Method for multi-satellite parallel access oriented to ICAN

Abstract

The application relates to the technical field of satellite communication, in particular to a multi-satellite parallel access method for ICAN, which can guarantee the throughput of communication users and meet the positioning accuracy of navigation users, characterized in that: firstly, a parallel multi-satellite access CMSA architecture based on a ZC-NOMA waveform is established, and multiple satellites simultaneously provide navigation and communication services to users in a 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; wherein the subcarrier and power allocation CMSSP algorithm under parallel satellite access comprises a subcarrier allocation method and a power allocation method, for power allocation, a two-concave function difference approximation method is used to convert a non-convex problem into a solvable convex problem, and for subcarrier allocation, a two-stage adaptive matching subcarrier allocation DAMSA algorithm is introduced.

Description

Technical Field

[0001] This invention relates to the field of satellite communication technology, specifically to a multi-satellite parallel access method for ICAN that ensures both the throughput of communication users and the positioning accuracy of navigation users. Background Technology

[0002] The Global Navigation Satellite System (GNSS) is a vital space infrastructure providing positioning services to numerous sectors worldwide. 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 from a large user base for high-precision positioning has spurred interest in enhancing GNSS services through the integration of various technologies.

[0003] GNSS navigation performance is typically related to two factors: accuracy and availability. The former is assessed through positioning error, while the latter is measured by the time of application. Therefore, improving GNSS navigation performance is crucial for enhancing vehicle positioning accuracy. Navigation satellites are usually located in medium to high orbits, at altitudes of 19 to 35 kilometers. This long-distance propagation weakens the strength of the GNSS signal received on Earth (to only about -133 to -122 dBm). Furthermore, GNSS navigation signals are susceptible to various unforeseen factors such as satellite clock errors, ephemeris errors, and ionospheric and tropospheric delays. Therefore, the actual positioning accuracy of GNSS outdoors is typically around 10 meters.

[0004] Low Earth Orbit (LEO) satellites offer a promising solution for improving the availability and accuracy of navigation systems. The inherent advantages of LEO satellites in signal strength, geometric accuracy, and fast convergence make them an attractive option for enhancing GNSS services. Furthermore, the strong interest in LEO satellites for their broad coverage and flexible, cost-effective connectivity aligns well with the Beyond 5G (B5G) paradigm. This trend is evidenced by the more than 11 emerging broadband constellations under development, offering a total data throughput of approximately 30 Tbps. Unlike terrestrial cellular networks, satellite communications are not limited by complex geographical conditions and can operate in remote areas inaccessible to terrestrial networks, such as forests, deserts, and oceans. Moreover, satellites deployed outside the Earth's atmosphere possess inherent resilience, minimizing the impact of natural disasters or unforeseen events, thus ensuring high communication reliability. These advancements in navigation and communications highlight the potential of LEO satellites in integrated solutions, leveraging the synergies between these technologies. Therefore, the concept of Integrated Communication and Navigation (NAVCOM) emerged, aiming to integrate communication and navigation functions into a unified system. By leveraging the synergy between these areas, NAVCOM systems promise to improve performance, efficiency, and reliability, while providing a scalable and interoperable platform for future technological advancements.

[0005] A novel ICAN waveform, named ZC-NOMA, superimposes a communication signal occupying only a portion of the carrier on top of a broadband navigation signal in an orthogonal frequency-division multiplexing (OFDM) shape, facilitating the integration of communication and navigation functions. Since the navigation signal waveform is fixed and known to the receiver, communication users can easily cancel interference with the navigation signal, thereby reducing the overall interference level for communication users. Summary of the Invention

[0006] This invention takes into account the mutual interference between navigation and communication signals, and proposes a multi-satellite parallel access method for ICAN that can solve the inter-satellite interference (ISI) caused by parallel satellite access, while ensuring the throughput of communication users and meeting the positioning accuracy of navigation users.

[0007] This invention achieves its purpose through the following measures:

[0008] A multi-satellite parallel access method for ICAN is characterized by the following steps: First, 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 within 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 allowable transmission power, while simultaneously meeting the positioning accuracy requirements of navigation users and the rate requirements of communication users.

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

[0010] This invention considers a joint multi-satellite parallel access system, in which at least four LEO satellites are involved. Capable of broadcasting integrated communication and navigation waveforms, with the number of satellites being [number missing]. On the ground, there are Navigation User and Name of communication users Considering the downlink from satellite to user, 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. Unlike terrestrial networks and traditional satellite networks, each communication user can choose the number of satellites to access and the number of carriers to map as needed, thus providing greater flexibility and redundancy for communication.

[0011] In this system, the integrated waveform for satellite broadcasting is ZC-NOMA, derived from... The communication signals from the satellites occupied all available subcarriers. For each satellite It occupies only one consecutive set of subcarriers out of all subcarriers. ,in It is a satellite The starting position of the occupied subcarrier, It is a satellite The number of subcarriers occupied, where all subcarriers have the same subcarrier spacing, the navigation portion of the signals 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 allocated 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 simultaneously 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 carrier. In order to reduce the interference of navigation signals, communication users need to first receive the navigation signals from all satellites and reconstruct these signals based on the prior information of the navigation signals. By using the reconstructed navigation signals, the navigation components in ZC-NOMA can be eliminated, thereby obtaining independent communication signals.

[0013] definition For satellite To communication users In the The channel coefficients on each subcarrier are determined by... Given, among which This indicates large-scale fading that depends on distance. This indicates a small-scale fading effect. It is a satellite transmit antenna gain, Communication user The receive antenna gain is defined as the correlation coefficient between the subcarrier and the user. ,in That is, when At that time, it indicates the satellite The Subcarriers and communication users The connection is the same, and vice versa;

[0014] let Indicates communication user In subcarrier SNR on:

[0015] (1),

[0016] in Representative satellite For communication users In subcarrier The power allocated above, It is a satellite In subcarrier The frequency response of the filter used. Represents noise power, where It is the power spectral density of random noise. Representing communication users In relation to satellites Interference encountered during communication, here This indicates interference with navigation signals from all satellites, while This indicates interference caused by spectrum leakage due to asynchronous access from multiple satellites;

[0017] (2),

[0018] in It is the interference cancellation coefficient formed by the communication user based on known information from the navigation signal; for Ignoring the effects of carrier frequency offset (CFO) and considering only the effects of time offset (TO), a closed-form expression for inter-satellite interference caused by asynchronous access is given:

[0019] (3)

[0020] Due to users from The signals received by the satellites are not perfectly synchronized, leading to interference. It contains three parts. Item Representative satellite Receiving satellites of When symbols are used, for communication users subcarrier from The resulting interference, here,

[0021] (4),

[0022] in,

[0023] (5),

[0024] Representative vector The N-point Discrete Fourier Transform (DFT), similarly, vectors The N-point inverse discrete Fourier transform (IDFT) is given by the following equation:

[0025] (6),

[0026] in, (7),

[0027] in

[0028] (8), and (9),

[0029] Here, Represents the filter length. Represents the channel length. Indicates satellite With satellite For communication users The time difference. Indicates from satellite Transmitted to communication users TOA; (10)

[0030] Here, It is the speed of signal propagation. yes and The distance between them;

[0031] It can be obtained from satellites On carrier Communication users on the service The communication rate is:

[0032] (11),

[0033] in Given the subcarrier spacing, the total communication rate in the system can be expressed as:

[0034] (12)

[0035] For each communication user The communication rate is,

[0036] (13).

[0037] Navigation user in this invention Positioning is achieved by simultaneously receiving navigation signals from satellites. During this process, the user independently detects signals from different positioning nodes, therefore the TOA (Time of Arrival) measurement errors are uncorrelated. Consequently, the ranging information provided by different positioning nodes can be directly superimposed. Based on the lower bound of the mean square error (MSE) for TOA positioning (SPEB), the navigation user... SPEB satisfy:

[0038] (14), among which, yes Position estimation. Matrix Navigation user The Integrated Equivalent Fisher Information Matrix (IEFIM) is the visible range The sum of ranging information provided by each satellite, i.e. , Representing navigation users From satellite Distance information obtained from transmitted signals;

[0039] Distance measurement information is a matrix, defined as follows:

[0040] (15), of which, It is a direction vector, which only depends on and The angular relationship between them, azimuth angle and pitch angle Determined by a system of nonlinear equations

[0041] (16), and It is a scalar, representing a satellite. To navigation users The ranging signal strength depends on the channel's transmission parameters and channel conditions;

[0042] The signal strength of SPEB is expressed as:

[0043] (17), it is The sum of signal strengths on each carrier, where It is the channel coefficient. represent The mean square bandwidth. The shaping pulse of OFDM is usually a sinc function, so the mean square bandwidth can be expressed as...

[0044] (18) Representing the The navigation power of each satellite. It should be noted that the power level is specific for all subcarriers of the same satellite. Power representing random noise, Representing navigation users Receiving, synchronizing, and capturing data from satellites The signal suffers from non-noise interference. Since the cross-correlation coefficient of ZC sequences with different root values ​​is zero, interference from navigation signals from other satellites can be ignored. It consists only of interference from communication signals on the same carrier wave, i.e. ;therefore,

[0045] (19), of which Representative from satellite To navigation users The channel coefficient, yes The receiving antenna gain.

[0046] The optimization problem (20) in this invention is as follows:

[0047] (20)

[0048] Its goal is to maximize the sum of channel capacity for all communication users within the CMSA-ICAN paradigm by allocating communication and navigation power to each subcarrier and by allocating users and subcarriers to satellites. Indicates the first The navigation power of each satellite on each subcarrier Indicates the first The first satellite The subcarrier is assigned to the first The power of each communication user, and It is the carrier allocation factor, where Indicates the first The first satellite The subcarrier is assigned to the first For each user, the opposite is also true;

[0049] constraint Ensure navigation users SPEB should be less than the threshold. ,constraint Ensure communication users The channel capacity is greater than its minimum channel capacity requirement. ,constraint Ensure allocation to satellites The sum of its communication and navigation power is less than the maximum power that the satellite can provide. ,constraint Indicates carrier allocation factor It is a binary variable, with constraints Ensure that each subcarrier can be allocated to at most one satellite and one user, constraining... and Ensure that both communication and navigation power are positive, and impose constraints. Ensure navigation users From satellite The strength of the received navigation signal is greater than its reception threshold. This threshold is determined by the receiver performance and constrains... Guarantee the upper limit of the number of carriers that each communication user can use.

[0050] This invention solves the subproblems of power allocation and subcarrier allocation iteratively and independently until convergence, ultimately obtaining the desired optimal solution through iteration. The power allocation algorithm PA is as follows:

[0051] Step 1: Apply equation (9) Transformed into equation (31):

[0052] (31),

[0053] Convert constraint C2 into equation (32):

[0054] (32),

[0055] Using a quadratic transformation, we obtain equation (42):

[0056] (42),

[0057] Introduce a new variable To replace in equation (45) , in, (45)

[0058] Equation (46) is obtained:

[0059] (46);

[0060] Step 2: Initialize variables within the feasible region , and Reuse (28) update ,

[0061] (28)

[0062] Use equation (34) to update ,

[0063] (34),

[0064] Use formula (43) to update ,

[0065] (43),

[0066] For fixed Update by solving equation (48) , and This continues until the convergence criterion or the maximum number of iterations is reached.

[0067] To effectively solve the subcarrier allocation problem (SA), this invention proposes the DAMSA algorithm, which consists of two parts: DAMSA-I and DAMSA-II. During execution, initially, DAMSA-I is used to establish a stable match. If this cannot be achieved, the algorithm will enter the second stage of DAMSA. In the first stage, a polynomial-time algorithm is designed to find a stable match between the subcarrier and the user. If a stable match cannot be achieved, the algorithm will report that it does not exist.

[0068] First, we introduce the non-negative loss capacity. Quantify communication users The difference between the current data rate achieved under the existing matching and its target data rate:

[0069] The invariants that need to be maintained during the matching process are defined as follows:

[0070] (49)

[0071] in , Indicates communication with users The currently matched first Single-carrier data rate of each subcarrier It is the first Index of a matching subcarrier,

[0072] (50),

[0073] initial, Set as threshold As the allocation process proceeds, each subcarrier is assigned to... hour, The value will be dynamically adjusted when a new subcarrier is successfully allocated and the invariant A is maintained. The data rate contribution of this newly added subcarrier is updated and reduced accordingly; however, if accepting a new subcarrier results in a violation of invariant A (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 is the rate difference provided by the newly added and removed subcarriers; in order to always satisfy invariant B, Updates should be made in a decreasing manner until they approach zero, for communication users. Select the list of matches to reject The subcarrier with the lowest speed.

[0074] This invention optimizes for subcarriers, but this is not advantageous from the user's perspective, often referred to as "subcarrier optimal, user worst." To illustrate this, consider a given user... Two stable matching schemes and , respectively represented as and ,

[0075] If an index m' exists ( ), where for all ,have And at index $m'$, ,mean So, the user In matching The middle is considered superior to the middle in terms of lexicographical order. In this case, it indicates that at the first distinct index m', the match... Provided users with more A better result is that this feature stems from the fact that the algorithm starts from the perspective of the subcarrier and makes suggestions to the communication user, and the user has the right to accept or reject these suggestions, but does not have the right to make suggestions from his own perspective;

[0076] When DAMSA-I could not find a stable match, a suboptimal DAMSA-II was 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 certain communication user is met, the allocation of subcarriers to it is suspended until the requirements of all communication users are met.

[0077] Compared with existing technologies, this invention ensures both the throughput of communication users and the positioning accuracy of navigation users. By finely adjusting the power allocation and subcarrier allocation strategies, it greatly optimizes the overall system performance and achieves an effective balance between navigation and communication. Attached Figure Description

[0078] Appendix Figure 1 This is the CMSA-ICAN architecture diagram in this invention.

[0079] Figure 2 This is a schematic diagram of the ZC-NOMA time-frequency structure in this invention.

[0080] Figure 3 This is a schematic diagram of multi-satellite coverage analysis in an embodiment of the present invention.

[0081] Figure 4 This is the convergence curve in an embodiment of the present invention.

[0082] Figure 5 This is a schematic diagram illustrating the influence of satellite power on speed in an embodiment of the present invention, wherein... Figure 5 (a) Interference cancellation coefficient , Figure 5 (b) Navigation and positioning accuracy m.

[0083] Figure 6 This is an embodiment of the invention showing the impact of the number of satellite access users on the speed, wherein... Figure 6 (a) is a schematic diagram illustrating the impact of the number of communication users on the speed. Figure 6 (b) is a schematic diagram illustrating the impact of the number of navigation users on the speed.

[0084] Figure 7 This is a schematic diagram illustrating the impact of filtering parameters on the combined rate of communication users in an embodiment of the present invention.

[0085] Figure 8 This is a graph showing the impact of communication user rate demand on the rate in an embodiment of the present invention.

[0086] Figure 9 This is a schematic diagram illustrating the interruption probability under different power and QoS requirements in an embodiment of the present invention. Detailed Implementation

[0087] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0088] This invention considers a such Figure 1 The scenario shown involves joint multi-satellite parallel access, in which at least four LEO satellites are used in the system. Capable of broadcasting integrated communication and navigation waveforms, with the number of satellites being [number missing]. On the ground, there are Navigation User and Name of communication users .

[0089] Considering the downlink from satellite to user, navigation users need to receive integrated waveforms from at least four satellites to achieve navigation functionality, 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. Notably, unlike terrestrial networks and traditional satellite networks, each communication user can select the number of satellites to access and the number of carriers to map as needed, thus providing greater flexibility and redundancy for communication.

[0090] In this system, the integrated waveform for satellite broadcasting is ZC-NOMA, and its time-frequency structure is as follows: Figure 2 As shown in the figure. It can be seen from the graph that... The communication signals from the satellites occupied all available subcarriers. For each satellite It occupies only one consecutive set of subcarriers out of all subcarriers. ,in It is a satellite occupy

[0091] According to the starting position of the subcarrier, It is a satellite The number of subcarriers occupied. All subcarriers have the same subcarrier spacing. The navigation portion 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 allocated to the same satellite) at the transmitting end and performing corresponding matched filtering at the receiving end.

[0092] Navigation users need to simultaneously receive integrated signals from four satellites and use the navigation components in ZC-NOMA to achieve their positioning. The primary objective of communication users is to acquire the information carried on their corresponding carrier wave. To reduce interference with navigation signals, communication users first need to receive navigation signals from all satellites and reconstruct these signals based on prior information. By using the reconstructed navigation signals, they can eliminate the navigation components in ZC-NOMA, thereby obtaining independent communication signals.

[0093] We define For satellite To communication users In the The channel coefficients on each subcarrier are determined by... Given, among which This indicates large-scale fading that depends on distance. This indicates a small-scale fading effect. It is a satellite transmit antenna gain, It is a communication user The receive antenna gain. Furthermore, we define the subcarrier-to-user correlation coefficient as... ,in That is, when At that time, it indicates the satellite The Subcarriers and communication users The connection is the same, and vice versa.

[0094] let Indicates communication user In subcarrier SNR on:

[0095] (1),

[0096] in Representative satellite For communication users In subcarrier The power allocated above, It is a satellite In subcarrier The frequency response of the filter used. Represents noise power, where It is the power spectral density of random noise. Representing communication users In relation to satellites Interference encountered during communication. Here This indicates interference with navigation signals from all satellites, while This indicates interference caused by spectrum leakage due to asynchronous access from multiple satellites.

[0097] (2), of which It is the interference cancellation coefficient formed by the communication user based on known information about the navigation signal.

[0098] for Existing technologies have proposed multiphase analysis methods for analyzing interference problems under non-ideal synchronization conditions, and have incorporated 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 for inter-satellite interference caused by asynchronous access.

[0099] (3),

[0100] Due to users from The signals received by the satellites are not perfectly synchronized, leading to interference. It contains three parts. Item Representative satellite Receiving satellites of When symbols are used, for communication users subcarrier from The resulting interference.

[0101] Here,

[0102] (4),

[0103] in,

[0104] (5),

[0105] Representative vector The N-point Discrete Fourier Transform (DFT), similarly, vectors The N-point inverse discrete Fourier transform (IDFT) is given by the following equation:

[0106] (6),

[0107] in,

[0108] (7),

[0109] in

[0110] (8),

[0111] and

[0112] (9),

[0113] Here, Represents the filter length. Represents the channel length. Indicates satellite With satellite For communication users The time difference. Indicates from satellite Transmitted to communication users TOA.

[0114] (10)

[0115] Here, It is the speed of signal propagation. yes and The distance between them.

[0116] Therefore, it is possible to obtain information from satellites. On carrier Communication users on the service The communication rate is

[0117] (11), of which This refers to the subcarrier spacing. The total communication rate in the system can be expressed as...

[0118] (12) For each communication user Their communication rate is

[0119] (13) Navigation users Positioning is achieved by simultaneously receiving navigation signals from satellites. In this process, the user independently detects signals from different positioning nodes, therefore the TOA (Time of Arrival) measurement errors are independent, and the ranging information provided by different positioning nodes can be directly superimposed. Based on the lower bound of the mean square error (MSE) SPEB for TOA positioning, navigation users... SPEB satisfy

[0120] (14), among which, yes Location estimation.

[0121] matrix Navigation user The Integrated Equivalent Fisher Information Matrix (IEFIM) is the visible range The sum of ranging information provided by each satellite, i.e. , Representing navigation users From satellite Distance information obtained from the transmitted signal.

[0122] Distance measurement information is a matrix, defined as follows:

[0123] (15), of which, It is a direction vector, which only depends on and The angular relationship between them, azimuth angle and pitch angle Determined by a system of nonlinear equations:

[0124] (16)

[0125] and It is a scalar, representing a satellite. To navigation users The ranging signal strength depends on the channel's transmission parameters and channel conditions.

[0126] The signal strength of SPEB is expressed as follows:

[0127] (17)

[0128] It is The sum of signal strengths on each carrier, where It is the channel coefficient. represent The mean square bandwidth. The shaping pulse of OFDM is usually a sinc function, so the mean square bandwidth can be expressed as...

[0129] (18)

[0130] Representing the The navigation power of each satellite. It should be noted that the power level is specific for all subcarriers of the same satellite. Power representing random noise.

[0131] Representing navigation users Receiving, synchronizing, and capturing data from satellites The signal suffers from non-noise interference. Since the cross-correlation coefficient of ZC sequences with different root values ​​is zero, navigation signal interference from other satellites can be ignored. It consists only of interference from communication signals on the same carrier wave, i.e. .

[0132] therefore,

[0133] (19), of which Representative from satellite To navigation users The channel coefficient, yes The receiving antenna gain.

[0134] The problem is modeled as follows:

[0135] (20)

[0136] The objective of optimization problem (20) is to maximize the sum of channel capacity for all communication users within the CMSA-ICAN paradigm by allocating communication and navigation power to each subcarrier and allocating users and subcarriers to satellites. Indicates the first The navigation power of each satellite on each subcarrier Indicates the first The first satellite The subcarrier is assigned to the first The power of each communication user, and It is the carrier allocation factor, where Indicates the first The first satellite The subcarrier is assigned to the first For each user, the same applies to the other.

[0137] constraint Ensure navigation users SPEB should be less than the threshold. ,constraint Ensure communication users The channel capacity is greater than its minimum channel capacity requirement. ,constraint Ensure allocation to satellites The sum of its communication and navigation power is less than the maximum power that the satellite can provide. .constraint Indicates carrier allocation factor It is a binary variable, with constraints Ensure that each subcarrier can be allocated to at most one satellite and one user, constraining... and Ensure that both communication and navigation power are positive, and impose constraints. Ensure navigation users From satellite The strength of the received navigation signal is greater than its reception threshold. This threshold is determined by the receiver performance and constrains... Guarantee the upper limit of the number of carriers that each communication user can use.

[0138] The original optimization problem is difficult to find an optimal solution due to its non-convex and nonlinear characteristics. Therefore, we propose an iterative carrier and power allocation algorithm called CMSSP. This algorithm solves the subproblems of power allocation and subcarrier allocation independently through iteration until convergence, and finally obtains the desired optimal solution through iteration.

[0139]

[0140] PA (Power Allocation) and SA (Subcarrier Allocation) correspond to respectively and The PA problem can be described as follows:

[0141] (twenty one),

[0142] The SA problem can be described as...

[0143] (twenty two),

[0144] However, we found that these two subproblems remain difficult to solve due to their nonlinear and nonconvex characteristics. Therefore, corresponding algorithms are proposed for the PA and SA subproblems respectively.

[0145] First, consider the power allocation problem, where power allocation is based on the carrier allocation result obtained in the previous iteration. Due to the non-convexity of the objective function and constraints, we use the DC approximation method to transform the PA optimization problem into a solvable concave function problem. Therefore, the objective function of PA can be equivalently rewritten in DC form:

[0146] (twenty three),

[0147] in and These are two concave functions, expressed by the following formulas:

[0148] (twenty four),

[0149] and

[0150] (25)

[0151] in,

[0152] (26)

[0153] and

[0154] (27)

[0155] in, Is for In other words, carrier arrive carrier The interference propagation factor. Since (23) is composed of the difference of two concave functions, it is not a definite concave function. The first-order Taylor approximation is used to... It is approximately a linear function, and its expression is:

[0156] (28), among which,

[0157] (29), and

[0158] (30) Based on this, the PA problem is transformed into a concave function, and formula (23) can be reformulated as:

[0159] (31) The same strategy applies to constraints. It can be converted to:

[0160] (32), among which,

[0161] (33), and (34), among which,

[0162] (35) will To each and Taking the derivative, we get (36), and (37) Therefore, by adopting the DC approximation, the constraints are... Successfully converted to a convex constraint.

[0163] The PA problem now takes the form of:

[0164] (38) In the PA problem, we find constraints and constraints It remains a non-convex constraint.

[0165] Lemma 1: Constraints It is a non-convex constraint.

[0166] Proof: Note It is about The convex function, due to yes A linear combination, it is also about The convex function. However, due to and and The complex nonlinear relationship between them It is about and The non-convex function ultimately makes Become about and The non-convex function.

[0167] For (17), an equivalent treatment is achieved by performing a quadratic transformation on the numerator and denominator of each ratio term.

[0168] (39) and (40), at this time

[0169] (41) Through a second transformation, we can obtain:

[0170] (42), let pass Iterative updates, and retrieve The closed expression is:

[0171] (43), It is about The function is convex, therefore constraint C1 becomes

[0172] (44), among which, (45), of which and It is about and affine function. When When fixed, due to (39) The coefficient is positive and ,therefore It is a concave function. It is an affine function, therefore we know It is a concave function. Therefore It is about and Non-convex functions, constraints It is a non-convex constraint. To ensure... It is a convex constraint, and we introduce a new variable. Replace (45) ,therefore

[0173] (46), and the constraint must be satisfied.

[0174] (47);

[0175] Lemma 2: Under constraint (47), (44) is a convex constraint, and it is related to constraint (47). There are equivalent transformations between them.

[0176] Proof: For a fixed , It is about , and The affine function. Furthermore, due to It is a convex and non-increasing function, while It is a concave and non-decreasing function, therefore constraint (47) ensures that and They are equivalent. Moreover, in the optimal... Under the conditions, constraints The first-order condition is the same as that of (44), and the iterative algorithm will make (44) converge to the same level. The same stable point ensures the equivalence of the quadratic transformation. Meanwhile, It is a convex function, therefore it is determined that under constraint (47), (44) is a convex constraint, and it is consistent with the constraint There are equivalent transformations between them.

[0177] At this point, we obtain a solvable PA problem, which can be solved using mature convex optimization tools.

[0178] (48) The complete PA algorithm is shown in Algorithm 1.

[0179] Algorithm 1: Power Allocation Algorithm PA

[0180]

[0181] To effectively address the SA (subcarrier allocation) problem specified in (22), this paper proposes the DAMSA algorithm, which comprises two important components: DAMSA-I and DAMSA-II. Initially, DAMSA-I is used to establish a stable match. If this fails, the algorithm proceeds to the second stage of DAMSA, which aims to provide a suboptimal but practical matching solution. This bifurcation strategy ensures that the SA challenge yields a robust solution that prioritizes stability while also providing effective alternatives to maintain system performance.

[0182] The classic Gale-Shapley algorithm performs poorly in matching processes constrained by upper and lower bounds. In our problem context, constraints such as minimum throughput requirements per user and the maximum number of accessible subcarriers make the Gale-Shapley algorithm infeasible. A polynomial-time algorithm is designed in the first stage to find stable matches between subcarriers and users. If a stable match cannot be achieved, the algorithm reports that no match exists.

[0183] The general approach of this invention allows subcarriers to begin pairing with communication users according to their preferences. Users respond to these contacts based on specific criteria (described in detail later), accepting or rejecting the pairing. A rejected subcarrier then approaches the next user in its list. This process continues until every 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 bounds defined for all categories. If these criteria are met, the pairing is considered stable; otherwise, stable pairings are considered not to exist in a given scenario.

[0184] The effectiveness of the DAMSA-I algorithm heavily relies on the strategy of communication users in accepting or rejecting subcarrier proposals. This decision is constrained. and The guidance primarily considers whether accepting additional subcarriers would cause the total number of allocated subcarriers to exceed the user's limit. If the limit is exceeded, the protocol requires a re-evaluation of current matches to potentially reject existing subcarriers (not necessarily the most recently proposed ones). This mechanism ensures compliance with defined constraints and improves the overall efficiency of the subcarrier allocation process.

[0185] Next, we solve the constraints of the SA problem by defining the invariants that must be maintained during the two matching processes. We introduce the "loss capacity," denoted as... This is a non-negative value, quantifying the communication user. The difference between the current data rate achieved under the existing matching and its target data rate.

[0186] The invariants that need to be maintained during the matching process are defined as follows:

[0187] (49), of which , Indicates communication with users The currently matched first Single-carrier data rate of each subcarrier It is the first Index of a matching subcarrier.

[0188] (50),

[0189] initial, Set as threshold As the allocation process proceeds, each subcarrier is assigned to... hour, The value will be dynamically adjusted. Specifically, when a new subcarrier is successfully allocated and maintains the invariant A, Update and reduce accordingly

[0190] This contributes to the data rate of the newly added subcarrier.

[0191] Algorithm 2 DAMS-I

[0192]

[0193] However, if accepting new subcarriers results in a violation of invariant A (i.e., the number of subcarriers allocated exceeds the limit), some subcarriers must be removed from the matching list to re-satisfy invariant A. In this case, The reduction is the rate difference provided by the newly added and removed subcarriers. To always satisfy invariant B, It should be updated in a decreasing manner until it approaches zero. In our algorithm, the communication user... Select the list of matches to reject The subcarrier with the lowest speed. The pseudocode of the algorithm is described in detail in Algorithm 2.

[0194] Please note that our algorithm is optimized for subcarriers, but is not very advantageous from the user's perspective; this is often referred to as "subcarrier optimal, user worst." To illustrate this, consider a given user... Two stable matching schemes and , respectively represented as and .

[0195] If an index m' exists ( ), where for all ,have And at index $m'$, ,mean So, the user In matching The middle is considered superior to the middle in terms of lexicographical order. This indicates that at the first distinct index m', the match... Provided users with more A better result. This feature stems from the fact that the algorithm starts from the perspective of the subcarrier, making suggestions to the communication user, who has the right to accept or reject these suggestions, but does not have the right to make suggestions from their own perspective.

[0196] When DAMSA-I fails to find a stable match, we propose a suboptimal DAMSA-II to address the problem. Unlike DAMSA-I, DAMSA-II aims to meet the minimum capacity requirements of all users. When the rate requirement of a particular user is met, subcarrier allocation for that user is suspended until the requirements of all users are met.

[0197] Algorithm 3 DAMS-II

[0198]

[0199] A detailed description of the DAMS-II algorithm is in Algorithm 3.

[0200] The performance of the SMSSP algorithm in CMSA-ICAN is verified through simulation.

[0201] This example considers four satellites distributed in one orbital plane, 500 km above the ground, to ensure visibility between the satellites and the observer (ground station). The elevation angle is the distance between the satellites and the observer's horizontal plane. The minimum should be 10 degrees. Since receiving navigation information requires simultaneous acquisition of navigation messages from at least four satellites, we only consider areas that can be covered by four satellites simultaneously. LEO ground coverage area radius. It can be represented as:

[0202] (51),

[0203] in Represents the Earth's radius. This indicates the distance from the LEO satellite to the ground. For According to equation (54). It is 1547 KM.

[0204] Figure 3 This demonstrates the shared coverage area of ​​multiple satellites. When all satellites are distributed within a radius of... When the plane is in the same direction, the radius of the common coverage area is The central projection points of the two planes overlap, which leads to the conclusion that... Therefore, when communication and navigation users are distributed within a radius... Within a range of 947 km, they can maintain connections with four satellites simultaneously.

[0205] This example verifies the convergence properties of the proposed SMSSP algorithm. Figure 4 To achieve different maximum navigation user accuracies, the SMSSP algorithm is used when the total satellite power is... The convergence curves are shown below. From the graph, we can observe that for navigation users with low positioning accuracy, both the communication rate and the overall rate converge rapidly after three iterations. When the positioning accuracy is 10m, a total rate of 1.52Mbps can be obtained, and it can be seen that a decrease in navigation positioning accuracy will benefit the improvement of the overall communication rate.

[0206] Figure 5 The maximum power of the satellite was evaluated. Impact on the total rate of communication users. Figure 5 (a) shows the variation of the sum rate with the power of the communication user under different interference cancellation factors. Two points need to be represented. and Two extreme cases, This means that for communication users, the navigation signals have not undergone any interference cancellation, and users will receive navigation signals from four satellites at full power, resulting in high-intensity interference to themselves; This represents a limiting case where the communication user can completely cancel the navigation signal's interference based on its prior characteristics, thereby eliminating the navigation signal's impact on the communication user. It is clear from the figure that... and At dBm, the system's total transmission rate is only 0.43 Mbps, while In this case, it can reach 1.41 Mbps. The other three curves represent... The value ranges from 0.97 to 0.99, falling between these two extreme cases.

[0207] Figure 5 (b) An assessment was conducted on how the total transmission rate of communication users changes with satellite power under different positioning accuracy requirements of navigation users. Changes. The four curves correspond to the changes from... Navigation accuracy ranges from 1 meter to 26 meters. It was observed that... dBm and At a speed of meters, the total transmission rate is 1.25 Mbps, while... The speed increased from 10 meters to 1.36 Mbps, an increase of 0.11 Mbps. As the positioning accuracy for navigation users decreased from 10 meters to 18 meters, and then from 18 meters to 26 meters, the corresponding... The speeds increased by 0.03 Mbps and 0.02 Mbps. This indicates that as navigation and positioning accuracy decreases, the overall transmission rate improvement for the same degree of accuracy reduction also decreases. This phenomenon is not only observed in… Observed at dBm, and from This was observed across all power levels from dBm to 54 dBm. This can be attributed to the lower power levels of the navigation component in the lower accuracy region, resulting in relatively lower interference levels for communication users, and thus a smaller impact from the reduction in navigation accuracy.

[0208] exist Figure 6 In this study, the changes in communication user throughput and rate relative to the number of users were evaluated under different numbers of subcarriers. Figure 6 (a) illustrates different numbers of subcarriers Below, the number of communication users Total transmission rate within range The changes. We observed that for a given number of users... Total transmission rate With the number of subcarriers It increased significantly with the increase. Especially for , They increased by 0.52 Mbps and 0.53 Mbps respectively, with The number increased from 16 to 20, and from 20 to 24. hour, along with The increase is gradual due to the expansion of user distribution, which increases the flexibility of resource allocation. Conversely, in hour, Not with It continues to increase with the increase; it is increasing. It reaches its peak at that time. It stabilized and, The timeframe begins to decline after 14 seconds. This decline is attributed to strict communication user capacity limitations. .when At that time, the trend showed that from It started to decline, and the algorithm could not provide... Provide a feasible solution. This is because in hour, This means that some communication users are only allocated to the edge of the satellite filter passband, failing to meet the minimum capacity requirement, thus preventing the algorithm from producing a feasible solution. This indicates that the CMSSP algorithm inherently creates a "guard interval" (even if not explicitly specified) to avoid allocating edge subcarriers to communication users. In strict... Under these constraints, the number of supportable communication users will be less than [number missing]. .

[0209] Figure 7 This demonstrates the effects of various filter types and their parameters on the total rate under different numbers of subcarriers. The impact, of which (a) number of carriers (b) Number of carriers (c) Number of carriers (d) Number of carriers The performance impact of two types of window functions—Hamming window and Kaiser window—as well as 3rd and 10th order Butterworth filters was evaluated. The study found that the number of subcarriers... or maximum transmission power The increase in invariably leads to the degradation of all types of filters. Increase. At a constant level. and The third-order Butterworth filter performed the worst, while the tenth-order Butterworth filter performed the best. Higher filter orders not only indicate increased complexity but also a better filter shape, thus improving performance. Comparing the resultant rates under different carrier numbers, it can be found that increasing power has the smallest performance improvement for the third-order Butterworth filter. This is because the third-order Butterworth filter has the worst filter shape, making the power increase ineffective in improving the resultant rate. Figure 8The impact of communication user rate requirements on different numbers of communication users was evaluated. The impact can be observed when the QoS requirement is 105kbps. This increases with the number of users because a denser user base means more flexible allocation strategies can be implemented. With the increase in QoS, regardless of... We can observe how much or how little. The decrease is intuitive; stricter QoS requirements reduce the flexibility of allocation, especially for... In comparison to ,when At that time, as QoS increases, Rapid decline, At kbps It has dropped to the level of The timing phases are close, and as QoS continues to increase, when When the speed reaches kbps, it is no longer possible to obtain a valid feasible solution, which means that it is no longer possible to satisfy all the constraints. This is similar to the conclusion obtained in Figure (6). Figure 9 The outage probability was evaluated under different power and QoS requirements. It can be seen that when the power is constant, as... As the power increases, the probability of interruption gradually increases. At the same time, it can be seen that increasing the power can effectively reduce the probability of interruption, but for strict QoS requirements, there is still a possibility of interruption of more than 10% after the satellite power reaches 52 dBm.

[0210] This invention constructs a CMSA architecture for use in the ICAN scenario of low-Earth orbit satellites. The core innovation of its CMSA framework lies in using ZC-NOMA waveforms to superimpose navigation and communication signals in the frequency domain. This invention also features a meticulously designed subcarrier and power allocation algorithm (CMSSP) for parallel satellite access. This algorithm significantly optimizes the overall system performance by finely adjusting power and subcarrier allocation strategies. The introduction of the CMSSP algorithm ensures both navigation accuracy and the high throughput requirements of communication users, achieving an effective balance between navigation and communication.

Claims

1. A method for parallel access to multiple satellites for ICAN, characterized in that, First, a parallel multi-satellite access (CMSA) architecture based on ZC-NOMA waveform is established. In this architecture, multiple satellites simultaneously provide navigation and communication services to users within 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 allowable transmission power, while meeting the positioning accuracy requirements of navigation users and the rate requirements of communication users. The CMSSP algorithm for subcarrier and power allocation under parallel satellite access includes a subcarrier allocation method and a power allocation method. For power allocation, the difference between two concave functions 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. By iteratively solving the subproblems of power allocation and subcarrier allocation independently until convergence, the desired optimal solution can be obtained through iteration. The power allocation algorithm PA is as follows: Step 1: Apply equation (9) Transformed into equation (31): （31）， Convert constraint C2 into equation (32): （32）， Using a quadratic transformation, we obtain equation (42): （42）， Introduce a new variable To replace in equation (45) , in, (45) （46）， Step 2: Initialize variables within the feasible region , and , Reusable (28) update , （28）， Use equation (34) to update , (34), use equation (43) to update , （43）， For fixed Update by solving equation (48) , and Continue until the convergence criterion or the maximum number of iterations is reached: ， To effectively solve the subcarrier allocation problem (SA), the DAMSA algorithm was proposed, which consists of two parts: DAMSA-I and DAMSA-II. During execution, DAMSA-I is used initially to establish a stable match. If this fails, the algorithm will enter the second stage of DAMSA. In the first stage, a polynomial-time algorithm is designed to find a stable match between the subcarrier and the user. If a stable match cannot be achieved, the algorithm will report that it does not exist. First, we introduce the non-negative loss capacity. Quantify communication users 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: (49) in , Indicates communication with users The currently matched first The single-carrier data rate of each subcarrier It is the first Index of a matching subcarrier, （50）， initial, Set as threshold As the allocation process proceeds, each subcarrier is assigned to... hour, The value will be dynamically adjusted when a new subcarrier is successfully allocated and the invariant A is maintained. The data rate contribution of this newly added subcarrier is updated and reduced accordingly; if accepting a new subcarrier causes invariant A to be violated, i.e., the number of allocated subcarriers exceeds the limit, then some subcarriers must be removed from the matching list to re-satisfy invariant A. In this case, The reduction is the rate difference provided by the newly added and removed subcarriers; in order to always satisfy invariant B, Updates should be made in a decreasing manner until they approach zero, for communication users. Select the list of matches to reject The subcarrier with the lowest speed.

2. The multi-satellite parallel access method for ICAN according to claim 1, characterized in that, Consider a joint multi-satellite parallel access system with at least four LEO satellites. Capable of broadcasting integrated communication and navigation waveforms, with the number of satellites being [number missing]. On the ground, there are Navigation User and Name of communication users ; Considering the downlink from satellite to user, 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. Unlike terrestrial networks and traditional satellite networks, each communication user can choose the number of satellites to access and the number of carriers to map as needed, thus providing greater flexibility and redundancy for communication. In this system, the integrated waveform for satellite broadcasting is ZC-NOMA, derived from... The communication signals from the satellites occupied all available subcarriers. For each satellite It occupies only one consecutive set of subcarriers out of all subcarriers. ,in It is a satellite The starting position of the occupied subcarrier, It is a satellite The number of subcarriers occupied, where all subcarriers have the same subcarrier spacing, the navigation portion of the signals 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 at the transmitting end, i.e., a group of adjacent carriers allocated to the same satellite, and performing corresponding matched filtering at the receiving end. Navigation users need to simultaneously receive integrated signals from four satellites and use the navigation components in ZC-NOMA to achieve their positioning. The primary goal of communication users is to acquire the information carried on their corresponding carrier wave. To reduce navigation signal interference, communication users first need to receive navigation signals from all satellites and reconstruct these signals based on prior information. By using the reconstructed navigation signals, the navigation components in ZC-NOMA can be eliminated, thus obtaining an independent communication signal. For satellite To communication users In the The channel coefficients on each subcarrier are determined by... Given, among which This indicates large-scale fading that depends on distance. This indicates a small-scale fading effect. It is a satellite transmit antenna gain, Communication user The receive antenna gain is defined as the correlation coefficient between the subcarrier and the user. ,in That is, when At that time, it indicates the satellite The Subcarriers and communication users Related, and vice versa; let Indicates communication user In subcarrier SNR on: （1）， in Representative satellite For communication users In subcarrier The power allocated above, It is a satellite In subcarrier The frequency response of the filter used. Represents noise power, where It is the power spectral density of random noise. Representing communication users In relation to satellites Interference encountered during communication, here This indicates interference with navigation signals from all satellites, while This indicates interference caused by spectrum leakage due to asynchronous access from multiple satellites; （2）， in It is the interference cancellation coefficient formed by the communication user based on known information from the navigation signal; for Ignoring the effect of carrier frequency offset (CFO) and considering only the effect of time offset (TO), a closed-form expression for inter-satellite interference caused by asynchronous access is given: (3) Due to the user from The signals received by the satellites are not perfectly synchronized, leading to interference. It consists of three parts. Representative satellite Receiving satellites of When symbols are used, for communication users subcarrier from The resulting interference, here, (4), of which, (5) represents a vector The N-point Discrete Fourier Transform (DFT), similarly, vectors The N-point inverse discrete Fourier transform (IDFT) is given by the following equation: (6), among which, （7）， in (8), and (9) Here, Represents the filter length. Represents the channel length. Indicates satellite With satellite For communication users Time difference, Indicates from satellite Transmitted to communication users TOA; (10) It is the speed of signal propagation. yes and The distance between them; It can be obtained from satellites On carrier Communication users on the service The communication rate is: （11）， in Given the subcarrier spacing, the total communication rate in the system can be expressed as: （12）， For each communication user The communication rate is, （13）。 3. The multi-satellite parallel access method for ICAN according to claim 1, characterized in that, Navigation users Positioning is achieved by simultaneously receiving navigation signals from satellites. During this process, the user independently detects signals from different positioning nodes, therefore the TOA (Time of Arrival) measurement errors are uncorrelated. Consequently, the ranging information provided by different positioning nodes can be directly superimposed. Based on the lower bound of the mean square error (MSE) for TOA positioning (SPEB), the navigation user... SPEB satisfy: (14), among which, yes Position estimation, matrix Navigation user The Integrated Equivalent Fisher Information Matrix (IEFIM) is the visible range The sum of ranging information provided by each satellite, i.e. , Representing navigation users From satellite The ranging information obtained from the transmitted signal; the ranging information is a matrix, defined as follows: (15), of which, It is a direction vector, which only depends on and The angular relationship between them, azimuth angle and pitch angle Determined by a system of nonlinear equations: (16), and It is a scalar, representing a satellite. To navigation users The ranging signal strength depends on the channel's transmission parameters and channel conditions; the SPEB signal strength is expressed as... (17), it is The sum of signal strengths on each carrier, where It is the channel coefficient. represent The mean square bandwidth is given by the fact that the shaping pulse of an FDM is typically a sinc function; therefore, the mean square bandwidth can be expressed as... (18) Representing the The navigation power of a satellite is specific across all subcarriers of the same satellite. Power representing random noise, Representing navigation users Receiving, synchronizing, and capturing data from satellites The signal suffers from non-noise interference. Since the cross-correlation coefficient of ZC sequences with different root values ​​is zero, interference from navigation signals from other satellites can be ignored. It consists only of interference from communication signals on the same carrier wave, i.e. ;therefore, (19), of which Representative from satellite To navigation users The channel coefficient, yes The receiving antenna gain.

4. The multi-satellite parallel access method for ICAN according to claim 1, characterized in that, The optimization problem (20) is as follows: （20）， Its goal is to maximize the sum of channel capacity for all communication users within the CMSA-ICAN paradigm by allocating communication and navigation power to each subcarrier and by allocating users and subcarriers to satellites. Indicates the first The navigation power of each satellite on each subcarrier Indicates the first The first satellite The subcarrier is assigned to the first The power of each communication user, and It is the carrier allocation factor, where Indicates the first The first satellite The subcarrier is assigned to the first For each user, the opposite is also true; constraint Ensure navigation users SPEB should be less than the threshold. ,constraint Ensure communication users The channel capacity is greater than its minimum channel capacity requirement. ,constraint Ensure allocation to satellites The sum of its communication and navigation power is less than the maximum power that the satellite can provide. ,constraint Indicates carrier allocation factor It is a binary variable, with constraints Ensure that each subcarrier can be allocated to at most one satellite and one user, constraining... and Ensure that both communication and navigation power are positive, and impose constraints. Ensure navigation users From satellite The strength of the received navigation signal is greater than its reception threshold. This threshold is determined by the receiver performance and constrains... Guarantee the upper limit of the number of carriers that each communication user can use.

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