A robust multi-channel power allocation method based on double-twist risk metric

Abstract

The application discloses a kind of robust multi-channel power configuration methods based on double twist risk measure, comprising: the total utility of wireless communication system is expressed as the weighted linear combination of each channel utility, and parameterized double twist function is introduced, construct twist risk measure and embed the worst case consideration of CSI parameter uncertainty;Using the closed-form solution under the first-order second-moment uncertainty set, the inner worst-case performance shortage or optimal case performance shortage of twist risk measure is expressed as linear mean term+second-order cone standard deviation term;Design CSI uncertainty set to carry out SOCP modeling and solving, obtain optimal power weight;The potential slow fading state transition point of single channel is determined using moving average technology index, forming the scheduling scheme of power weight size+scheduling opportunity parallel. The application can effectively deal with channel parameter uncertainty, improve the QoS stability and robustness of communication system in extreme channel environment.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and signal processing technology, and specifically relates to a multi-channel power configuration method based on distortion risk measurement and robust optimization. Background Technology

[0002] With the increasing complexity of modern wireless communication systems, the optimal allocation and coordinated management of power resources for multiple channels or users within the system presents a significant challenge. Especially when external channel conditions fluctuate drastically or system model parameters change rapidly, rationally allocating multi-channel power resources while balancing total system throughput and Quality of Service (QoS) has become a crucial issue that system designers urgently need to address.

[0003] Traditional configuration methods primarily rely on the Markowitz mean-variance framework, aiming to control fluctuations by minimizing the variance of the combined system output, and assuming that the output of each channel capacity follows a normal distribution. However, in the real world, the output distribution of channel capacity (such as Rayleigh or Ricean fading) often exhibits heavy-tailed and skewed characteristics. Especially when the system encounters external shocks (such as deep fading), the probability of extremely adverse results is significantly higher than expected under the normal distribution assumption, thus causing the mean-variance model to have a significant bias in characterizing system performance deficiencies. Furthermore, this model is highly dependent on the mean and covariance parameters estimated from historical data (i.e., channel statistical characteristics). Once these parameters deviate from the future true distribution (caused by user movement or environmental changes), it can easily lead to overfitting of the optimization results, potentially causing a significant deterioration in system quality of service (QoS) in extreme cases.

[0004] To more effectively characterize tail performance, the industry has gradually introduced single tail performance metrics such as outage probability (similar to VaR) and average outage utility (similar to CVaR) in recent years to improve sensitivity to distributed tail features. However, these methods also have inherent limitations: VaR can reveal specific quantiles of excess performance shortages, but it cannot reflect information on the scale of the shortage; CVaR measures the expected value of tail performance shortages, but it is not responsive enough to performance changes at different confidence levels and cannot fully cover the tail performance structure.

[0005] Current wireless resource management (VRRM) technologies face three main challenges: First, tail performance measurement methods are relatively simplistic. Traditional VaR methods focus only on the performance shortage threshold at specific quantiles, ignoring the severity of excess shortages. While CVaR improves upon this, its sensitivity to confidence level selection makes it difficult to comprehensively reflect the diversity of tail performance. Second, the parameter uncertainty of Channel State Information (CSI) significantly impacts performance evaluation. Existing methods typically treat the mean and covariance matrices estimated from historical samples as fixed parameters, neglecting the risk of parameter deviations caused by sample estimation errors and sudden changes in system structure, potentially leading to systematic misestimation of system performance. Finally, model robustness is insufficient. Standard mean-variance models or single CVaR optimization frameworks exhibit instability in out-of-sample testing, particularly struggling to maintain stable performance control under extreme channel conditions. Existing robust optimization methods often focus on a single performance metric, failing to effectively integrate multi-level tail characteristics and multiple sources of uncertainty, thus limiting their practical application. Therefore, there is an urgent need for a method that can control the tail performance at multiple levels. This method can not only characterize the key features of the output distribution at multiple confidence levels, but also be applicable to wireless power configuration scenarios with multiple users and high real-time requirements when parameters are uncertain. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a stroke rehabilitation assessment device based on electroencephalogram (EEG) graph theory features.

[0007] The objective of this invention is achieved through the following technical solution: a robust multi-channel power configuration method based on a dual-twist risk metric, comprising:

[0008] The total utility of the wireless communication system is represented as a weighted linear combination of the utility of each channel. A parameterized double twist function is introduced to integrate the single quantile risk and the tail average risk through a convex combination, constructing a twist risk measure and embedding the worst-case consideration of the uncertainty of the CSI parameter.

[0009] By utilizing the closed-form solution under the first and second moment uncertainty sets, the inner worst-case performance shortage or best-case performance shortage of the distortion risk measure is expressed as a linear mean term plus a second-order cone standard deviation term, thereby equivalencing the original problem to the standard SOCP form.

[0010] Design the CSI uncertainty set to model and solve SOCP, and obtain the optimal power weights;

[0011] For a single channel, the potential slow fading state transition time is determined using the moving average technique. The obtained weights are then combined with the optimal time to form a scheduling scheme that combines power weight magnitude with scheduling timing, and power allocation instructions are generated.

[0012] Furthermore, distorting risk measurement for:

[0013]

[0014] in, Let the total utility of the wireless communication system be a random variable. and Let be the probability distortion function. To adjust the parameters, and These are measures of single quantile risk and tail average risk, respectively.

[0015] Furthermore, the worst-case consideration of CSI parameter uncertainty is embedded, including:

[0016] Given a weight vector mean vector With covariance matrix In this scenario, the power allocation problem falls into two categories of optimization objectives: the objective of minimizing performance shortages is:

[0017]

[0018] The objective of maximizing the risk-adjusted utility scenario is:

[0019]

[0020] Where P is the CSI uncertainty set, Let i be the utility of the i-th channel. Weight vector The power configuration weight of the i-th channel, where n is the number of channels.

[0021] Furthermore, by utilizing the closed-form solution under the uncertainty set of first and second moments, the worst-case or best-case performance deficit of the distorted risk measure will be expressed as a linear mean term plus a second-order cone standard deviation term, thereby equivaling the original problem to the standard SOCP form, including:

[0022] Total utility of wireless communication system The first and second moments are respectively expressed as and According to the Shao & Zhang theorem, minimizing the performance-shortage scenario objective yields the following closed form:

[0023]

[0024] To maximize the risk-adjusted utility scenario objective, we obtain the following closed-form:

[0025]

[0026] Let be the total utility of the wireless communication system, with its mean and standard deviation being respectively... and The superscript T indicates the transpose operation;

[0027] The objective of minimizing performance shortage scenarios then becomes:

[0028]

[0029] The objective of maximizing the risk-adjusted utility scenario is transformed into:

[0030] .

[0031] Furthermore, a CSI uncertainty set is designed for SOCP modeling and solution to obtain the optimal power weights, including:

[0032] Based on the requirements for CSI estimation error, a box-shaped uncertainty set is constructed, and the objective and constraints containing mean and covariance offsets are transformed into a standard SOCP model. The optimal weights are then efficiently solved using optimization tools.

[0033] Furthermore, the set of box-shaped uncertainties is:

[0034]

[0035]

[0036]

[0037] in, Let represent the half-width of the confidence interval for the covariance estimation between the i-th channel and the j-th channel. It is a standard normal distribution quantile of a quantile point For channel The sample standard deviation; Obtained through guided methods or based on the standard error formula of moment estimation;

[0038] Based on the box-shaped uncertainty set, worst-case analysis is performed on the variance and mean terms, yielding the following results:

[0039]

[0040]

[0041] Introduce the following constants and variables: Let

[0042]

[0043] Introducing auxiliary variables ,make , Then rewritten as:

[0044]

[0045]

[0046] Its constraints include: total power constraints Non-negative weights Second-order cone constraint , equivalent to .

[0047] Furthermore, moving average techniques are used to determine the potential slow fading state transition times for individual channels, including:

[0048] Obtain channel quality sequence And using moving average techniques, short-term... With long-term moving average ;

[0049] Minimize the direction of shortage: when the short-term moving average Crossing the long-term moving average from bottom to top When this happens, a "channel degradation" signal is generated; when the short-term moving average... Crossing the long-term moving average from top to bottom At that time, a "channel improvement" signal is generated; the corresponding crossover points are denoted as follows: and ;

[0050] Maximizing utility direction: The signal direction is opposite to minimizing shortage.

[0051] Furthermore, it also includes: performing historical simulation tests on the output scheduling logs, and calculating multi-dimensional indicators such as system throughput curves, performance-fluctuation ratio, outage probability measurement, and maximum performance rollback.

[0052] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described robust multi-channel power configuration method based on a double-twist risk metric.

[0053] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described robust multi-channel power configuration method based on a dual-twist risk metric.

[0054] The technical concept of this invention is as follows: First, the total system utility of a multi-channel system is expressed as a linear combination of weights and the utility of each channel. Two parameterized distortion functions are introduced, and a comprehensive double-distortion risk measure is constructed by convex combination of VaR and CVaR to balance quantile performance shortage and tail mean. Then, worst-case considerations of the uncertainty of mean and covariance (CSI) parameters are embedded in the combinatorial optimization objective. The double-distortion measures for the two scenarios of maximizing utility and minimizing shortage are transformed into closed-form expressions of "linear mean term + second-order cone variance term", and equivalent to a standard second-order cone programming (SOCP) model using the Shao & Zhang theorem. Next, for two uncertainty sets, box-shaped and ellipsoidal, the contributions of mean shift and covariance shift to the performance measure under worst-case conditions are analyzed, and these worst-case values ​​are incorporated into the SOCP constraints. Finally, the optimal configuration weights obtained are linked with the moving average signal of a single channel to generate a parallel scheduling scheme of "power weight + scheduling timing". The efficiency-fluctuation ratio, VaR / CVaR, maximum drawdown and other multi-dimensional indicators are comprehensively evaluated in historical simulations.

[0055] The beneficial effects of this invention are as follows: Firstly, the multi-level dual-torsion performance metric can simultaneously capture both single-quantile performance deficiencies and tail-average performance deficiencies, enhancing sensitivity to distributed heavy-tailed and skewed characteristics, and can satisfy different QoS preferences by adjusting the torsion function parameters. Secondly, by transforming the inner worst-case problem into a closed-form "linear + second-order cone" expression, the original semi-infinite-dimensional robust optimization can be efficiently transformed into a solvable SOCP problem, taking into account both the numerical solvability and robustness of the model. Furthermore, the design for box-shaped and ellipsoidal uncertainty sets for parameter uncertainties retains fine control over extreme perturbations in each dimension while simplifying worst-case calculations through duality theory. Finally, by combining the combinatorial optimization results with technical indicator signals, the synergy between robust configuration and channel trend timing is achieved, improving the system throughput and policy stability after QoS adjustment under extreme channel environments. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is the overall flowchart of the present invention;

[0058] Figure 2 This is a schematic diagram of the double-twist risk metric and its convex hull of the present invention;

[0059] Figure 3 This diagram illustrates the performance shortcomings of the methodology of this invention compared to traditional methods. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features of the following embodiments and implementations can be combined with each other.

[0061] A robust multi-channel power configuration method based on a dual-twist performance metric is applied to a wireless communication system (hereinafter referred to as the system). The method includes:

[0062] (1) Define system utility and double-twist performance metrics, specifically including the following steps:

[0063] (1.1) System utility random variable. In the multi-channel power allocation problem, the total utility / performance deficit of the system can be regarded as a weighted linear combination of the utilities of multiple channel systems. Suppose the system contains... Channel type, the first The random system utility of a channel is denoted as The corresponding power allocation weight Then the total system utility It can be represented as:

[0064]

[0065] It needs to meet the total power constraint. and nonnegativity In the context of risk measurement, a negative value of the combined system utility is often regarded as a performance deficit. This is to ensure consistency with the definition and interpretation of risk measurement.

[0066] (1.2) Distortion Risk Measure. Distortion risk measures are a class of risk measurement methods that weight the tails of a distribution using a probability transformation function. Given a monotonically increasing distribution that satisfies... probability distortion function Its corresponding risk metric is defined as:

[0067]

[0068] in, Let the total utility of the system be a random variable. For probability quantiles, for The quantile function (i.e., the inverse function of the cumulative distribution function). For the twist function The differential.

[0069] By analyzing different intervals of the quantile curve (from...) (Definition) Apply different weights (by) The distortion risk measure, as defined, can flexibly characterize the different preferences of system designers for different parts of the performance shortage distribution. When the distortion function takes a specific form, this measure can degenerate into the common single quantile risk (VaR) or tail mean risk (CVaR). To balance the focus on single quantiles and tail means, two basic distortion functions can be introduced. and These correspond to the single quantile risk (VaR) and tail mean risk (CVaR) measures, respectively, and are measured using a proportional parameter. Perform convex combination Substituting this double-torsion function into the definition of the distortion risk measure, we obtain... By adjusting The model can smoothly transition between single quantile risk (VaR) and tail average risk (CVaR), thus better meeting the needs of different QoS preferences.

[0070] (2) Construct a robust optimization strategy framework, which includes the following steps:

[0071] (2.1) Two types of objectives for system optimization. Given a power allocation vector... mean vector With covariance matrix In this context, the power allocation problem can be divided into two categories of optimization objectives: For scenarios where the goal is to minimize performance shortages (hereinafter referred to as minimization scenarios), the optimization problem can be expressed as:

[0072]

[0073] in This refers to the minimum expected system throughput level set by the system designer.

[0074] In the scenario of maximizing risk-adjusted utility (hereinafter referred to as the maximization scenario), the focus is on the system utility potential while ensuring the maximization of the distortion risk measure. The corresponding problem is:

[0075]

[0076] The above model assumes parameters The data is precisely known, making it difficult to cope with extreme performance degradation events caused by estimation errors and sudden changes in the channel environment. Therefore, the next step is to optimize for the worst-case scenario under data uncertainty.

[0077] (2.2) Worst-case optimization under data uncertainty. In the robust multi-channel configuration problem, considering the data errors and uncertainties in the channel statistical model in the actual communication environment (e.g., the assumptions about the channel utility distribution, such as the Gaussian distribution, do not match the actual heavy-tailed distribution), optimization is not performed based solely on a single estimated parameter (such as the expected channel utility). With covariance matrix Optimizing such models often fails to achieve robust performance in real-world scenarios. To improve the fault tolerance and practicality of these models, a robust optimization strategy is introduced, which optimizes possible parameters (referring to channel utility)... The first moment (mean vector μ) and the second moment (covariance matrix Σ) of the perturbation set are modeled as a CSI uncertainty set P, and a worst-case optimization objective is constructed on this set to ensure that the strategy remains stable under adverse channel conditions.

[0078] Specifically, for the minimization scenario, where the system designer's goal is to construct a power combination that minimizes the worst-case performance deficit, the robust optimization model can be expressed as:

[0079]

[0080] The outer layer This represents the optimization decision made by the system designer when determining the combined weights; inner layer. This represents the worst-case performance deficit assessment under all possible uncertain parameter configurations. This structure ensures that regardless of the parameter settings the actual future channel state falls into, as long as it belongs to the uncertainty set P, the maximum combined performance deficit is always controlled within an optimal lower bound. This idea is particularly important when hedging tail performance risks or preventing structural misjudgments.

[0081] Conversely, for the maximization scenario, the model can be represented as:

[0082]

[0083] At this time, the inner layer The operation represents the utility response of the channel under the most conservative parameter estimates, outer layer This means that the system designer is trying to find a set of weights that maximizes the acceptable level of utility in all the most optimistic scenarios.

[0084] The two robust forms described above construct optimized response mechanisms for extreme situations from the perspectives of minimizing shortages and maximizing utility, respectively. The models can systematically resist estimation errors and environmental disturbances, improving the stability and real-world interpretability of performance metrics, reflecting the robustness-first design philosophy of communication system engineering.

[0085] (3) Based on the equivalent second-order cone programming transformation according to Shao & Zhang's theorem, the specific steps are as follows:

[0086] (3.1) Transformation from moment conditions to closed-form solutions. First, consider the total system utility. The first and second moments can be expressed as follows: and According to the Shao & Zhang theorem, minimizing the shortage objective yields the following closed-form:

[0087] For scenarios that minimize performance shortages (i.e., pursuing the worst-case QoS baseline), we need to focus on the inner worst-case scenario (maximizing risk / shortage), which corresponds to the following closed-form:

[0088]

[0089] Will Take as the utility of the combined system Their mean and standard deviation are respectively and This transforms the inner-layer maximization problem into a problem of... Maximize, where .

[0090] Similarly, for scenarios that maximize risk-adjusted utility (i.e., pursuing maximum utility in the worst-case scenario), we need to focus on the inner worst-case scenario (minimizing utility), which corresponds to the following closed-form...

[0091]

[0092] The meanings of each symbol are as follows: It represents the expected value (scalar) of the total utility of the combined system. The standard deviation (scalar) represents the total utility of the combined system. This represents the expected vector (n-dimensional vector) of the utility of each single channel. This represents the standard deviation of the utility of each individual channel. The distortion function, used to define the weighting of different quantiles, is a monotonically increasing function. The derivative of the distortion function reflects the local risk weights at different probability quantiles u. express The L2 norm is a constant determined by the distortion function, representing the sensitivity or penalty coefficient of the performance metric to volatility (standard deviation).

[0093] These two equivalent expressions lay the foundation for subsequently writing the robustness objective in the form of a second-order cone. No further assumptions about the specific distribution of Y are needed; simply ensuring that it satisfies the aforementioned moment conditions allows for the direct application of its closed-form equivalent results. The essence of this approach lies in completely encompassing the uncertainty of the distribution within the moment constraints, and using the expression for "linear mean term ± second-order cone standard deviation term" given by the theorem, obtaining upper and lower bounds for the double-torsion performance metric that are simultaneously applicable to any distribution satisfying the same moment conditions.

[0094] (3.2) Rewriting the SOCP of the minimization / maximization scenario problem. After obtaining the correspondence between the above moment conditions and closed-form solutions, the original SOCP can be rewritten. Top The maximization / minimization problem is equivalently transformed into solving the problem only in the moment space. Optimizations on the surface. Specifically,

[0095] as well as

[0096] This equivalence relation shows that solving for the extrema of a distribution is entirely reduced to analyzing its moment characteristics, thus avoiding the need to examine each distribution family individually.

[0097] With the inner closed expression carrying a huge risk, the original minimization scenario problem...

[0098]

[0099] It can be written directly as:

[0100]

[0101] In this formula, the objective function consists of linear terms. With second-order cone terms The weighted sum of the given components perfectly fits the standard form of second-order cone constrained convex optimization (SOCP). Therefore, it can be solved efficiently using mature numerical optimization tools, thus transforming the semi-infinite-dimensional optimization problem caused by uncertain distributions into a deterministic and computable second-order cone programming problem.

[0102] Similarly, for the maximization scenario problem:

[0103]

[0104] The dual closed expression can be obtained:

[0105]

[0106] At this point, the objective function is the sum of linear terms and negative second-order cone terms, which also falls within the scope of second-order cone programming. This transformation not only corresponds one-to-one with the minimization scenario problem in form, but also provides a unified numerical solution approach for studying decision-makers' strategies under different QoS preferences.

[0107] (4) Design the uncertainty set for SOCP modeling and solution, specifically including the following steps:

[0108] (4.1) Set of box-shaped uncertainties The concept lies in applying independent upper and lower bound constraints to each dimension of the parameter, thereby ensuring the robustness of the model while preserving the solvability of the problem to the greatest extent possible. This is achieved by setting...

[0109]

[0110] in These are the lower / upper bound vectors of the expected system output rate for each channel, ensuring... ; Define the bounds of the covariance matrix (based on corresponding element components) and ensure that... ; The covariance is forced to be positive semi-definite. This restricts uncertainty to a "hyperrectangle," causing each element of the expected utility and covariance matrix of each channel to fluctuate within a specified interval. The greatest advantage of this design is that the worst-case scenario often occurs only at the endpoints of each component—that is, the search for the global extremum can be completed by taking only one of the upper and lower bounds for each dimension. More importantly, by using duality theory, the inner-layer maximization operation can be transformed into several linear or quadratic cone constraints, reducing the optimization problem, which originally contained uncertainty, to a form solvable by the mature SOCP, greatly improving the efficiency and stability of the numerical solution.

[0111] Based on historical channel utility sequences, the sample mean for each channel is first calculated. With the sample covariance matrix ,set up Let n be the random utility vectors of the channels (where...) This represents the random utility value of the i-th channel, such as instantaneous channel capacity or signal-to-noise ratio; the superscript T indicates a transpose operation.

[0112]

[0113] Then, based on the given confidence level (e.g., 95%) and sample size... , construct confidence intervals for the mean and covariance components respectively: for the mean, we have

[0114]

[0115] in This represents the half-width of the confidence interval for the mean estimate of the i-th channel (i.e., the radius of uncertainty of the mean). It is a standard normal distribution quantile of a quantile point For channel The sample standard deviation. For the element in the i-th row and j-th column of the covariance matrix, we have

[0116]

[0117] in, The confidence interval half-width represents the covariance estimation between the i-th channel and the j-th channel; The standard error is obtained through the bootstrap method or based on the moment estimation formula. Here, the subscripts i and j both correspond to the channel index (i,j=1,......,n), and i refers to the same specific channel in both formulas, ensuring a one-to-one correspondence between the symbols.

[0118] Finally, the parameter space is constrained to a set of box-shaped uncertainties:

[0119]

[0120] Among them positive definite constraints Ensure the validity of the covariance matrix; if the lower bound of the diagonal elements is negative, it can be cut off to zero to maintain positive semidefiniteness. Box-shaped uncertainty sets have advantages over ellipsoidal sets in terms of computational simplicity and the ability to transform the dual problem into a linear or second-order conical form. Furthermore, they can be adjusted... The multiplier allows for flexible control of robustness, exhibiting good conservatism and operability in situations with a limited number of channel configurations.

[0121] (4.2) Worst-case analysis of the mean term. For the mean offset, since the box-shaped uncertainty set is defined as... With fixed weights Under these conditions, the inner layer is... Maximization simply requires each component Take its upper bound. Therefore, the worst-case value of the mean term is...

[0122] This result demonstrates the direct increment of mean deviation on risk measures under box-shaped uncertainty sets.

[0123] For the scenario of "maximizing risk-adjusted utility": we need to consider the lower bound of utility (i.e., the worst-case scenario). Inner layer... Minimization requires taking each component The lower bound of the mean. Therefore, the worst-case value of the mean term is:

[0124]

[0125] (4.3) Worst-case analysis of the variance term. In any scenario, an increase in variance (volatility) represents an increase in uncertainty risk; therefore, the worst-case scenario corresponds to maximizing variance. Regarding the variance term... Maximizing this is equivalent to maximizing the value of each covariance element. Find the boundary point that maximizes the value of the quadratic form. Let Let be a nonnegative matrix representing the covariance uncertainty, then the worst-case population covariance can be considered as... Thus, the variance term is in the worst case. Combining weights and distortion coefficients, the contribution of the variance side to the robustness objective is: Among them, let .

[0126] (4.4) Scenario 1: The SOCP model that minimizes performance shortages. Adding the upper bound of the mean to the variance term in this scenario yields the complete robust objective:

[0127]

[0128] Introducing auxiliary variables ,make The optimization problem then transforms into a standard second-order cone programming problem (SOCP):

[0129]

[0130] Its constraints include: total power constraints Non-negative weights ; , equivalent to ,in Solving this model yields the first set of optimal weights, denoted as... .

[0131] Scenario 2: The SOCP model that maximizes risk-adjusted utility. The objective of this scenario is to maximize (the mean in the worst-case scenario - the risk penalty), i.e.:

[0132]

[0133] To utilize convex optimization tools, "maximizing a convex function" is transformed into "minimizing the negative value of a concave function," which is equivalent to solving:

[0134]

[0135] make Similarly, by introducing an auxiliary variable t, the optimization problem becomes:

[0136]

[0137] Its constraints are the same as in scenario one. Solving this model yields the second set of optimal weights, denoted as... .

[0138] After the above steps, the solver will output two sets of candidate optimal power configuration weights: one focusing on defense. and offensive-oriented These two sets of weights will be fed into the subsequent step (6). The system will dynamically select one of them as the actual power allocation scheme at each moment based on the real-time channel trend signal (such as channel improvement or deterioration) determined in step (5).

[0139] (5) External signals are linked with weights, which specifically includes the following steps:

[0140] (5.1) Acquisition and preprocessing of historical channel quality data. For each channel or user (e.g., user 1, user 2), historical channel quality data is collected during the specified time period. Intra-channel quality To reduce the interference of short-term fluctuations on signal recognition, the original sequence can be denoised as needed (e.g., by filtering or logarithmic transformation).

[0141] (5.2) Construction of Moving Average Indicators. Using classic moving average techniques, short-term and long-term moving averages are constructed respectively:

[0142]

[0143]

[0144] in and These represent the short-term and long-term window lengths, respectively, and are typically taken as... (like , If the sequence contains missing values, a forward or backward imputation strategy can be used to ensure the continuity of the moving average calculation.

[0145] (5.3) Determining the trend of channel status.

[0146] Minimize the direction of shortage (channel quality degradation trend): when the short-term moving average Crossing the long-term moving average from bottom to top When this happens, a "channel degradation" signal is generated; when the short-term moving average... Crossing the long-term moving average from top to bottom At that time, a "channel improvement" signal is generated; the corresponding crossover points are denoted as follows: and .

[0147] Maximizing utility direction (channel quality improvement trend): This scenario primarily captures opportunities when the channel quality improves. That is, when the short-term moving average... Crossing the long-term moving average from top to bottom This is a "channel improvement" signal, when the short-term moving average... Crossing the long-term moving average from bottom to top The time is designated as the "channel degradation" signal; the corresponding crossover points are denoted as follows: and .

[0148] (5.4) Channel quality index recording and signal pool construction. At each signal determination time point... or Record the corresponding instantaneous channel quality level and This serves as a potential execution reference. For the first... For each channel / user, generate a set of record tuples containing timestamps, signal type, and quality values ​​to construct the potential state transition signal pool for that channel. These signals will serve as a critical timing gate reference for subsequent system-level power weight allocation and scheduling updates. Specifically, although step (4) calculates the optimal weight vector based on statistical characteristics... However, it does not specify the optimal timing for intervention. Using the signal pool recorded in this step, the system can establish a "weight-timing" matching mechanism in subsequent steps (5.5): that is, only when the optimal weight of channel i is reached... The signal is relatively high, and there is an effective "channel improvement" signal in the vicinity of the current time. Only when the system is in a certain condition will it execute the power allocation command in full or aggressively; otherwise, if a "channel degradation" signal is present, even if... At higher speeds, the system may also introduce minor execution delays or smoothing processes. This mechanism ensures that power resources are not only allocated to the statistically most robust channels, but also injected during the optimal window of time when the instantaneous trend of that channel is improving.

[0149] (5.5) Power weights are linked to scheduling timing. After obtaining the optimal combined configuration, we first extract the optimal power weights for each channel from the optimizer output. (Right now or They are then sorted in descending order of their numerical values ​​to construct scheduling priorities. For weights close to zero (e.g., less than 10), ... −6 This can be considered as the channel not participating in this round of configuration.

[0150] Then, the weighting results are combined with the potential state transition times for each channel determined in step (5.4). In its candidate time set In the process, select the signal point that is closest to the current time and best corresponds to its estimated channel utility and outage risk state, and denote it as... The specific selection logic is as follows:

[0151] Scenario 1 (Maximizing Utility After Risk Adjustment): In this scenario, the system's outage risk state is defined as "missed opportunity risk." Therefore, the strategy prioritizes selecting the nearest "channel improvement" signal point (i.e., For example, if the current short-term moving average crosses below the long-term moving average, it indicates that the channel quality is improving in the short term. In this case, power reallocation should be triggered first when the channel improves.

[0152] Scenario 2 (Minimizing Performance Shortage): In this scenario, the system's outage risk is defined as "QoS violation risk." Therefore, the strategy prioritizes selecting the nearest "channel degradation" signal point (i.e., For example, if the short-term moving average crosses below the long-term moving average, it indicates that the channel is about to fade. At this time, actions should be taken when the channel deteriorates (such as cutting off or injecting backup power).

[0153] The final output is the optimal power weight obtained by combining the solution from step (4). and the determined optimal execution time This generates the final power allocation command. The specific calculation formula is as follows:

[0154] .

[0155] This generates each scheduling log entry, which includes the channel / user name and the optimal execution time. Scheduling modes and corresponding power allocation.

[0156] In one embodiment, the method further includes step (6), which involves performing historical simulation tests on the output scheduling logs and calculating multi-dimensional indicators such as system throughput curve, performance-fluctuation ratio, outage probability metric, and maximum performance rollback. This consists of the following steps:

[0157] (6.1) The format of each generated scheduling log includes the channel / user name and the optimal execution time. The scheduling mode and corresponding power allocation are determined. This ensures that system-level performance deficiencies are minimized while fully considering the dynamic and trend signals of individual channels, thereby improving the overall system performance.

[0158] (6.2) Scheduling queue generation and execution process. For real-time system operation, when the optimal time point corresponding to the channel arrives, scheduling instructions are issued according to the preset scheduling mode and transaction performance parameters and allocated power are recorded in real time; in the simulation environment, the scheduling process is replayed based on historical transaction data and the actual simulation performance gain or loss is calculated.

[0159] (6.3) Real Performance and QoS Measurement. After the transaction is completed, a comprehensive evaluation of the simulation results is required. First, the utility contribution is calculated for each scheduling record:

[0160]

[0161] By summing up the utilities of all channels, we can obtain the evolution curve of the system's cumulative utility over time. Based on this curve, the following key performance indicators can be calculated: the utility-volatility ratio measures volatility-adjusted utility by the ratio of the expected value of the portfolio's excess utility to its volatility; VaR and CVaR characterize the magnitude of the portfolio's tail performance deficit at a specified confidence level; and the maximum drawdown measures the maximum decline in the portfolio's cumulative utility from its historical high during the backtesting period.

[0162] Finally, the system utility curve, drawdown curve, weight evolution diagram, and single-channel scheduling time point diagram are generated, and the average throughput, throughput volatility, utility-volatility ratio, VaR / CVaR, and maximum drawdown are summarized.

[0163] See Figure 1 This paper elucidates the mathematical transformation steps in the technical solution of the present invention, including the risk measurement defined in step (1.2) and the core mechanism of SOCP transformation in step (3).

[0164] sup M_φ(Y) is transformed into a solvable SOCP problem. The essence of this theorem is that the worst-case risk described above is mathematically equivalent to the risk defined by its convex hull function, i.e.:

[0165]

[0166] And based on convex hull risk value It possesses a closed-form solution that can be directly calculated, in the form of "linear mean term + second-order cone standard deviation term":

[0167]

[0168] Figure 2 This illustrates the transformation from a theoretically defined risk measure to a mathematically solvable computational tool. The horizontal axis in the figure represents probability quantiles. The vertical axis represents the value of the torsion function. The solid line represents the torsion function corresponding to the "double torsion risk metric" defined in step 1.2 of this invention. This function is defined identically to "GlueVaR" in the references, being a convex combination of VaR and CVaR. Its specific form is as follows: The interval is 0, in The interval is a horizontal line (reflecting the characteristics of VaR), in The interval is represented by a slanted line (reflecting the characteristics of CVaR). The dashed line represents the "convex envelope" of the above solid line function, denoted as . The convex hull is the largest convex function below the original function.

[0169] See Figure 3 The horizontal axis represents the risk confidence level. The value ranges from 0.95 to 1, representing the transition from general risk to extreme risk. The vertical axis represents the risk value. The colored curves represent the Standardized Value at Risk (SVaR) calculated by various traditional parametric models under the assumption that the channel system output follows a specific probability distribution (e.g., the blue line represents a Gaussian / normal distribution). The black dashed line represents the upper bound of the worst-case SVaR calculated by the theoretical framework cited in this invention, without any distributional assumptions and only knowing the mean and variance (i.e., k=2). Its calculation formula is:

[0170]

[0171] As discussed in the background section of this application, traditional models have significant biases in characterizing performance deficiencies. For example... Figure 3 As shown, with confidence level As the curve approaches 1 (i.e., enters the extreme tail), the blue curve representing the normal distribution shows a gradual increase, while the black dashed line representing the worst-case scenario rises sharply, creating a huge gap between the two. This significant gap vividly reveals that traditional methods severely underestimate the risks of extreme channels, which is the root cause of the vulnerability of multi-channel combinations in real-world communication crises. The robust optimization method employed in this invention aims to manage and control the significant performance shortcoming represented by this black dashed line, which is overlooked by traditional methods, thereby ensuring the stability and effectiveness of multi-channel combinations in uncertain environments.

[0172] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described robust multi-channel power configuration method based on a double-twist risk metric.

[0173] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described robust multi-channel power configuration method based on a dual-twist risk metric.

[0174] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0175] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0176] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0178] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

[0179] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A robust multi-channel power configuration method based on a dual-twist risk metric, characterized in that, include: The total utility of the wireless communication system is represented as a weighted linear combination of the utility of each channel. A parameterized double twist function is introduced to integrate the single quantile risk and the tail average risk through a convex combination, constructing a twist risk measure and embedding the worst-case consideration of the uncertainty of the CSI parameter. By utilizing the closed-form solution under the first and second moment uncertainty sets, the inner worst-case performance shortage or best-case performance shortage of the distortion risk measure is expressed as a linear mean term plus a second-order cone standard deviation term, thereby equivalencing the original problem to the standard SOCP form. Design the CSI uncertainty set to model and solve SOCP, and obtain the optimal power weights; For a single channel, the potential slow fading state transition time is determined using the moving average technique. The obtained weights are then combined with the optimal time to form a scheduling scheme that combines power weight magnitude with scheduling timing, and power allocation instructions are generated.

2. The robust multi-channel power configuration method based on a dual-twist risk metric according to claim 1, characterized in that, Distortion of risk measurement for: in, Let the total utility of the wireless communication system be a random variable. and Let be the probability distortion function. To adjust the parameters, and These are measures of single quantile risk and tail average risk, respectively.

3. The robust multi-channel power configuration method based on a dual-twist risk metric according to claim 1, characterized in that, The worst-case considerations for CSI parameter uncertainty are embedded, including: Given a weight vector mean vector With covariance matrix In this scenario, the power allocation problem falls into two categories of optimization objectives: the objective of minimizing performance shortages is: The objective of maximizing the risk-adjusted utility scenario is: Where P is the CSI uncertainty set, Let i be the utility of the i-th channel. Weight vector The power configuration weight of the i-th channel, where n is the number of channels.

4. A robust multi-channel power configuration method based on a dual-twist risk metric according to claim 3, characterized in that, By utilizing the closed-form solution under the uncertainty set of first and second moments, the inner worst-case or best-case performance deficit of the distorted risk measure will be expressed as a linear mean term plus a second-order cone standard deviation term, thus equivaling the original problem to the standard SOCP form, including: Total utility of wireless communication system The first and second moments are respectively expressed as and The objective of minimizing performance shortage scenarios is: The objective of maximizing risk-adjusted utility is: Let be the total utility of the wireless communication system, with its mean and standard deviation being respectively... and The superscript T indicates the transpose operation; The objective of minimizing performance shortage scenarios then becomes: The objective of maximizing the risk-adjusted utility scenario is transformed into: 。 5. A robust multi-channel power configuration method based on a dual-twist risk metric according to claim 1, characterized in that, Design the CSI uncertainty set for SOCP modeling and solution to obtain the optimal power weights, including: Based on the requirements for CSI estimation error, a box-shaped uncertainty set is constructed, and the objective and constraints containing mean and covariance offsets are transformed into a standard SOCP model. The optimal weights are then efficiently solved using optimization tools.

6. A robust multi-channel power configuration method based on a dual-twist risk metric according to claim 5, characterized in that, The set of box-shaped uncertainties is: in, Let represent the half-width of the confidence interval for the covariance estimation between the i-th channel and the j-th channel. For elements of the covariance matrix, It is a standard normal distribution quantile of a quantile point For channel The sample standard deviation; Obtained through guided methods or based on the standard error formula of moment estimation; Based on the box-shaped uncertainty set, worst-case analysis is performed on the variance and mean terms, yielding the following results: Introduce the following constants and variables: Let Introducing auxiliary variables ,make , Then rewritten as: Its constraints include: total power constraints Non-negative weights Second-order cone constraint , equivalent to .

7. A robust multi-channel power configuration method based on a dual-twist risk metric according to claim 1, characterized in that, For individual channels, the potential slow fading state transition time is determined using moving average techniques, including: Obtain channel quality sequence And using moving average techniques, short-term... With long-term moving average ; Minimize the direction of shortage: when the short-term moving average Crossing the long-term moving average from bottom to top When this happens, a "channel degradation" signal is generated; when the short-term moving average... Crossing the long-term moving average from top to bottom At that time, a "channel improvement" signal is generated; the corresponding crossover time points are denoted as follows: and ; Maximizing utility direction: The signal direction is opposite to minimizing shortage.

8. A robust multi-channel power configuration method based on a dual-twist risk metric according to claim 1, characterized in that, Also includes: Historical simulation tests are performed on the output scheduling logs to calculate system throughput curves, efficiency-fluctuation ratio, outage probability metric, maximum performance rollback, and other multi-dimensional indicators.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements a robust multi-channel power configuration method based on a dual-twist risk metric as described in any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a robust multi-channel power configuration method based on a dual-twist risk metric as described in any one of claims 1-8.

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