Clustering-greedy optimization based fbmc-ss non-uniform subband adaptive modulation method

Abstract

This invention relates to the field of shortwave communication, and specifically to an adaptive modulation method for non-uniform subbands in FBMC-SS based on clustering-greedy optimization. This method makes targeted improvements to the subband partitioning and bit allocation stages based on the multi-carrier structural characteristics of the FBMC-SS system. In the subband partitioning stage, a K-means++ clustering algorithm incorporating contour coefficients is used to achieve non-uniform subcarrier partitioning under different channel conditions. This not only enhances the compactness within subbands and the separation between subbands, but also improves robustness to outliers by introducing centroid update strategies such as median and truncated mean, laying a good foundation for subsequent bit allocation. In the bit allocation stage, the traditional greedy algorithm oriented towards subcarriers is improved to use subbands as units, employing the same bit and modulation scheme for subcarriers within the same subband, which is more conducive to maximum ratio combining at the FBMC-SS receiver. Furthermore, based on the rate adaptive criterion, the system transmission rate is maximized under constraints of total power and bit error rate.

Description

Technical Field

[0001] This invention relates to the field of shortwave communication, and particularly to a Clustering-Greedy Adaptive Modulation with Non-Uniform Subbands (CGAM-NUS, hereinafter referred to as CGAM) method for Filter Bank Multi-Carrier Spread Spectrum (FBMC-SS). CGAM consists of non-uniform subband partitioning based on a clustering algorithm and bit allocation based on an improved greedy algorithm. This method is designed based on a rate-adaptive criterion, aiming to maximize the data transmission rate of the FBMC-SS system while satisfying power and bit error rate constraints, and balancing the effectiveness and reliability of the FBMC-SS system. Background Technology

[0002] Due to the complexity of shortwave channel conditions, traditional shortwave communication systems often prioritize the reliability of the communication link, sacrificing data transmission rate and reducing the effectiveness of information transmission. Therefore, shortwave communication is often only used to transmit low-volume data such as keyword messages or short voice messages. With the increasing demand for shortwave communication, improving its effectiveness while ensuring reliability has become a crucial aspect of its future development. Filter bank multi-carrier spread spectrum (FBMC) is a novel multi-carrier communication system first proposed in 2012. This technology integrates the core advantages of Filter Bank Multi-Carrier (FBMC) and Spread Spectrum (SS) technologies, offering advantages such as lower out-of-band power leakage and weaker frequency offset sensitivity compared to traditional Orthogonal Frequency Division Multiplexing (OFDM). FBMC-SS systems transmit data using a large number of parallel subcarriers, with all subcarriers transmitting the same information for maximum ratio combining at the receiver. This effectively addresses multipath fading and partial frequency band interference in complex shortwave channels, providing strong communication reliability even under low signal-to-noise ratio conditions. Although the FBMC-SS system has good reliability in shortwave channels, its data transmission per unit time is relatively limited because each subcarrier transmits the same information for maximum ratio combining and the modulation method is relatively conservative. This makes it difficult to meet the future development needs of shortwave communication, especially when the channel conditions are good, which will result in redundancy and waste of spectrum resources.

[0003] Adaptive modulation technology can select the optimal communication scheme according to different channel states, effectively improving data transmission rate while ensuring reliable communication. This is of great significance for enhancing the effectiveness of FBMC-SS systems in future engineering applications. Currently, based on the subcarrier partitioning method, classical adaptive algorithms can be divided into two categories: subcarrier-based and subband-based adaptive modulation. Subcarrier-based adaptive modulation algorithms dynamically allocate the number of information bits, modulation order, or transmit power on each subcarrier to maximize the total system capacity or minimize the total transmit power, achieving globally optimal resource allocation. Typical subcarrier-based adaptive modulation algorithms include the Hughes-Hartogs algorithm, the Chow algorithm, and the Fischer algorithm. Among them, the Hughes-Hartogs algorithm has the best performance, but its high complexity makes it difficult to implement. In addition, when the number of subcarriers in the system is large, the computational load of subcarrier-based adaptive modulation algorithms increases dramatically, greatly limiting the performance of practical applications. Since adjacent subchannel states are usually quite similar and have a certain correlation, they can be merged into subbands for unified processing, thereby effectively reducing computational complexity. This is where subband-based adaptive modulation algorithms come in. Classical subband-based adaptive modulation algorithms include the Campello algorithm, the Simple Blockwise Loading Algorithm (SBLA), and the Nader-Esfahani algorithm. While the Campello algorithm reduces complexity compared to the Hughes-Hartogs algorithm, its bit error rate performance is not ideal. The SBLA algorithm uses fixed subband division for adjacent subcarriers, failing to consider scenarios where adjacent subchannels have significantly different channel conditions, resulting in poor performance in rapidly changing channels. The Nader-Esfahani algorithm employs a dynamic subband division approach, significantly improving system performance compared to the SBLA algorithm, but its grouping strategy lacks adaptability to dynamically changing channels, potentially leading to inaccurate grouping boundaries and impacting overall performance. Research on these traditional adaptive modulation algorithms primarily focuses on OFDM; no studies have been conducted specifically for FBMC-SS systems. Due to significant differences between FBMC-SS and OFDM, traditional methods cannot be directly applied; targeted improvements based on the structural characteristics of FBMC-SS systems are necessary.

[0004] Since FBMC-SS systems typically contain a large number of subcarriers, using a per-subcarrier bit allocation strategy would lead to overly complex algorithm implementations. Merging subcarriers with similar channel states into subbands for unified processing can effectively reduce computational complexity. Furthermore, all subcarriers in an FBMC-SS system usually transmit the same information for maximum ratio combining at the receiver; therefore, the same information needs to be transmitted using the same modulation scheme on a subband basis, rather than on a single subcarrier. Thus, FBMC-SS systems are better suited to subband-based adaptive modulation methods, requiring a redesign of both subband partitioning and bit allocation to balance data transmission rate, bit error rate, and computational complexity. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a clustering-greedy optimization-based non-uniform subband adaptive modulation method for FBMC-SS. This method makes targeted improvements to the subband partitioning and bit allocation stages based on the multi-carrier structural characteristics of the FBMC-SS system. In the subband partitioning stage, a K-means++ clustering algorithm incorporating contour coefficients is employed to achieve non-uniform subcarrier partitioning under different channel conditions. This not only enhances intra-subband compactness and inter-subband separation but also improves robustness to outliers by introducing centroid update strategies such as median and truncated mean, laying a solid foundation for subsequent bit allocation. In the bit allocation stage, the traditional subcarrier-oriented greedy algorithm is improved to operate on a subband-by-subband basis, using the same bit and modulation scheme for subcarriers within the same subband. This is more conducive to maximum ratio combining at the FBMC-SS receiver. Furthermore, based on the rate adaptive criterion, the system transmission rate is maximized under constraints of total power and bit error rate.

[0006] The technical solution adopted in this invention is as follows: an FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization, which provides four sequentially increasing modulation schemes: Binary Phase Shift Keying (BPSK), Quaternary Phase Shift Keying (QPSK), Octal Phase Shift Keying (8PSK), and 16-Quadrature Amplitude Modulation (16QAM). The method consists of the following steps:

[0007] S1 is a non-uniform subband partitioning based on a clustering algorithm:

[0008] S1.1 preprocesses the original signal-to-noise ratio of the subcarriers;

[0009] To avoid the influence of dimensions and ensure that the signal-to-noise ratio (SNR) data conforms to a zero-mean, unit-variance distribution for easier subsequent clustering calculations, the raw SNR of the subcarriers needs to be preprocessed; [Definition] The original signal-to-noise ratio of the subcarrier is represented by k, where k is the original sequence index of the subcarrier, k=1,2,…,N, and N represents the number of subcarriers;

[0010] The original signal-to-noise ratios of the subcarriers are sorted in descending order from high to low to facilitate subsequent classification and evaluation of the channel status of each subcarrier; [Definition] represents the signal-to-noise ratio after subcarrier sorting, where i is the sequence index of the sorted subcarriers, i=1,2,…,N;

[0011] Calculate the mean μ and standard deviation σ of the signal-to-noise ratio for all subcarriers:

[0012]

[0013] Z-score normalization is applied to the signal-to-noise ratio (SNR) of all subcarriers. The normalized SNR data satisfies a mean of 0 and a variance of 1. The signal-to-noise ratio of the i-th subcarrier after normalization is:

[0014]

[0015] S1.2 Initialize the centroids of the K-means++ algorithm:

[0016] S1.2.1 Randomly select the first centroid;

[0017] definition Let p represent the centroid of the p-th subband, where p is the sequence index of the subband, p = 1, 2, ..., P, and P represents the number of subbands. (The last part, "randomly selected from...", is a typo and can be left as is.) Select the first centroid .

[0018] S1.2.2 Calculate the distance to the nearest centroid for each signal-to-noise ratio;

[0019] definition This represents the distance from the normalized signal-to-noise ratio to the nearest centroid:

[0020]

[0021] Where v represents the number of centroids that have been determined so far, with the initial state v=1 and subsequent increments being v←v+1;

[0022] S1.2.3 Determine the next centroid using the roulette wheel selection method;

[0023] In the K-means++ algorithm, the selection of subsequent centroids is neither completely random nor directly choosing the farthest point. Instead, it uses a roulette wheel selection method to probabilistically select points that are far from the current centroids, avoiding getting trapped in local optima or overly biased towards outliers, thereby improving the clustering effect.

[0024] definition Represents the standardized signal-to-noise ratio The probability of being selected as the next centroid, after normalization, is expressed as:

[0025]

[0026] Define Q i This represents the probability of choosing the centroid. The cumulative probability obtained after summing:

[0027]

[0028] Where w represents the sequence index when traversing the subcarriers, w = 1, 2, ..., i, for example... And so on.

[0029] Generate uniform random numbers Finding Find the smallest index i and select As the next center of mass;

[0030] S1.2.4 Repeat steps S1.2.2 and S1.2.3 until the centroids of all subbands are initialized. ;

[0031] S1.3 Clustering iteration based on K-means++ algorithm:

[0032] After initializing the centroids of all sub-bands, the algorithm enters the iterative optimization phase. Next, the objective function needs to be determined, and the centroid and subcarrier allocations are iteratively clustered using the K-means++ algorithm to determine the optimal centroid and subcarrier allocation scheme.

[0033] S1.3.1 Determine the objective function;

[0034] definition This represents the intra-group dissimilarity, specifically the average distance between the signal-to-noise ratio (SNR) of the i-th subcarrier and other subcarriers within the subband. The smaller the value, the closer the subcarrier is to its subband. The expression is:

[0035]

[0036] Where j represents the sequence index of other subcarriers within the p-th subband, distinct from the i-th subcarrier. C p Let p represent the set of signal-to-noise ratios within the p-th subband. Indicates the difference within the sub-band The signal-to-noise ratio of other subcarriers, N p This represents the number of subcarriers contained in the p-th subband. It's important to note that when there is only one subband, the definition is... =0, at which point the contour coefficient is meaningless.

[0037] definition This represents the inter-group dissimilarity, specifically the minimum average distance between the i-th subcarrier and the subcarriers within other subbands in terms of signal-to-noise ratio. The larger the value, the more significant the difference between this subcarrier and other sub-bands; The expression is:

[0038]

[0039] Where q is the sequence index of other sub-bands, which is different from the p-th sub-band where the i-th subcarrier is located, q=1,2,…,P; Let r represent the signal-to-noise ratio of the r-th subcarrier within the q-th subband, where r is the sequence index of the subcarrier within the q-th subband, and q = 1, 2, ..., N. q N q C represents the number of subcarriers contained in the q-th subband; q Let represent the set of signal-to-noise ratios of subcarriers within the q-th subband. .

[0040] Define u(i) as the contour coefficient of a subcarrier. A larger contour coefficient indicates smaller intra-group differences and larger inter-group differences in sub-band division, meaning a more reasonable sub-band division. Its expression is:

[0041]

[0042] definition Mean profile coefficient:

[0043]

[0044] The objective function of the K-means++ algorithm is defined as maximizing the average silhouette coefficient.

[0045]

[0046] The silhouette coefficient is an evaluation metric used to measure the intra-group tightness and inter-group separation of sample data. Its value ranges from -1 to 1; a value close to 1 indicates reasonable sample grouping with small intra-group differences and large inter-group differences; a value close to -1 indicates that the samples may have been incorrectly grouped. Introducing the silhouette coefficient into subband partitioning allows for the simultaneous assessment of the similarity of channel conditions within subbands and the differences in channel conditions between subbands, making subband partitioning more scientific and reasonable.

[0047] S1.3.2 Assign subbands to subcarriers based on the minimum Euclidean distance;

[0048] According to the standard steps of the K-means++ algorithm, subcarriers need to be assigned to subbands based on the minimum Euclidean distance, that is, the subcarriers are assigned to the subbands where the nearest centroid is located.

[0049] calculate Find the sub-band sequence index that has the smallest Euclidean distance to the i-th subcarrier among all centroids, and then... Assigned to this sub-band, resulting in the set C of signal-to-noise ratios for the p-th sub-band. p :

[0050]

[0051] When all subcarriers have completed subband allocation, the optimal subband partitioning result can be expressed as follows: At this point, the number of subcarriers in each subband signal-to-noise ratio set is usually different, that is, non-uniform subband division is completed, which facilitates subsequent bit allocation by subband.

[0052] S1.3.3 Update the centroid;

[0053] The centroid of each sub-band is calculated using the following three strategies. Compare and select the strategy with the largest average profile coefficient:

[0054] Strategy 1: Arithmetic Mean Method

[0055] definition Let the centroid of the p-th subband be updated using the arithmetic mean method:

[0056]

[0057] in, This represents the signal-to-noise ratio of the j-th subcarrier within the p-th subband after standardization.

[0058] Strategy 2: Median Method

[0059] definition Let p be the centroid of the p-th subband after median-based update, and its expression is:

[0060]

[0061] Strategy 3: Cut-off Mean Method

[0062] Define η as the number of data points to be truncated, and its expression is:

[0063]

[0064] in, To indicate the truncation ratio, usually taken as... ; This indicates rounding down to the nearest integer.

[0065] definition Let p be the centroid of the p-th subband after updating using the truncated mean method, and its expression is:

[0066]

[0067] when When there are too few data points in the sub-band, the truncated mean method is equivalent to the arithmetic mean method.

[0068] The strategy that updates the centroid by selecting the one with the largest average profile coefficient is expressed as follows:

[0069]

[0070] in, Indicates use The average profile coefficient after the strategy updates the centroid.

[0071] S1.3.4 Iteration terminates;

[0072] The K-means++ algorithm will be executed if any of the following conditions are met during its iterative process: the centroid no longer changes, the change in the silhouette coefficient is less than a certain set threshold ε (e.g., ε = 0.01), or the maximum number of iterations T is reached. max When the reference value range is [30, 100], the K-means++ algorithm terminates its iteration and outputs the optimal subband partitioning result. .

[0073] S2 is a bit allocation based on an improved greedy algorithm:

[0074] After step S1, which performs non-uniform subband division on all subcarriers, subcarriers with similar channel states are grouped into the same subband. Subsequent processing is then performed on a subband-by-subband basis, effectively reducing computational complexity. Subsequently, in step S2, the original information bits are allocated to each subband, and the corresponding modulation scheme is determined. By ensuring that all subcarriers within the same subband transmit the same information bits and use the same modulation scheme, maximum ratio combining is facilitated at the receiver, thereby improving reception performance.

[0075] Since all subcarriers within a subband use the same modulation scheme, the definition is... Indicates the transmit power of the p-th subband:

[0076]

[0077] Among them, P p This represents the power of the p-th subband. b represents the signal-to-noise ratio threshold for different modulation methods. p b represents the number of bits. p =1,2,3,4, corresponding to the modulation schemes BPSK, QPSK, 8PSK, and 16QAM, respectively; These represent the manually set signal-to-noise ratio (SNR) thresholds for BPSK, QPSK, 8PSK, and 16QAM, respectively. Their values ​​cover the actual SNR range of the channel. Furthermore, since these four modulation schemes progressively increase in order and their SNR requirements gradually increase, they are typically set to... N0 represents the power spectral density of the noise; The average channel gain of the p-th subband is obtained by averaging the channel gains of all subcarriers within that subband.

[0078]

[0079] Among them, H p,l Let l represent the channel gain of the l-th subcarrier within the i-th subband, where l represents the sequence index of the subcarrier, l=1,2,…N p .

[0080] definition This represents the subband power increment when the bit is increased by 1:

[0081]

[0082] For example, when the modulation scheme of the p-th subband is changed from BPSK to QPSK, the power increment is: When QPSK is adjusted to 8PSK, the power increment is: .

[0083] S2.1 Algorithm Initialization;

[0084] First, set b p =1, meaning that all subbands are allocated at least 1 bit, using BPSK modulation.

[0085] Then, calculate the initial power increment when allocating 2 bits for each subband:

[0086]

[0087] Define Q as the set of system power increments, used to store the power increments of all sub-bands. And record the sub-band sequence index at this time. The expression for this set is:

[0088]

[0089] Calculate the initial total system power P at this point. T And system bit error rate E:

[0090]

[0091] in, This indicates that the p-th subband is assigned to b. p Bits and the bit error rate when using the corresponding modulation method. This represents the bit error rate when the p-th subband uses BPSK modulation.

[0092] S2.2 Extract the subband index p with the smallest power increment from Q. * ;

[0093] Define p * The subband index with the smallest power increment in Q is expressed as follows:

[0094]

[0095] Check bit limits, if Then remove index p from Q. * Record the error and repeat step S2.2; otherwise, proceed to the next step.

[0096] S2.3 Update bit allocation and modulation scheme;

[0097] tentative setup That is, try to be the pth * Each subband allocates one more bit and uses a higher-order modulation scheme. For example, from b p* =1 set b p* =2, which is the pth * Each subband is allocated one more bit, the modulation scheme is changed from BPSK to QPSK, and so on.

[0098] Calculate the corresponding power increment and update the total system power. and system bit error rate Their expressions are as follows:

[0099]

[0100] At the same time, check the power and bit error rate limits: if P0 and E0 represent the manually set power threshold and bit error rate threshold, respectively, which are typically set based on the transmitter's maximum power limit and the system's bit error rate requirements. Then use the modulation method to... Updated to Simultaneously update and Otherwise, revert to the original modulation scheme and maintain b. p* Remain unchanged, and remove the record with index p* from Q.

[0101] S2.4 Updates the system power increment set Q;

[0102] If b p* <4, you can continue to add bits and calculate. The value of b is updated and the power increment value at index p* in Q is updated; if b p* =4, the maximum bit allocation has been reached, remove the record with index p* from Q.

[0103] Repeat the iterative operations S2.2, S2.3, and S2.4 above until Q is an empty set, then terminate the iterative process and determine the information bits and modulation scheme transmitted on each subcarrier of the final FBMC-SS system.

[0104] S3 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion;

[0105] After subband division and bit allocation in steps S1 and S2, the information bits and modulation scheme transmitted on each subcarrier of the FBMC-SS system are determined. Then, shaping filtering and up-conversion are required to generate the final transmit signal of the FBMC-SS system.

[0106] Define s k (t) represents s k [n] is the transmission symbol obtained after upsampling, and its expression is:

[0107]

[0108] Among them, s k [n] represents the transmitted symbol of the original information bits s[n] on the k-th subcarrier after steps S1 and S2; k represents the original sequence index of the subcarrier, k=1,2,…,N; n represents the discrete time sequence index; T s For periodicity, δ(t-nT) s ) indicates that T s A periodic impulse train sequence.

[0109] Define x(t) as the transmitted signal of the FBMC-SS system, which is composed of the s signals on each subcarrier. k[n] is obtained by upsampling, shaping filtering, and upconversion, followed by time-domain superposition. Its expression is:

[0110]

[0111] Where h(t) represents the prototype filter; γ k The phase perturbation factor has an amplitude of Phase at The upper part follows a uniform random distribution; The center frequency f of the k-th subcarrier is represented. k That is, up-conversion.

[0112] S4 calculates the data transmission rate of the transmitter in the FBMC-SS system.

[0113] Since the p-th subband contains N p There are 10 subcarriers, and all subcarriers within the same subband use the same modulation scheme and are allocated the same number of bits (b). p Then the p-th subband in each period T s The total number of bits transmitted internally is N p b p Define R p This represents the data transmission rate of the p-th subband:

[0114]

[0115] Define R total The total data transmission rate of the FBMC-SS system transmitter is obtained by summing the data transmission rates of all P subbands:

[0116] .

[0117] The beneficial effects of this invention are as follows:

[0118] ① An outline coefficient is introduced into the K-means++ clustering algorithm to perform non-uniform subband division for subcarriers under different channel conditions, ensuring high density within subbands and significant separation between subbands, further improving the rationality of subband division and laying a good foundation for bit and modulation scheme allocation. In addition to the arithmetic mean, two new centroid update strategies, median and truncated mean, are added to enhance the algorithm's robustness to outliers;

[0119] ② The greedy algorithm originally used for subcarriers was improved into a subband-based bit allocation algorithm, which is more in line with the structural characteristics of the FBMC-SS system. This algorithm allocates bits and modulation schemes on a subband basis, keeping the bits and modulation schemes of subcarriers within the same subband the same, and maximizes the system transmission rate under the constraints of total power and bit error rate according to the rate adaptation criterion;

[0120] ③ Simulation results show that, compared with traditional methods, the method proposed in this invention significantly improves the data transmission rate while maintaining strong anti-interference capability, thus balancing the reliability and effectiveness of the FBMC-SS system. Attached Figure Description

[0121] Figure 1 : A flowchart of the method described in this invention;

[0122] Figure 2 FBMC-SS transmitter;

[0123] Figure 3 Signal-to-noise ratio random distribution plot;

[0124] Figure 4 Subcarrier distribution diagram after non-uniform subband division;

[0125] Figure 5 : Distribution diagram of bit count, subcarrier count, and modulation scheme for each subband;

[0126] Figure 6 : Distribution diagram of transmission rates for each subband;

[0127] Figure 7 Comparison of data transmission rates for different adaptive modulation methods;

[0128] Figure 8 Comparison of bit error rate performance of different adaptive modulation methods. Detailed Implementation

[0129] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0130] Figure 1 This is a flowchart of the method described in this invention. Figure 2 The transmitter structure of FBMC-SS is shown. This invention proposes an adaptive modulation method for non-uniform subbands of FBMC-SS based on clustering-greedy optimization, which consists of the following steps:

[0131] S1 is a non-uniform subband partitioning based on a clustering algorithm:

[0132] S1.1 preprocesses the original signal-to-noise ratio of the subcarriers;

[0133] S1.2 Initialize the centroids of the K-means++ algorithm:

[0134] S1.2.1 Randomly select the first centroid;

[0135] S1.2.2 Calculate the distance to the nearest centroid for each signal-to-noise ratio;

[0136] S1.2.3 Determine the next centroid using the roulette wheel selection method;

[0137] S1.2.4 Repeat steps S1.2.2 and S1.2.3 until the centroids of all sub-bands are determined during initialization. ;

[0138] S1.3 Clustering iteration based on K-means++ algorithm:

[0139] S1.3.1 Determine the objective function;

[0140] S1.3.2 Assign subbands to subcarriers based on the minimum Euclidean distance;

[0141] S1.3.3 Update the centroid;

[0142] S1.3.4 Iteration terminates;

[0143] S2 is a bit allocation based on an improved greedy algorithm:

[0144] S2.1 Algorithm Initialization;

[0145] S2.2 Extract the subband index p* with the smallest power increment from Q;

[0146] S2.3 Update bit allocation and modulation scheme;

[0147] S2.4 Updates the system power increment set Q;

[0148] S3 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion;

[0149] S4 calculates the data transmission rate of the transmitter in the FBMC-SS system.

[0150] This section analyzes the performance of the clustering-greedy optimization-based non-uniform subband adaptive modulation method for FBMC-SS in the FBMC-SS system through multiple sets of numerical simulation results. The basic parameter configuration of the FBMC-SS system is shown in Table 1, with a total transmission of 1000 bits (800 information bits + 200 pilot bits), and block pilots (pilot spacing) are set. The system will employ four modulation schemes (BPSK / QPSK / 8PSK / 16QAM) depending on different signal-to-noise ratios, and the prototype filter will use a square root raised cosine (SRRC) filter. Since this invention primarily focuses on adaptive modulation at the transmitter, the receiver can be designed in reverse based on the transmitter structure with the addition of maximum ratio combining; details will not be elaborated here.

[0151]

[0152] Figure 3 This figure illustrates the random signal-to-noise ratio (SNR) distribution of 200 subcarriers before any subband partitioning or optimization. The distribution characteristics show that the SNR of each subcarrier exhibits significant randomness and irregularity, which is a typical manifestation of frequency-selective fading in wireless multipath propagation environments. In actual wireless communication environments, due to factors such as building reflection, scattering, and the Doppler effect, signals at different frequencies experience varying degrees of fading, resulting in inconsistent channel quality across subcarriers. As shown in the figure, some subcarrier regions exhibit relatively concentrated high SNR values ​​(e.g., the blue area, with an SNR range of [10, 20], suitable for high-order modulation), while other areas show severe signal attenuation (e.g., the red area, with an SNR range of [-20, -10], only supporting low-order modulation). Without proper resource management and optimization, this random SNR distribution leads to low system spectrum utilization and decreased transmission reliability. Therefore, subsequent non-uniform subband partitioning is necessary to rationally configure the channel and fully utilize its transmission potential.

[0153] Figure 4 This paper demonstrates the results of non-uniform subband partitioning of subcarriers using the algorithm proposed in this invention. The originally randomly distributed subcarriers are divided into 10 non-uniform subbands based on their signal-to-noise ratio (SNR). Subcarriers within each subband have similar SNRs, representing similar channel conditions. The figure illustrates the average SNR of each subband, which gradually decreases from 18.6 dB in subband 1 to -16.7 dB in subband 10, exhibiting a clear sequential distribution. This partitioning strategy effectively transforms subcarriers from random scattered points to ordered groups, significantly reducing SNR fluctuations within each subband and making transmission conditions more stable. This structure lays an important foundation for subsequent adaptive bit allocation: the system can independently select the optimal modulation and coding scheme for each subband, employing higher-order modulation for high SNR subbands to improve transmission efficiency and robust lower-order modulation for low SNR subbands to ensure communication reliability, thereby improving spectral efficiency while further optimizing the overall system performance.

[0154] Figure 5The bit allocation of each subband is visually illustrated using a pie chart, with the legend indicating the number of subcarriers, their proportion, and the modulation scheme for each subband. Subband 2 received 156 bits (19.5% of the total bits), receiving the most bits despite not having the highest signal-to-noise ratio (SNR) (15.0 dB). Subband 1, while having the highest SNR (18.6 dB), only received 133 bits (16.6%) due to its smaller number of subcarriers (only 6). This reflects the algorithm's comprehensive optimization strategy: considering not only SNR but also factors such as the number of subcarriers and modulation efficiency. Regarding modulation scheme selection, subbands with higher SNR employ higher-order modulation schemes such as 16QAM to maximize data transmission rate; while subbands with poorer channel conditions use BPSK or QPSK modulation with stronger noise immunity to ensure communication reliability. The legend also indicates the number and proportion of subcarriers in each subband. Subband 4 contains the most subcarriers (33, accounting for 16.5%), reflecting the non-uniform distribution of resources in actual channels. Overall, this allocation strategy embodies the core idea of ​​the rate adaptive principle: under the condition of limited total power, more bit resources and higher-order modulation schemes are allocated to subbands with better channel conditions, while fewer bits and lower-order modulation schemes are allocated to subbands with poorer channel conditions; at the same time, it ensures that each subband can meet the basic communication quality requirements, thereby maximizing the total system transmission rate while meeting the bit error rate performance requirements.

[0155] Figure 6 The transmission rate performance of each subband is illustrated, with the average signal-to-noise ratio (SNR) and modulation scheme of each subband also marked in the figure. Subband 2 maximizes its transmission rate due to its superior SNR (15.0 dB), a larger number of subcarriers (23), and efficient 8PSK modulation. Subband 1, despite having an SNR of 18.6 dB and using 16QAM modulation, suffers from a limited transmission rate due to the allocation of only 6 subcarriers. Subband 3, with a similar modulation scheme, also has a lower rate (48.0 kbps) due to its smaller number of subcarriers (9). This demonstrates that transmission performance depends not only on the SNR but also on the combined influence of the number of subcarriers and the modulation scheme. Overall, the system achieves a total transmission rate exceeding 300 kbps, with the highest rate (subband 2) reaching 60.0 kbps and the lowest rate (subband 6) reaching 14.4 kbps. This indicates that the proposed method not only achieves efficient utilization of high-quality channel resources but also ensures basic transmission capabilities under poor channel conditions. Compared with traditional subband modulation methods, the method proposed in this invention can better adapt to the channel characteristics of frequency-selective fading. While meeting the bit error rate requirements, it significantly improves the spectral efficiency and transmission rate of the system, providing a useful reference scheme for improving the effectiveness of FBMC-SS systems.

[0156] Figure 7 The relationship between the number of subcarriers and the data transmission rate in the FBMC-SS system under different adaptive modulation methods is illustrated using scatter plots and fitted curves. Here, "SBLA" and "NE" represent the Simple Group Allocation Algorithm and the Nader-Esfahani algorithm in the traditional classical algorithms, respectively, while "CGAM" represents the non-uniform subband adaptive modulation method based on clustering-greedy optimization proposed in this invention. SBLA exhibits a high initial rate due to its simplest fixed subband number partitioning strategy, directly allocating the modulation scheme based on the average channel quality of each subband. Although this algorithm avoids complex constraint checks and can quickly determine subband partitioning and modulation schemes when the number of subcarriers is small, its linear allocation mechanism leads to weak performance growth in the later stages of system transmission rate, with the curve quickly flattening out and exhibiting obvious asymptotic characteristics. NE's performance falls between SBLA and CGAM. This algorithm adopts a dynamic subband partitioning approach, and although the system performance is significantly improved compared to SBLA, achieving stable linear growth, it lacks further optimization for high-quality channels, resulting in a relatively gentle growth slope. CGAM, although having the lowest initial performance, has the steepest growth slope, ultimately achieving a performance reversal. This is because when the number of subcarriers is small, the clustering algorithm may get stuck in a local optimum when processing sparse data, while as the number of subcarriers increases, the advantages of CGAM in fine-grained allocation of channel resources can be fully demonstrated.

[0157] Figure 8 The relationship between the number of subcarriers and the bit error rate (BER) of the FBMC-SS system under different adaptive modulation methods was illustrated using scatter plots and fitted curves. Overall, the BER of all three methods generally decreases with increasing subcarrier count, but fluctuates to some extent in certain ranges. The results indicate that while increasing the number of subcarriers helps improve the system's maximum ratio combining performance and enhances anti-interference capability, it does not increase monotonically with the number of subcarriers, but rather is the result of multiple factors. Furthermore, the significant randomness of channel environment changes poses a considerable challenge to the robustness of the three methods. Specifically, SBLA performs poorly in frequency-selective fading channels due to its fixed subband division; its BER performance decreases relatively slowly with increasing subcarrier count (the BER only reaches approximately 10% when the number of subcarriers reaches 400). -2 (On the order of magnitude); NE, by dividing subcarriers with similar channel gains into the same subband for processing, significantly improves system performance compared to the SBLA algorithm, but it is still not ideal (basically remaining at 10). -3 -10 -2Within the order of magnitude); the CGAM algorithm significantly outperforms the two classical methods mentioned above, achieving a lower bit error rate (generally maintained at 10%) with the same number of subcarriers. -3 Below the order of magnitude, and rapidly approaching 10 as the number of subcarriers increases. -4 (On the order of magnitude). This demonstrates that the targeted improvements made to the CGAM algorithm in the subband partitioning and bit allocation stages are effective, not only increasing the data transmission rate of the FBMC-SS system but also maintaining good anti-interference performance, thus balancing the reliability and effectiveness of the system.

Claims

1. FBMC-SS non-uniform sub-band adaptive modulation method based on clustering-greedy optimization, characterized in that, This method consists of the following steps: S1 is a non-uniform subband partitioning based on a clustering algorithm: S1.1 preprocesses the original signal-to-noise ratio of the subcarriers; definition The original signal-to-noise ratio of the subcarrier is represented by k, where k is the original sequence index of the subcarrier, k=1,2,…,N, and N represents the number of subcarriers; The original signal-to-noise ratios of the subcarriers are sorted in descending order from high to low to facilitate subsequent classification and evaluation of the channel status of each subcarrier; [Definition] represents the signal-to-noise ratio after subcarrier sorting, where i is the sequence index of the sorted subcarriers, i=1,2,…,N; Calculate the mean μ and standard deviation σ of the signal-to-noise ratio for all subcarriers: ， Z-score normalization is applied to the signal-to-noise ratio (SNR) of all subcarriers. The normalized SNR data satisfies a mean of 0 and a variance of 1. The signal-to-noise ratio of the i-th subcarrier after normalization is: ； S1.2 Initialize the centroids of the K-means++ algorithm: S1.2.1 Randomly select the first centroid; definition Let p represent the centroid of the p-th subband, where p is the sequence index of the subband, p = 1, 2, ..., P, and P represents the number of subbands. (The last part, "randomly selected from...", is a typo and can be left as is.) Select the first centroid ; S1.2.2 Calculate the distance to the nearest centroid for each signal-to-noise ratio; Definitions denotes the distance of the normalized signal-to-noise ratio to the nearest centroid: ， Where v represents the number of centroids that have been determined so far, with the initial state v=1 and subsequent increments being v←v+1; S1.2.3 Determine the next centroid using the roulette wheel selection method; In the K-means++ algorithm, the selection of subsequent centroids is neither completely random nor directly choosing the farthest point. Instead, it uses a roulette wheel selection method to probabilistically select points that are far from the current centroids, avoiding getting trapped in local optima or overly biased towards outliers, thereby improving the clustering effect. Definitions normalized signal-to-noise ratio the probability of being chosen as the next centroid, normalized expression of which is: ， Definition Q i representing the centroid selection probability cumulative probability after accumulation: ， Where w represents the sequence index when traversing the subcarriers, w=1,2,…,i; Generating uniform random numbers , find the smallest index i such that and select as the next centroid; S1.2.4 Repeat steps S1.2.2 and S1.2.3 until the centroids of all subbands are initialized. ; S1.3 Clustering iteration based on K-means++ algorithm: S1.3.1 Determine the objective function; definition This represents the intra-group dissimilarity, specifically the average distance between the signal-to-noise ratio (SNR) of the i-th subcarrier and other subcarriers within the subband. The smaller the value, the closer the subcarrier is to its subband. The expression is: ， Where j represents the sequence index of other subcarriers within the p-th subband, distinct from the i-th subcarrier. C p Let p represent the set of signal-to-noise ratios within the p-th subband. Indicates the difference within the sub-band compared to The signal-to-noise ratio of other subcarriers, N p This represents the number of subcarriers contained in the p-th subband; when there is only one subband, it is defined as follows: =0, at which point the profile coefficient is meaningless; definition This represents the inter-group dissimilarity, specifically the minimum average distance between the i-th subcarrier and the subcarriers within other subbands in terms of signal-to-noise ratio. The larger the value, the more significant the difference between this subcarrier and other sub-bands; The expression is: ， Where q is the sequence index of other sub-bands, which is different from the p-th sub-band where the i-th subcarrier is located, q=1,2,…,P; Let r represent the signal-to-noise ratio of the r-th subcarrier within the q-th subband, where r is the sequence index of the subcarrier within the q-th subband, and q = 1, 2, ..., N. q N q C represents the number of subcarriers contained in the q-th subband; q Let represent the set of signal-to-noise ratios of subcarriers within the q-th subband. ; Define u(i) as the contour coefficient of a subcarrier. A larger contour coefficient indicates smaller intra-group differences and larger inter-group differences in sub-band division, meaning a more reasonable sub-band division. Its expression is: ， Definitions denotes the average profile coefficient: ， The objective function of the K-means++ algorithm is defined as maximizing the average silhouette coefficient. ， The silhouette coefficient is an evaluation index used to measure the tightness of sample data within groups and the separation between groups. The value ranges from [-1, 1]. A value close to 1 indicates that the sample is reasonably grouped with small differences within groups and large differences between groups; a value close to -1 indicates that the sample may have been misgrouped. S1.3.2 Assign subbands to subcarriers based on the minimum Euclidean distance; calculate Find the sub-band sequence index that has the smallest Euclidean distance to the i-th subcarrier among all centroids, and then... Assigned to this sub-band, resulting in the set C of signal-to-noise ratios for the p-th sub-band. p : ， When all subcarriers complete subband allocation, the optimal subband division result is represented as ; complete non-uniform subband division, facilitate subsequent bit allocation by subband; S1.3.3 Update the centroid; The centroid of each subband is calculated according to the following three strategies The strategy of comparing and selecting the largest average profile coefficient among them: Strategy 1: Arithmetic Mean Method Definitions is the centroid of the pth subband after updating by the arithmetic mean method. ， in, This represents the signal-to-noise ratio of the j-th subcarrier within the p-th subband after standardization. Strategy 2: Median Method Definitions is the centroid of the pth subband after median filtering, and its expression is ， Strategy 3: Cut-off Mean Method Define η as the number of data points to be truncated, and its expression is: ， wherein, denotes the proportion of truncation, denotes the floor function; Definitions is the centroid of the pth subband after the truncated mean method is updated, and its expression is ， when At this point, the truncated mean method is equivalent to the arithmetic mean method; The strategy that updates the centroid by selecting the one with the largest average profile coefficient is expressed as follows: ， wherein, indicates the use of the average profile coefficient after the policy update of the centroid; S1.3.4 Iteration terminates; When the K-means++ algorithm iteration process meets any one of the following conditions, i.e., the centroid no longer changes, the silhouette coefficient changes less than a certain set threshold ε, or the maximum number of iterations T of the algorithm is reached max , the K-means++ algorithm terminates iteration and outputs the optimal sub-band partition result ; S2 is a bit allocation based on an improved greedy algorithm: Since all subcarriers within a subband use the same modulation scheme, the definition is... Indicates the transmit power of the p-th subband: ， Among them, P p This represents the power of the p-th subband. b represents the signal-to-noise ratio threshold for different modulation schemes. p b represents the number of bits. p =1,2,3,4, corresponding to the modulation schemes BPSK, QPSK, 8PSK, and 16QAM, respectively; These represent the manually set signal-to-noise ratio (SNR) thresholds for BPSK, QPSK, 8PSK, and 16QAM, respectively. Their values ​​cover the actual SNR range of the channel. Furthermore, since these four modulation schemes progressively increase in order and their SNR requirements gradually increase, these thresholds are set accordingly. N0 represents the power spectral density of the noise. The average channel gain of the p-th subband is obtained by averaging the channel gains of all subcarriers within that subband. ， Among them, H p,l Let l represent the channel gain of the l-th subcarrier within the i-th subband, where l represents the sequence index of the subcarrier, l=1,2,…N p ; Definitions Subband power increment when bit is increased by 1: ； S2.1 Algorithm Initialization; First, set b p =1, meaning that all subbands are allocated at least 1 bit and BPSK modulation is used; Then, calculate the initial power increment when allocating 2 bits for each subband: ， Define Q as the set of system power increments, used to store the power increments of all sub-bands. And record the sub-band sequence index at this time. The expression for this set is: ， Calculate the initial system total power P at this time T and the system bit error rate E: ， in, This indicates that the p-th subband is assigned to b. p Bits and the bit error rate when using the corresponding modulation method. This represents the bit error rate when the p-th subband uses BPSK modulation; S2.2 Take out the sub-band index p with the minimum power increment from Q * ; Definition of p * is the index of the subband with the minimum power increment in Q, which is expressed as ， Check bit limits, if Then remove index p from Q. * Record the error and repeat step S2.2; otherwise, proceed to the next step. S2.3 Update bit allocation and modulation scheme; tentative setup That is, try to be the pth * Each subband is allocated one more bit and uses a higher-order modulation scheme; Calculate the corresponding power increment and update the total system power. and system bit error rate Their expressions are as follows: ， At the same time, check the power and bit error rate limits: if P0 and E0 represent the manually set power threshold and bit error rate threshold, respectively. Using this modulation method, the following will be achieved: Updated to Simultaneously update and Otherwise, revert to the original modulation scheme and maintain b. p* Remain unchanged, and remove the record with index p* from Q; S2.4 Updates the system power increment set Q; If b p* <4, you can continue to add bits and calculate. The value of b is updated and the power increment value at index p* in Q is updated; if b p* =4, the maximum bit allocation has been reached, remove the record with index p* from Q; Repeat the iterative operations of S2.2, S2.3, and S2.4 above until Q is an empty set, then terminate the iterative process and determine the information bits and modulation scheme transmitted on each subcarrier of the final FBMC-SS system; S3 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion; S4 calculates the data transmission rate of the transmitter in the FBMC-SS system.

2. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: In S1.3.3, the truncation ratio Pick .

3. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: In S1.3.4, the threshold ε is set to 0.

01.

4. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: In S1.3.4, the maximum number of iterations T of the algorithm max The reference value range is [30, 100].

5. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: In S2.3, the manually set power threshold and bit error rate thresholds P0 and E0 are set according to the transmitter's maximum power limit and the system's bit error rate requirements.

6. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 5, characterized in that: In S2.3, the manually set power threshold and bit error rate thresholds P0 and E0 are taken as follows: .

7. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: The process by which S3 generates the transmit signal of the FBMC-SS system through shaping filtering and up-conversion is as follows: Definition s k (t) represents s k [n] is the transmitted symbol after upsampling, which is expressed as ， Among them, s k [n] represents the transmitted symbol of the original information bits s[n] on the k-th subcarrier after steps S1 and S2; k represents the original sequence index of the subcarrier, k=1,2,…,N; n represents the discrete time sequence index; T s For periodicity, δ(t-nT) s ) indicates that T s A periodic impulse train sequence; Define x(t) as the transmitted signal of the FBMC-SS system, which is composed of the s signals on each subcarrier. k [n] is obtained by upsampling, shaping filtering, and upconversion, followed by time-domain superposition. Its expression is: ， Where h(t) represents the prototype filter; γ k The phase perturbation factor has an amplitude of Phase at The upper part follows a uniform random distribution; The center frequency f of the k-th subcarrier is represented. k That is, up-conversion.

8. The FBMC-SS non-uniform subband adaptive modulation method based on clustering-greedy optimization according to claim 1, characterized in that: The process of S4 calculating the data transmission rate of the FBMC-SS system transmitter is as follows: Since the p-th subband contains N p There are 10 subcarriers, and all subcarriers within the same subband use the same modulation scheme and are allocated the same number of bits (b). p Then the p-th subband in each period T s The total number of bits transmitted internally is N p b p Define R p This represents the data transmission rate of the p-th subband: ， Definition of R total denotes the total data transmission rate of the FBMC-SS system transmitter, which is the sum of the data transmission rates of all P subbands: 。

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