Adaptive filter weight optimization method and system based on LMS algorithm

Abstract

The invention discloses an adaptive filter weight optimization method and system based on an LMS algorithm, and relates to the field of wireless communication, and the method comprises the steps: obtaining a composite receiving signal containing the superposition of a public message and a private message; performing common message decoding on the composite receiving signal, and removing the decoded common message from the receiving signal to obtain a residual signal for filtering processing; inputting the residual signal into a fractional order variable step length LMS filter, and generating a filtering output signal based on a filter weight and a fractional order differential item; calculating an error signal according to a difference value between the filtering output signal and an ideal symbol of the corresponding private message; updating a filter weight by using the error signal and the residual signal, and respectively updating a step length and a fractional order gain parameter based on the error signal; and outputting a final optimized target filter weight under the condition that the error signal is detected to meet a preset convergence condition. Therefore, precise suppression of SIC error propagation and stability improvement of weight updating are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and particularly relates to an adaptive filter weight optimization method and system based on an LMS (Least Mean Squares) algorithm. BACKGROUND

[0002] With the rapid development of the Internet of Things, Vehicle-to-Everything (V2X) and the fifth generation mobile communication (5G) technology, wireless communication systems need to handle more and more user connections and data traffic, and the requirements for spectrum efficiency, system reliability and anti-interference ability are increasingly stringent.

[0003] Traditional Orthogonal Multiple Access (OMA) technology is limited by low spectrum efficiency and is difficult to meet the demand for large-scale connection. Although the Non-Orthogonal Multiple Access (NOMA) technology can effectively improve the spectrum utilization, it depends on the SIC (Successive Interference Cancellation) process, and is easily affected by channel time variation, channel estimation error, hardware limitation and decoding error accumulation, resulting in prominent error propagation problem and reduced system reliability.

[0004] Therefore, how to effectively overcome the error propagation in the SIC process and improve the performance of the RSMA (Rate-Splitting Multiple Access) system is an important problem to be solved at present. SUMMARY

[0005] The present application provides an adaptive filter weight optimization method and system based on an LMS algorithm, a storage medium, a computer program product and an electronic device, which at least solve the problems of serious error propagation in the SIC process and insufficient adaptability to channel dynamic changes in the related art.

[0006] In a first aspect, an embodiment of the present application provides an adaptive filter weight optimization method based on an LMS algorithm, implemented by an RSMA receiving end, and the method comprises the following steps: obtaining a composite received signal containing superimposed public messages and private messages; decoding the public messages from the composite received signal, and removing the decoded public messages from the received signal to obtain a residual signal for filter processing; inputting the residual signal into a fractional order variable step LMS filter, generating a filter output signal based on filter weights and a fractional order differential term; calculating an error signal according to a difference between the filter output signal and ideal symbols corresponding to the private messages; updating the filter weights using the error signal and the residual signal, and updating a step size and a fractional order gain parameter of the fractional order variable step LMS filter based on the error signal; and outputting a final optimized target filter weight when it is detected that the error signal satisfies a preset convergence condition.

[0007] In a second aspect, an embodiment of the present application provides an adaptive filter weight optimization system based on an LMS algorithm, arranged in an RSMA receiving end, and the system comprises the following units: a signal receiving unit, configured to obtain a composite received signal containing superimposed public messages and private messages; a public message eliminating unit, configured to decode the public messages from the composite received signal, and remove the decoded public messages from the received signal to obtain a residual signal for filter processing; a filter signal generating unit, configured to input the residual signal into a fractional order variable step LMS filter, and generate a filter output signal based on filter weights and a fractional order differential term; an error signal calculating unit, configured to calculate an error signal according to a difference between the filter output signal and ideal symbols corresponding to the private messages; a parameter adaptive updating unit, configured to update the filter weights using the error signal and the residual signal, and update a step size and a fractional order gain parameter of the fractional order variable step LMS filter based on the error signal; and an iterative convergence output unit, configured to output a final optimized target filter weight when it is detected that the error signal satisfies a preset convergence condition.

[0008] In a third aspect, an electronic device is provided, which comprises at least one processor, and a memory connected with the at least one processor in communication, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the steps of the adaptive filter weight optimization method based on an LMS algorithm of any embodiment of the present application.

[0009] In a fourth aspect, an embodiment of the present application provides a storage medium having a computer program stored thereon, and the program, when executed by a processor, implements the steps of the adaptive filter weight optimization method based on an LMS algorithm of any embodiment of the present application.

[0010] Fifthly, embodiments of this application provide a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the adaptive filter weight optimization method based on the LMS algorithm of any embodiment of this application.

[0011] The adaptive filter weight optimization method and system based on the LMS algorithm provided in this application can achieve at least the following technical effects:

[0012] (1) By decoding and removing the public message before filtering, the residual signal composed of private message and noise is accurately focused. This not only cuts off the interference coupling between public and private messages, but also retains a purer residual signal for private message detection and processing, which significantly improves the symbol recognition accuracy of private message extraction.

[0013] (2) The fractional-order variable-step-size LMS algorithm is introduced into the RSMA receiver for adaptive filter weight optimization of the residual signal. The introduction of fractional-order derivatives enhances the filter's memory of historical error information and improves the ability of the filter output to fit the signal characteristics. At the same time, the variable-step-size mechanism dynamically adjusts the update speed according to the current error level. When the error is large, the step size is increased to accelerate convergence, and when the error decreases, the step size is reduced to suppress oscillation. This achieves a balance between convergence speed and stability, significantly shortens the filter adaptation process, and reduces the final error level.

[0014] (3) Not only are the filter weights updated synchronously based on the residual signal and the error signal, but the fractional step size and gain parameter are also adjusted separately using the same error signal, forming a multi-parameter collaborative adaptive optimization mechanism. Through error-driven joint updates, error propagation caused by SIC residual error or channel estimation deviation is effectively suppressed. Furthermore, the iteration is intelligently terminated by preset convergence conditions, which avoids unnecessary computational overhead and ensures the stability and reliability of the final output weights.

[0015] This technical solution utilizes adaptive weight optimization combining fractional variable step size LMS filtering and convergence detection to achieve precise suppression of SIC error propagation, accelerated convergence speed, reduced steady-state error, and improved stability of weight updates, significantly enhancing the spectral efficiency and reliability of the RSMA system. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating an example of an adaptive filter weight optimization method based on the LMS algorithm according to an embodiment of this application is shown.

[0018] Figure 2 A flowchart illustrating an example of graphical smoothing of a filtered output signal according to an embodiment of this application is shown;

[0019] Figure 3 A schematic diagram illustrating an example of adaptive filter weight optimization based on the LMS algorithm according to an embodiment of this application is shown.

[0020] Figure 4 A comparative simulation diagram of the adaptive filter weight optimization method based on the LMS algorithm according to an embodiment of this application and an example of a filter using the traditional fixed step size LMS algorithm is shown.

[0021] Figure 5 A block diagram of an example of an adaptive filter weight optimization system based on the LMS algorithm according to an embodiment of this application is shown. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] With the widespread deployment of Internet of Things (IoT) devices and Vehicle-to-Everything (V2X) networks, the number of terminals is experiencing explosive growth. Simultaneously, fifth-generation (5G) and 6G-oriented evolution technologies continue to advance in areas such as spectrum resources, network slicing, and edge computing, requiring wireless networks to find a balance between ultra-high connection density, ultra-low latency, and ultra-high reliability. On the one hand, applications such as smart manufacturing, autonomous driving, and telemedicine place stringent demands on end-to-end latency and reliability at the millisecond or even sub-millisecond level; on the other hand, the massive number of terminals (including sensors, cameras, drones, etc.) requires networks to possess extremely high spectrum utilization and concurrent access capabilities. Traditional designs cannot simultaneously meet these conflicting demands, necessitating innovative multiple access solutions.

[0024] In orthogonal multiple access (OMA) technologies, such as Time Division Multiple Access (TDMA), Frequency Division Multiple Access (FDMA), and Orthogonal Frequency Division Multiple Access (OFDMA), mutual interference is avoided by allocating different users to independent time or frequency resources. Although this approach has simple signal decoding logic and stable implementation, its resource utilization is limited by reserved blank intervals. In large-scale access scenarios, it often exhibits a spectrum waste phenomenon of alternating "resource idleness" and "resource saturation," making it difficult to support the concurrent data transmission needs of massive terminals.

[0025] Non-orthogonal multiple access (NOMA) significantly improves spectral efficiency by superimposing multiple user signals in the power or code domain. Specifically, different transmit powers are allocated according to the user channel gain, with high power for distant users and low power for near users. Furthermore, by employing successive interference cancellation (SIC), the "strongest" signal is first decoded and reconstructed at the receiver before being cancelled, and so on.

[0026] However, the SIC process has several drawbacks: estimation errors caused by channel time-varying characteristics result in inaccurate reconstruction of the decoded signal; additional distortion is introduced by hardware non-ideals (such as ADC quantization errors and power amplifier nonlinearities); and decoding errors accumulate and amplify across multiple SIC stages, creating a "avalanche effect" that significantly reduces system reliability. These drawbacks are particularly pronounced in high-speed mobile or high-interference environments, making it difficult for NOMA systems to fully leverage their advantages in practical deployments.

[0027] Rate Division Multiple Access (RSMA) is an extension and optimization of NOMA. Its core idea is to divide each user's information into a "common message" (which all users must decode) and a "private message," then superimpose the power of both. Specifically, through superset coding, all users first decode the common message, which helps eliminate some multi-user interference. After removing the common message interference, each user decodes their own private message. The power allocation between the common and private messages can be dynamically adjusted to balance spectral efficiency and reliability.

[0028] RSMA performs well in mitigating multi-stage SiC error propagation in NOMA, but it still has some problems, specifically: 1) the power of the common message is limited, making it difficult to guarantee successful decoding of the common message under extremely poor channel conditions; 2) after removing the common message, residual interference between private messages is still difficult to completely suppress. Furthermore, current research generally focuses on static power allocation or coding design, lacking adaptive, low-latency compensation methods for residual interference.

[0029] In summary, how to efficiently compensate for and adaptively optimize residual interference and error accumulation online within the RSMA framework has become a key technical bottleneck for improving system reliability and spectral efficiency.

[0030] In view of this, Figure 1 A flowchart illustrating an example of an adaptive filter weight optimization method based on the LMS algorithm according to an embodiment of this application is shown, which realizes interference compensation based on fractional-order LMS, hypergradient metaparameter adaptation, and graph signal smoothing.

[0031] Regarding the execution subject of the method in the embodiments of this application, it can be any controller or processor with computing or processing capabilities, and is deployed at the RSMA receiver. By introducing the fractional-order variable step size LMS adaptive filtering algorithm, the error propagation problem of the SIC process in the RSMA system is effectively suppressed, the private message decoding accuracy and system reliability are improved, and stronger robustness and spectrum utilization efficiency are demonstrated under dynamic channel changes and non-ideal hardware conditions.

[0032] In some examples, it can be integrated into an electronic device or terminal through software, hardware, or a combination of both, and the type of terminal or electronic device can be diverse, such as mobile phones, tablets, or desktop computers, etc.

[0033] like Figure 1 As shown, in step S110, a composite received signal containing superimposed public and private messages is obtained.

[0034] It should be noted that in an RSMA communication system, the transmitter encodes and multiplexes the data streams from multiple users into two parts: "common messages" and "private messages," before sending them to the receiver. Common messages represent information shared by multiple users, while private messages are personalized data specific to a particular user. To improve spectral efficiency, these messages are weighted and superimposed using a power allocation strategy and transmitted through a wireless channel. Due to multi-user multiplexing and channel interference, the signal received by the RSMA receiver is essentially a composite superposition of multiple signals in both the frequency and power domains.

[0035] Here, the RSMA receiver needs to receive this composite signal from the antenna and perform primary downlink processing to preserve the complete public and private information. In some implementations, the RF signal received by the antenna first passes through a low-noise amplifier (LNA), a band filter, and a downconverter to obtain a baseband analog signal. Subsequently, the analog signal enters a high-speed analog-to-digital converter (ADC) for quantization at a sampling rate more than twice the signal bandwidth to ensure the integrity of the signal spectrum. Oversampling and a high-precision ADC ensure that the spectral energy of the analog signal is not lost. In the digital baseband, the preamble is detected by the frame synchronization and symbol timing module to locate the start times of the public and private messages in the received frame structure, providing accurate frame and symbol synchronization, ensuring clear boundaries between public and private messages, and achieving precise time-frequency synchronization and channel tracking. In addition, the uplink pilot or reference signal can be used to estimate the channel gain of each channel using the minimum mean square error (MMSE) algorithm, providing accurate channel parameters for subsequent decoding and filtering.

[0036] In step S120, the composite received signal is decoded for common messages, and the decoded common messages are removed from the received signal to obtain a residual signal for filtering.

[0037] It should be noted that since the public message is information shared by all users, the RSMA receiver must prioritize separating it from the received composite signal. Correct decoding of the public message is a prerequisite for subsequent processing. By stripping away the public message, a cleaner residual signal can be obtained for processing private information, significantly reducing the level of multi-user interference. Only after successfully recovering and rigidly removing the public component does the residual signal mainly consist of the superposition of various private messages and noise, thus preventing the filter weight update from being "misled" by the high-power components of the residual public data.

[0038] In some implementations, based on known received signal and channel state information, such as using previously completed frame synchronization and channel estimation results, the transmitted symbol that maximizes the posterior probability is selected as the decision result. For example, for systems employing LDPC (Low-Density Parity-Check) codes, soft decision feedback can be introduced in the decoder to generate symbol estimates, thereby improving the decoding reliability of common messages. The soft / hard decision symbols output by the decoder are mapped and reconstructed, multiplied by the estimated common channel gain to generate a reconstructed signal, and then subtracted from the composite received samples sample by sample in the digital baseband to obtain the residual signal after removing common interference.

[0039]

[0040] In the formula, y(n) represents the composite received signal sample obtained by the receiving antenna at time n after down-conversion, which includes the common message after power allocation, the superposition of private messages and noise. α represents the reconstructed signal of the common components at time n. c This represents the power normalization coefficient allocated by the transmitter for the common message, used to reconstruct the amplitude of the common component. This represents the channel gain estimate corresponding to the common message at time n, obtained through the MMSE algorithm using the preamble symbol or pilot. Let r(n) represent the decoded output symbol of the common message at time n, which represents the transmitted symbol that the common message should have after decoding and remapping. r(n) represents the residual signal at time n after removing the reconstructed common components.

[0041] Furthermore, before performing complex subtraction, the carrier phase error (CPE) correction module can be used to ensure... The phase reference of y(n) is consistent to avoid subtraction residue caused by phase shift. Thus, by using phase correction, the common components are accurately aligned and completely stripped away, and the residue is mainly private interference and noise, which greatly simplifies the input characteristics of adaptive filtering.

[0042] In this embodiment, after decoding the common message and reconstructing the common component using the estimated channel gain, the high-power portion is removed from the received signal. This allows the remaining signal to primarily reflect the mutual interference between private users and background noise. The filter does not need to adjust its weights under significant common interference; instead, it directly compensates for the private residuals. Its iteration direction is most relevant to the private message decoding, enhancing the filter's ability to locate and suppress multi-user private interference. Therefore, the residual signal obtained after removing the common message has a narrower dynamic range and more pronounced private mutual interference characteristics due to the elimination of most of the concentrated power components. This allows subsequent adaptive filtering to converge quickly within a lower mean square error region. Simultaneously, the filter update is no longer "masked" by the common component, greatly improving the system's bit error rate performance and decoding reliability under conditions of dense multi-user access and time-varying channels.

[0043] In step S130, the residual signal is input into a fractional-order variable step-size LMS filter, and a filtered output signal is generated based on the filter weights and fractional-order differential terms.

[0044] It should be noted that traditional LMS filters adjust weights based only on first-order gradient information. In this embodiment, a fractional differential operator is introduced to capture the multi-scale dynamic characteristics of the signal and channel, and a variable step size mechanism is used to adapt to channel changes in real time, thereby enhancing its robustness under time-varying channels and non-ideal interference conditions.

[0045] In some examples of embodiments of this application, the most recent L sampled values ​​{r(n),r(n-1),…,r(n-L+1)} of the residual signal are stored in the shift register buffer.

[0046] It should be noted that each iteration of the adaptive filter requires the use of current and past residual signal samples to estimate the next output. In order to support the operation of both the traditional integer-order FIR (Finite Impulse Response) part and the fractional-order derivative part, the system accurately caches the residual sample values ​​from multiple recent time steps, which can be called in parallel and without conflict at any time.

[0047] For example, in an FPGA design, a shift register array of depth L is configured to store the latest residual signal sample {r(n), r(n-1), ..., r(n-L+1)}. Whenever a new sample r(n+1) is received, all register contents are shifted one bit to the right through cascading shifts, and the new sample is written to the front of the array.

[0048] Using the Grünwald-Retnikov fractional binomial coefficients pre-stored in read-only memory Read the most recent M residual samples from the shift register buffer, perform fractional-order differential weighted summation, and calculate the fractional-order compensation term using the following formula:

[0049]

[0050] In the formula, M represents the memory window length of the fractional derivative, specifies the number of past residual samples participating in the fractional derivative, M≥L, and L represents the total number of taps; j represents the cumulative index of the Grünwald-Letnikov summation, and ν represents the fractional derivative operator; D ν [r(n)] is the result of the fractional differential operator applied to r(n), representing the weighted difference of the latest M residual samples, which is used as a compensation term.

[0051] It should be noted that traditional integer-order filters can only linearly combine current residuals and finite history, but their compensation capability is limited for channel abrupt changes or slowly changing residual interference. Fractional-order differential D ν By applying power-order weights to historical samples, the Grünwald-Letnikov fractional binomial coefficients naturally possess "long memory" characteristics: they can respond quickly to sudden changes and act as low-pass filters for stationary conditions, thus compensating for the shortcomings of integer-order filters in non-stationary scenarios.

[0052] Specifically, on an FPGA, a multiply-accumulate pipeline of length M+1 can be used: the first stage performs M+1 multiplications in parallel. Then sum all the products and apply (-1) jReverse the sign for even / odd indices. On a DSP, loops can be unrolled, processed into multiple terms, and then summed to reduce loop branching overhead.

[0053] Furthermore, the value of the memory window length M can be selected based on system resources and the required memory length, and should be determined at the beginning of the design. If resources are limited, a value close to L can be chosen; if a stronger memory effect is desired, M can be appropriately increased and sparse access or approximate algorithms can be used to reduce the amount of computation.

[0054] Therefore, accumulating historical samples has a natural low-pass property, suppressing high-frequency jitter and random noise. In addition, fractional derivatives have a sensitive response to signal abrupt changes (such as sudden increases in deep fading), enabling non-stationary interference tracking and allowing the filter to quickly adjust its output at the moment of abrupt change.

[0055] Regarding the selection and calibration of the Grünwald-Letnikov binomial coefficients, offline simulations can be performed on typical channel samples (including deep fading abrupt changes and slow drift scenarios) to traverse the possible combinations of ν∈(0,1) and M, compare their corresponding steady-state MSE and convergence rate, and then select the parameters that achieve the best balance between the two. In actual deployment, the ν and M obtained from the above offline calibration can be solidified into the device.

[0056] Based on the filter weights at the current time The filtered output signal is generated using the fractional-order gain β(n) as follows:

[0057]

[0058] In the formula, β(n) represents the filtered output signal generated by the fractional-order variable-step-size LMS filter at time n; β(n) is the fractional-order compensation gain, which represents the strength of the fractional-order differential term used to adjust the strength at time n.

[0059] It should be noted that the residual interference after the superposition of private messages often exhibits two typical modes: abrupt change or slow drift, due to user power, channel time-varying characteristics, and hardware non-ideals. Traditional integer-order LMS only performs a weighted summation of the current residual, making it difficult to account for both types of dynamic characteristics; while fractional-order derivative D ν [r(n)](ν∈(0,1)) contains a power-weighted memory of historical samples, which can simultaneously respond to abrupt changes and filter out steady noise, providing a "long-term memory" correction path for the filter.

[0060] After separating the common message and calculating the fractional-order compensation term, the FIR part continues to suppress the current residual linear interference. By weighted averaging the latest L residual samples, it corrects the "local" interference profile and, together with the fractional-order compensation, constructs the filtered output, resulting in the FIR weighted summation output.

[0061] In the embodiments of the present application, local linear compensation for the current residual signal and long-memory weighting for historical interference are combined simultaneously, so as to achieve double suppression of sudden and slow-changing interference in a multi-user time-varying channel environment. First, the most recent L residual samples are cached in parallel to ensure timely response to the latest cross interference. Then, the past M samples are weighted and accumulated through fractional-order differentiation to achieve "memory" compensation for historical residuals. Finally, within the same clock cycle, the weighted average result of the traditional FIR part and the fractional-order compensation are added according to the adjustable gain β(n) to generate the final filter output. Thus, through the fractional-order weighted compensation for historical residuals, the influence of low-frequency drift and slow changes is significantly reduced, further compressing the steady-state mean square error, enabling both rapid convergence and maintaining low-jitter steady-state performance in dynamic multi-user access scenarios.

[0062] It should be noted that setting the memory window length M to be greater than or equal to the filter tap number L is to ensure that the fractional-order differential term covers all historical residual samples participating in FIR weighting. Specifically, the FIR part performs a linear combination based on the most recent L samples, while the fractional-order compensation needs to weight them and earlier samples to reflect the long-memory effect. If M < L, some important historical information used by FIR will be omitted, weakening the effect of fractional-order compensation. By ensuring M ≥ L, both the accurate suppression of current interference by FIR and the compensation of slow-changing trends or sudden residuals by the fractional-order term on a wider time scale are retained, achieving the collaborative optimization of the two.

[0063] In step S140, an error signal is calculated according to the difference between the filtered output signal and the ideal symbol of the corresponding private message.

[0064] The error signal e(n) is the core feedback of the LMS-like algorithm, which quantifies the instantaneous gap between the filtered output and the ideal target. In the RSMA system, the ideal symbol d(n) is obtained from the symbol estimation after stripping the aforementioned common message and making a decision feedback on the private message. By calculating the difference between the two in real time, the system can accurately identify the magnitude and direction of the current residual interference, and use this to guide the update of the filter weights in the direction of minimizing the mean square error.

[0065] Details regarding the acquisition and alignment of the ideal symbol can be After output, the symbol estimation generated by the decoder module performing a soft decision on the private message. Specifically, the receiver can calculate the posterior probability or log-likelihood ratio (LLR) by demodulating the residual signal, and then construct the confidence of each modulation symbol, and generate a continuous-valued symbol estimation in a weighted average manner as a reference value for filtering error calculation. In addition, before calculating the error, it can also be corrected by a carrier phase error estimation (CPE) module The phase must be consistent with the phase reference of d(n); otherwise the difference will include phase offset error.

[0066] Furthermore, the error signal e(n) can be calculated using the following formula:

[0067]

[0068] In the formula, d(n) represents the relationship between... The corresponding ideal symbol for the private message at time n is given by e(n), which represents the error signal at time n.

[0069] Therefore, based on precise synchronization and prior pilot, the comparison error signal directly quantifies the performance deviation of the filter at the current moment, so that the error signal can truly reflect the vector deviation between the filter output and the ideal symbol, providing a reliable direction indication for the adaptive algorithm.

[0070] In step S150, the filter weights are updated using the error signal and the residual signal, and the step size and fractional gain parameters of the fractional-order variable step size LMS filter are updated based on the error signal.

[0071] Here, in order to improve the system's long-term adaptive capability and short-term tracking capability, a joint update mechanism based on error signal driving is designed. At the same time, the filter weights, step size factor and fractional gain are adjusted to form a multi-parameter collaborative adaptive mechanism, so that the update processes are linked to each other and comprehensively suppress the SIC residual error and channel estimation deviation.

[0072] In some examples of embodiments of this application, the filter weights are updated in the following manner:

[0073] w i (n+1)=w i (n)+μ(n)e(n)r(ni), formula (7)

[0074]

[0075] In the formula, n represents the discrete time index, i represents the filter tap index, and L represents the total number of taps; r(n) represents the residual signal sample at time n, r(ni) represents the delayed sample of the residual signal at time (ni), and μ(n) represents the variable step size at time n. base (n) represents the baseline step size at time n, μ0 represents the initial step size constant, γ represents the balance factor, and w i (n) represents the stored value of the i-th order filter weight at time n, w i (n+1) represents the updated value of the i-th order filter weight at time n+1.

[0076] Equation (8) provides an initial / reference step size based on the current error magnitude, which accelerates convergence when the error is large and finely adjusts it when the error is small, ensuring an initial balance between convergence speed and steady-state jitter. In one example of an embodiment of this application, μ(n) = μ base μ(n) allows the filter weights to be directly given by empirical formulas. In another example of this application embodiment, μ(n) can also be μ base The value determined by further optimization (e.g., supergradient iterative fine-tuning) based on (n) should not be restricted here.

[0077] In equation (7), the error signal, the current step size, and the residual are combined to complete the adaptive adjustment of the weight of each tap. The weight update can be completed in each sampling period, so that the filter continuously approaches the optimum. It should be noted that the traditional LMS directly uses the original received signal as the update input, which makes it difficult to distinguish between common messages and private interference. Under the RSMA framework, common messages are first removed by SIC, and then the residual is preliminarily processed by fractional-order LMS filtering. The residual signal r(ni) at this time is used for weight increment calculation, so that it can directly focus on the private message cross-interference that needs to be suppressed. This makes each iteration fine-tuned on the basis of the signal with "common parts removed + filtered compensation", which enhances the targeting and effectiveness of the update. Thus, by using the residual signal as the update input, the filter weight update can accurately match the current private interference characteristics and is no longer interfered with by common messages or unprocessed noise, thereby improving the overall spectral efficiency and reliability of the system.

[0078] In this embodiment, the error signal e(n) and the residual signal sample r(ni) are used together for weight iteration, and the step size μ(n) is adjusted in real time according to the error magnitude. This accelerates weight convergence when the error is large and automatically reduces the step size for fine correction when the error is small. Thus, the filter behavior is tightly coupled with the channel and interference characteristics through closed-loop feedback, ensuring that the filter always updates the weights in the optimal direction under dynamic multi-user interference environment.

[0079] In some examples of embodiments of this application, the step size hypergradient is calculated using the following formula:

[0080]

[0081] In the formula, g μ (n) is the hypergradient of the step size at time n, representing the direction and magnitude of the error's sensitivity to the step size.

[0082] Update the step size according to the following formula:

[0083] μ(n+1)=μ base (n)-η μ g μ(n), Equation (10)

[0084] Where, η μ is the step size learning rate constant, and μ(n+1) represents the updated value of the step size at time n+1.

[0085] Here, based on the baseline step size value given by the closed-loop update in the previous iteration, we further use the first derivative information of the influence of the error on the step size to fine-tune it, and treat the step size as a "weight" to perform gradient descent together, so as to converge to the optimal step size region more precisely and obtain the step size used for weight update.

[0086] In this embodiment, the supergradient is updated based on the error signal e(n), and the filter reference step size μ is set. base (n) is considered an optimizable meta-parameter, and the magnitude of each weight adjustment is determined by the filter's baseline step size, which has a significant impact on the algorithm's convergence speed and steady-state error. The hypergradient of the step size is calculated by equation (9), and iteratively updated using equation (10). The step size is regarded as a learnable meta-parameter, which automatically amplifies or shrinks in the direction of sensitivity to real-time error and residual signal, closely conforming to the current signal environment. This can significantly reduce the number of convergence iterations and improve steady-state accuracy.

[0087] Therefore, a two-stage step size update strategy combining closed-loop baseline step size and supergradient fine-tuning is adopted. The baseline step size provides a safe initial value, and the supergradient fine-tuning performs fine optimization, ultimately producing the step size that is actually used for weight update.

[0088] Using the fractional differential term D already calculated in the fractional variable step size LMS filter ν Calculate the fractional-order gain hypergradient using [r(n)] and the error signal e(n):

[0089] g β (n)=-e(n)D ν [r(n)], Equation (11)

[0090] In the formula, g β (n) represents the fractional gain hypergradient at time n, indicating the sensitivity of the error to the fractional gain.

[0091] Update the fractional-order gain parameter according to the following formula:

[0092] β(n+1)=β(n)-η β g β (n), Equation (12)

[0093] In the formula, η β β is the fractional gain learning rate constant, and β(n+1) is the updated value of the fractional gain, used for fractional compensation at time n+1.

[0094] It should be noted that the fractional compensation gain β(n) determines the fractional differential term D. ν The weighting ratio of [r(n)] in the filter output signal: too high a weighting ratio will amplify differential noise, while too low a weighting ratio will prevent the long memory advantage from being utilized. The contribution of the historical residual memory term to the filter output is controlled by the fractional-order compensation gain β(n). Its optimal value dynamically changes based on channel abrupt changes and drift characteristics, and is iteratively updated. β is automatically adjusted with the product of instantaneous error and the long memory term, ensuring that the fractional-order compensation neither excessively amplifies historical noise nor loses the ability to track slowly changing trends.

[0095] g β β(n) is proportional to the product of the current error and the fractional-order compensation term, reflecting the instantaneous impact of gain changes on the error. When the channel exhibits abrupt changes, the product of the error and the derivative tends to increase, driving β(n) to enhance fractional-order compensation; when the channel is stable, the fractional-order weights are automatically reduced to avoid jitter caused by excessive "memory". Thus, the hypergradient mechanism avoids the scenario limitations caused by artificially fixing β, enhances the comprehensive suppression capability of fractional-order filtering against multi-scale interference, and enables the system to exhibit good robustness and performance stability in both short-term and long-term dynamically changing environments.

[0096] In step S160, if the error signal is detected to meet the preset convergence condition, the final optimized target filter weights are output.

[0097] Here, when the system detects that the error signal sequence meets the preset convergence criteria within a given window (e.g., fluctuation amplitude convergence or average error decrease rate is lower than a set threshold), it stops the iteration and uses the current weights as the final optimization result, avoiding oscillations or unnecessary calculations caused by over-updates. Therefore, the convergence condition is adaptively determined based on the error signal, ensuring automatic convergence and real-time control of the filtering process, and improving system operating efficiency.

[0098] In some examples of embodiments of this application, the primary indicator of filter convergence is that the error signal |e(n)| fluctuates within a small range. To quickly and in real-time determine whether the error is sufficiently small, the absolute value of the error at each moment needs to be compared with a preset threshold ε. For example, in each iteration, it is determined whether the absolute value of the error signal e(n) is less than the preset threshold ε. If e(n) < ε, the step counter increments by 1; otherwise, the counter is reset to 0. When the counter value reaches a preset integer N, a convergence status signal is output, and the current filter weights are latched as the final optimized target filter weights.

[0099] It should be noted that a single occurrence of |e(n)| < ε may be the result of sporadic noise or pulse jitter and cannot be used as sufficient evidence of convergence. Only when "local convergence" occurs continuously within a sufficiently long time window can the global convergence of the filter be reliably determined. The counter management module is responsible for triggering the final convergence determination under the condition of "continuous occurrence". Once the counter reaches the preset number of times, it can be considered that the filter weights have converged stably. At this point, the current weights are latched and subsequent adaptive updates are stopped, thereby achieving dynamic stopping of weights with minimal computational overhead and the most reliable determination criteria. Thus, by using the dual criteria of "error threshold + continuous counting", misjudgments caused by random noise or transient jitter are effectively avoided, significantly improving the reliability of convergence determination.

[0100] Figure 2 A flowchart illustrating an example of graphical smoothing of a filtered output signal according to an embodiment of this application is shown.

[0101] like Figure 2 As shown, in step S210, the filtered output signal is decomposed into K filtered output components, and the k-th filtered output component is used as the residual interference vector of the k-th user.

[0102] After fractional-order variable-step LMS filtering is completed in step S130, a filtered output sequence that slides with the frame is obtained. It is actually a weighted combination of residual private messages from different users. In order to perform targeted suppression in the graph domain, the overall output needs to be "split" back into the residual interference amounts corresponding to each user, thereby constructing a multi-dimensional "graph signal".

[0103] Specifically, the system filters the output. Processing is done frame by frame, with each frame containing T sampling points. Each frame can be viewed as a vector of length T. If the system frame length is equal to the number of concurrent users K, parallel processing can be performed all at once; otherwise, window sliding or batch iterative decomposition can be used.

[0104] At the RSMA transmitter, private messages use a fixed or dynamic power allocation coefficient {α} when superimposed in the power domain. k The receiver can use the estimated α k h k (n) Proportional relationships are used to reconstruct the initial contribution of each private message. Specifically, the proportions will be... Power channel response for each user The k-th path contribution is obtained by multiplying the channel estimate by the dot product:

[0105]

[0106] The above formula can be viewed as a strategy based on least mean square decomposition, ensuring

[0107] For each signal Frame-by-frame aggregation forms a vector of length T, which is the residual interference vector:

[0108]

[0109] Stacking the K vectors yields a matrix.

[0110] Therefore, the star-shaped decomposition method based on power and channel estimation reduces the decomposition error, and the decomposition results in... It accurately addresses residual interference for each user, enabling the differentiation of signal sources.

[0111] In step S220, based on the channel gain estimates of user p and user q, the correlation coefficient between users is calculated, the off-diagonal terms of the correlation matrix are filled with the correlation coefficient, and the diagonal elements of the correlation matrix are set as the sum of the elements of the corresponding rows, thereby obtaining the degree matrix.

[0112] It should be noted that although multi-user residual interference is approximately independent in the time domain, it often exhibits statistical correlation in power allocation and channel fading. The correlation matrix describes how nodes (users) are "adjacent" on the graph, while the degree matrix measures the overall connectivity strength of each node. Together, they provide the basis for the subsequent Laplace matrix.

[0113] Specifically, for any two users p and q, their channel estimation sequences are used... and Calculate cross-correlation:

[0114]

[0115] Take the absolute value |ρ pq | As a correlation weight, it reflects the spatial coupling degree of residual interference.

[0116] The correlation matrix A is of size K×K, with off-diagonal terms A ij =|ρ ij |, fill in 0 for the diagonal terms first; A is a real symmetric matrix, which is easy to decompose later.

[0117] The degree matrix D is a diagonal matrix, and each diagonal element is... It represents the total correlation between the i-th user and all other users.

[0118] The correlation matrix is ​​based on real channel estimation and intuitively reflects the spatial distribution of residual interference among multiple users, achieving accurate modeling. In addition, the correlation calculation only involves dot multiplication and accumulation, which is easy to parallelize on multi-core CPUs.

[0119] Here, the residual interference vector of each user is naturally mapped to a node in the correlation graph, because the residual interference obtained after decomposing the filtered output signal precisely reflects the interference status of different users at the current moment; and the interference coupling between users due to power domain superposition and channel time-varying nature can be characterized by the correlation coefficient between their channel gain estimation sequences. Using the channel gain correlation coefficient between user p and user q as the weight of the edge in the graph ensures that the graph structure can truly reflect the spatial mutual influence intensity of each residual interference.

[0120] Therefore, by adopting the edge connection method based on the channel gain correlation coefficient, graph smoothing can "leverage" user nodes that actually have coupling interference, and mutually correct the highly correlated residual estimation information during the smoothing process. This effectively suppresses abnormal residual peaks caused by single-path deep fading or local filtering errors, thereby reducing the mean square error (MSE) overall and reducing the negative impact of bit error propagation on system performance.

[0121] In step S230, the Laplace matrix of the user association graph is constructed using the association matrix and the degree matrix.

[0122] It should be noted that the graph Laplacian matrix L=DA plays the role of a "discrete second-order differential operator" in signal smoothing, and its eigenstructure determines the spectral characteristics of the smoothing operation. Specifically, it compares the signal value of each node with the average value of its neighboring nodes, thereby identifying and suppressing high-frequency (abrupt) components, achieving low-pass filtering on the graph structure. This allows the node values ​​to retain the overall trend while weakening the parts that are inconsistent with the neighboring values, thus achieving collaborative suppression of residual cross-interference from multiple users.

[0123] Specifically, L is positive semi-definite, with the smallest eigenvalue being 0, corresponding to the eigenspace of a constant vector.

[0124] In addition, if local contrast is desired, normalized Laplacian can be used:

[0125] L norm =D -1 / 2 (DA)D -1 / 2 Equation (16)

[0126] The normalized form reduces the impact of differences in degree between different nodes, making it suitable for scenarios with uneven distribution of node degree.

[0127] Therefore, the inherent characteristics of the Laplace result in smooth spatial frequency band characteristics, which can filter out high-frequency components of the graph. In addition, the positive semi-definite property ensures that negative eigenvalues ​​do not interfere during subsequent matrix inversion or decomposition.

[0128] In step S240, a graph smoothing operation is performed on the decomposed K-path residual interference vectors based on the Laplace matrix to generate smoothed K-path filtered output components, thereby obtaining the smoothed filtered output signal.

[0129] Here, graph smoothing can be seen as performing low-pass filtering on the residual interference field on the user association graph, smoothing the residual of each node by "borrowing from its neighbors", further suppressing cross-interference and enhancing overall consistency.

[0130] In some implementations, common operators are used.

[0131] S=(I+ηL) -1 Equation (17)

[0132] Where η>0 is the smoothing factor, applied to... The smoothed result is obtained:

[0133]

[0134] Here, the smoothing factor can be tuned online. A larger η emphasizes global consistency and may lead to over-smoothing; a smaller η retains more local differences and weakens the suppression ability. Therefore, with the goal of minimizing the mean squared error within the sliding window, η is adjusted through gradient descent or meta-search.

[0135] Graph smoothing based on the Laplace operator can effectively reduce high-frequency jitter and local deviations in node signals, and distribute residual interference in the graph domain evenly. This adds a layer of spatial domain denoising on top of mature time-domain filtering, thereby significantly reducing the fluctuation range of residual estimation and improving the system's bit error rate performance and decoding reliability.

[0136] Finally, the result will be In Reassembled into a smoothed overall filter output:

[0137]

[0138] Will As input for the next step of error calculation, replacing the original

[0139] In this embodiment, based on the inter-user correlation coefficient obtained from channel estimation, a correlation graph reflecting the intensity of residual cross-interference can be constructed. Each filtered output is regarded as a node in the graph, and a smoothing operation is performed on the graph signal through the Laplace matrix. That is, while retaining its own filtering effect, it "borrows" the better estimates of neighboring nodes to perform weighted correction on abnormally high or low residuals, thereby further reducing the impact of multi-user cross-interference on the basis of time-domain filtering.

[0140] Through the embodiments of this application, graph smoothing operation can calibrate the residual estimates of different users at the same time in the graph structure, reducing the local error caused by deep fading of a single path or filter jitter, and significantly reducing the overall mean square error (MSE). Secondly, in multi-user dense access scenarios, this method can maintain the consistency and robustness of the filter output estimates of each path, effectively suppressing the residual collapse phenomenon caused by channel mutation or power allocation differences, thereby significantly improving the bit error rate (BER) performance and decoding reliability of the system.

[0141] Figure 3 A schematic diagram illustrating an example of adaptive filter weight optimization based on the LMS algorithm according to an embodiment of this application is shown.

[0142] like Figure 3 The upper part illustrates the system-level closed-loop flow from the residual signal input to the filtered output. Specifically, the residual signal r(n) obtained after stripping the common message first enters the fractional-order variable-step-size LMS filter module, which internally performs conventional FIR weighted summation and fractional-order differential compensation operations based on Grünwald–Letnikov binomial coefficients in parallel. Based on the FIR, it is then processed by the fractional-order operator D. ν After processing (corresponding to the fractional-order differential formula), multiply by the current gain β(n) (corresponding to the fractional-order gain update formula) to generate the final filtering result. At the same time, the filter will change the current weight vector {w i {r(ni)} and the residual samples {r(ni)} are fed into the hypergradient update unit to calculate the step-size hypergradient g. μ (n) and gain hypergradient g β (n), and combined with the graph smoothing fusion module, μ and β are smoothed and adjusted in real time to adapt to the time-varying channel and multi-user interference characteristics. Finally, the updated μ(n+1) and β(n+1) are fed back to the filter module to realize the online adaptation of the binary parameters.

[0143] like Figure 3 The lower half of the diagram illustrates the weight iteration logic within the filter. Specifically, the input residual r(n) passes through a series of L-stage delay units z. -1 Then, with weight w i (n) Parallel multiplication and accumulation generate FIR components, which are then multiplied by the fractional compensation term β(n)D. ν Adding [r(n)] together, we get Subsequently, the error signal e(n) is generated by subtracting the private message ideal symbol d(n) from the subtraction unit.

[0144] Based on this, the closed-loop reference step size μ base (n) and hypergradient g μ(n),g β (n) respectively drive the step size update μ(n) and the fractional-order gain update β(n+1), and then use the final step size μ(n+1) to complete the weight update w. i (n+1)=w i (n)+μ(n+1)e(n)r(ni).

[0145] Therefore, through a two-stage closed-loop operation that integrates external parameter supergradients and graph smoothing, and internal error-driven weight fine-tuning, it not only has the ability to respond quickly to sudden disturbances, but also maintains an extremely low steady-state mean square error in the stable phase, providing an efficient and reliable filter weight optimization solution for multi-user private message decoding in RSMA systems.

[0146] Figure 4 A schematic diagram showing the comparative simulation results of an example of an adaptive filter weight optimization method based on the LMS algorithm according to an embodiment of this application and a filter based on the traditional fixed step size LMS algorithm is presented.

[0147] like Figure 4 The vertical axis of the coordinate system represents the mean squared error (MSE), and the horizontal axis represents the number of iterations. The yellow curve represents the performance of the traditional fixed-step-size LMS algorithm, and the orange curve represents the simulation results of the fractional-order variable-step-size LMS filter weight optimization method based on closed-loop reference step size and supergradient fine-tuning proposed in this embodiment of the invention. It can be seen that the method provided in this embodiment accelerates the iteration with a larger step size in the early stages, causing the MSE to decrease rapidly. Within the iteration number range of 1-10, the MSE is significantly lower than that of the traditional curve, demonstrating the rapid convergence capability under the synergistic effect of fractional-order memory compensation and variable step size. In the later stages of iteration, supergradient fine-tuning effectively reduces the step size, suppresses jitter, and keeps the steady-state MSE below the lower limit of the traditional method, demonstrating superior steady-state performance.

[0148] Thus, on the one hand, by fusing fractional derivatives and graph smoothing, the filter fits multi-user residual interference more accurately, improving the initial convergence speed; on the other hand, by utilizing closed-loop reference step size and super-gradient iteration for dual optimization, it achieves effective suppression of steady-state error while achieving fast convergence, thereby balancing convergence efficiency and steady-state accuracy overall, which has significant advantages over the traditional fixed-step LMS algorithm.

[0149] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of combined actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Secondly, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application. In the above embodiments, the descriptions of each embodiment have their own emphasis; for parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0150] Figure 5 A block diagram of an example of an adaptive filter weight optimization system based on the LMS algorithm according to an embodiment of this application is shown.

[0151] like Figure 5 As shown, the adaptive filter weight optimization system 500 based on the LMS algorithm can be set at the RSMA receiver, which includes a signal receiving unit 510, a common message cancellation unit 520, a filter signal generation unit 530, an error signal calculation unit 540, a parameter adaptive update unit 550, and an iterative convergence output unit 560.

[0152] The signal receiving unit 510 is used to acquire a composite received signal that includes superimposed public and private messages.

[0153] The common message cancellation unit 520 is used to decode the common message of the composite received signal and remove the decoded common message from the received signal to obtain a residual signal for filtering.

[0154] The filter signal generation unit 530 is used to input the residual signal into a fractional-order variable step size LMS filter and generate a filtered output signal based on the filter weights and fractional-order differential terms.

[0155] The error signal calculation unit 540 is used to calculate the error signal based on the difference between the filtered output signal and the ideal symbol corresponding to the private message.

[0156] The parameter adaptive update unit 550 is used to update the filter weights using the error signal and the residual signal, and to update the step size and fractional gain parameters of the fractional-order variable step size LMS filter based on the error signal.

[0157] The iterative convergence output unit 560 is used to output the final optimized target filter weights when the error signal is detected to meet the preset convergence conditions.

[0158] In some embodiments, this application provides a non-volatile computer-readable storage medium storing one or more programs including execution instructions. The execution instructions can be read and executed by an electronic device (including but not limited to a computer, server, or network device) to perform the steps of any of the adaptive filter weight optimization methods based on the LMS algorithm described above.

[0159] In some embodiments, this application also provides a computer program product, the computer program product including a computer program stored on a non-volatile computer-readable storage medium, the computer program including program instructions, which, when executed by a computer, cause the computer to perform the steps of any of the above-described adaptive filter weight optimization methods based on the LMS algorithm.

[0160] In some embodiments, this application also provides an electronic device, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform steps of an adaptive filter weight optimization method based on the LMS algorithm.

[0161] The above-described product can perform the methods provided in the embodiments of this application, and has the corresponding functional modules and beneficial effects for performing the methods. Technical details not described in detail in this embodiment can be found in the methods provided in the embodiments of this application.

[0162] The electronic devices in this application embodiments exist in various forms, including but not limited to:

[0163] (1) Mobile communication devices: These devices are characterized by their mobile communication capabilities and primarily aim to provide voice and data communication. These terminals include smartphones, multimedia phones, feature phones, and low-end phones.

[0164] (2) Ultra-mobile personal computer devices: These devices fall under the category of personal computers, possessing computing and processing capabilities, and generally also have mobile internet access features. These terminals include: PDAs, MIDs, and UMPCs, etc.

[0165] (3) Portable entertainment devices: These devices can display and play multimedia content. This category includes audio and video players, handheld game consoles, e-book readers, as well as smart toys and portable car navigation devices.

[0166] (4) Other airborne electronic devices with data interaction capabilities, such as vehicle-mounted systems installed on vehicles.

[0167] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0168] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented using software plus a general-purpose hardware platform, or of course, using hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. An adaptive filter weight optimization method based on the LMS algorithm, implemented by an RSMA receiver, the method comprising: Acquire a composite received signal that includes both public and private messages; The composite received signal is decoded using a common message, and the decoded common message is removed from the received signal to obtain a residual signal for filtering. The residual signal is input into a fractional-order variable-step-size LMS filter, and a filtered output signal is generated based on the filter weights and fractional-order differential terms. Calculate the error signal based on the difference between the filtered output signal and the ideal symbol corresponding to the private message; The filter weights are updated using the error signal and the residual signal, and the step size and fractional gain parameters of the fractional-order variable step size LMS filter are updated based on the error signal, respectively. If the error signal is detected to meet the preset convergence condition, the final optimized target filter weights are output.

2. The method according to claim 1, wherein, After inputting the residual signal into a fractional-order variable-step-size LMS filter and generating a filtered output signal based on the filter weights and fractional-order differential terms, the method further includes: The filtered output signal is decomposed into K filtered output components, and the kth filtered output component is used as the residual interference vector of the kth user. Based on the channel gain estimates of user p and user q, the correlation coefficient between users is calculated, the off-diagonal terms of the correlation matrix are filled with the correlation coefficient, and the diagonal elements of the correlation matrix are set as the sum of the elements of the corresponding rows to obtain the degree matrix; Construct the Laplacian matrix of the user association graph using the association matrix and the degree matrix; Based on the Laplace matrix, a graph smoothing operation is performed on the decomposed K-path residual interference vectors to generate smoothed K-path filtered output components, thereby obtaining the smoothed filtered output signal.

3. The method according to claim 1, wherein, The step of updating the filter weights using the error signal and the residual signal includes: w i (n+1)=w i (n)+µ(n)e(n)r(ni), In the formula, n represents the discrete time index, i represents the filter tap index, and L represents the total number of taps; r(n) represents the residual signal sample at time n, and r(ni) represents the delayed sample of the residual signal at time (ni). Let d(n) represent the filtered output signal generated by the fractional-order variable-step-size LMS filter at time n, and let d(n) represent the signal generated by the filter at time n. The corresponding ideal symbol for the private message at time n, e(n) represents the error signal at time n, μ(n) represents the variable step size at time n, and μ base (n) represents the baseline step size at time n, μ0 represents the initial step size constant, γ represents the balance factor, and w i (n) represents the stored value of the i-th order filter weight at time n, w i (n+1) represents the updated value of the i-th order filter weight at time n+1.

4. The method according to claim 1 or 3, wherein, The step of inputting the residual signal into a fractional-order variable-step-size LMS filter and generating a filtered output signal based on the filter weights and fractional-order differential terms includes: Store the most recent L sampled values ​​of the residual signal {r(n),r(n-1),…,r(n-L+1)} into the shift register buffer; Using the pre-stored Grünwald-Retnikov fractional binomial coefficients in read-only memory Read the most recent M residual samples from the shift register buffer, perform fractional-order differential weighted summation, and calculate the fractional-order compensation term using the following formula: In the formula, M represents the memory window length of the fractional derivative, specifying the number of past residual samples participating in the fractional derivative, M≥L; j represents the accumulation index of the Grünwald-Letnikov summation, ν represents the fractional derivative operator; D ν [r(n)] is the result of the fractional differential operator applied to r(n), representing the weighted difference of the latest M residual samples, which is used as a compensation term; Based on the filter weights at the current time The filtered output signal is generated using the fractional-order gain β(n) as follows: In the formula, β(n) is the fractional compensation gain, which represents the strength of the fractional differential term used to adjust the strength at time n.

5. The method according to claim 4, wherein, The step size and fractional-order gain parameters of the fractional-order variable-step-size LMS filter, respectively, based on the error signal, include: Calculate the step-size hypergradient: In the formula, g μ (n) is the hypergradient of the step size at time n, which represents the direction and magnitude of the error’s sensitivity to the step size; Update the step size according to the following formula: μ(n+1)=μ base (n)-n μ g μ (n), Where, η μ Let μ be the step size learning rate constant, and μ(n+1) represent the updated value of the step size at time n+1. Using the fractional differential term D already calculated in the fractional variable step size LMS filter ν Calculate the fractional-order gain hypergradient using [r(n)] and the error signal e(n): g β (n)=-e(n)D ν [r(n)], In the formula, g β (n) represents the fractional gain hypergradient at time n, indicating the sensitivity of the error to the fractional gain; Update the fractional-order gain parameter according to the following formula: β(n+1)=β(n)-n β g β (n), In the formula, η β β is the fractional gain learning rate constant, and β(n+1) is the updated value of the fractional gain, used for fractional compensation at time n+1.

6. The method according to claim 1, wherein, The step of outputting the final optimized target filter weights when the error signal is detected to meet the preset convergence condition includes: In each iteration, it is determined whether the absolute value of the error signal |e(n)| is less than the preset threshold ε; If |e(n)|<ε, the step counter increments by 1; otherwise, the counter is reset to 0. When the counter value reaches the preset integer N, the convergence status signal is output and the current filter weight is latched as the final target filter weight for optimization.

7. An adaptive filter weight optimization system based on the LMS algorithm, set at an RSMA receiver, the system comprising: The signal receiving unit is used to acquire a composite received signal that includes superimposed public and private messages; A common message elimination unit is used to decode the common messages of the composite received signal and remove the decoded common messages from the received signal to obtain a residual signal for filtering processing. The filtered signal generation unit is used to input the residual signal into a fractional-order variable step-size LMS filter and generate a filtered output signal based on the filter weights and fractional-order differential terms. An error signal calculation unit is used to calculate an error signal based on the difference between the filtered output signal and the ideal symbol corresponding to the private message; The parameter adaptive update unit is used to update the filter weights using the error signal and the residual signal, and to update the step size and fractional gain parameters of the fractional-order variable step size LMS filter based on the error signal, respectively. An iterative convergence output unit is used to output the final optimized target filter weights when the error signal is detected to meet the preset convergence conditions.

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