Intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system and joint optimization method

Abstract

This invention relates to the field of wireless communication technology and proposes an intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system and a joint optimization method. The method includes the following steps: establishing an equivalent channel model for the transmitter, intelligent reflector, and receiver; based on the equivalent channel model, deriving an analytical expression for the receiver's performance index and an expression for the radio frequency harvesting power of the energy harvesting circuit; constructing a three-variable joint optimization problem concerning power allocation weights, power segmentation factors, and phase shifts of each reflector unit, with the goal of maximizing the receiver's performance index; and using an alternating optimization framework to decompose the three-variable joint optimization problem into two sub-problems that are iteratively executed: updating the phase shift of each reflector unit unit by unit. This invention significantly improves the communication performance and energy harvesting efficiency of the orthogonal time-frequency spatial data-energy simultaneous transmission system in high-speed mobile scenarios by actively reconstructing the wireless propagation path and expanding the degrees of freedom of the joint optimization.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to a smart reflector-assisted orthogonal time-frequency spatial data transmission system and a joint optimization method. Background Technology

[0002] In high-speed mobile communication scenarios (such as high-speed rail, low-orbit satellite, and drone communication), the relative motion between the transmitter and receiver generates significant Doppler frequency shift, which disrupts the subcarrier orthogonality of traditional Orthogonal Frequency Division Multiplexing (OFDM) modulation schemes, resulting in severe inter-carrier interference and a sharp decline in system performance. Orthogonal Time-Frequency Space (OTFS) modulation maps information symbols to the time-delay-Doppler domain for transmission. By fully utilizing the time-delay-Doppler domain sparsity of the channel, it transforms the time-varying multipath channel into an approximately time-invariant two-dimensional channel, thereby effectively resisting interference caused by high Doppler spread and becoming a powerful candidate waveform technology for high-speed mobile communication scenarios.

[0003] With the explosive growth in the number of IoT devices in wireless networks, how to continuously power a massive number of low-power devices has become an urgent problem to be solved. Wireless Powered Communication (SWIPT) technology, by introducing a power division mechanism at the receiver, allows the same radio frequency signal to be used simultaneously for information decoding and radio frequency energy harvesting, effectively extending the device's operating life. Combining SWIPT technology with OTFS modulation to build an OTFS data-power simultaneous transmission system is of great significance for supporting low-power IoT communication in high-speed mobile scenarios. In such systems, the transmitter optimizes signal energy distribution by applying power allocation weights to each time-frequency grid point, while the receiver balances information decoding performance and energy harvesting efficiency by adjusting the power division factor, thereby jointly maximizing the receiver's signal-to-noise ratio.

[0004] However, existing OTFS (Over-the-Air) data transmission systems rely entirely on the natural wireless propagation environment. Channel conditions are passively determined by the positional relationship between the communicating parties and surrounding scatterers. The system can only adjust resource allocation under given channel conditions by optimizing two variables: the transmitter power allocation weight and the receiver power segmentation factor. When the direct link experiences deep fading due to obstacles or excessive distance, system performance deteriorates significantly. Relying solely on bivariate joint optimization at the transmitter and receiver is no longer sufficient to effectively compensate for the performance loss caused by insufficient channel conditions, and the optimization freedom is fundamentally limited.

[0005] Intelligent reflectors consist of a large number of passive reflective elements with independently controllable phase shifts. By applying a programmable phase shift to the incident electromagnetic wave, they construct a controllable additional propagation path between the transmitter and receiver, thereby actively reconstructing the wireless propagation environment. Existing research has introduced intelligent reflectors into MIMO or OFDM systems and has made preliminary explorations into the introduction of intelligent reflectors into OTFS systems. However, none of these studies have combined intelligent reflectors with OTFS data-power simultaneous transmission systems, nor have they considered the joint optimization of the three variables—power allocation weights, power segmentation factors, and phase shifts of each reflective element—after the introduction of intelligent reflectors. There is a significant gap in the existing technology. Summary of the Invention

[0006] Based on this, it is necessary to address the technical problem that the existing OTFS data and energy transmission system lacks the ability to actively control the wireless propagation path, and to provide an intelligent reflector-assisted orthogonal time-frequency spatial data and energy transmission system and a joint optimization method, which has the characteristics of high communication performance and energy harvesting efficiency.

[0007] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows: A smart reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system includes a transmitter, a smart reflector, and a receiver. The smart reflector comprises multiple passive reflective units, each of which can independently adjust its phase shift. These units receive wireless signals from the transmitter and reflect them to the receiver with a controllable phase shift, thus forming a composite propagation link together with the direct path from the transmitter to the receiver. The receiver receives signals from the smart reflector and the transmitter and includes an information decoding branch and an energy harvesting circuit. A frequency domain linear equalizer is provided in the information decoding branch of the receiver.

[0008] A joint optimization method for the intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system includes the following steps: Establish an equivalent channel model: The equivalent channel response of each time-frequency grid point is modeled as the sum of the direct component from the transmitter to the receiver and the reflected component controlled by the phase shift of each reflection unit of the intelligent reflector, so as to characterize the active control effect of the intelligent reflector on the composite propagation link. Derivation of performance index expressions: Based on the equivalent channel model, the analytical expression of the receiver performance index of the information decoding branch after equalization by the frequency domain linear equalizer is derived, as well as the expression of the radio frequency harvesting power of the energy harvesting circuit. Construct a joint optimization problem: With the goal of maximizing the performance index of the receiver, under the constraints of total transmit power, minimum power of energy harvesting, power division factor range, and constant mode of phase shift of each reflector, construct a three-variable joint optimization problem concerning power allocation weight, power division factor, and phase shift of each reflector. Alternating optimization solution: The three-variable joint optimization problem is decomposed into two sub-problems using an alternating optimization framework and executed iteratively: the phase shift of each reflection unit is fixed, and the power allocation weight and the power segmentation factor are solved; the power allocation weight and the power segmentation factor are fixed, and the phase shift of each reflection unit is iteratively updated unit by unit until the algorithm converges.

[0009] Furthermore, the frequency domain linear equalizer is a zero-forcing equalizer; the equalization weight of the zero-forcing equalizer at the i-th time-frequency grid point. satisfy:

[0010] in, For the transmitter in the The power allocation weights applied to each time-frequency grid point For the first Equivalent channel response at each time-frequency grid point For the number of subcarriers, The number of time slots; the zero-forcing equalizer completely eliminates inter-channel interference in the time and frequency domains through the above grid-by-grid inversion operation.

[0011] Furthermore, the frequency domain linear equalizer is a minimum mean square error equalizer; the minimum mean square error equalizer in the first... Equilibrium weights at each time-frequency grid point satisfy:

[0012] in, For the first Power allocation weights for each time-frequency grid point For the first Equivalent channel response at each time-frequency grid point The transmission power for each time-delay-Doppler domain information symbol, This refers to the antenna thermal noise power. Additional noise power introduced for the information decoding branch. The power division factor is... For the number of subcarriers, The number of time slots is denoted as ; the minimum mean square error equalizer suppresses noise amplification effect while suppressing inter-channel interference by introducing a noise power regularization term in the denominator, and has stronger noise robustness compared to the zero-forcing equalizer.

[0013] Furthermore, in the equivalent channel model, the first... Equivalent channel response at each time-frequency grid point Determined by the following formula:

[0014] in, For the transmitter-to-receiver direct link in the 1st Channel response at each time-frequency grid point; The total number of reflective units of the intelligent reflective surface; For the first The phase shift of the nth reflecting unit, that is, the nth phase shift of each reflecting unit. One component; For the transmitter to the The first reflector unit at the... The incident channel response at each time-frequency grid point; For the first The first reflector unit to the receiver at the second... The outgoing channel response at each time-frequency grid point; the equivalent channel response at each time-frequency grid point together constitutes the time-frequency domain diagonal equivalent cascaded channel.

[0015] Furthermore, the frequency-domain linear equalizer is a zero-forcing equalizer, and the receiver performance index is the signal-to-noise ratio after zero-forcing equalization. Its parsing expression is:

[0016] in, The normalized equivalent noise gain is determined by the following formula:

[0017] The expression for the radio frequency collection power is:

[0018] The three-variable joint optimization problem is specifically as follows:

[0019] in, The power division factor is... The transmission power for each time-delay-Doppler domain information symbol, For the first Power allocation weights for each time-frequency grid point For the first Equivalent channel response at each time-frequency grid point This refers to the antenna thermal noise power. Additional noise power introduced for the information decoding branch. For the radio frequency energy conversion efficiency of the energy harvesting circuit, For the number of subcarriers, This represents the number of time slots.

[0020] Furthermore, the frequency domain linear equalizer is a minimum mean square error equalizer, and the receiver performance index is the signal-to-interference-noise ratio after minimum mean square error equalization. Its parsing expression is:

[0021] The three-variable joint optimization problem is specifically as follows: .

[0022] Furthermore, the subproblems of fixing the phase shift of each reflecting unit and solving the power allocation weights and power division factors are solved using a two-layer decomposition method: Inner layer: Fixed power division factor Introducing Lagrange multipliers corresponding to the total transmit power constraint and the Lagrange multiplier corresponding to the minimum power constraint for energy harvesting The square of the power allocation weights for each time-frequency grid point of the Lagrangian function. Taking the partial derivative and setting it to zero, we obtain the first... The optimal power allocation weights for each time-frequency grid point satisfy:

[0023] in ; using the subgradient method , Perform iterative updates until the constraints are met; Outer layer: Utilizing the objective function with respect to the power division factor The unimodality, in The optimal power division factor that maximizes the receiver's performance index is found using the golden section search method within the feasible interval. .

[0024] Furthermore, the solution steps for the subproblem of fixed power allocation weights and power segmentation factors, and iteratively updating the phase shift of each reflection unit in a unit-by-unit manner, in the zero-forcing equilibrium scenario are as follows: Regarding the first One reflective unit ( ), define the phase shift of the remaining reflection units after fixing them. The composite channel residual for each time-frequency grid point is:

[0025] Definition of the first The first reflector unit at the... The channel contribution of each time-frequency grid point is ,thereby ; Introducing auxiliary variables Its closed-form update is:

[0026] fixed Afterwards, regarding the first The optimal phase shift is obtained by calculating the argument of the phase shift of each reflecting unit:

[0027] right Update the phase shift matrix one by one according to the above steps, and repeat until convergence.

[0028] Furthermore, the solution steps for the subproblem of fixed power allocation weights and power segmentation factors, and iteratively updating the phase shift of each reflection unit in a unit-by-unit manner, under the minimum mean square error equilibrium scenario are as follows: Regarding the first One reflective unit ( ),by , The composite channel residual and channel contribution are defined in the same way, and the first... The phase shift parameter of each reflector unit is denoted as ; Introducing auxiliary variables Its closed-form update is:

[0029] in For the current iteration round Equivalent channel response at each time-frequency grid point; Fixed auxiliary variables Then, define the intermediate auxiliary quantities for each time-frequency grid point:

[0030] For the objective function with respect to the phase angle Find the partial derivative and set it to zero to obtain the first... The optimal closed-form solution for the phase shift of a single reflecting unit:

[0031] right Update the phase shift matrix one by one according to the above steps, and repeat until convergence. The closed-form solution does not require the calculation of the Riemannian manifold gradient, and the computational complexity is significantly lower than the phase shift update method based on Riemannian manifold optimization.

[0032] The beneficial effects of this invention are as follows: This invention introduces an intelligent reflective surface containing multiple passive reflective units into the system architecture. This allows the controllable reflection path formed by the intelligent reflective surface to form a composite propagation link together with the direct path from the transmitter to the receiver. This overcomes the fundamental limitation of existing OTFS data and energy simultaneous transmission systems, which rely entirely on the natural propagation environment. Even in scenarios where the direct link is severely degraded due to obstacles or deep fading, the equivalent channel gain can still be reconstructed by actively adjusting the phase shift of each reflective unit, ensuring reliable communication and significantly expanding the applicable scenarios of the OTFS data and energy simultaneous transmission system.

[0033] This invention also introduces a joint optimization method, which simultaneously optimizes the power allocation weights of each time-frequency grid point of the transmitter, the power division factor of the receiver, and the phase shift of each reflector unit of the smart reflector. The optimization variables are expanded from the two variables of power allocation weights and power division factors in the prior art to three variables for joint optimization. This fully explores the joint degrees of freedom of the three dimensions of transmitter power allocation, receiver energy allocation, and wireless propagation path. Compared with the OTFS data and energy transmission system without the introduction of a smart reflector, it can achieve improved bit error rate performance in the zero-forcing equalization scenario and in the minimum mean square error equalization scenario.

[0034] This invention realizes a system architecture of centralized optimization and distributed execution, enabling the optimal configuration of the three optimization variables to be deployed in a coordinated manner among the various components of the system, supporting the engineering implementation of practical communication systems. Attached Figure Description

[0035] Figure 1 This is a system block diagram of an intelligent reflector-assisted orthogonal time-frequency spatial data and energy transmission system according to an embodiment of the present invention.

[0036] Figure 2 This is a flowchart illustrating a joint optimization method for an intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system according to an embodiment of the present invention.

[0037] Figure 3 This is a schematic diagram of the transceiver signal processing flow of an intelligent reflector-assisted orthogonal time-frequency spatial data transmission system according to an embodiment of the present invention.

[0038] Figure 4 This is a graph illustrating the change of the outer objective function with the power division factor in one embodiment of the present invention.

[0039] Figure 5 This is a comparison chart of the convergence curves of the normalized objective function value and the number of iterations of the proposed alternative optimization algorithm in one embodiment of the present invention.

[0040] Figure 6This is a graph showing the comparison of bit error rate and signal-to-noise ratio between a smart reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system and a system without a smart reflector, as illustrated in one embodiment of the present invention.

[0041] Figure 7 This is a comparison curve of the system bit error rate under different numbers of intelligent reflective surface reflective units in one embodiment of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0043] Example 1 This embodiment constructs an intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system, such as... Figure 1 As shown, the system consists of three parts: a transmitter (Tx), a smart reflector (IRS), and a receiver (Rx). The smart reflector includes... Each transmitter has an independently adjustable phase-shift passive reflector unit; the receiver includes a power division module, a frequency-domain linear equalizer, and an energy harvesting circuit. A direct path exists between the transmitter and receiver, while a reflection path is formed from the transmitter to the receiver via a smart reflector; these two paths together constitute a composite propagation link. Assume the reflection amplitude of each reflector unit... This means that each reflecting unit only adjusts the signal phase without changing the amplitude. In the simulation verification, the channel parameters of the three links—the transmitter-to-receiver direct link, the transmitter-to-smart reflector link, and the smart reflector-to-receiver link—are set to the same value.

[0044] like Figure 3 As shown, the bandwidth of each OTFS frame is (Hz), duration is (s), where the subcarrier spacing , The number of time slots, This represents the number of subcarriers. Each frame consists of... Information symbol The symbols are arranged in the time-delay-Doppler domain, and each symbol is modulated using 4QAM. Let the variance of each symbol be... .

[0045] OTFS modulation and power allocation: Delay-Doppler domain signal vector ( The dimension is mapped to the time-frequency domain via inverse symplectic finite Fourier transform (ISFFT):

[0046] in for 3D time-frequency domain signal vector, For the first The first time slot, the first Time-frequency domain signal on each subcarrier for Point-normalized Discrete Fourier Transform (DFT) matrix, This represents the Kronecker product operation.

[0047] Power allocation: Applying a power allocation matrix to the time-frequency domain signal. , for The diagonal matrix whose first... The diagonal elements are ( , This is used to apply different power allocation weights to each time-frequency grid point. The power-allocated signal... A Heisenberg transform is applied to generate a time-domain transmit signal, which is then transmitted via a wireless channel.

[0048] Two-select channel model: This model assumes that each propagation link in the system experiences a two-select fading channel, and each link has... There are 3 independent propagation paths, and the channel impulse response is:

[0049] in, , , The first Channel coefficients, time delays, and Doppler shifts for each path; Follows a pattern with a mean of zero and a variance of . Cyclic symmetric complex Gaussian distribution (Rayleigh fading); path delay Evenly distributed in Above; Doppler frequency shift Based on the user's movement speed using Jakes' formula Generate. In the simulation, the number of paths for each link is set to... Large-scale path loss is dB, the channel matrix is ​​assumed to be perfectly estimable.

[0050] Time-frequency domain channel response: using the biorthogonal pulse assumption, a single time-frequency grid point The time-frequency domain channel response at that point is:

[0051] IRS-assisted system channel matrix definition: In the time-frequency domain, the direct link channel... Transmitter to Smart Reflector (Tx→IRS) Channel Smart reflector to receiver (IRS→Rx) channel All are modeled as diagonal matrices in the time-frequency domain, where and The first The incident channel matrix and the output channel matrix corresponding to each reflecting unit ( The diagonal elements of each matrix are given by equation (3).

[0052] The phase shift matrix of the intelligent reflector is defined as:

[0053] in For the first The phase angle of each reflecting unit. Define the extended phase shift matrix. .

[0054] Time-frequency equivalent concatenated channel: The time-frequency equivalent concatenated channel from transmitter to receiver for Diagonal matrix:

[0055] Each time-frequency grid point ( The equivalent channel response at point () is:

[0056] in For the first The row vector of the outgoing channel from each time-frequency grid point IRS to the receiver. Let be the column vector of the incident channel from the transmitter to the IRS. The equivalent channel responses at each time-frequency grid point together constitute the diagonally concatenated channel in the time-frequency domain.

[0057] Received signal model and power division: Time-frequency domain received signal: The receiver converts the time-domain signal back to the time-frequency domain using a Wigner transform. Under the assumption of biorthogonal pulses, the time-frequency domain received signal is:

[0058] in Let be a time-frequency domain Gaussian white noise vector, and its i-th element satisfy , This represents the antenna thermal noise power.

[0059] Power division: The power division module uses a power division factor. Received signals in the time and frequency domain According to amplitude proportion The power is split so that the ratio of the two power paths is... It is divided into: Information Decoding (ID) Branch: ,in The additional noise introduced by power segmentation follows a zero-mean, covariance matrix of... Circularly symmetric complex Gaussian distribution; Energy harvesting (EH) branch: .

[0060] Energy harvesting power: Since noise power is negligible compared to signal power, the RF harvesting power of the energy harvesting circuit is:

[0061] Time-delay-Doppler domain signal recovery: Applying frequency-domain linear equalization to the ID branch signal yields the equalized time-frequency domain signal. The time-delay-Doppler domain signal is then recovered by symplectic finite Fourier transform (SFFT):

[0062] in This refers to the radio frequency energy conversion efficiency of the energy harvesting circuit.

[0063] Example 2 like Figure 2 As shown, a joint optimization method based on the intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system includes the following steps: Establish an equivalent channel model: The equivalent channel response of each time-frequency grid point is modeled as the sum of the direct component from the transmitter to the receiver and the reflected component controlled by the phase shift of each reflection unit of the intelligent reflector, so as to characterize the active control effect of the intelligent reflector on the composite propagation link. Derivation of performance index expressions: Based on the equivalent channel model, the analytical expression of the receiver performance index of the information decoding branch after equalization by the frequency domain linear equalizer is derived, as well as the expression of the radio frequency harvesting power of the energy harvesting circuit. Construct a joint optimization problem: With the goal of maximizing the performance index of the receiver, under the constraints of total transmit power, minimum power of energy harvesting, power division factor range, and constant mode of phase shift of each reflector, construct a three-variable joint optimization problem concerning power allocation weight, power division factor, and phase shift of each reflector. Alternating optimization solution: The three-variable joint optimization problem is decomposed into two sub-problems using an alternating optimization framework and executed iteratively: the phase shift of each reflection unit is fixed, and the power allocation weight and the power segmentation factor are solved; the power allocation weight and the power segmentation factor are fixed, and the phase shift of each reflection unit is iteratively updated unit by unit. Until the algorithm converges, the optimal power allocation weight is sent to the transmitter, the optimal power division factor is sent to the receiver, and the optimal phase shift of each reflector is sent to the smart reflector.

[0064] This embodiment uses a zero-forcing equalizer as an example to detail the complete implementation process of the joint optimization method.

[0065] Zero-forcing equalizer: In the ID branch, a zero-forcing equalizer is applied to the time-frequency domain signal, and the equalization matrix... .because and All are diagonal matrices. It is also a diagonal matrix, and its position is... The equilibrium weights at each time-frequency grid point are:

[0066] Inverting the signal point by point completely eliminates inter-channel interference in the time-frequency domain. The equalized time-frequency domain signal is:

[0067] in For effective signal components, To equalize the channel noise components, Introduce noise components to the ID.

[0068] Equivalent SNR Derivation: Obtained by applying SFFT to the equalized signal. The covariance matrix of the channel noise components is:

[0069] because It is a diagonal matrix (where Since it is a real number, ),through and The transformation of two unitary matrices yields a block cyclic matrix, in which all diagonal elements are equal, denoted as . :

[0070] Similarly, the equivalent power of the noise component introduced by ID is .

[0071] Define the normalized equivalent noise gain:

[0072] The equivalent signal-to-noise ratio after ZF equalization is:

[0073] ZF Scenario Joint Optimization Problem: In this embodiment, to maximize To achieve the goal, construct a weighting scheme for power allocation. Power division factor Phase shift of each reflecting unit Three-variable joint optimization problem:

[0074]

[0075]

[0076]

[0077]

[0078] Where constraint (C1) is the total transmit power constraint, The total power that can be allocated; constraint (C2) is the minimum power constraint for energy harvesting. The minimum energy required to be collected by the EH branch; constraint (C3) is the power division factor range constraint; constraint (C4) is the phase shift constant mode constraint for each reflecting unit. The non-convexity of this problem mainly stems from the three variables. , , The complex coupling and constant modulus constraint (C4) make it impossible to solve directly.

[0079] Alternating Optimization Framework and Complete Algorithm: The alternating optimization framework is adopted to decompose the three-variable joint optimization problem into two subproblems that are solved iteratively in alternation.

[0080] Algorithm 1: IRS-assisted OTFS-SWIPT system joint optimization of AO algorithm Input: Channel matrix , , Noise parameters , Transmit power parameters Total power constraint EH energy constraint Energy conversion efficiency Maximum number of iterations Convergence threshold ; With Θ fixed, solve for {p²} i Subproblems of λ: fixed back, In a fixed, government-managed scenario, the problem degenerates into:

[0081] The solution is obtained by using a two-layer decomposition method: Inner layer – Fixed λ, Lagrange multiplier method to solve {p² i}: fixed Maximizing is equivalent to minimizing the denominator. .

[0082] Construct the Lagrangian function:

[0083] in and Let be Lagrange multipliers, corresponding to constraints (C1) and (C2), respectively. For Find the partial derivative and set it to zero:

[0084] Organized into the first Closed-form solution for optimal power allocation weights at each time-frequency grid point:

[0085] Must meet Lagrange multipliers , Iterative updates are performed using the subgradient method—when a constraint is violated, the corresponding multiplier is increased to intensify the penalty; when the constraint is satisfied, the multiplier shrinks towards zero.

[0086]

[0087] in , Step size, For inner iterative index, The physical meaning of equation (15): When the total power exceeds the upper limit... hour( ), Increase, suppress power; when the constraint is satisfied, the multiplier remains unchanged. Equation (16) is similar: when the collected power is lower than hour( ,Right now ), The increase forces more energy to be allocated to EH. Repeating equations (14) to (16) until constraints (C1) and (C2) are satisfied yields the given... Optimal power allocation .

[0088] Outer layer – Golden section search method to solve for λ: Substituting the optimal power allocation of the inner layer, the outer layer objective function is equivalent to:

[0089] Based on the parameters in Table 1, in Under the conditions of SNR=0 dB and randomly initialized IRS phase, a fixed channel is used to implement and plot the results. and Relationship curves, such as Figure 4 As shown, simulation verification indicates about exist The above is a unimodal function. Therefore, the Golden Section Search (GSS) method can be directly used to find the feasible interval. Search for the optimal power division factor It eliminates the need to calculate gradients, resulting in high search efficiency.

[0090] Table 1 Simulation parameters of the IRS-OTFS-SWIPT system

[0091] Fix {P, λ}, optimize the phase shift Θ of each reflector: fix the power allocation weights. and power division factor back, Maximize a constant Equivalent to minimizing the normalized equivalent noise gain .make The objective function simplifies to:

[0092] Introducing auxiliary variables, we construct an auxiliary problem for fractional programming: Introducing real auxiliary variables Construct the following auxiliary optimization problem:

[0093] right and Solving the problem using an alternating optimization strategy: Fix Θ, update the auxiliary variable γ: right About each Find the partial derivative and set it to zero: We obtain closed-form updates for auxiliary variables:

[0094] With γ fixed, BCD updates the phase shift of each reflection element element by element: fixed After that, ignore with irrelevant The constant term, the original minimization problem is equivalent to:

[0095] Update the element-wise using Block Coordinate Descent (BCD). Phase shift of each reflecting unit ( Fix the remaining units ( ).

[0096] Vectorization techniques: Utilizing the equivalence between the product of a diagonal matrix and a vector:

[0097] make ( vector), for The If there are 1 element, then .

[0098] BCD unit decomposition: Fixed ( ),make:

[0099] but The objective function expands to:

[0100] Ignore and irrelevant After the constant term, it is equivalent to:

[0101] make Under constant modulus constraint Below, maximize We need to make the cosine function reach its maximum value of 1, that is... , got the first Optimal closed-form solution for each reflecting unit:

[0102] right Update one by one following the steps above (each update) Immediately afterwards and with the updated Calculate the next unit This completes one round of BCD updates. Steps (a) and (b) are executed alternately until the objective function converges.

[0103] In this embodiment, a simulation verification of the ZF equilibrium scenario is performed: Simulation parameters: As shown in Table 1, carrier frequency GHz, subcarrier spacing kHz, number of subcarriers Number of time slots User movement speed km / h, allowing for the allocation of total power dBm, EH requires energy harvesting dBm, energy conversion efficiency Channel noise power W,ID Additional Noise Power W, number of multipath paths .

[0104] like Figure 5 Convergence verification shown: Figure 5 (a) shows the convergence curve when using a zero-forcing equalizer. Figure 5 (b) shows the convergence curve when using the minimum mean square error equalizer. SNR=0 dB, the maximum number of iterations for the ZF scene is 20, and the phase of each reflection unit is randomly initialized. Figure 5 The relationship between the normalized objective function of the AO algorithm and the number of iterations under ZF equalization is presented. It can be seen that the objective function value converges at approximately 10 iterations, rapidly increasing from the initial value of 48% to 100%, demonstrating a fast convergence speed and verifying the effectiveness of the proposed AO algorithm in ZF scenarios.

[0105] like Figure 6 The BER-SNR performance shown: Settings The maximum number of AO iterations is 15, and the phase of each reflection unit is randomly initialized. Figure 6 The relationship between bit error rate (BER) and signal-to-noise ratio (SNR) for three schemes using a ZF equalizer is presented: ① IRS + phase optimization (this invention); ② IRS + initial random phase (without phase shift optimization); ③ no IRS. The results show that this invention significantly improves BER performance compared to the scheme without IRS; compared to the scheme using IRS but without phase shift optimization, the average SNR gain is approximately 2.5 dB at the same BER, verifying the necessity of joint optimization of the phase shift of each reflecting unit.

[0106] like Figure 7 The BER-K performance shown: Figure 7 This study compares the bit error rate (BER) performance of three schemes: IRS phase shift optimization, IRS random phase shift, and no IRS, under two scenarios: using a zero-forcing equalizer and a minimum mean square error equalizer. The SNR is set to 10 dB, the maximum number of AO iterations is 10, and the phase of each reflection unit is randomly initialized. The number of reflection units is then compared. BER performance for different values. In the ZF scenario, the system BER decreases as the number of reflection units increases; as... As the number of iterations increases, the equivalent cascaded channel becomes more complex, and the ZF equalizer becomes more sensitive to noise amplification. The BER decrease trend becomes more gradual. At this point, the maximum number of AO iterations can be appropriately increased to further reduce the BER.

[0107] Example 3 This embodiment uses the minimum mean square error (MMSE) equalizer as an example to detail the complete implementation process of the joint optimization method. The system architecture and channel modeling are the same as in Embodiment 1.

[0108] MMSE Equilibrium and Equivalent SSINR Derivation Minimum mean square error equalizer: In the ID branch, a minimum mean square error equalizer is applied to the time-frequency domain signal. Because and Both are diagonal matrices and It is a real number (therefore) The MMSE equalization matrix degenerates into element-wise operations on a time-frequency grid, the first... The equilibrium weights at each time-frequency grid point are:

[0109] In the denominator This is a noise power regularization term. This term enables the minimum mean square error equalizer to suppress noise amplification while suppressing inter-channel interference in the time and frequency domains, resulting in stronger noise robustness compared to zero-forcing equalizers. The equalized time-frequency domain signal... The number of grid point components is:

[0110] Equivalent SSINR derivation: Similar to the ZF scenario, utilizing the property that the covariance matrix of the diagonal matrix after SFFT / ISFFT unitary transformation is a block cyclic matrix with equal diagonal elements, the equivalent signal-to-interference-noise ratio (SSINR) after MMSE equalization is derived as follows:

[0111] Joint optimization issues in MMSE scenarios: With the objective of maximizing SSINR, and the constraints being the same as those in the ZF scenarios (C1) to (C4), a three-variable joint optimization problem is constructed:

[0112] The AO framework from Algorithm 1 is also used to solve the problem, where step 1 ( and (Optimization) and step 2 ( The optimizations are performed separately for the MMSE objective function.

[0113] With Θ fixed, solve for {p²} i Subproblems of λ: In MMSE scenarios, fixed back, and The subproblem-solving framework is the same as that of the ZF scenario, both employing a two-layer decomposition: an inner layer fixed... The power allocation weights of each time-frequency grid point are updated using the Lagrange multiplier method (Equations (13) to (16)). (Both the numerator and denominator in the objective function are related to...) Monotonic, similar Lagrangian functions can be constructed); outer verification of the MMSE objective function with respect to Similarly, forming a unimodal function (verified numerically under the same simulation conditions), the golden section search method is used in... Solving for the optimal power division factor .

[0114] With {P, λ} fixed, optimize the phase shift Θ of each reflection unit: fixed and back, For constants, in the MMSE scenario The subproblems are:

[0115] Introducing auxiliary variables, we construct an auxiliary problem for fractional programming: Introducing real auxiliary variables Applying a quadratic transformation to the above fraction and objective function, we construct an auxiliary optimization problem:

[0116] (a) Fix Θ, update the auxiliary variable γ (execute once before each round of BCD): Utilize the current Calculate each grid point ,right about Take the partial derivative and set it to zero. We obtain closed-form updates for auxiliary variables:

[0117] (b) With γ fixed, BCD updates the phase shift of each reflection element element by element: fixed Then, ignore the constant term. The objective function simplifies to:

[0118] Defined in the same way as equation (21) , For the first The BCD update of each reflection unit is performed, and its phase shift parameterization is... In the current iteration round Value (denoted as) )calculate:

[0119] With respect to the objective function (25a) and the phase angle To find the partial derivative, use:

[0120] Substituting and simplifying, we get:

[0121] Setting the partial derivatives to zero, define the intermediate auxiliary quantities for each time-frequency grid point:

[0122] in From equation (26), From equation (26a) before the update Calculate. Let:

[0123] The equation with zero partial derivatives simplifies to: Multiply both sides have to:

[0124] Solve for the optimal phase angle That is, the first The optimal closed-form solution for the phase shift of a single reflecting unit is:

[0125] renew Effective immediately upon update Recalculate ,Enter Unit updates. After completing each step, you will get a new one. , and then with new renew (Return to step (a)) and loop until convergence.

[0126] The closed-form solution of equation (29) only requires... Intermediate auxiliary quantities at each grid point The argument is obtained by weighting and superimposing according to formula (28). The computational complexity is significantly lower than that of the Riemann manifold optimization method, which requires the calculation of the Riemann manifold gradient and the Riemann exponent mapping.

[0127] In this embodiment, the simulation verification of the MMSE equalization scenario is as follows: Convergence verification as follows Figure 5 As shown: Settings SNR=0 dB, maximum number of iterations is 15, and the phase of each reflective unit is randomly initialized. Figure 5 The relationship between the normalized objective function and the number of iterations for the AO algorithm under the MMSE equalizer is also presented. It can be seen that the objective function converges at approximately 7 iterations, with an initial convergence of 89%, indicating a relatively smooth convergence. This is because the MMSE equalizer considers noise power, and at a fixed... Only optimization and The phase has already achieved good performance, and the additional gains from subsequent phase-shift optimization are relatively small.

[0128] BER-SNR performance such as Figure 6 As shown: Settings The maximum number of iterations for AO is 15. Figure 6 The BER-SNR curves for three comparative schemes under the MMSE equalizer are presented. In the MMSE scenario, the average SNR gain of the IRS phase-optimized scheme is about 0.5 dB compared to the unoptimized scheme, which is much smaller than the 2.5 dB in the ZF scenario, further verifying the robustness of the MMSE equalizer to channel interference.

[0129] BER-K performance such as Figure 7 As shown: With SNR set to 10 dB, the maximum number of AO iterations is 10. The system BER also varies under the MMSE scenario. As the BER curve increases and decreases, the slope of the BER curve decreases only slightly. The increased response is more stable than in the ZF scenario, demonstrating the robustness of the MMSE equalizer to changes in channel complexity.

Claims

1. A smart reflective surface-assisted orthogonal time-frequency spatial data and energy transmission system, characterized in that, The system includes a transmitter, a smart reflector, and a receiver. The smart reflector comprises multiple passive reflective elements, each of which can independently adjust its phase shift. These elements receive wireless signals from the transmitter and reflect them to the receiver with a controllable phase shift, thus forming a composite propagation link together with the direct path from the transmitter to the receiver. The receiver receives signals from the smart reflector and the transmitter and includes an information decoding branch and an energy harvesting circuit. A frequency domain linear equalizer is provided in the information decoding branch of the receiver.

2. A joint optimization method for the intelligent reflector-assisted orthogonal time-frequency spatial data-energy simultaneous transmission system, characterized in that, Includes the following steps: Establish an equivalent channel model: The equivalent channel response of each time-frequency grid point is modeled as the sum of the direct component from the transmitter to the receiver and the reflected component controlled by the phase shift of each reflection unit of the intelligent reflector, so as to characterize the active control effect of the intelligent reflector on the composite propagation link. Derivation of performance index expressions: Based on the equivalent channel model, the analytical expression of the receiver performance index of the information decoding branch after equalization by the frequency domain linear equalizer is derived, as well as the expression of the radio frequency harvesting power of the energy harvesting circuit. Construct a joint optimization problem: With the goal of maximizing the performance index of the receiver, under the constraints of total transmit power, minimum power of energy harvesting, power division factor range, and constant mode of phase shift of each reflector, construct a three-variable joint optimization problem concerning power allocation weight, power division factor, and phase shift of each reflector. Alternating optimization solution: The three-variable joint optimization problem is decomposed into two sub-problems using an alternating optimization framework and executed iteratively: the phase shift of each reflection unit is fixed, and the power allocation weight and the power segmentation factor are solved; the power allocation weight and the power segmentation factor are fixed, and the phase shift of each reflection unit is iteratively updated unit by unit until the algorithm converges.

3. The joint optimization method according to claim 2, characterized in that, The frequency domain linear equalizer is a zero-forcing equalizer; the equalization weight of the zero-forcing equalizer at the i-th time-frequency grid point... satisfy: in, For the transmitter in the The power allocation weights applied to each time-frequency grid point For the first Equivalent channel response at each time-frequency grid point For the number of subcarriers, The number of time slots; the zero-forcing equalizer completely eliminates inter-channel interference in the time and frequency domains through the above grid-by-grid inversion operation.

4. The joint optimization method according to claim 2, characterized in that, The frequency domain linear equalizer is a minimum mean square error equalizer; the minimum mean square error equalizer is in the first... Equilibrium weights at each time-frequency grid point satisfy: in, For the first Power allocation weights for each time-frequency grid point For the first Equivalent channel response at each time-frequency grid point The transmission power for each time-delay-Doppler domain information symbol, This refers to the antenna thermal noise power. Additional noise power introduced for the information decoding branch. The power division factor is... For the number of subcarriers, The number of time slots is denoted as ; the minimum mean square error equalizer suppresses noise amplification effect while suppressing inter-channel interference by introducing a noise power regularization term in the denominator, and has stronger noise robustness compared to the zero-forcing equalizer.

5. The joint optimization method according to claim 2, characterized in that, The equivalent channel model in the first Equivalent channel response at each time-frequency grid point Determined by the following formula: in, For the transmitter-to-receiver direct link in the 1st Channel response at each time-frequency grid point; The total number of reflective units of the intelligent reflective surface; For the first The phase shift of the nth reflecting unit, that is, the nth phase shift of each reflecting unit. One component; For the transmitter to the The first reflector unit at the... The incident channel response at each time-frequency grid point; For the first The first reflector unit to the receiver at the second... The outgoing channel response at each time-frequency grid point; the equivalent channel response at each time-frequency grid point together constitutes the time-frequency domain diagonal equivalent cascaded channel.

6. The joint optimization method according to claim 3, characterized in that, The frequency-domain linear equalizer is a zero-forcing equalizer, and the receiver performance metric is the signal-to-noise ratio after zero-forcing equalization. Its parsing expression is: in, The normalized equivalent noise gain is determined by the following formula: The expression for the radio frequency collection power is: The three-variable joint optimization problem is specifically as follows: in, The power division factor is... The transmission power for each time-delay-Doppler domain information symbol, This refers to the antenna thermal noise power. Additional noise power introduced for the information decoding branch. For the radio frequency energy conversion efficiency of the energy harvesting circuit, For the number of subcarriers, This represents the number of time slots.

7. The joint optimization method according to claim 4, characterized in that, The frequency domain linear equalizer is a minimum mean square error equalizer, and the receiver performance index is the signal-to-interference-to-noise ratio after minimum mean square error equalization. Its parsing expression is: The three-variable joint optimization problem is specifically as follows: 。 8. The joint optimization method according to any one of claims 6 or 7, characterized in that, The subproblem of fixing the phase shift of each reflection unit and solving the power allocation weight and power division factor is solved using a two-level decomposition method: Inner layer: Fixed power division factor Introducing Lagrange multipliers corresponding to the total transmit power constraint and the Lagrange multiplier corresponding to the minimum power constraint for energy harvesting The square of the power allocation weights for each time-frequency grid point of the Lagrangian function. Taking the partial derivative and setting it to zero, we obtain the first... The optimal power allocation weights for each time-frequency grid point satisfy: in ; using the subgradient method , Perform iterative updates until the constraints are met; Outer layer: Utilizing the objective function with respect to the power division factor The unimodality, in The optimal power division factor that maximizes the receiver's performance index is found using the golden section search method within the feasible interval. .

9. The joint optimization method according to claim 8, characterized in that, The solution steps for the subproblem of fixed power allocation weights and power division factors, and iteratively updating the phase shift of each reflection unit in the zero-forcing equilibrium scenario are as follows: Regarding the first One reflective unit ( ), define the phase shift of the remaining reflection units after fixing them. The composite channel residual for each time-frequency grid point is: Definition of the first The first reflector unit at the... The channel contribution of each time-frequency grid point is ,thereby ; Introducing auxiliary variables Its closed-form update is: fixed Afterwards, regarding the first The optimal phase shift is obtained by calculating the argument of the phase shift of each reflecting unit: right Update the phase shift matrix one by one according to the above steps, and repeat until convergence.

10. The joint optimization method according to claim 8, characterized in that, The solution steps for the subproblem of fixed power allocation weights and power segmentation factors, and iteratively updating the phase shift of each reflection unit on a unit-by-unit basis, in the minimum mean square error equilibrium scenario are as follows: Regarding the first One reflective unit ( ),by , The composite channel residual and channel contribution are defined in the same way, and the first... The phase shift parameter of each reflector unit is denoted as ; Introducing auxiliary variables Its closed-form update is: in For the current iteration round Equivalent channel response at each time-frequency grid point; Fixed auxiliary variables Then, define the intermediate auxiliary quantities for each time-frequency grid point: For the objective function with respect to the phase angle Find the partial derivative and set it to zero to obtain the first... The optimal closed-form solution for the phase shift of a single reflecting unit: right Update the phase shift matrix one by one according to the above steps, and repeat until convergence. The closed-form solution does not require the calculation of the Riemannian manifold gradient, and the computational complexity is significantly lower than the phase shift update method based on Riemannian manifold optimization.

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