ICAN-oriented multi-satellite parallel access method

Abstract

The invention relates to the technical field of satellite communication, in particular to an ICAN-oriented multi-satellite parallel access method, which not only ensures the throughput of a communication user, but also meets the positioning precision of a navigation user, and is characterized by comprising the following steps of: firstly, establishing a ZC-NOMA waveform-based parallel multi-satellite access CMSA architecture; a plurality of satellites provide navigation and communication services for users in the coverage area at the same time; at a receiving end, through a subcarrier and power distribution CMSSP algorithm under parallel satellite access, the total throughput of a communication user is maximized within the maximum allowable transmission power, and the positioning precision requirement of a navigation user and the rate requirement of the communication user are met at the same time; wherein the subcarrier and power distribution CMSSP algorithm under parallel satellite access comprises a subcarrier distribution method and a power distribution method, for power distribution, a difference approximation method of two concave functions is adopted to convert a non-convex problem into a solvable convex problem, and for subcarrier distribution, a dual-stage adaptive matching subcarrier distribution DAMSA algorithm is introduced.

Description

Technical field:

[0001] The invention relates to the field of satellite communication technology, in particular to an ICAN-oriented multi-satellite parallel access method which not only guarantees the throughput of communication users but also satisfies the positioning accuracy of navigation users. Background technology:

[0002] The Global Navigation Satellite System (GNSS) is a critical space infrastructure that provides positioning services to numerous areas around the world. However, its reliability in dense urban and indoor environments is compromised by multipath and non-line-of-sight (NLOS) propagation and low carrier-to-noise ratio. The growing demand for high-precision positioning from a large user community has stimulated interest in enhancing GNSS services by integrating multiple technologies.

[0003] The navigation performance of GNSS is usually related to two factors: accuracy and availability. The former is evaluated by positioning error, and the latter is measured by applicable time. Therefore, improving the navigation performance of GNSS is crucial to enhancing the positioning accuracy of vehicles. Typically, navigation satellites are located in medium-high orbits, with altitudes of 19 to 35 kilometers. This long-distance propagation weakens the strength of the GNSS signal received on the earth (only about -133 to -122dBm). In addition, GNSS navigation signals are susceptible to various unexpected conditions such as satellite clock errors, ephemeris errors, ionospheric and tropospheric delays. Therefore, the actual positioning accuracy of GNSS is usually about 10 meters outdoors.

[0004] Low Earth Orbit satellites (LEO satellites) offer a promising solution to improve the availability and accuracy of navigation systems. The inherent advantages of LEO satellites in terms of signal strength, geometric accuracy, and fast convergence make them an attractive option for enhancing GNSS services. Moreover, the strong interest in LEO satellites to provide widespread coverage and flexible, cost-effective connectivity fits well with the Beyond 5G (B5G) paradigm. This trend is evidenced by the more than 11 emerging broadband constellations under development, providing a total data throughput of approximately 30Tbps. Unlike terrestrial cellular networks, satellite communications are not constrained by complex geographical conditions and are able to operate in remote areas that cannot be reached by terrestrial networks, such as forests, deserts, and oceans. In addition, satellites deployed outside the Earth’s atmosphere are inherently resilient, minimizing the impact of natural disasters or unforeseen events, thereby ensuring high communication reliability. This advancement in navigation and communications highlights the potential of LEO satellites in integrated solutions, leveraging the synergistic relationship between these technologies. Therefore, the concept of Integrated Communication and Navigation (NAVCOM) was born, which aims to merge communication and navigation functions into a unified system. By leveraging the synergy between these areas, the NAVCOM system is expected to improve performance, increase efficiency and enhance reliability, while providing a scalable and interoperable platform for future technological advances.

[0005] The novel ICAN waveform named ZC-NOMA superimposes a communication signal that occupies only part of the carrier on top of a broadband navigation signal in the shape of Orthogonal Frequency-Division Multiplexing (OFDM), facilitating the integration of communication and navigation functions. Considering that the navigation signal waveform is fixed and known to the receiver, communication users can easily eliminate interference with the navigation signal, thereby reducing the overall interference level of communication users. Summary of the invention:

[0006] The present invention takes into account the mutual interference between navigation and communication signals, and proposes an ICAN-oriented multi-satellite parallel access method that can solve the inter-satellite interference (ISI) caused by parallel satellite access, which not only guarantees the throughput of communication users but also meets the positioning accuracy of navigation users.

[0007] The present invention is achieved by the following measures:

[0008] A multi-satellite parallel access method for ICAN is characterized in that, firstly, a parallel multi-satellite access CMSA architecture based on ZC-NOMA waveform is established, in which multiple satellites simultaneously provide navigation and communication services to users in the coverage area; at the receiving end, a subcarrier and power allocation CMSSP algorithm under parallel satellite access is used to maximize the total throughput of communication users within the maximum allowed transmission power, while meeting the positioning accuracy requirements of navigation users and the rate requirements of communication users;

[0009] Among them, the subcarrier and power allocation CMSSP algorithm under parallel satellite access includes a subcarrier allocation method and a power allocation method. For power allocation, the difference between two concave functions approximation method is used to transform the non-convex problem into a solvable convex problem. For subcarrier allocation, a two-stage adaptive matching subcarrier allocation DAMSA algorithm is introduced.

[0010] The present invention considers a joint multi-satellite parallel access system, in which there are at least four LEO satellites s = {s1, s2, ..., s K} Capable of broadcasting integrated communication and navigation waveforms, with K satellites and J navigation users on the ground and I communication users Consider the downlink from satellite to user, where navigation users need to receive integrated waveforms from more than four satellites to achieve navigation functions, while communication users need to receive broadcast integrated waveforms from at least one satellite and extract their communication information through demodulation, decoding and carrier mapping. Different from terrestrial networks and traditional satellite networks, each communication user can choose the number of satellites to access and the number of mapped carriers as needed, thus providing higher flexibility and redundancy for communication;

[0011] In this system, the integrated waveform of satellite broadcasting is ZC-NOMA, and the communication signals from K satellites occupy all available subcarriers {SC1, SC2, …, SC N}, for each satellite s k , which only occupies a group of consecutive subcarriers among all subcarriers where n k Satellites k The starting position of the occupied subcarrier, N k Satellites k The number of occupied subcarriers, where all subcarriers have the same subcarrier spacing, the navigation part of the signal broadcast by all satellites occupies all subcarriers, and the navigation allocations of different satellites are superimposed in the power domain. Different satellites can transmit signals at any time without synchronization. Carrier interference can be avoided by filtering each group of carriers (i.e., a group of adjacent carriers assigned to the same satellite) at the transmitting end and performing corresponding matched filtering at the receiving end;

[0012] Navigation users need to receive integrated signals from four satellites at the same time and use the navigation components in ZC-NOMA to achieve their own positioning. The main goal of communication users is to obtain the information carried on their corresponding carriers. In order to reduce the interference of navigation signals, communication users need to first receive navigation signals from all satellites and reconstruct these signals based on the prior information of navigation signals. By using the reconstructed navigation signals, the navigation components in ZC-NOMA can be eliminated, thereby obtaining independent communication signals.

[0013] Define h k,i,n For satellites k To communication users The channel coefficient on the nth subcarrier is given by Given, where g k,i represents the distance-dependent large-scale fading, β k,i,n represents the small-scale fading effect, Satellites k The transmit antenna gain, Is a communication user The receiving antenna gain is defined as Δ = {δ k,n,i}, where δ k,n,i ∈{0,1}, that is, when δ k,n,i =1, indicating satellite s k The nth subcarrier and the communication user association and vice versa;

[0014] Let σ k,n,i Indicates communication user In subcarrier SC n SNR on:

[0015]

[0016] in Representative satellites k For communication user ui C In subcarrier SC n The power distributed on the k t (n) is satellite s k In subcarrier SC n The frequency response of the filter used on represents the noise power, where N0 is the power spectral density of random noise, Representative communication user In conjunction with satellites k Interference encountered during communication, here Indicates the interference of navigation signals from all satellites, and Represents the interference caused by spectrum leakage due to asynchronous access of multiple satellites;

[0017]

[0018] where α k,i is the interference elimination coefficient formed by the communication user based on the known information of the navigation signal; Ignoring the influence of carrier frequency offset (CFO) and only considering the influence of time offset (TO), the closed-form expression of inter-satellite interference caused by asynchronous access is given:

[0019]

[0020] Because the user The signals received from K satellites are not perfectly synchronized, resulting in interference It contains three parts. Representative satellites k′ In receiving satellite k Lambda th Symbol, for communication users Subcarrier SC n From SC n′ The interference generated here is

[0021]

[0022] in,

[0023]

[0024] represents the N-point discrete Fourier transform (DFT) of vector v. Similarly, the N-point inverse discrete Fourier transform (IDFT) of vector v is given by:

[0025]

[0026] in,

[0027]

[0028] in

[0029] and

[0030] Here, L f Represents the filter length, L chi represents the channel length, Δ kk′ =|t i,k -t i,k′ | indicates satellitesk With satellites k′ For communication users The time difference of i,k Indicates the satellite s k =(s x,k ,s y,k ,s z,k ) T Transmit to communication users TOA;

[0031] Here, c is the signal propagation speed, d j,k yes With s k The distance between

[0032] Available from satellite k In carrier SC n Communication users of the service The communication rate is:

[0033] r k,n,i =Δf·log2(1+ψ k,n,i ) (11),

[0034] Where Δf is the subcarrier spacing, the total communication rate in the system can be expressed as:

[0035]

[0036] For each communication user The communication rate is,

[0037]

[0038] Navigation user in the present invention Positioning is achieved by simultaneously receiving navigation signals from satellites. In this process, the user independently detects signals from different positioning nodes, so the TOA measurement errors are unrelated. Therefore, the ranging information provided by different positioning nodes can be directly superimposed. Based on the mean square error (MSE) lower bound SPEB of TOA positioning, the navigation user SPEB satisfy:

[0039] in, yes The position of the matrix

[0040] Is a navigation user The integrated equivalent Fisher information matrix (IEFIM) is the sum of the ranging information provided by K satellites within the visible range, that is, Represents navigation user From satellites k Ranging information obtained from the transmitted signal;

[0041] The ranging information is a matrix defined as

[0042] Among them, q j,k is the direction vector, which depends only on a k and u j The angular relationship between j,k and the pitch angle φ j,k Determined by a system of nonlinear equations

[0043] And μ j,k is a scalar, representing the satellite s k To navigation user The ranging signal strength depends on the transmission parameters and channel conditions of the channel;

[0044] The signal intensity of SPEB is expressed as

[0045] It is the sum of the signal strengths on N carriers, where is the channel coefficient, and β represents the mean square bandwidth of p(t). OFDM shaped pulses are usually sinc functions, so the mean square bandwidth can be expressed as

[0046] represents the navigation power of the kth satellite. It should be noted that for all subcarriers of the same satellite, the power level is specific, represents the power of random noise, Represents navigation user In receiving, synchronizing and acquiring satellite k The signal is subjected to non-noise interference. Since the mutual correlation coefficient of ZC sequences with different root values ​​is zero, the interference of navigation signals from other satellites can be ignored. Therefore, It is composed only of interference caused by communication signals on the same carrier, that is, SC n ;therefore,

[0047] in Represents the satellite k To navigation user The channel coefficients, yes The receiving antenna gain.

[0048] The optimization problem (20) in the present invention is as follows:

[0049]

[0050] The goal is to maximize the sum of the channel capacities of all communication users by allocating communication and navigation power to each subcarrier and assigning users and subcarriers to satellites under the CMSA-ICAN paradigm, where represents the navigation power of the kth satellite on each subcarrier, represents the power of the nth subcarrier of the kth satellite allocated to the i-th communication user, and δ k,n,i is the carrier allocation factor, where δ k,n,i =1 means that the nth subcarrier of the kth satellite is allocated to the i-th user, and vice versa;

[0051] Constraint C1 ensures that the navigation user The SPEB should be less than the threshold Constraint C2 ensures communication users The channel capacity is greater than its minimum channel capacity requirement Constraint C3 ensures that the sum of the communication and navigation power allocated to satellite k is less than the maximum power P that the satellite can provide k ,Constraint C4 indicates that the carrier allocation factor δk,n,i is a binary variable, constraint C5 ensures that each subcarrier can be assigned to at most one satellite and one user, constraints C6 and C7 ensure that the communication and navigation powers are both positive, and constraint C8 ensures that the navigation user u j From satellites k The received navigation signal strength is greater than its receiving threshold Θ j , the threshold is determined by the receiver performance, and constraint C9 guarantees the upper limit of the number of carriers that each communication user can use.

[0052] The present invention solves the sub-problems of power allocation and subcarrier allocation independently by iteration until convergence, and finally obtains the desired optimal solution by iteration, wherein the power allocation algorithm PA is as follows:

[0053] Step 1: Substitute equation (9) Convert to formula (31):

[0054]

[0055] Transform constraint C2 into equation (32):

[0056]

[0057] Using the quadratic transformation, we get formula (44):

[0058]

[0059] Introduce a new variable t k,n,jTo replace the We get formula (46):

[0060]

[0061] Step 2: Initialize variables in the feasible region and t k,n,j ,

[0062] Repeatedly use formula (28) to update

[0063]

[0064] Use equation (34) to update

[0065]

[0066] Use equation (43) to update

[0067]

[0068] For fixed By solving equation (48), we can update and t k,n,j , until the convergence criterion or the maximum number of iterations is reached.

[0069] In order to effectively solve the subcarrier allocation problem SA, the present invention proposes a DAMSA algorithm, which includes two components: DAMSA-I and DAMSA-II. When executed, initially, DAMSA-I is used to establish a stable match. If it cannot be achieved, the algorithm will enter the second stage of DAMSA, in which a polynomial time algorithm is designed in the first stage to find a stable match between subcarriers and users. If a stable match cannot be achieved, the algorithm will report that it does not exist;

[0070] Firstly, we introduce the non-negative loss capacity ΔC(i) to quantify the communication user The difference between the current data rate achieved under existing matching and its target data rate:

[0071] The invariants that need to be maintained during the matching process are defined as follows:

[0072]

[0073] in Indicates the communication user The single carrier data rate of the currently matched m-th subcarrier, a im is the index of the mth matching subcarrier,

[0074]

[0075] Initially, ΔC(i) is set as the threshold As the allocation process proceeds, each subcarrier is assigned to , the value of ΔC(i) is dynamically adjusted. When a new subcarrier is successfully allocated and invariant A is maintained, ΔC(i) is updated accordingly and reduces the data rate contribution of the newly added subcarrier. However, if accepting a new subcarrier causes invariant A to be violated (i.e., the number of allocated subcarriers exceeds the limit), some subcarriers must be removed from the matching list to re-satisfy invariant A. In this case, the reduction in ΔC(i) is the rate difference provided by the newly added and removed subcarriers. In order to always meet invariant B, ΔC(i) should be updated in a decreasing manner until it approaches zero, and the communication user Select the subcarrier with the lowest rate in the rejection matching list μ(i).

[0076] The present invention optimizes subcarriers, but is not very favorable from the user's perspective, which is often referred to as "best subcarrier and worst user". To illustrate this point, consider a given user The two stable matching schemes μ and μ′ are expressed as:

[0077]

[0078] and

[0079] If there exists an index m'(1≤m'≤M) where for all j<m', And at index $m'$, mean Then the user In matching μ, it is considered lexicographically superior to in μ'. This situation indicates that, at the first different index m', matching μ provides a more preferred result for the user than μ'. This property stems from the fact that the algorithm starts from the subcarrier point of view and makes proposals to the communicating user, while the user has the right to accept or reject these proposals without having the right to make proposals from his own point of view;

[0080] When DAMSA-I cannot find a stable match, a suboptimal DAMSA-II is further proposed to solve the problem. Unlike DAMSA-I, DAMSA-II aims to meet the minimum capacity requirements of all users. When the rate requirement of a communication user is met, the allocation of subcarriers to it is suspended until the requirements of all communication users are met.

[0081] Compared with the prior art, the present invention not only ensures the throughput of communication users, but also satisfies the positioning accuracy of navigation users. By finely adjusting the power allocation and subcarrier allocation strategies, the operating performance of the entire system is greatly optimized, achieving an effective balance between navigation and communication. Description of the drawings:

[0082] Figure 1 This is the CMSA-ICAN architecture diagram of the present invention.

[0083] Figure 2 It is a schematic diagram of the ZC-NOMA time-frequency structure in the present invention.

[0084] Figure 3 2 is a schematic diagram of multi-satellite coverage analysis in an embodiment of the present invention.

[0085] Figure 4 It is the convergence curve in the embodiment of the present invention.

[0086] Figure 5 Schematic diagram of the effect of satellite power on the sum rate in an embodiment of the present invention, wherein Figure 5 In (a), the interference elimination coefficient α = {0, 0.97, 0.98, 0.99, 1}, Figure 5 (b) Navigation positioning accuracy

[0087] Figure 6 is the effect of the number of satellite access users on the sum rate in the embodiment of the present invention, where Figure 6 (a) is a schematic diagram showing the effect of the number of communication users on the sum rate. Figure 6 (b) Schematic diagram of the impact of the number of navigation users on the sum rate.

[0088] Figure 7 Schematic diagram of the effect of filtering parameters on the combined rate of communication users in an embodiment of the present invention.

[0089] Figure 8 It is a curve diagram showing the influence of the communication user rate demand on the sum rate in an embodiment of the present invention.

[0090] Fig. 9 It is a schematic diagram of the interruption probability under different power and QoS requirements in an embodiment of the present invention. Specific implementation method:

[0091] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0092] The present invention considers a Figure 1 The joint multi-satellite parallel access scenario shown in the figure, in this system, there are at least four LEO satellites s = {s1, s2, ..., s K} Capable of broadcasting integrated communications and navigation waveforms, with K satellites. On the ground, there are J navigation users and I communication users

[0093] Consider the downlink from the satellite to the user, where the navigation user needs to receive integrated waveforms from more than four satellites to achieve navigation functions, while the communication user needs to receive the broadcast integrated waveform from at least one satellite and extract their communication information through demodulation, decoding and carrier mapping. In particular, unlike terrestrial networks and traditional satellite networks, each communication user can choose the number of satellites to access and the number of mapped carriers as needed, thereby providing higher flexibility and redundancy for communication.

[0094] In this system, the integrated waveform of satellite broadcasting is ZC-NOMA, and its time-frequency structure is as follows: Figure 2 As shown in the figure, the communication signals from K satellites occupy all available subcarriers {SC1, SC2, …, SC N}. For each satellite s k , which only occupies a group of consecutive subcarriers among all subcarriers where n k Satellites k occupy

[0095] The starting position of the subcarrier, N k Satellites k The number of subcarriers occupied. All subcarriers have the same subcarrier spacing. The navigation part of the signal broadcast by all satellites occupies all subcarriers, and the navigation allocations of different satellites are superimposed in the power domain. Different satellites can transmit signals at any time without synchronization. Carrier interference can be avoided by filtering each group of carriers (i.e. a group of adjacent carriers assigned to the same satellite) at the transmitting end and performing corresponding matched filtering at the receiving end.

[0096] Navigation users need to receive integrated signals from four satellites at the same time and use the navigation components in ZC-NOMA to achieve their own positioning. The main goal of communication users is to obtain the information carried on their corresponding carriers. In order to reduce the interference of navigation signals, communication users need to first receive the navigation signals of all satellites and reconstruct these signals based on the prior information of the navigation signals. By using the reconstructed navigation signals, they can eliminate the navigation components in ZC-NOMA and obtain independent communication signals.

[0097] We define h k,i,n For satellites k To communication users The channel coefficient on the nth subcarrier is given by Given, where gk,i represents the distance-dependent large-scale fading, β k,i,n represents the small-scale fading effect, Satellites k The transmit antenna gain, Is a communication user In addition, we define the subcarrier-to-user correlation coefficient as Δ = {δ k,n,i}, where δ k,n,i ∈{0,1}, that is, when δ k,n,i =1, indicating satellite s k The nth subcarrier and the communication user association and vice versa.

[0098] Let σ k,n,i Indicates communication user In subcarrier SC n SNR on:

[0099]

[0100] in Representative satellites k For communication user ui C In subcarrier SC n The power distributed on the k t (n) is satellite s k In subcarrier SC n The frequency response of the filter used on represents the noise power, where N0 is the power spectral density of random noise, Representative communication user In conjunction with satellites k Interference encountered during communication. Indicates the interference of navigation signals from all satellites, and Represents the interference caused by spectrum leakage due to asynchronous access of multiple satellites.

[0101] where α k,i It is the interference cancellation coefficient formed by the communication user based on the known information of the navigation signal.

[0102] for The prior art has proposed a multiphase analysis method to analyze the interference problem under non-ideal synchronization conditions, and added an additional time-frequency transformation. Based on this method, the influence of carrier frequency offset (CFO) is ignored, and only the influence of time offset (TO) is considered, giving a closed-form expression of inter-satellite interference caused by asynchronous access.

[0103]

[0104] Because the user The signals received from K satellites are not perfectly synchronized, resulting in interference It contains three parts. Representative satellites k′ In receiving satellite k Lambda th Symbol, for communication users Subcarrier SC n From SC n′ The interference generated.

[0105] Here,

[0106]

[0107] in,

[0108]

[0109] represents the N-point discrete Fourier transform (DFT) of vector v. Similarly, the N-point inverse discrete Fourier transform (IDFT) of vector v is given by:

[0110]

[0111] in,

[0112]

[0113] in

[0114]

[0115] and

[0116]

[0117] Here, L f Represents the filter length, L chi represents the channel length, Δ kk′ =|t i,k -t i,k′ | indicates satellites k With satellites k′ For communication users The time difference of i,k Indicates the satellite s k =(s x,k ,s y,k ,s z,k ) T Transmit to communication users TOA.

[0118]

[0119] Here, c is the signal propagation speed, d j,k yes With s k The distance between.

[0120] Therefore, we can get the k In carrier SC n Communication users of the service The communication rate is

[0121] r k,n,i =Δf·log2(1+ψ k,n,i )(11), where Δf is the subcarrier spacing. The total communication rate in the system can be expressed as

[0122] For each communication user Their communication rate is

[0123] Navigation User Positioning is achieved by simultaneously receiving navigation signals from satellites. In this process, the user independently detects signals from different positioning nodes, so the TOA measurement errors are uncorrelated, and the ranging information provided by different positioning nodes can be directly superimposed. Based on the mean square error (MSE) lower bound SPEB of TOA positioning, the navigation user SPEB satisfy

[0124] in, yes position estimate.

[0125] matrix Is a navigation user The integrated equivalent Fisher information matrix (IEFIM) is the sum of the ranging information provided by K satellites within the visible range, that is, Represents navigation user From satellites k The transmitted signal obtains the ranging information.

[0126] The ranging information is a matrix defined as

[0127]

[0128] Among them, q j,k is the direction vector, which depends only on a k and u j The angular relationship betweenj,k and the pitch angle φ j,k Determined by a system of nonlinear equations:

[0129]

[0130] And μ j,k is a scalar, representing the satellite s k To navigation user The ranging signal strength depends on the channel transmission parameters and channel conditions.

[0131] The signal strength of SPEB is expressed as:

[0132]

[0133] It is the sum of the signal strengths on N carriers, where is the channel coefficient, and β represents the mean square bandwidth of p(t). OFDM shaped pulses are usually sinc functions, so the mean square bandwidth can be expressed as

[0134]

[0135] represents the navigation power of the kth satellite. It should be noted that for all subcarriers of the same satellite, the power level is specific, Represents the power of random noise.

[0136] Represents navigation user In receiving, synchronizing and acquiring satellite k The signal is subjected to non-noise interference. Since the mutual correlation coefficient of ZC sequences with different root values ​​is zero, the interference of navigation signals from other satellites can be ignored. Therefore, It is composed only of interference caused by communication signals on the same carrier, that is, SC n .

[0137] therefore,

[0138] in Represents the satellite k To navigation user The channel coefficients, yes The receiving antenna gain.

[0139] The problem is modeled as follows:

[0140]

[0141] The goal of the optimization problem (20) is to maximize the sum of the channel capacities of all communication users by allocating communication and navigation power to each subcarrier and assigning users and subcarriers to satellites under the CMSA-ICAN paradigm. represents the navigation power of the kth satellite on each subcarrier, represents the power of the nth subcarrier of the kth satellite allocated to the i-th communication user, and δ k,n,i is the carrier allocation factor, where δ k,n,i =1 means that the nth subcarrier of the kth satellite is allocated to the i-th user, and vice versa.

[0142] Constraint C1 ensures that the navigation user The SPEB should be less than the threshold Constraint C2 ensures communication users The channel capacity is greater than its minimum channel capacity requirement Constraint C3 ensures that the sum of the communication and navigation power allocated to satellite k is less than the maximum power P that the satellite can provide k Constraint C4 indicates that the carrier allocation factor δk,n,i is a binary variable, constraint C5 ensures that each subcarrier can be allocated to at most one satellite and one user, constraints C6 and C7 ensure that the communication and navigation powers are positive, and constraint C8 ensures that the navigation user u j From satellites k The received navigation signal strength is greater than its receiving threshold Θ j , the threshold is determined by the receiver performance, and constraint C9 guarantees the upper limit of the number of carriers that each communication user can use.

[0143] The original optimization problem is difficult to find the optimal solution due to its non-convex and nonlinear characteristics. Therefore, we propose an iterative carrier and power allocation algorithm called CMSSP, which solves the sub-problems of power allocation and sub-carrier allocation independently by iteration until convergence, and finally obtains the desired optimal solution through iteration.

[0144]

[0145] PA (power allocation) and SA (subcarrier allocation) correspond to Prob1 and Prob2 respectively. The PA problem can be described as:

[0146]

[0147] stC1-C3,C6-C8 (21),

[0148] The SA problem can be described as

[0149]

[0150] stC2,C4,C5,C9 (22),

[0151] However, we find that these two sub-problems are still difficult to solve due to the existence of nonlinear and non-convex characteristics. Therefore, corresponding algorithms are proposed for the PA and SA sub-problems respectively.

[0152] First, consider the power allocation problem, in which power allocation is performed based on the carrier allocation results obtained in the previous iteration. Due to the non-convexity of the objective function and the constraints, we use the DC approximation method to transform the PA optimization problem into a solvable concave function problem. Therefore, the objective function of the PA can be equivalently rewritten in DC form:

[0153] γ=T(P com ,P nav )-G(P com ,P nav ) (twenty three),

[0154] Where T(P) and G(P) are two concave functions, respectively expressed by the following formulas:

[0155]

[0156] and

[0157]

[0158] in,

[0159]

[0160] and

[0161]

[0162] in, is for For k′ Carrier SC n′ to k Carrier SC n Since (23) is composed of the difference between two concave functions, it is not a definite concave function. The first-order Taylor approximation is used to approximate G(P) as a linear function, which is expressed as:

[0163] in,

[0164] and

[0165] Based on this, the PA problem is transformed into a concave function, and formula (23) can be restated as:

[0166] The same strategy applies to constraint C2, which can be transformed into:

[0167] in,

[0168] and in,

[0169] G 2,i (P com ,P nav ) respectively and Taking the derivative, we get and Therefore, by adopting the DC approximation, constraint C2 is successfully converted into a convex constraint.

[0170] At this time, the form of the PA problem is:

[0171] In the PA problem, we find that constraints C1 and C8 are still non-convex constraints.

[0172] Lemma 1: Constraint C1 is a non-convex constraint.

[0173] Proof: Notice that About is a convex function, since is μ j, k, which is also related to μ j,k However, due to μ j,k and and The complex nonlinear relationship between j,k About and A non-convex function, which eventually makes Become about and Non-convex function of .

[0174] For (17), an equivalent treatment is performed by performing a quadratic transformation on the numerator and denominator of each ratio term.

[0175] and at this time

[0176] Through the second transformation we can get:

[0177] Let y k,n,j pass Iterate and update, and take y k,n,j The closed form expression is:

[0178] About is a convex function, so constraint C1 becomes

[0179] in,

[0180] Among them A k,j,n and B k,j,n It's about P nav and P com The affine function of . k,n,j When fixed, due to (39) The coefficient of is positive and therefore is a concave function, is an affine function, so we know is a concave function. Therefore It's about P com and P nav The constraint C1 is a non-convex constraint. To ensure that C1 is a convex constraint, we introduce a new variable t k,n,j To replace (45) therefore

[0181] And the constraints must be satisfied

[0182]

[0183] Lemma 2: Under constraint (47), (44) is a convex constraint, and there is an equivalent transformation between it and constraint C1. Proof: For a fixed It is about t,P com and P nav In addition, since f(m) is a convex and non-increasing function, is a concave and non-decreasing function, so constraint (47) ensures that t k,n,j and are equivalent. Moreover, at the optimal y * Under this condition, the first-order conditions of constraint C1 and (44) are the same, and the iterative algorithm will make (44) converge to the same stable point as C1, thus ensuring the equivalence of the quadratic transformation. At the same time, tr{(·) -1} is a convex function, so it is determined that under constraint (47), (44) is a convex constraint, and there is an equivalent transformation between it and constraint C1.

[0184] At this point, a solvable PA problem can be obtained, which can be solved using mature convex optimization tools.

[0185] The complete PA algorithm is shown in Algorithm 1.

[0186] Algorithm 1 Power Allocation Algorithm PA

[0187]

[0188] To effectively solve the SA (subcarrier assignment) problem specified in (22), this paper proposes the DAMSA algorithm, which consists of two important components: DAMSA-I and DAMSA-II. Initially, DAMSA-I is used to establish a stable matching. If it cannot be achieved, the algorithm will enter the second stage of DAMSA, which aims to provide a suboptimal but practical matching solution. This bifurcation strategy ensures that the SA challenge is solved robustly, with a focus on stability but also providing effective alternatives to maintain system performance.

[0189] The classical Gale-Shapley algorithm falls short in matching processes subject to upper and lower bounds. In the context of our problem, constraints such as the minimum throughput requirement for each user and the maximum number of accessible subcarriers make the Gale-Shapley algorithm infeasible. A polynomial-time algorithm is designed in the first phase to find a stable matching between subcarriers and users. If a stable matching cannot be achieved, the algorithm reports that one does not exist.

[0190] The overall approach of the present invention is to allow subcarriers to begin pairing with communicating users according to their preferences. Users respond to these contacts by accepting or rejecting the pairing according to specific criteria (described in detail later). The rejected subcarrier then approaches the next user in its list. This process continues until each subcarrier is paired or its list is exhausted. The algorithm finally determines the stability of the pairing by evaluating whether the final pairing meets the upper and lower limits defined by all categories. If these criteria are met, the pairing is considered stable; otherwise, a stable pairing is considered to not exist in the given scenario.

[0191] The effectiveness of the algorithm DAMSA-I relies heavily on the strategy of the communicating user to accept or reject subcarrier proposals. This decision is guided by constraints C2 and C9, and the main consideration is whether accepting additional subcarriers causes the total number of allocated subcarriers to exceed the user's limit. If the limit is exceeded, the protocol requires re-evaluation of the current match to potentially reject existing subcarriers (not necessarily those that were recently proposed). This mechanism ensures compliance with the defined constraints and improves the overall efficiency of the subcarrier allocation process.

[0192] Next, we solve the constraints of the SA problem by defining invariants that must hold during the two matching processes. We introduce a “deficit capacity”, denoted as ΔC(i), which is a non-negative value that quantifies the number of communicating users. The difference between the current data rate achieved under existing matching and its target data rate.

[0193] The invariants that need to be maintained during the matching process are defined as follows:

[0194] in

[0195] Indicates the communication user The single carrier data rate of the currently matched m-th subcarrier, a im is the index of the mth matching subcarrier.

[0196]

[0197] Initially, ΔC(i) is set as the threshold As the allocation process proceeds, each subcarrier is assigned to Specifically, when a new subcarrier is successfully allocated and the invariant A is maintained, ΔC(i) is updated accordingly and reduces the data rate contribution of the newly added subcarrier.

[0198] Algorithm 2 DAMS-I

[0199]

[0200] However, if accepting new subcarriers causes invariant A to be violated (i.e., the number of allocated subcarriers exceeds the limit), some subcarriers must be removed from the matching list to re-satisfy invariant A. In this case, ΔC(i) is reduced by the rate difference provided by the newly added and removed subcarriers. In order to always satisfy invariant B, ΔC(i) should be updated in a decreasing manner until it approaches zero. In our algorithm, the communicating users The subcarrier with the lowest rate in the rejection matching list μ(i) is selected. The pseudo code of the algorithm is described in detail in Algorithm 2.

[0201] Note that our algorithm is optimized for subcarriers, but not so favorable from the user perspective, often referred to as “subcarrier-optimal and user-worst”. To illustrate this, consider a given user The two stable matching schemes μ and μ' are expressed as:

[0202] and If there exists an index m'(1≤m'≤M) where for all j<m', And at index $m'$, mean Then the user In matching μ, it is considered lexicographically better than in μ'. This case indicates that at the first different index m', matching μ provides a more preferred result for the user than μ'. This property stems from the fact that the algorithm starts from the subcarrier point of view and makes proposals to the communicating user, who has the right to accept or reject these proposals, without having the right to make proposals from his own point of view.

[0203] When DAMSA-I cannot find a stable match, we further propose the suboptimal DAMSA-II to solve the problem. Unlike DAMSA-I, DAMSA-II aims to meet the minimum capacity requirements of all users. When the rate requirement of a communication user is met, the allocation of subcarriers to it is suspended until the requirements of all communication users are met.

[0204] Algorithm 3 DAMS-II

[0205]

[0206] The detailed description of the DAMS-II algorithm is given in Algorithm 3.

[0207] Next, the performance of SMSSP algorithm in CMSA-ICAN is verified and evaluated through simulation.

[0208] In this example, four satellites are distributed in an orbital plane, 500 km above the ground, to ensure visibility between the satellite and the observer (ground station). The horizontal plane (i.e., pitch angle) ε0 between the satellite and the observer should be at least 10$ degrees. Since receiving navigation information requires obtaining navigation messages from at least four satellites at the same time, we only consider the area that can be covered by four satellites at the same time. The radius R0 of the LEO ground coverage area can be expressed as:

[0209]

[0210] Where R e represents the radius of the Earth, H s represents the distance from the LEO satellite to the ground. For ε0 = 10°, according to equation (51), R0 is 1547 km.

[0211] Figure 3 The figure shows the common coverage area of ​​multiple satellites. When all satellites are distributed in a radius of R s When the common coverage area is in the plane of u The central projection points of the two planes overlap each other, and we can get Ru =R0-R s Therefore, when communication and navigation users are distributed in the radius R u With a range of 947km, they can maintain connection with four satellites simultaneously.

[0212] This example verifies the convergence characteristics of the proposed SMSSP algorithm. Figure 4 The SMSSP algorithm is used to calculate the maximum navigation user accuracy under different conditions when the total satellite power is P. k =46dBm. From the figure, we can see that for the navigation user positioning accuracy, the communication user and rate converge quickly after three iterations. When the positioning accuracy is 10m, a total rate of 1.52Mbps can be obtained, and it can be seen that the decrease in navigation positioning accuracy will be conducive to the improvement of the communication rate.

[0213] Figure 5 The maximum satellite power P k Impact on the total rate of communication users. Figure 5 (a) shows how the sum rate changes with the communication user power under different interference elimination factors. The two lines need to represent the two extreme cases of α = 0 and α = 1. α = 0 means that for the communication user, the navigation signal has not undergone any interference elimination, and the user will receive the navigation signals from four satellites at full power, forming a high-intensity interference to itself; α = 1 represents an extreme case. In this case, the communication user can completely eliminate the interference of the navigation signal based on the prior characteristics of the navigation signal, thereby eliminating the impact of the navigation signal on the communication user. It can be clearly seen from the figure that when α = 0 and P k = 48dBm, the total transmission rate of the system is only 0.43Mbps, while it can reach 1.41Mbps when α = 1. The other three curves, representing α values ​​from 0.97 to 0.99, are between these two extreme cases.

[0214] Figure 5 (b) Evaluate how the total transmission rate of communication users changes with the satellite power P under different positioning accuracy requirements of navigation users. k The four curves correspond to The navigation accuracy ranges from $m to $26$m. k =48dBm and When the total transmission rate is 1.25Mbps, When the navigation user positioning accuracy decreases from 10 meters to 18 meters, and then from 18 meters to 26 meters, the corresponding γ increases by 0.03Mbps and 0.02Mbps. This shows that as the navigation positioning accuracy decreases, the total transmission rate improvement of the same degree of accuracy reduction is also decreasing. This phenomenon is not only in P k = 48dBm, and from P k = 46dBm to 54dBm. This can be attributed to the lower power levels in the navigation part in the lower accuracy area, resulting in relatively low interference levels for the communication users and therefore less impact on the reduction in navigation accuracy.

[0215] exist Figure 6 In this paper, the variation of communication user throughput and rate with respect to the number of users is evaluated for different numbers of subcarriers. Figure 6 (a) shows the number of communication users under different subcarrier numbers N = {16, 20, 24} We observe that for a given number of users The total transmission rate γ increases significantly with the increase of the number of subcarriers N. γ increases by 0.52Mbps and 0.53Mbps, respectively, as N increases from 16 to 20 and from 20 to 24. When N = 24, γ increases with This is because the expansion of user distribution increases the flexibility of resource allocation. On the contrary, when N = 20, γ does not increase with increases with the increase of It reaches its peak at stabilized and After 14:00, it began to decline. This decline is attributed to strict communication user capacity restrictions When N=16, the trend shows starts to decrease, and the algorithm cannot Provides a feasible solution. This is because when N = 16, This means that some communication users are only assigned to the edge of the satellite filter passband, which cannot meet the minimum capacity requirement, making the algorithm unable to produce a feasible solution. This shows that the CMSSP algorithm inherently creates a "guard interval" (even if it is not explicitly specified) to avoid allocating edge subcarriers to communication users. In a strict Under the constraint, the number of supported communication users will be less than N.

[0216] Figure 7The effects of various filter types and their parameters on the total rate γ for different numbers of subcarriers are shown, where (a) the number of carriers N = 16, (b) the number of carriers N = 20, (c) the number of carriers N = 24, and (d) the number of carriers N = 28. The performance impact of two types of window functions - Hamming window and Kaiser window, as well as 3rd and 10th order Butterworth filters are evaluated. The study found that the number of subcarriers N or the maximum transmission power P k The increase of , without exception, leads to an increase of γ for all types of filters. k and N, the third-order Butterworth filter performs the worst, while the tenth-order Butterworth filter performs the best. A higher filter order not only means increased complexity, but also means a better filter shape, thereby improving performance. Comparing the combined rate under different numbers of carriers, it can be found that the increase in power has the smallest performance improvement under the third-order Butterworth filter. This is because the third-order Butterworth filter has the worst filter shape, so the increase in power cannot effectively affect the increase in the combined rate. Figure 8 The impact of communication user rate requirements on γ under different numbers of communication users is evaluated. It can be observed that when the QoS requirement is 105kbps, γ increases with the increase in the number of users. This is because more dense users mean a more flexible allocation strategy. For any value, we can observe a decrease in γ, which is in line with intuition. More stringent QoS requirements reduce the freedom of allocation, especially for The situation, compared to when When QoS increases, γ decreases rapidly, r req =117kbps, γ has dropped to the same level as The time phase is close, and as QoS continues to increase, when r req = 135 kbps, no effective feasible solution can be obtained, which means that all constraints cannot be met at this time. Figure 6 The conclusions obtained in are similar. Fig. 9 The outage probability under different power and QoS requirements is evaluated. It can be seen that when the power is constant, as r req With the increase of , the interruption probability gradually increases. At the same time, it can be seen that increasing the power can effectively reduce the interruption probability. However, for strict QoS requirements, there is still a possibility of more than 10% interruption after the satellite power reaches 52dBm.

[0217] The present invention constructs a CMSA architecture for use in low-orbit satellite ICAN scenarios. The core innovation of the CMSA framework is the use of ZC-NOMA waveforms to achieve the superposition of navigation signals and communication signals in the frequency domain. The present invention carefully designs a subcarrier and power allocation algorithm CMSSP under parallel satellite access. The algorithm greatly optimizes the operating performance of the entire system by fine-tuning the power allocation and subcarrier allocation strategies. The introduction of the CMSSP algorithm ensures that while ensuring navigation accuracy, it can also meet the high throughput requirements of communication users, achieving an effective balance between navigation and communication.

Claims

1. A multi-satellite parallel access method for ICAN, characterized in that: Firstly, a parallel multi-satellite access CMSA architecture based on the ZC-NOMA waveform is established. In this architecture, multiple satellites simultaneously provide navigation and communication services to users in the coverage area. At the receiving end, the subcarrier and power allocation CMSSP algorithm under parallel satellite access is used to maximize the total throughput of communication users within the maximum allowed transmission power, while meeting the positioning accuracy requirements of navigation users and the rate requirements of communication users. Among them, the subcarrier and power allocation CMSSP algorithm under parallel satellite access includes a subcarrier allocation method and a power allocation method. For power allocation, the difference between two concave functions approximation method is used to transform the non-convex problem into a solvable convex problem. For subcarrier allocation, a two-stage adaptive matching subcarrier allocation DAMSA algorithm is introduced.

2. The ICAN-oriented multi-satellite parallel access method according to claim 1, characterized in that: Consider a joint multi-satellite parallel access system, in which there are at least four LEO satellites s = {s1, s2, …, s K } Capable of broadcasting integrated communication and navigation waveforms, with K satellites and J navigation users on the ground and I communication users Consider the downlink from satellite to user, where navigation users need to receive integrated waveforms from more than four satellites to achieve navigation functions, while communication users need to receive broadcast integrated waveforms from at least one satellite and extract their communication information through demodulation, decoding and carrier mapping. Different from terrestrial networks and traditional satellite networks, each communication user can choose the number of satellites to access and the number of mapped carriers as needed, thus providing higher flexibility and redundancy for communication; In this system, the integrated waveform of satellite broadcasting is ZC-NOMA, and the communication signals from K satellites occupy all available subcarriers {SC1, SC2, …, SC N }, for each satellite s k , which only occupies a group of consecutive subcarriers among all subcarriers where n k Satellites k The starting position of the occupied subcarrier, N k is the number of subcarriers occupied by satellite sk, where all subcarriers have the same subcarrier spacing, the navigation part of the signal broadcast by all satellites occupies all subcarriers, and the navigation allocations of different satellites are superimposed in the power domain. Different satellites can transmit signals at any time without synchronization. Carrier interference can be avoided by filtering each group of carriers (i.e., a group of adjacent carriers assigned to the same satellite) at the transmitting end and performing corresponding matched filtering at the receiving end; Navigation users need to receive integrated signals from four satellites at the same time and use the navigation components in ZC-NOMA to achieve their own positioning. The main goal of communication users is to obtain the information carried on their corresponding carriers. In order to reduce the interference of navigation signals, communication users need to first receive navigation signals from all satellites and reconstruct these signals based on the prior information of navigation signals. By using the reconstructed navigation signals, the navigation components in ZC-NOMA can be eliminated to obtain independent communication signals. Define h k,i,n For satellites k To communication users The channel coefficient on the nth subcarrier is given by Given, where g k,i represents the distance-dependent large-scale fading, β k,i,n represents the small-scale fading effect, Satellites k The transmit antenna gain, Is a communication user The receiving antenna gain is defined as Δ = {δ k,n,i }, where δ k,n,i ∈{0,1}, that is, when δ k,n,i =1, indicating satellite s k The nth subcarrier and the communication user association and vice versa; Let σ k,n,i Indicates communication user In subcarrier SC n SNR on: in Representative satellites k For communication user ui C In subcarrier SC n The power allocated on Satellites k In subcarrier SC n The frequency response of the filter used on represents the noise power, where N0 is the power spectral density of random noise, Representative communication user In conjunction with satellites k Interference encountered during communication, here Indicates the interference of navigation signals from all satellites, and Represents the interference caused by spectrum leakage due to asynchronous access of multiple satellites; where α k,i is the interference elimination coefficient formed by the communication user based on the known information of the navigation signal; Ignoring the influence of carrier frequency offset (CFO) and only considering the influence of time offset (TO), the closed-form expression of inter-satellite interference caused by asynchronous access is given: Because the user The signals received from K satellites are not perfectly synchronized, resulting in interference It contains three parts: Representative satellites k′ In receiving satellite k Lambda th Symbol, for communication users Subcarrier SC n From SC n′ The interference generated here is in, represents the N-point discrete Fourier transform (DFT) of vector v. Similarly, the N-point inverse discrete Fourier transform (IDFT) of vector v is given by: in, in and Here, L f Represents the filter length, L chi represents the channel length, Δ kk′ =|t i,k -t i,k′ | indicates satellites k With satellites k′ For communication users The time difference of i,k Indicates the satellite s k =(s x,k ,s y,k ,s z,k ) T Transmit to communication users TOA; c is the signal propagation speed, d j,k yes With s k The distance between Available from satellite k In carrier SC n Communication users of the service The communication rate is: r k,n,i =Δf·log2(1+ψ k,n,i ) (11), Where Δf is the subcarrier spacing, the total communication rate in the system can be expressed as: For each communication user The communication rate is, 3. The ICAN-oriented multi-satellite parallel access method according to claim 1, characterized in that: Navigation User Positioning is achieved by simultaneously receiving navigation signals from satellites. In this process, the user independently detects signals from different positioning nodes, so the TOA measurement errors are unrelated. Therefore, the ranging information provided by different positioning nodes can be directly superimposed. Based on the mean square error (MSE) lower bound SPEB of TOA positioning, the navigation user SPEB satisfy: in, yes The position of the matrix Is a navigation user The integrated equivalent Fisher information matrix (IEFIM) is the sum of the ranging information provided by K satellites within the visible range, that is, Represents navigation user From satellites k The ranging information obtained by the transmitted signal; the ranging information is a matrix defined as Among them, q j,k is the direction vector, which depends only on a k and u j The angular relationship between j,k and the pitch angle φ j,k Determined by a system of nonlinear equations: And μ j,k is a scalar, representing the satellite s k To navigation user The ranging signal strength depends on the transmission parameters and channel conditions of the channel; the signal strength of SPEB is expressed as It is the sum of the signal strengths on N carriers, where is the channel coefficient, β represents the mean square bandwidth of p(t), and the shaped pulse of FDM is usually a sinc function, so the mean square bandwidth can be expressed as represents the navigation power of the kth satellite. For all subcarriers of the same satellite, the power level is specific. represents the power of random noise, Represents navigation user In receiving, synchronizing and acquiring satellite k The signal is subjected to non-noise interference. Since the mutual correlation coefficient of ZC sequences with different root values ​​is zero, the interference of navigation signals from other satellites can be ignored. Therefore, It is composed only of interference caused by communication signals on the same carrier, that is, SC n ;therefore, in Represents the satellite k To navigation user The channel coefficients, yes The receiving antenna gain.

4. The ICAN-oriented multi-satellite parallel access method according to claim 1, characterized in that: The optimization problem (20) is as follows: The goal is to maximize the sum of the channel capacities of all communication users by allocating communication and navigation power to each subcarrier and assigning users and subcarriers to satellites under the CMSA-ICAN paradigm, where represents the navigation power of the kth satellite on each subcarrier, represents the power of the nth subcarrier of the kth satellite allocated to the i-th communication user, and δ k,n,i is the carrier allocation factor, where δ k,n,i =1 means that the nth subcarrier of the kth satellite is allocated to the i-th user, and vice versa; Constraint C1 ensures that the navigation user The SPEB should be less than the threshold Constraint C2 ensures communication users The channel capacity is greater than its minimum channel capacity requirement Constraint C3 ensures that the sum of the communication and navigation power allocated to satellite k is less than the maximum power P that the satellite can provide k ,Constraint C4 indicates that the carrier allocation factor δk,n,i is a binary variable, constraint C5 ensures that each subcarrier can be assigned to at most one satellite and one user, constraints C6 and C7 ensure that the communication and navigation powers are positive, and constraint C8 ensures that the navigation user u j From satellites k The received navigation signal strength is greater than its receiving threshold Θ j , the threshold is determined by the receiver performance, and constraint C9 guarantees the upper limit of the number of carriers that each communication user can use.

5. The ICAN-oriented multi-satellite parallel access method according to claim 1, characterized in that: The sub-problems of power allocation and subcarrier allocation are solved independently by iteration until convergence. Finally, the desired optimal solution can be obtained through iteration, where the power allocation algorithm PA is as follows: Step 1: Substitute equation (9) Convert to formula (31): Transform constraint C2 into equation (32): Using the quadratic transformation, we get formula (42): Introduce a new variable t k,n,j To replace the We get formula (46): Step 2: Initialize variables in the feasible region and t k,n,j , Repeatedly use formula (28) to update Use equation (34) to update Use equation (43) to update For fixed By solving equation (48), we can update and t k,n,j , until the convergence criterion or the maximum number of iterations is reached.

6. The ICAN-oriented multi-satellite parallel access method according to claim 1, characterized in that: In order to effectively solve the subcarrier allocation problem SA, the DAMSA algorithm is proposed, which consists of two components: DAMSA-I and DAMSA-II. When executed, initially, DAMSA-I is used to establish a stable match. If it cannot be achieved, the algorithm will enter the second stage of DAMSA, where a polynomial time algorithm is designed in the first stage to find a stable match between subcarriers and users. If a stable match cannot be achieved, the algorithm will report that it does not exist; Firstly, we introduce the non-negative loss capacity ΔC(i) to quantify the communication user The difference between the current data rate achieved under the existing matching and its target data rate: The invariants that need to be maintained during the matching process are defined as follows: in Indicates the communication user The single carrier data rate of the currently matched m-th subcarrier, a im is the index of the mth matching subcarrier, Initially, ΔC(i) is set as the threshold As the allocation process proceeds, each subcarrier is assigned to , the value of ΔC(i) is dynamically adjusted. When a new subcarrier is successfully allocated and invariant A is maintained, ΔC(i) is updated accordingly and reduces the data rate contribution of the newly added subcarrier. If accepting a new subcarrier causes invariant A to be violated (i.e., the number of allocated subcarriers exceeds the limit), some subcarriers must be removed from the matching list to re-satisfy invariant A. In this case, the reduction in ΔC(i) is the rate difference provided by the newly added and removed subcarriers. In order to always meet invariant B, ΔC(i) should be updated in a decreasing manner until it approaches zero, and the communication user Select the subcarrier with the lowest rate in the rejection matching list μ(i).

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