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

Abstract

The application discloses a robust nonlinear transceiver design method based on a multicarrier MIMO SWIPT system. The method comprises the following steps: considering the case that there is a channel estimation error in the multicarrier MIMO SWIPT system, a receiving signal model of the transceiver is established; based on the receiving signal model of the transceiver, an optimization problem of joint precoding matrix, equalization matrix, feedback matrix and power splitting ratio is established with the total mean square error of the receiving signal being minimized as the target; the optimization problem is transformed, a preset algorithm is used to solve the transformed optimization problem, and the optimal precoding matrix, the optimal equalization matrix, the optimal feedback matrix and the optimal power splitting ratio of the subcarrier corresponding to the minimum total mean square error of the receiving signal are obtained. The method can realize the design of the nonlinear transceiver suitable for the multicarrier MIMO SWIPT system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of nonlinear transceiver, more particularly, to a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system. BACKGROUND

[0002] In the 6G era, wireless simultaneous wireless information and power transfer (SWIPT) is a technology with great development potential, which can wirelessly power a large number of Internet of Things devices and effectively extend the working cycle of energy-constrained Internet of Things networks. The transceiver undertakes the work of signal transmission and reception of wireless SWIPT, and is an important part of wireless SWIPT.

[0003] Traditional transceivers are mainly linear transceivers. For the case of perfect channel state information (CSI), the existing technology has studied the power splitting (PS) based multi-carrier MIMO SWIPT system, and under different constraint conditions, different mean square error (MSE) functions are minimized and the energy efficiency is maximized. For the case of imperfect channel state information, the existing technology proposes a robust beamforming scheme for the PS based MIMO SWIPT network, and under the constraints of signal-to-interference-plus-noise ratio (SINR), EH and transmit power, the secrecy rate of data is maximized. The existing technology extends to the PS based MIMO SWIPT IoT network, and under the premise of meeting the secrecy rate of data and the total transmit power constraint, the minimum energy harvesting power in all users is maximized. The existing technology studies the amplify-and-forward and decode-and-forward based MIMO SWIPT relay system, and under the constraints of source node transmit power and relay node transmit power, the mutual information is maximized. The existing technology studies a full-duplex MIMO SWIPT IoT network, and under the constraints of EH and transmit power, the worst-case secure energy efficiency of the system is maximized. For traditional wireless information transmission systems, nonlinear transceivers can improve the communication performance of MIMO systems. Considering the design complexity of energy-limited terminals, the Tomlinson-Harashima precoding (THP) technology is more suitable for application in MIMO SWIPT IoT networks, because the transmitter can bear the computational overhead required by the nonlinear signal processing process. So far, the existing technology has proposed a robust design scheme for the THP based single-carrier MIMO SWIPT system, and under the premise of meeting the EH and transmit power constraints, the average MSE of the received signal is minimized. However, the separate receiver scheme in the existing technology is not suitable for IoT terminal devices, because in actual application, equipping the terminal with a dedicated EH receiver increases the cost. In addition, the single-carrier transmission scheme in the existing technology is not suitable for frequency-selective fading channel scenarios, because the matrix optimization based algorithm in the existing technology has high complexity, making it difficult to extend to the multi-carrier MIMO scenario.

[0004] The prior art discloses a robust multi-carrier MIMO wireless power carrying system design method under non-ideal channel information, comprising the following steps: S1: considering channel error, establishing a channel estimation error model; S2: according to the channel estimation error model, establishing a receiving signal model of a transceiver of the wireless power carrying communication system; S3: establishing a transceiver signal optimization problem, the optimization problem aims to minimize the MSE of the transceiver information decoder equalization signal under the premise of meeting the given transmission power constraint and the average collection power constraint; S4: using an alternating optimization algorithm to solve the transceiver signal optimization problem, and obtaining an optimal transceiver design scheme. The method mainly aims at linear transceivers, and does not aim at nonlinear transceivers. SUMMARY

[0005] The present application aims at the technical blank that nonlinear transceivers are not applied to the multi-carrier MIMO SWIPT system, and proposes a robust nonlinear transceiver design method based on the multi-carrier MIMO SWIPT system, so as to realize the design of the nonlinear transceiver suitable for the multi-carrier MIMO SWIPT system.

[0006] The primary object of the present application is to solve the above technical problems, and the technical scheme of the present application is as follows:

[0007] The robust nonlinear transceiver design method based on the multi-carrier MIMO SWIPT system comprises:

[0008] S1: considering the case that there is a channel estimation error in the multi-carrier MIMO SWIPT system, establishing a receiving signal model of a transceiver;

[0009] S2: based on the receiving signal model of the transceiver, establishing an optimization problem of jointly optimizing the precoding matrix, the equalization matrix, the feedback matrix and the power splitting ratio of the subcarrier, with the total mean square error of the receiving signal being minimized as the target;

[0010] S3: transforming the optimization problem, and using a preset algorithm to solve the transformed optimization problem, so as to obtain the optimal precoding matrix, the optimal equalization matrix, the optimal feedback matrix and the optimal power splitting ratio of the subcarrier corresponding to the minimum total mean square error of the receiving signal.

[0011] Further, the optimization problem of jointly optimizing the precoding matrix, the equalization matrix, the feedback matrix and the power splitting ratio of the subcarrier is as follows:

[0012]

[0013] C3: 0≤β≤1

[0014] Tr represents a trace in linear algebra, M kMSE matrix of the kth subcarrier, k represents the subcarrier number, N represents the total number of subcarriers, P k precoding matrix of the kth subcarrier, β represents the power division ratio, C k feedback matrix of the kth subcarrier, G k equalization matrix of the kth subcarrier, P th maximum transmission power of the system, E in input power of the energy collector, E th energy collection power requirement of the system design, input power requirement of the energy collector about the system design.

[0015] Further, the step S3 comprises:

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

[0017] S30102: solving the joint optimization problem about the precoding matrix and the power division ratio to obtain the optimized precoding matrix and the optimized power division ratio;

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

[0019] S30104: repeating steps S30102-S30103 until the joint optimization problem about the precoding matrix and the power division ratio converges to a preset accuracy to obtain the optimal precoding matrix, the optimal power division ratio, the optimal equalization matrix and the optimal feedback matrix.

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

[0021]

[0022] optimized equalization matrix of the kth subcarrier, P k precoding matrix of the kth subcarrier, estimated channel matrix of the kth subcarrier, C k feedback matrix of the kth subcarrier, R yk indicates a calculation intermediate quantity;

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

[0024]

[0025] Q k denotes the lower triangular matrix of the kth subcarrier, L k denotes the number of symbols carried by the kth subcarrier, [Q k ] i,j denotes the data of the kth subcarrier in the ith row and jth column, k denotes the subcarrier index.

[0026] Further, the joint optimization problem about the precoding matrix and the power splitting ratio is as follows:

[0027]

[0028] C3: 0≤β≤1

[0029]

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

[0031] Further, the step S3 comprises:

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

[0033] S30202: fixing the power splitting ratio, solving the joint scalar optimization problem about the power allocation and the power splitting ratio to obtain a power allocation scheme and an optimal precoding matrix;

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

[0035] S30204: calculating an optimal equalization matrix and an optimal feedback matrix according to the joint optimization problem of the precoding matrix, the equalization matrix, the feedback matrix and the power splitting ratio of the subcarrier, the optimal precoding matrix and the optimal power splitting ratio.

[0036] Furthermore, the expression for the joint scalar optimization problem concerning power allocation and power splitting ratios is as follows:

[0037]

[0038] E ** This indicates that intermediate quantities are being calculated. This represents the input power requirement of the energy harvester for the system design, β represents the power split ratio, and z k,i P represents the power of the i-th symbol on the k-th subcarrier. th This represents the system's maximum transmit power, where i and k represent the serial numbers, and L... k Let {} denote the number of symbols carried by the k-th subcarrier, {} denote a set, F0 denote a function, and μ k,i v k,i This indicates that intermediate quantities are being calculated.

[0039] Further, in step S30202, the joint scalar optimization problem concerning power allocation and power splitting ratio is solved as follows:

[0040]

[0041] E ** This indicates that intermediate quantities are being calculated. This represents the input power requirement of the energy harvester for the system design, β represents the power split ratio, and z k,i P represents the power of the i-th symbol on the k-th subcarrier. th This represents the system's maximum transmit power, where i and k represent the serial numbers, and L... k Let {} represent the number of symbols carried by the k-th subcarrier, {} represent a set, and F1 represent a function. This indicates that intermediate quantities are being calculated.

[0042] Further, in step S30202, the joint scalar optimization problem concerning power allocation and power splitting ratio is solved as follows:

[0043]

[0044] E ** This indicates that intermediate quantities are being calculated. This represents the input power requirement of the energy harvester for the system design, β represents the power split ratio, and z k,i P represents the power of the i-th symbol on the k-th subcarrier. th This represents the system's maximum transmit power, where i and k represent the serial numbers, and L... k t represents the number of symbols carried by the k-th subcarrier. k Let g represent the slack variable of the k-th subcarrier. k hk represents a calculation intermediate quantity.

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

[0046]

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

[0048] Compared with the prior art, the present application has the beneficial effects that:

[0049] The present application establishes a transceiver receiving signal model in the case of existing channel estimation error in a multi-carrier MIMO SWIPT system; based on the transceiver receiving signal model, an optimization problem of jointly optimizing a precoding matrix, an equalization matrix, a feedback matrix and a power split ratio of a subcarrier is established with the minimization of total mean square error of a received signal as the target; the optimization problem is transformed, a preset algorithm is used to solve the transformed optimization problem, and the optimal precoding matrix, the optimal equalization matrix, the optimal feedback matrix and the optimal power split ratio of the subcarrier corresponding to the minimum total mean square error of the received signal are obtained. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 A flowchart of a robust nonlinear transceiver design method based on a multi-carrier MIMO SWIPT system provided for embodiment 1.

[0051] Figure 2 A structure diagram of a transceiver receiving signal model provided for embodiment 1.

[0052] Figure 3 A flowchart of optimization problem transformation and solution provided for embodiment 1.

[0053] Figure 4 A flowchart of optimization problem transformation and solution provided for embodiment 1.

[0054] Figure 5 A unimodal characteristic curve diagram of a power split ratio provided for embodiment 1.

[0055] Figure 6 A comparison diagram of algorithm complexity analysis provided for embodiment 1.

[0056] Figure 7 A simulation parameter diagram provided for embodiment 1.

[0057] Figure 8 A comparison diagram of average total mean square error and transmit power provided for embodiment 1.

[0058] Figure 9 A plot of the bit error rate versus the transmit power for Example 1.

[0059] Figure 10 A plot of the average total mean square error versus the transmit power for Example 1. DETAILED DESCRIPTION

[0060] The accompanying drawings are included to provide a further understanding of the present application and are incorporated in and constitute a part of this specification, illustrate embodiments of the present application and together with the description serve to explain the principles of the present application.

[0061] To make the present embodiments more readable, some parts of the drawings are omitted, enlarged or reduced, and do not represent the actual size of the product.

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

[0063] The technical solutions of the present application will be further described below in combination with the drawings and embodiments.

[0064] Example 1

[0065] As shown in the robust nonlinear transceiver design method based on a multicarrier MIMO SWIPT system, the method comprises: Figure 1

[0066] S1: considering the case that there is a channel estimation error in the multicarrier MIMO SWIPT system, a received signal model of the transceiver is established;

[0067] S2: based on the received signal model of the transceiver, an optimization problem of jointly optimizing the precoding matrix, the equalization matrix, the feedback matrix and the power splitting ratio of the subcarriers is established, with the minimization of the total mean square error of the received signal as the target;

[0068] S3: the optimization problem is transformed, and a preset algorithm is used to solve the transformed optimization problem, so as to obtain the optimal precoding matrix, the optimal equalization matrix, the optimal feedback matrix and the optimal power splitting ratio of the subcarriers corresponding to the minimum total mean square error of the received signal.

[0069] As shown in the robust nonlinear transceiver design method based on a multicarrier MIMO SWIPT system, the method comprises: Figure 2 A multicarrier MIMO SWIPT system with N t roots of transmitting antennas and N r roots of receiving antennas, the total bandwidth W of the system is evenly distributed to N subcarriers. Influenced by the time-varying characteristics of the wireless channel and the limited length of the pilot symbol, channel estimation error cannot be avoided. 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 follows independent and identically distributed CN(0, 1), σ e,k represents the variance of channel estimation error. This technique assumes that both the transmitter and the receiver have the same imperfect CSI.

[0072] Let the information symbol vector carried by the kth subcarrier be denoted as L k ≤ min{N t ,N r}, s k All elements of s k are modulated by M-QAM and have mean 0 and variance 1. Before transmission, s k is first sent to a THP unit for processing. The THP unit includes a modulo operation and a strictly lower triangular feedback matrix The detailed operation of the modulo operation is where represents the largest integer not exceeding z. Then, the THP unit outputs a signal vector The nth element of v may be denoted as and is a complex vector that limits the elements of v k to the region of According to the above analysis, we have

[0073]

[0074] where is a lower triangular matrix with unit diagonal elements, u k = s k + i k is the effective signal vector. If M is large enough, we have Next, a frequency domain precoding matrix is used to process v k and obtain the transmitted signal. After the transmitted signal propagates through the wireless channel, the received signal can be denoted as

[0075]

[0076] where is an additive white Gaussian noise vector.

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

[0078]

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

[0080] For energy collection, the total input power of the energy collector is According to the Parseval theorem, it can be further obtained:

[0081]

[0082] The derivation process in equation (1.6) applies: if the elements of X follow CN(0, σ 2 ), E[XMX H ] = σ 2 Tr(M)I. The technology adopts a nonlinear EH model, that is, the energy collection power γ(E in ) is a nonlinear function of E in , which can be specifically represented as:

[0083]

[0084] where, E m and E0 represent the input power of the energy collector and the activation power of the energy collector, respectively, and parameters τ and v determine the curve characteristics of function γ(E in ). Let E th represent the EH requirement of system design, so the EH constraint condition of system design can be obtained as γ(E in ) ≥ E th , and the equivalent constraint condition is obtained after derivation:

[0085]

[0086] where

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

[0088]

[0089] where, is an automatic gain control factor used to simplify the derivation. The MSE matrix of the kth subcarrier, may be further derived as:

[0090]

[0091] wherein,

[0092] Further, the optimization problem of the precoding matrix, the equalization matrix, the feedback matrix and the power splitting ratio of the joint subcarriers 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 splitting ratio, C k represents the feedback matrix of the kth subcarrier, G k represents the equalization matrix of the kth subcarrier, P th represents the maximum transmit power of the system, E in represents the input power of the energy collector, E th represents the energy collection power requirement of the system design, represents the input power requirement of the energy collector about the system design.

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

[0097] Further, as shown in Figure 3 , the step S3 comprises:

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

[0099] S30102: solving the joint optimization problem about the precoding matrix and the power splitting ratio to obtain the optimized precoding matrix and the optimized power splitting ratio;

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

[0101] S30104: repeating steps S30102-S30103 until the joint optimization problem about the precoding matrix and the power splitting ratio converges to a preset precision, obtaining the optimal precoding matrix, the optimal power splitting ratio, the optimal equalization matrix and the optimal feedback matrix.

[0102] To minimize the total mean square error of the received signal, it is required that The first-order derivative of G k with respect to R

[0103]

[0104] denotes the optimized equalization matrix of the kth subcarrier, P k denotes the precoding matrix of the kth subcarrier, denotes the estimated channel matrix of the kth subcarrier, C k denotes the feedback matrix of the kth subcarrier, R yk denotes a calculation intermediate quantity;

[0105] Equation (1.11) is a well-known Wiener filter. Substituting equation (1.11) into equation (1.10) and using the matrix inversion lemma, we can obtain:

[0106]

[0107] wherein

[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] wherein is the i-th column of . According to equation (1.13), the minimization of different [M k ] i,i can be performed independently. Let T k be the Cholesky decomposition of wherein Q k is a lower triangular matrix, and thus we can obtain:

[0111]

[0112] wherein is a lower triangular matrix, and has From equation (1.14), if we want to minimize the MSE, the summation term of equation (1.14) must be zero, and the optimal expression of the feedback matrix is as follows:

[0113]

[0114] Q k Lkdenotes the lower triangular matrix of the kth subcarrier, k Qkdenotes the number of symbols carried by the kth subcarrier, k i,j dkijdenotes the data of the kth subcarrier in the ith row and jth column, and k denotes the subcarrier number.

[0115] It should be noted that, and are feedback matrices, and wherein, the diagonal of the matrix is all 0, the diagonal of the matrix is all 1.

[0116] Substituting equation (1.15) into equation (1.12) 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 convert P 2 into a convex SDP problem, a slack variable is introduced: and Therefore, P 2 can be equivalent to the following formula:

[0121]

[0122] s.t.C3: 0≤β≤1

[0123]

[0124] P k denotes the precoding matrix of the kth subcarrier, denotes the estimated channel matrix of the kth subcarrier, k denotes the feedback matrix of the kth subcarrier, k denotes the equalization matrix of the kth subcarrier, k denotes the slack variable, β denotes the power division ratio, and Tr denotes the trace in linear algebra, ​a third MSE expression of the kth subcarrier, denotes a calculation intermediate quantity, denotes a unit matrix, L k denotes the number of symbols carried by the kth subcarrier, δ k,sp denotes the standard deviation of the signal processing noise, denotes the input power requirement of the energy collector with respect to system design, E * (X k ) denotes the received signal power.

[0125]

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

[0127] Further, as Figure 4 indicated, the step S3 comprises:

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

[0129] S30202: fixing the power splitting ratio, solving the joint scalar optimization problem of power allocation and power splitting ratio to obtain a power allocation scheme and an optimal precoding matrix;

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

[0131] S30204: according to the optimization problem of the joint precoding matrix, equalization matrix, feedback matrix and power splitting ratio of the joint subcarrier, the optimal precoding matrix and the optimal power splitting ratio, calculating the optimal equalization matrix and the optimal feedback matrix.

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

[0133]

[0134] C3: 0≤β≤1

[0135]

[0136] a second MSE expression of the kth subcarrier, Tr denotes the trace in linear algebra, k denotes the subcarrier number, N denotes the total number of subcarriers, P kLet P represent the precoding matrix of the k-th subcarrier, β represent the power split ratio, and P represent the precoding matrix of the k-th subcarrier. th E represents the system's maximum transmit power. in E represents the input power of the energy harvester. th This indicates the energy harvesting power requirements of the system design. Q represents the input power requirement of the energy harvester in the system design. k This represents the lower triangular matrix of the k-th subcarrier.

[0137] As can be seen, P4 is still a concept about {P} k This paper addresses the nonconvex optimization problem involving β and β. To solve this problem, a two-layer optimization algorithm is proposed. Specifically, β is fixed in the inner optimization layer, and then the precoding matrix {P} is optimized. k The optimization of the outer layer involves using the GSS algorithm to search for the optimal PS ratio.

[0138] For a fixed β, P4 can be rewritten as with respect to the precoding matrix {P} k Optimization problem of}:

[0139]

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

[0141] Proposition 1: For problem P5, the optimal precoding matrix... It has the following structure:

[0142]

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

[0144]

[0145] Where, λ k,i yes The i-th largest eigenvalue.

[0146] Proof: For a fixed β, if the constraint C2 can be satisfied, P 5 degenerates to the problem of minimizing the total mean square error (MSE) under the given transmit power constraint.

[0147] Substituting (1.18) and (1.19) into P 5, the precoding matrix optimization problem is simplified to a scalar power allocation optimization problem P6:

[0148]

[0149] E ** denotes a calculation intermediate quantity, denotes the input power requirement of the energy harvester with respect to the system design, β denotes the power split ratio, z k,i denotes the power of the i-th symbol of the k-th subcarrier, P th denotes the maximum transmit power of the system, i, k denote the serial number, L k denotes the number of symbols carried by the k-th subcarrier, {} denotes a set, F0denotes a function, μ k,i , v k,i denotes a calculation intermediate quantity.

[0150] wherein,

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

[0152] For the APA method, it can be observed that denotes the power allocated to the k-th subcarrier. In order to obtain an approximate convex form of P 6, it is necessary to let while keeping the constraint unchanged, at this time P 6 can be transformed into P7:

[0153]

[0154] E ** denotes a calculation intermediate quantity, denotes the input power requirement of the energy harvester with respect to the system design, β denotes the power split ratio, z k,i denotes the power of the i-th symbol of the k-th subcarrier, P th denotes the maximum transmit power of the system, i, k denote the serial number, L k denotes the number of symbols carried by the k-th subcarrier, {} denotes a set, F1denotes a function, represents a calculation intermediate quantity.

[0155]

[0156] Since all the constraints of problem P 7 are affine, P 7 is a convex optimization problem, which can be verified by proving that the Hessian matrix of the objective function is positive semi-definite, and then can be solved using the Lagrangian dual algorithm. According to the Karush-Kuhn-Tucker (KKT) conditions, the expression of the joint scalar optimization problem about power allocation and power splitting ratio can be obtained as follows:

[0157]

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

[0159] For the SCA method, in order to obtain an approximate convex form of P 6, a relaxation variable {t k} is introduced to the objective function, and then an equivalent upper mirror form of P 6 is obtained:

[0160]

[0161] It can be seen that the non-convex term in P 8 is only C 10 , and by using logarithmic conversion, C 10 can be further converted into:

[0162]

[0163] wherein, In order to obtain an approximate convex form of C 11 , a first-order Taylor expansion can be used to convert f k into an affine approximation form:

[0164]

[0165] wherein, is the optimal solution of the mth iteration of the SCA method. Thus, the approximate convex form of P8 at the (n+1)th iteration can be obtained, i.e., solving the joint scalar optimization problem with respect to the power allocation and power splitting ratio, the expression of P9 is as follows:

[0166]

[0167] E ** denotes a calculation intermediate quantity, denotes the input power requirement of the energy harvester with respect to the system design, β denotes the power splitting ratio, z k,i denotes the power of the ith symbol of the kth subcarrier, P th denotes the maximum transmit power of the system, i, k denote the serial number, L k denotes the number of symbols carried by the kth subcarrier, t k denotes the relaxation variable of the kth subcarrier, g k , h k denotes a calculation intermediate quantity.

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

[0169]

[0170] wherein, u, v and w k are non-negative dual variables with respect to the constraint conditions C8, C9 and C 12 , respectively.

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

[0172]

[0173] G denotes a unimodal function with respect to β, denotes the power allocation scheme, F denotes the power splitting ratio optimization problem, and β denotes the power splitting ratio.

[0174] It should be noted that generally, β can be obtained by using the exhaustive search method, but the corresponding complexity is relatively high. Because it is a unimodal function, the GSS (Golden-section-search) algorithm is used to solve it with higher efficiency.

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

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

[0177] The following is a proof that G is a unimodal function with respect to β:

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

[0179] β1and β2are any feasible power split ratios, and θ ∈ [0, 1]. It can be proven that F({z k,i}, β) is a monotonically increasing function with respect to β, and thus it can be concluded that:

[0180]

[0181] Assuming β1≤ β2, denotes the power allocation result of the inner optimization in step S30202 when β2is fixed, and the above equation can be derived as:

[0182]

[0183] denotes the power allocation result of the inner optimization in step S30202 when β1is fixed.

[0184] If holds, then

[0185]

[0186] Otherwise, it can be concluded that:

[0187]

[0188] Combining the above equations, it can be finally derived that:

[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 each of the above schemes is shown in FIG. 3: Figure 6 ​​

[0192] AO (alternating optimization) denotes the alternating optimization algorithm, which is the algorithm shown in steps S30101-S30104.

[0193] SS (structural solution) denotes the structural solution algorithm, which is the algorithm shown in steps S30201-S30204.

[0194] For both the AO algorithm and the SS algorithm, updating {G k} once according to equation (1.11) involves matrix inversion and matrix multiplication operations, and the total number of arithmetic operations required is Updating {C k} once according to equation (1.15) involves Cholesky decomposition, matrix inversion, and matrix multiplication operations, and the total number of arithmetic operations required is

[0195] For the optimization of {P k , β}, the alternating optimization algorithm requires a computational complexity of where ∈ is the solution accuracy. For the SS algorithm, the complexity of optimizing {P k , β} mainly comes from matrix operations and the solution of P 7 or P 9 by the Lagrangian dual algorithm. Specifically, the matrix operations involve eigenvalue decomposition, GMD decomposition, and the calculation of , which requires a computational complexity of and Therefore, the total computational complexity of the matrix operations is In addition, the complexity of solving P 7 and P 9 using the Lagrangian dual algorithm is and which 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. In the simulation process, it can be observed that typical values are: N1≈300, N2≈10, N3≈5, which further verifies that the SS algorithm has lower complexity than the AO algorithm.

[0197] Simulations were performed according to the parameters shown in Figure 7 , and 3000 independent channel implementations were obtained, with the following results:

[0198] As shown in Figure 8 , as the transmit power P thAs the power density increases, the total mean square error (TMS) for all design schemes decreases. For the same algorithm, the TMS of the nonlinear transceiver (THP - Tomlinson-Harashima precoding) is always better than that of the linear transceiver. Regardless of whether it's a nonlinear or linear transceiver, robust designs always outperform non-robust designs. Furthermore, the performance of the nonlinear transceiver in the GSS+SCA algorithm is almost identical to that of the alternating optimization algorithm; however, in the lower transmit power region, 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 always reaches a local optimum of the objective function.

[0199] Figure 9 This demonstrates that, for the same algorithm, the bit error rate (BER) of a nonlinear transceiver is consistently better than that of a linear transceiver, due to the nonlinear transceiver's ability to suppress inter-symbol interference. Furthermore, it can be observed that, for nonlinear transceivers, in the medium-to-high transmit power region, the BER of a robust design is significantly better than that of a non-robust design. However, this conclusion does not hold for linear transceivers, meaning that minimizing the total mean square error (TSE) is more beneficial for reducing the BER of nonlinear transceivers. Additionally, it is worth noting that, for nonlinear transceivers, the BER of the alternating optimization algorithm is not always optimal among all robust algorithms; for example, when P... th =31dBm, because the design goal of this technology is to minimize the total mean square error rather than the bit error rate.

[0200] like Figure 10 As shown, when E th When the channel estimation error σ = -5dBm, e,k As σ increases from 0.001 to 0.0032, the performance gap between robust and non-robust designs also widens. e,k When E = 0.0032, as E th As the transmit power increases from -10dBm to -5dBm, the total mean square error performance of all robust algorithms deteriorates in the low transmit power region. This is because, under these conditions, the receiver needs to allocate more received power to the energy harvesting branch, leading to a decrease in the performance of the information decoding branch. Therefore, in practical applications, a trade-off must be struck between energy harvesting performance and information decoding performance.

[0201] The same or similar labels correspond to the same or similar parts;

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

[0203] Obviously, the above embodiments of the present application are merely exemplary but not intended to limit the embodiments of the present application. Based on the above description, any other variations or changes can be made by those skilled in the art without departing from the spirit and principles of the present application. It is not necessary to list all the embodiments here. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present application shall fall within the scope of the claims of the present application.

Claims

1. A method for robust nonlinear transceiver design based on multicarrier MIMO SWIPT systems, characterized in that, The method comprises the following steps: S1: considering the case that there is channel estimation error in a multi-carrier MIMO SWIPT system, a receiver signal model of a transceiver is established; S2: based on the receiver signal model of the transceiver, an optimization problem of joint precoding matrix, equalization matrix, feedback matrix and power division ratio of subcarriers is established, with the total mean square error of the received signal being minimized as the target; S3: the optimization problem is transformed, and a preset algorithm is used to solve the transformed optimization problem, so that the optimal precoding matrix, the optimal equalization matrix, the optimal feedback matrix and the optimal power division ratio of the subcarriers corresponding to the minimum total mean square error of the received signal are obtained; The optimization problem of the joint precoding matrix, equalization matrix, feedback matrix and power division ratio of the subcarriers is as follows: s.t. C1: C2： C3： denotes a trace in linear algebra, denotes an MSE matrix of the kth subcarrier, k denotes a subcarrier number, and N denotes a total number of subcarriers, denotes a precoding matrix of the kth subcarrier, denotes a power split ratio, denotes a feedback matrix of the kth subcarrier, denotes an equalization matrix of the kth subcarrier, denotes a maximum transmission power of a system, denotes an input power of an energy harvester, denotes an energy harvesting power requirement of a system design, denotes an input power requirement of an energy harvester with respect to a system design; Step S3 comprises: S30101: the optimization problem of the joint precoding matrix, equalization matrix, feedback matrix and power division ratio of the subcarriers is transformed into a joint optimization problem about the precoding matrix and the power division ratio; S30102: the joint optimization problem about the precoding matrix and the power division ratio is solved, and the optimized precoding matrix and the optimized power division ratio are obtained; S30103: the equalization matrix and the feedback matrix are updated according to the optimized precoding matrix and the optimized power division ratio; S30104: steps S30102-S30103 are repeated until the joint optimization problem about the precoding matrix and the power division ratio converges to a preset precision, and the optimal precoding matrix, the optimal power division ratio, the optimal equalization matrix and the optimal feedback matrix are obtained.

2. The method of claim 1, wherein the method is based on a robust nonlinear transceiver design for a multicarrier MIMO SWIPT system. In the step S30103, the optimal expression of the equalization matrix is as follows: an equalization matrix representing the kth subcarrier after optimization, a precoding matrix representing the kth subcarrier, an estimated channel matrix representing the kth subcarrier, a feedback matrix representing the kth subcarrier, represents a calculation intermediate quantity; The optimal expression of the feedback matrix is as follows: a lower triangular matrix representing the kth subcarrier, a number of symbols carried by the kth subcarrier, data of the kth subcarrier, k represents the subcarrier number. 3.The method of claim 1, wherein, The joint optimization problem about the precoding matrix and the power division ratio is as follows: s.t. C1: C2： C3： a second MSE expression representing the kth subcarrier, denotes a trace in linear algebra, k denotes a subcarrier number, and N denotes a total number of subcarriers, denotes a precoding matrix of the kth subcarrier, denotes a power split ratio, denotes a maximum transmission power of a system, denotes an input power of an energy harvester, denotes an energy harvesting power requirement of a system design, denotes an input power requirement of an energy harvester with respect to a system design, denotes a unit lower triangular matrix of the kth subcarrier.

4. The method of claim 1, wherein the robust nonlinear transceiver design for a multicarrier MIMO SWIPT system is characterized by, The step S3 comprises: S30201: the optimization problem of the joint precoding matrix, equalization matrix, feedback matrix and power division ratio of the subcarriers is transformed into a joint scalar optimization problem about power allocation and power division ratio; S30202: the joint scalar optimization problem about power allocation and power division ratio is solved by fixing the power division ratio, and a power allocation scheme and an optimal precoding matrix are obtained; S30203: the optimal power division ratio is searched according to the power allocation scheme and the joint scalar optimization problem about power allocation and power division ratio; S30204: the optimal equalization matrix and the optimal feedback matrix are calculated according to the optimization problem of the joint precoding matrix, equalization matrix, feedback matrix and power division ratio of the subcarriers, the optimal precoding matrix and the optimal power division ratio.

5. The method of claim 4, wherein, The expression of the joint scalar optimization problem about power allocation and power division ratio is as follows: s.t. C8: C9： represents a calculation intermediate quantity, represents an input power requirement of an energy harvester with respect to system design, represents a power division ratio, represents power of the i-th symbol of the k-th subcarrier, represents a maximum transmission power of a system, i, k represent serial numbers, represents a number of symbols carried by the k-th subcarrier, {} represents a set, represents a function, , represents a calculation intermediate quantity.

6. The method of claim 4, wherein the method is characterized by, In step S30202, the joint scalar optimization problem about power allocation and power division ratio is solved as follows: s.t. C8: C9： denotes a calculation intermediate quantity, denotes the input power requirement of the energy harvester with respect to the system design, denotes the power split ratio, denotes the power of the i-th symbol of the k-th subcarrier, denotes the maximum transmit power of the system, i, k denote the index, denotes the number of symbols carried by the k-th subcarrier, {} denotes a set, denotes a function, , denotes a calculation intermediate quantity. 7.The method of claim 4, wherein, In step S30202, the joint scalar optimization problem about power allocation and power division ratio is solved as follows: s.t. C8: C9： C12： denotes a calculation intermediate quantity, denotes the input power requirement of the energy harvester with respect to the system design, denotes the power split ratio, denotes the power of the i-th symbol of the k-th subcarrier, denotes the maximum transmit power of the system, i, k denote the index, denotes the number of symbols carried by the k-th subcarrier, denotes the slack variable of the k-th subcarrier, , denotes a calculation intermediate quantity. 8.The method of claim 4, wherein, In step S30203, the optimization problem of searching for the optimal power division ratio is as follows: denotes a unimodal function with respect to denotes a unimodal function with respect to denotes a power allocation scheme, denotes a power split ratio optimization problem, denotes a power split ratio.

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