Receiving and transmitting parameter design method based on retransmission air computing system

Abstract

The invention relates to the technical field of air computing, in particular to a receiving and transmitting parameter design method based on a retransmission air computing system, which comprises the following steps of: according to a channel coefficient from each edge node to a central node under each time slot and the number distribution of the edge nodes; an optimization problem is constructed according to the frequency of signal transmission, the fluctuation condition of additive white Gaussian noise at the center node, the distribution condition of transmitting power of all edge nodes under each time slot and the number of signal transmission times; and solving the optimization problem to obtain the optimal emission amplitude of each edge node in each time slot and the optimal denoising factor of the center node in each time slot. According to the method, the accuracy of an air calculation result and the anti-interference capability of an air calculation system can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of air computing, and in particular to a method for designing receiving and transmitting parameters based on a retransmission air computing system. Background Art

[0002] Over-the-air computation (Aircomp) technology is a wireless communication aggregation technology. Over-the-air computation systems usually include a central node and multiple edge nodes, and the nodes can be single-antenna or multi-antenna. During the over-the-air computation process, all edge nodes transmit their signals to the central node at the same time and frequency. Due to the signal superposition characteristics of the wireless multiple access channel (MAC), the signal received by the central node is the superposition of the signals transmitted by all edge nodes. This means that the "summation" calculation process is completed directly during the signal transmission process, eliminating the step of restoring the signals of each edge node and then calculating them at the receiving end, greatly improving the communication calculation efficiency and saving time and frequency resources.

[0003] In the prior art, the peak value of the transmission power of each edge node in each time slot is used as a constraint, and the transmit and receive parameters are designed by minimizing the deviation of the air calculation results. However, this method does not jointly optimize the transmit and receive parameters, resulting in insufficient ability to dynamically adjust the receiving parameters according to the quality of the communication environment, making it perform poorly in a low signal-to-noise ratio (SNR) environment, which in turn leads to low accuracy of the air calculation results. Summary of the invention

[0004] In order to solve the technical problem that the method for optimizing parameters in the prior art is insufficient in its ability to dynamically adjust according to environmental conditions, thereby resulting in low accuracy of the in-flight calculation results, the purpose of the present invention is to provide a method for designing transceiver parameters based on a retransmission in-flight calculation system, and the technical solution adopted is as follows:

[0005] During the data transmission process of the retransmission air computing system, the channel coefficient from each edge node to the central node in each time slot is obtained;

[0006] According to the channel coefficient from each edge node to the central node in each time slot and the number distribution of edge nodes, as well as the fluctuation of additive Gaussian white noise at the central node, the distribution of the transmission power of all edge nodes in each time slot and the number of signal transmissions, an optimization problem is constructed;

[0007] A Lagrangian function is constructed based on the optimization problem, and the Lagrangian function is solved to obtain an optimal transmission amplitude of each edge node in each time slot and an optimal denoising factor of the central node in each time slot.

[0008] Preferably, the optimization problem includes a first condition and a second condition;

[0009] Determining a first condition based on a minimum value of a mean square error of the retransmission air computing system;

[0010] The second condition is determined based on the sum of squares of transmission amplitudes of all edge nodes in all time slots.

[0011] Preferably, the mean square error of the retransmission air calculation system is specifically:

[0012]

[0013] Where MSE represents the mean square error of the retransmission air computing system, K represents the number of edge nodes, T represents the number of transmissions, and |h k (t)| represents the modulus of the channel coefficient from the kth edge node to the central node in the tth time slot, σ z 2 represents the variance of the additive Gaussian white noise at the central node; b k (t) represents the amplitude of the transmission coefficient of the kth edge node in the tth time slot; g(t) represents the denoising factor applied by the central node in the tth time slot.

[0014] Preferably, the second condition is specifically:

[0015]

[0016] Among them, P max It represents the maximum value of the sum of the transmit powers of all edge nodes in each time slot.

[0017] Preferably, constructing a Lagrangian function based on the optimization problem specifically includes:

[0018]

[0019] Among them, L({b k (t), g(t), μ}) represents the Lagrangian function, and μ is the Lagrangian multiplier.

[0020] Preferably, solving the Lagrangian function to obtain the optimal transmission amplitude of each edge node in each time slot and the optimal denoising factor of the central node in each time slot specifically includes:

[0021] According to any given Lagrange multiplier μ greater than 0, solve the nonlinear equation group to obtain the optimal denoising factor of the central node in each time slot; update the transmission coefficient amplitude of the edge node to the central node in each time slot according to the optimal denoising factor;

[0022] According to the optimal denoising factor and the updated transmission coefficient amplitude, a dual function of the optimization problem is constructed; the optimal solution when the dual function takes the maximum value is solved to obtain the optimal transmission amplitude corresponding to the transmission coefficient of each edge node in each time slot.

[0023] Preferably, the nonlinear equation group is specifically:

[0024]

[0025] Among them, |h k (i)|The modulus of the channel coefficient from the kth edge node to the central node in the i-th time slot, g(i) represents the denoising factor applied by the central node in the i-th time slot.

[0026] Preferably, updating the transmission coefficient amplitude of the edge node to the central node in each time slot according to the optimal denoising factor specifically includes:

[0027]

[0028] in, It represents the updated transmission coefficient amplitude from the kth edge node to the central node in the tth time slot.

[0029] Preferably, constructing a dual function of the optimization problem according to the optimal denoising factor and the updated emission coefficient amplitude specifically includes:

[0030]

[0031] Among them, G(μ) represents the dual function, g * (t) represents the optimal denoising factor of the central node in the tth time slot.

[0032] Preferably, the method for calculating the optimal transmission amplitude is specifically as follows:

[0033]

[0034] in, represents the optimal transmission amplitude of the kth edge node to the central node in the tth time slot, μ * represents the optimal solution value of the Lagrange multiplier, g * (i) represents the optimal denoising factor of the central node in the i-th time slot.

[0035] The embodiments of the present invention have at least the following beneficial effects:

[0036] Under the condition that the sum of the transmission power of all edge nodes in each time slot is constrained, the present invention transforms the optimization problem into the dual problem by minimizing the MSE of the retransmission air computing system, and finally determines the denoising factor and the optimal transmission amplitude. The present invention can effectively improve the accuracy of the air computing results and the anti-interference ability of the air computing system. The provided solution greatly improves the performance of the air computing system at the cost of less time resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 It is a flow chart of the steps of a receiving and transmitting parameter optimization method corresponding to a receiving and transmitting parameter design method based on a retransmission air computing system provided by the present invention;

[0039] Figure 2 It is a flow chart of the process of solving the optimization problem provided by the present invention;

[0040] Figure 3 It is a flow chart of the steps of the solution method provided by the present invention. DETAILED DESCRIPTION

[0041] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of the specific implementation method, structure, features and effects of a method for designing transceiver parameters based on a retransmission air computing system proposed by the present invention in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0042] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0043] The following describes in detail a specific scheme of a method for designing transceiver parameters based on a retransmission air computing system provided by the present invention in conjunction with the accompanying drawings.

[0044] The specific implementation scenario targeted by the embodiment of the present invention is as follows: This embodiment mainly designs a scheme for obtaining the transmission coefficients of all edge nodes in each time slot and the receiving coefficients of the central node in each time slot in a retransmission air computing system. The scheme uses retransmission to improve the gain of the wireless channel, and jointly optimizes the receiving and transmitting parameters across time slots based on the CSI of all transmission time slots, which can effectively improve the accuracy of the air computing results and the anti-interference capability of the air computing system.

[0045] The main purpose of the embodiment of the present invention is to obtain the optimal transmission power of the edge node in each time slot and the optimal denoising factor of the central node in each time slot, that is, the receiving coefficient, based on the channel coefficients from all edge nodes to the central node and the number of edge nodes, as well as the sum of the transmission powers of all edge nodes in each time slot and the total number of transmissions.

[0046] See also Figure 1 , which shows a flowchart of the steps of the receiving and transmitting parameter optimization method corresponding to the receiving and transmitting parameter design method based on the retransmission air computing system provided by an embodiment of the present invention, the method comprising the following steps:

[0047] Step S100, in the data transmission process of the retransmission air computing system, the channel coefficient from each edge node to the central node in each time slot is obtained.

[0048] First, it is necessary to obtain all channel coefficients of all edge nodes in the entire transmission process. The channel coefficients from each edge node to the central node in the first time slot can be measured by channel reciprocity. The remaining channel coefficients are calculated using the channel prediction model constructed by the first-order Gauss-Markov process. The calculation process is specifically expressed as:

[0049]

[0050] Among them, h k (t+1) represents the channel coefficient from the kth edge node to the central node in the t+1th time slot, h k (t) represents the channel coefficient from the kth edge node to the central node in the tth time slot, K represents the total number of edge nodes, represents the set of all time slots, the channel difference term e~CN(0,1-∈ 2 ), CN represents the complex normal distribution, and the coefficient ∈ quantifies the channel correlation between two consecutive time slots = J0(2π·f d ·T0). J0(·) represents the zero-order Bessel function of the first kind, f d represents the maximum Doppler frequency, f d =vfc / c, v represents the moving speed of the edge node, fc represents the carrier frequency, c represents the speed of light, and T0 represents the period of channel change.

[0051] Step S200, construct an optimization problem based on the channel coefficient from each edge node to the central node in each time slot and the number distribution of edge nodes, the fluctuation of additive Gaussian white noise at the central node, the distribution of transmission power of all edge nodes in each time slot and the number of signal transmissions.

[0052] In traditional communication systems, the receiving end needs to first restore the data of each edge node and then perform calculations. This process usually requires a large amount of data transmission and processing. By performing calculations directly during signal transmission, the receiving end can omit the complete recovery of the data of each edge node, thereby reducing the amount of data required to be transmitted. In other words, the receiving end does not need to restore the data of each edge node to obtain the calculation results, thereby improving the communication calculation efficiency and saving resources.

[0053] In an air computing system, mean squared error (MSE) can be used to measure the accuracy of the air computing results. The smaller the MSE, the more accurate the air computing results. MSE is generally composed of signal deviation and thermal noise of the system.

[0054] When performing air calculations, you can usually adjust the transmission coefficient of the edge node to reduce signal deviation, and increase the receiving coefficient of the central node to reduce the impact of thermal noise. However, increasing the receiving coefficient means that a larger transmission coefficient is required to reduce signal deviation, that is, the node's transmission power is greater. But in practical applications, the transmission power of edge nodes is limited, so in order to make the MSE as small as possible, it is necessary to find a suitable receiving coefficient.

[0055] Based on this, an optimization problem is constructed and solved to obtain the optimal transmission power of the edge node and the optimal denoising factor of the central node. Specifically, the optimization problem includes a first condition and a second condition; the first condition is determined based on the minimum value of the mean square error of the retransmission air calculation system; the second condition is determined based on the sum of the squares of the transmission amplitudes of all edge nodes in all time slots.

[0056] The first condition can be expressed as: Among them, min represents the minimum value function, and MSE represents the mean square error of the retransmission air calculation system.

[0057] The mean square error of the retransmission air calculation system is specifically:

[0058]

[0059] Where MSE represents the mean square error of the retransmission air computing system, K represents the number of edge nodes, T represents the number of transmissions, and |h k(t)| represents the modulus of the channel coefficient from the kth edge node to the central node in the tth time slot, σ z 2 represents the variance of the additive Gaussian white noise at the central node; b k (t) represents the transmission coefficient amplitude of the kth edge node in the tth time slot; g(t) represents the denoising factor applied by the central node in the tth time slot.

[0060] The second condition is specifically:

[0061]

[0062] Among them, P max It represents the maximum value of the sum of the transmit powers of all edge nodes in each time slot.

[0063] Step S300: construct a Lagrangian function based on the optimization problem, and solve the Lagrangian function to obtain the optimal transmission amplitude of each edge node in each time slot and the optimal denoising factor of the central node in each time slot.

[0064] like Figure 2 , which shows a flow chart of the solution process. Since the original optimization problem is non-convex, the original optimization problem is transformed into its dual problem. First, it is necessary to construct a Lagrangian function based on the optimization problem, which specifically includes:

[0065]

[0066] Among them, L({b k (t), g(t), μ}) represents the Lagrangian function, μ is the Lagrangian multiplier, also known as the dual variable, and its value is a number greater than 0.

[0067] like Figure 3 As shown, the flowchart of the solution method can be implemented by steps S301 to S304.

[0068] Step S301: Solve the nonlinear equations to obtain the optimal denoising factor of the central node in each time slot according to any given Lagrange multiplier greater than 0.

[0069] According to the total number of all edge nodes K, the number of transmissions T, the modulus of the channel coefficients from each edge node to the central node in each time slot, and the variance σ of the additive Gaussian white noise at the central node z 2 , combined with any given dual variable μ greater than 0, the optimal denoising factor can be determined, that is, solving the nonlinear equations can obtain the optimal denoising factor g of the central node in the tth time slot *(t), in this embodiment, the nonlinear equations can be solved by the built-in function or optimization toolbox in Matlab, and the nonlinear equations can be specifically expressed as:

[0070]

[0071] Among them, |h k (i)|The modulus of the channel coefficient from the kth edge node to the central node in the i-th time slot, g(i) represents the denoising factor applied by the central node in the i-th time slot.

[0072] Step S302: updating the transmission coefficient amplitude of the edge node to the central node in each time slot according to the optimal denoising factor.

[0073] According to the number of transmissions T, the modulus of the channel coefficients from each edge node to the central node in each time slot, and the optimal denoising factor g of the central node in the tth time slot * (t), determine the function of the dual variable μ, and update the transmission coefficient amplitude of each edge node to the central node in each time slot, which can be specifically expressed as:

[0074]

[0075] in, It represents the updated transmission coefficient amplitude from the kth edge node to the central node in the tth time slot.

[0076] Step S303, constructing a dual function of the optimization problem according to the optimal denoising factor and the updated transmission coefficient amplitude;

[0077] According to the updated transmission coefficient amplitude of the kth edge node to the central node in the tth time slot The maximum value P of the sum of the transmission power of all edge nodes in each time slot max , combined with σ z 2 , K, T and g * (t), the dual function of the original optimization problem can be determined, which can be specifically expressed as:

[0078]

[0079] Among them, G(μ) represents the dual function, g * (t) represents the optimal denoising factor of the central node in the tth time slot.

[0080] Step S304, solving the optimal solution when the dual function takes the maximum value, and obtaining the optimal transmission amplitude corresponding to the transmission coefficient of each edge node in each time slot.

[0081] According to the dual problem of the original optimization problem, the optimal solution of the dual problem can be obtained, that is, the optimal solution value μ of the dual variable * , where the dual problem can be expressed as:

[0082]

[0083] stμ≥0

[0084] Among them, max μ G(μ) represents the maximum value of the dual function, and st is the abbreviation of "subject to", which means "under the condition of..." The dual problem can be solved by the built-in functions or optimization toolbox in Matlab.

[0085] Furthermore, the calculation process for determining the optimal transmission amplitude can be expressed as:

[0086]

[0087] in, represents the optimal transmission amplitude of the kth edge node to the central node in the tth time slot, μ * represents the optimal solution value of the Lagrange multiplier, g * (i) represents the optimal denoising factor of the central node in the i-th time slot.

[0088] It should be noted that in the process of solving the optimal denoising factor and the optimal transmission amplitude, multiple loop iterations can be performed under the condition that the dual variable is greater than 0, and the above solution steps are repeated. In this embodiment, an optimal solution with a relatively stable effect is obtained after 5 loop iterations.

[0089] Furthermore, the transmission coefficient of the edge node is in complex form, the modulus of the transmission coefficient, that is, the modulus of the complex number is the transmission amplitude, and the transmission power is the square of the modulus of the transmission coefficient, that is, the square of the transmission amplitude. The channel coefficients from all edge nodes to the central node are complex numbers. In the process of deriving MSE, let To compensate the phase of the channel coefficient. So the optimization problem is for the transmission amplitude b k (t) is optimized. Among them, b ′ k (t) represents the transmission coefficient of the kth edge node in the tth time slot, which is in the form of a complex number, Represents the conjugate of the channel coefficient from the kth edge node to the central node in the tth time slot.

[0090] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for designing transceiver parameters based on a retransmission air computing system, characterized in that: The method includes: During the data transmission process of the retransmission air computing system, the channel coefficient from each edge node to the central node in each time slot is obtained; According to the channel coefficient from each edge node to the central node in each time slot and the number distribution of edge nodes, as well as the fluctuation of additive Gaussian white noise at the central node, the distribution of the transmission power of all edge nodes in each time slot and the number of signal transmissions, an optimization problem is constructed; A Lagrangian function is constructed based on the optimization problem, and the Lagrangian function is solved to obtain an optimal transmission amplitude of each edge node in each time slot and an optimal denoising factor of the central node in each time slot.

2. A method for designing transceiver parameters based on a retransmission air computing system according to claim 1, characterized in that: The optimization problem includes a first condition and a second condition; Determining a first condition based on a minimum value of a mean square error of the retransmission air computing system; The second condition is determined based on the sum of squares of transmission amplitudes of all edge nodes in all time slots.

3. A method for designing transceiver parameters based on a retransmission air computing system according to claim 2, characterized in that: The mean square error of the retransmission air calculation system is specifically: Where MSE represents the mean square error of the retransmission air computing system, K represents the number of edge nodes, T represents the number of transmissions, and |h k (t)| represents the modulus of the channel coefficient from the kth edge node to the central node in the tth time slot, σ z 2 represents the variance of the additive Gaussian white noise at the central node; b k (t) represents the transmission coefficient amplitude of the kth edge node in the tth time slot; g(t) represents the denoising factor applied by the central node in the tth time slot.

4. A method for designing transceiver parameters based on a retransmission air computing system according to claim 3, characterized in that: The second condition is specifically: Among them, P max It represents the maximum value of the sum of the transmit powers of all edge nodes in each time slot.

5. A method for designing transceiver parameters based on a retransmission air computing system according to claim 4, characterized in that: The constructing of the Lagrangian function based on the optimization problem specifically includes: Among them, L({b k (t), g(t), μ}) represents the Lagrangian function, and μ is the Lagrangian multiplier.

6. A method for designing transceiver parameters based on a retransmission air computing system according to claim 5, characterized in that: Solving the Lagrangian function to obtain the optimal transmission amplitude of each edge node in each time slot and the optimal denoising factor of the central node in each time slot specifically includes: According to any given Lagrange multiplier μ greater than 0, solve the nonlinear equation group to obtain the optimal denoising factor of the central node in each time slot; update the transmission coefficient amplitude of the edge node to the central node in each time slot according to the optimal denoising factor; According to the optimal denoising factor and the updated transmission coefficient amplitude, a dual function of the optimization problem is constructed; the optimal solution when the dual function takes the maximum value is solved to obtain the optimal transmission amplitude corresponding to the transmission coefficient of each edge node in each time slot.

7. A method for designing transceiver parameters based on a retransmission air computing system according to claim 6, characterized in that: The nonlinear equations are specifically: Among them, |h k (i)|The modulus of the channel coefficient from the kth edge node to the central node in the i-th time slot, g(i) represents the denoising factor applied by the central node in the i-th time slot.

8. A method for designing transceiver parameters based on a retransmission air computing system according to claim 7, characterized in that: The updating of the transmission coefficient amplitude of the edge node to the central node in each time slot according to the optimal denoising factor specifically includes: in, It represents the updated transmission coefficient amplitude from the kth edge node to the central node in the tth time slot.

9. A method for designing transceiver parameters based on a retransmission air computing system according to claim 8, characterized in that: The step of constructing a dual function of the optimization problem according to the optimal denoising factor and the updated emission coefficient amplitude specifically includes: Among them, G(μ) represents the dual function, g * (t) represents the optimal denoising factor of the central node in the tth time slot.

10. A method for designing transceiver parameters based on a retransmission air computing system according to claim 9, characterized in that: The calculation method of the optimal transmission amplitude is specifically as follows: in, represents the optimal transmission amplitude of the kth edge node to the central node in the tth time slot, μ * represents the optimal solution value of the Lagrange multiplier, g * (i) represents the optimal denoising factor of the central node in the i-th time slot.

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