 Tr represents the trace in linear algebra, M k represents the MSE matrix of the kth subcarrier, k represents the subcarrier number, N represents the total number of subcarriers, P k represents the precoding matrix of the kth subcarrier, β represents the power division ratio, C k represents the feedback matrix of the kth subcarrier, G k represents the equalization matrix of the kth subcarrier, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, Represents the input power requirement of the energy harvester with respect to the system design.

3. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 1, characterized in that: The step S3 comprises: S30101: converting the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint optimization problem of the precoding matrix and the power division ratio; S30102: Solving the joint optimization problem of the precoding matrix and the power split ratio to obtain an optimized precoding matrix and an optimized power split ratio; S30103: updating an equalization matrix and a feedback matrix according to the optimized precoding matrix and the optimized power division ratio; S30104: Repeat steps S30102 to S30103 until the joint optimization problem of the precoding matrix and the power split ratio converges to a preset accuracy, and obtains the optimal precoding matrix, the optimal power split ratio, the optimal equalization matrix and the optimal feedback matrix.

4. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 3, characterized in that: In step S30103, the optimal expression of the equalization matrix is ​​as follows: represents the optimized equalization matrix of the kth subcarrier, P k represents the precoding matrix of the kth subcarrier, represents the estimated channel matrix of the kth subcarrier, C k represents the feedback matrix of the kth subcarrier, R yk Indicates calculation of intermediate quantities; The optimal expression of the feedback matrix is ​​as follows: Q k represents the lower triangular matrix of the kth subcarrier, L k represents the number of symbols carried by the kth subcarrier, [Q k ] i，j Represents the data of the i-th row and j-th column of the k-th subcarrier, where k represents the subcarrier number.

5. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 3, characterized in that: The joint optimization problem of the precoding matrix and the power split ratio is as follows: C3：0≤β≤1 represents the second MSE expression of the kth subcarrier, Tr represents the trace in linear algebra, k represents the subcarrier number, N represents the total number of subcarriers, P k represents the precoding matrix of the kth subcarrier, β represents the power division ratio, P th Indicates the maximum transmit power of the system, E in represents the input power of the energy harvester, E th represents the energy harvesting power requirement of the system design, represents the input power requirement of the energy harvester for system design, Q k represents the unit lower triangular matrix of the k-th subcarrier.

6. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 1, characterized in that: The step S3 comprises: S30201: Convert the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power division ratio of the joint subcarrier into a joint scalar optimization problem of power allocation and power division ratio; S30202: fix the power split ratio, solve the joint scalar optimization problem about power allocation and power split ratio, and obtain a power allocation scheme and an optimal precoding matrix; S30203: searching for an optimal power split ratio according to the power allocation scheme and the joint scalar optimization problem regarding power allocation and power split ratio; S30204: Calculate an optimal equalization matrix and an optimal feedback matrix based on the optimization problem of the precoding matrix, equalization matrix, feedback matrix and power split ratio of the joint subcarrier, the optimal precoding matrix and the optimal power split ratio.

7. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 6, characterized in that: The expression of the joint scalar optimization problem of power allocation and power split ratio is as follows: E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F0 represents a function, μ k，i 、v k,i Indicates the calculation of intermediate quantities.

8. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 6, characterized in that: In step S30202, the joint scalar optimization problem of power allocation and power split ratio is solved as follows: E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, {} represents a set, F1 represents a function, Indicates the calculation of intermediate quantities.

9. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 6, characterized in that: In step S30202, the joint scalar optimization problem of power allocation and power split ratio is solved as follows: E ** Indicates the calculation of intermediate quantities. represents the input power requirement of the energy harvester for system design, β represents the power split ratio, and z k,i represents the power of the i-th symbol of the k-th subcarrier, P th Indicates the maximum transmission power of the system, i and k represent the sequence number, L k represents the number of symbols carried by the kth subcarrier, t k represents the relaxation variable of the kth subcarrier, g k 、h k Indicates the calculation of intermediate quantities.

10. The robust nonlinear transceiver design method based on multi-carrier MIMO SWIPT system according to claim 6, characterized in that: In step S30203, the optimization problem of searching for the optimal power split ratio is as follows: G represents a unimodal function about β, represents the power allocation scheme, F represents the power split ratio optimization problem, and β represents the power split ratio.

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