Interference suppression processing method and device for satellite-ground integrated network and electronic equipment

Abstract

The application provides a satellite-ground fusion network interference suppression processing method and device and electronic equipment, and belongs to the field of wireless communication. The method comprises the following steps: acquiring statistical channel information of a satellite user terminal and network side information provided by a ground network side, wherein the network side information comprises position information of a ground base station; based on the position information of the ground base station and the spatial distribution statistical characteristics of the ground user terminal in the coverage area of the ground base station, a statistical interference integral model for representing the average interference power of the satellite transmission signal to the ground user terminal is constructed; under the condition of satisfying the interference power constraint and the satellite transmission power constraint of the statistical interference integral model, the communication performance index of the satellite user terminal is optimized as the target, and a precoding matrix of a satellite transmission end is solved; and the signal is processed according to the precoding matrix and transmitted to the satellite user terminal.

Description

Technical Field

[0001] This application relates to the field of wireless communication, and in particular to a method, apparatus, electronic device, and computer program product for interference suppression processing in a satellite-ground integrated network. Background Technology

[0002] In integrated terrestrial and satellite networks (ITSNs), satellite and terrestrial communication systems share spectrum resources to improve utilization, but this also introduces severe inter-system co-channel interference. Currently, interference suppression mainly relies on the accurate acquisition and sharing of channel state information (CSI), such as beamforming based on perfect instantaneous channel state information (iCSI), robust design based on statistical CSI, joint satellite-terrestrial precoding, and satellite-independent precoding based on interference thresholds. However, these methods generally face problems such as strong dependence on cross-system CSI sharing, high signaling overhead, high algorithm complexity, and poor real-time performance. Furthermore, they lack unified protocol support, making practical deployment in dynamic, large-scale integrated terrestrial and satellite networks difficult. Summary of the Invention

[0003] This application provides an interference suppression processing method, apparatus, electronic device, and computer program product for a space-ground integrated network, which can solve the problems of existing methods such as strong dependence on cross-system CSI sharing, large signaling overhead, high algorithm complexity, and poor real-time performance.

[0004] In a first aspect, embodiments of this application provide an interference suppression method for a satellite-ground fusion network, the method comprising the following steps: The system acquires statistical channel information from satellite user terminals and network-side information provided by the ground network, including the location information of ground base stations. Based on the location information of ground base stations and the spatial distribution statistical characteristics of ground user terminals within their coverage areas, a statistical interference integral model is constructed to characterize the average interference power of satellite transmitted signals to ground user terminals. To satisfy the interference power constraints and satellite transmit power constraints of the statistical interference integral model, and with the goal of optimizing the communication performance indicators of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving the problem. The signal is processed according to the precoding matrix and then sent to the satellite user terminal.

[0005] Secondly, embodiments of this application provide an interference suppression processing device for a satellite-to-ground fusion network, the device comprising the following: The information acquisition module is used to acquire statistical channel information of satellite user terminals and network-side information provided by the ground network side, wherein the network-side information includes the location information of ground base stations; The interference modeling module is used to construct a statistical interference integral model to characterize the average interference power of satellite-transmitted signals to ground user terminals based on the location information of ground base stations and the spatial distribution statistical characteristics of ground user terminals within their coverage area. The precoding solution module is used to solve for the precoding matrix of the satellite transmitter, under the conditions of interference power constraints and satellite transmit power constraints of the statistical interference integral model, with the objective of optimizing the communication performance indicators of the satellite user terminal; and The signal processing module is used to process the signal according to the precoding matrix and send it to the satellite user terminal.

[0006] Thirdly, embodiments of this application provide an electronic device including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of the interference suppression processing method for the satellite-ground fusion network as described in the first aspect.

[0007] Fourthly, embodiments of this application provide a computer program product, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, the program instructions being executed by a computer to implement the steps of the interference suppression processing method for the satellite-ground fusion network as described in the first aspect.

[0008] This application's embodiments are based on easily obtainable and slowly changing network-side information such as satellite-side statistical channel information and ground base station location information for modeling and optimization. It eliminates the need for real-time, precise iCSI interaction between satellite and ground systems, significantly reducing reliance on cross-system coordination protocols and data sharing mechanisms, minimizing massive signaling overhead, and enhancing the independence and flexibility of system deployment. By introducing an integral model based on the statistical characteristics of user spatial distribution, the interference impact of satellites on a massive number of discrete ground users is transformed into continuous integral calculation over the base station coverage area, allowing for a more accurate description of aggregated interference in large-scale user scenarios. The precoding design, constrained by both interference power thresholds and satellite transmit power, supports optimization with the goal of maximizing weighted sum rate or minimizing mean square error. For high-throughput scenarios, iterative optimization algorithms can be used to approximate the performance upper limit, while for low-complexity real-time requirements, closed-form solutions can be obtained combined with rapid parameter adjustment strategies, providing flexible and robust interference suppression methods for different service scenarios and resource conditions. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating an interference suppression method for a satellite-ground fusion network provided in an embodiment of this application. Figure 2 This is a flowchart illustrating another interference suppression method for a satellite-ground fusion network provided in this application embodiment; Figure 3 This is a system architecture diagram of a satellite-ground integrated network provided in an embodiment of this application; Figure 4 This is a schematic diagram illustrating the relationship between the approximate mean square error of interference and the radius of the ground base station provided in the embodiments of this application; Figure 5 This is a schematic diagram of the satellite beam provided in an embodiment of this application; Figure 6 This is a schematic diagram of satellites and their rates versus SNR provided in an embodiment of this application; Figure 7 This is a schematic diagram of the average interference power provided in an embodiment of this application; Figure 8 This is a schematic diagram of satellite and rate convergence provided in an embodiment of this application; Figure 9 This is a schematic diagram of satellites and their rates and interference thresholds provided in an embodiment of this application; Figure 10 This is a schematic diagram of the average interference power and interference threshold provided in the embodiments of this application; Figure 11 This is a schematic diagram illustrating the satellites, their speeds, and the number of satellite user terminals provided in the embodiments of this application; Figure 12 This is a schematic diagram of satellites and their rates versus SNR provided in an embodiment of this application; Figure 13 This is a schematic diagram of the average interference power of the various schemes provided in the embodiments of this application; Figure 14 This is a schematic diagram of the structure of an interference suppression processing device for a satellite-ground fusion network provided in an embodiment of this application; Figure 15 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0011] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0012] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0013] In existing Integrated Terrestrial and Satellite Networks (ITSNs), to address the inter-system interference problem caused by spectrum sharing, research mainly focuses on "transmitter beamforming" technology. Specific technical solutions are as follows: (I) Transmit Beamforming Scheme Based on Perfect Instantaneous CSI Currently widely used classical beamforming algorithms include Maximum Ratio Transmission (MRT), Zero Forcing (ZF), Minimum Mean Square Error (MMSE), and Weighted Minimum Mean Square Error (WMMSE). These algorithms can significantly improve user signal quality or system capacity, but they require the satellite to acquire high-precision instantaneous channel state information (iCSI) from all ground user terminals (UTs). However, in low Earth Orbit (LEO) satellite scenarios, obtaining perfect iCSI faces significant challenges due to the high relative motion between the satellite and the ground, time delays, and instability of the feedback link. Therefore, these methods are costly and impractical in practice.

[0014] (II) Robust Beamforming Design Based on Statistical CSI To reduce reliance on iCSI, some studies have begun to use statistical CSI (e.g., user angle distribution, path loss, and power information) for beam design. For example, a design method that maximizes the average signal-to-interference plus-noise ratio (SINR) using angle distribution and power information has been proposed. This type of method performs well in terms of multi-user average performance and can improve system robustness. Building on this, some studies have further introduced angle uncertainty modeling, taking into account the Angle of Departure (AoD) error in the design, and employing mechanisms such as daily antenna power constraints for robust optimization, thus improving adaptability in real-world scenarios.

[0015] (III) Satellite-Ground Joint Precoding Design Existing technologies also include joint optimization methods based on CSI sharing mechanisms. In such schemes, satellite and ground systems jointly participate in beam design, with objective functions including minimizing total system interference power, maximizing system capacity, or ensuring SINR constraints for each user. For example, by sharing channel matrix information, precoding is jointly optimized between satellite and ground systems to simultaneously meet the minimum SINR requirements of multiple UTs. Although joint design theoretically offers the best performance, it relies on the real-time and accurate sharing of all CSI between satellite and ground, resulting in extremely high signaling overhead and dependence on coordination mechanisms between cross-system operators, posing significant obstacles to engineering deployment.

[0016] (iv) Satellite-side independent precoding design based on interference threshold constraints Considering the practical limitations of sharing CSI between satellite and ground systems, some studies have attempted to perform precoding optimization independently on the satellite side and introduce constraints on the interference power of the ground-based UT (Underground User) into the optimization problem. For example, CSI can be centrally acquired using a cloud platform, and an interference threshold can be set in the beam design to maximize the communication performance of the satellite-side UT. Furthermore, ground user rate guarantee constraints are introduced, and by optimizing satellite precoding, the throughput of the satellite system can be improved without significantly reducing the performance of ground users.

[0017] While existing technologies have mitigated interference issues caused by satellite-to-ground spectrum sharing to some extent, significant shortcomings remain in areas such as engineering deployment, complexity control, and protocol support. These shortcomings are specifically reflected in the following aspects: (1) It is highly dependent on CSI sharing and lacks protocol support. Most existing beamforming designs rely on sharing precise channel information between satellite and ground systems. This mechanism requires terrestrial communication systems to upload their users' CSI (Communications Information System) to the satellite system in real time via satellite links or cloud platforms. However, current satellite-terrestrial converged architectures lack a unified cross-domain protocol standard, and data collaboration mechanisms between cross-system operators are absent. Furthermore, the sheer number of ground-based ground units (UTs) and the massive volume of their iCSI information make it difficult for the system to meet practical requirements in terms of signaling resources, latency control, and synchronization accuracy.

[0018] (2) The algorithm has high complexity and is difficult to deploy in real time. In particular, the joint beam design method involves precoding vectors of multiple systems as its optimization variables, resulting in high optimization dimensionality. The problem to be solved is a non-convex, multi-constraint, and multi-objective complex domain optimization problem, which requires iterative algorithms (such as interior point method, convex approximation method, etc.) to solve, resulting in high computational complexity and making it difficult to meet the real-time requirements of fast dynamic interference suppression in practical systems.

[0019] This application proposes an interference modeling method based on satellite-side statistical CSI (based on angular distribution and free space loss), eliminating the dependence on iCSI of the ground-based UT (Underground Terminal Unit), enabling the satellite system to independently perform precoding to suppress interference to the ground-based UT and improve the alignment and rate of the satellite UT. An approximate interference modeling method based on ground station (BS) location information is introduced. By combining the known spatial location information of the ground BS, the satellite-to-ground interference integral model is approximately simplified, significantly reducing the complexity of interference calculation, improving modeling efficiency, and enhancing the feasibility of the solution in large-scale deployments and dynamic environments. A multi-criteria robust precoding design framework is constructed, with two types of optimization objectives for different service scenarios: (i) a weighted sum rate maximization scheme for high throughput requirements; and (ii) a minimum mean square error (MMSE) scheme for low complexity and real-time requirements. By introducing a joint constraint mechanism of interference threshold and transmit power, a flexible trade-off between ground interference suppression and satellite communication performance is achieved.

[0020] The following is in conjunction with the appendix Figures 1 to 15 This application provides a detailed description of an interference suppression method, apparatus, electronic device, and computer program product for a satellite-ground fusion network through specific embodiments and application scenarios.

[0021] Figure 1 This application illustrates an embodiment of an interference suppression method for a satellite-to-ground integrated network. This method can be executed by an electronic device, which may include a server and / or terminal devices. In other words, the method can be executed by software or hardware installed on the server and / or terminal devices, and includes the following steps: Step 110: Obtain statistical channel information of the satellite user terminal and network-side information provided by the ground network side, wherein the network-side information includes the location information of the ground base station.

[0022] Satellite user terminals include user equipment that communicates directly via satellite links. Statistical channel information includes long-term statistical characteristics of the channel, specifically including but not limited to: average path loss between the satellite and the user terminal, Rice factor (K-factor), spatial angular distribution of users (e.g., statistical mean and spread range of AoD), and channel correlation matrix. This information changes slowly and can be obtained through long-term measurements or estimation based on geographical location and historical data, without requiring high-frequency feedback.

[0023] The terrestrial network side includes the terrestrial mobile communication network portion that shares spectrum with the satellite network. Network-side information includes semi-static or static network configuration and topology information provided by terrestrial network operators or network management systems, which is independent of real-time user dynamics. The location information of terrestrial base stations, i.e., the geographical coordinates (e.g., latitude, longitude, and altitude) of each base station, is determined after deployment, easily obtainable, and virtually unchanging. Network-side information may further include: the coverage radius of the terrestrial base stations, antenna configuration parameters, and statistical characteristics of user distribution within their service area (e.g., uniform distribution density function), for more refined interference modeling.

[0024] Step 120: Based on the location information of the ground base station and the spatial distribution statistical characteristics of the ground user terminals within its coverage area, construct a statistical interference integral model to characterize the average interference power of satellite transmitted signals to ground user terminals.

[0025] The location information of the ground base stations can be used as known reference points to determine the geometric center of interference assessment. The spatial distribution statistics of ground user terminals are usually described in the form of a probability density function, which describes the possible location distribution of ground users within the coverage area of ​​the base stations they serve (e.g., uniform distribution).

[0026] The statistical interference integral model transforms the statistical expectation of the instantaneous interference power of the satellite to a large number of discrete and randomly distributed ground users into a mathematical integral over the entire continuous coverage area of ​​the ground base station, thus avoiding the complexity of calculating and summarizing for a massive number of users individually.

[0027] Step 130: Under the conditions of satisfying the interference power constraints and satellite transmission power constraints of the statistical interference integral model, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving.

[0028] This step aims to solve a mathematical problem with the precoding matrix as the optimization variable. This problem must simultaneously satisfy two key constraints. The interference power constraint, based on the statistical interference integral model constructed in step 120, requires that the average interference power caused by the satellite's transmitted signals to ground users must not exceed a preset threshold. The satellite transmit power constraint requires that the total transmit power of the satellite must not exceed its power budget.

[0029] Under the premise of satisfying the above constraints, the solution is proposed with the goal of optimizing the communication performance indicators of satellite users. Specifically, corresponding optimization objectives and solution schemes can be provided according to the needs of different application scenarios.

[0030] For example, maximizing the weighted sum rate, which aims to maximize the sum of data rates for all satellite users, is suitable for scenarios that prioritize total system throughput. This can be achieved using an alternating optimization algorithm based on multidimensional complex quadratic transformations. This algorithm decomposes the complex non-convex problem into a series of more manageable convex optimization subproblems by introducing auxiliary variables and problem transformation. Through alternating iterative solutions, it ultimately converges to a high-performance precoding matrix.

[0031] For example, minimizing the mean square error (MSE) aims to minimize signal distortion at satellite user receivers, focusing on improving the reception reliability of individual users. This approach typically yields computationally efficient solutions and can be achieved using a penalty function method. This method incorporates the interference power constraint as a penalty term into the objective function, transforming the original constrained optimization problem into an unconstrained optimization problem (excluding the power constraint). Solving this problem directly yields a closed-form solution for the precoding matrix. Subsequently, adjusting the penalty factor through a simple binary search ensures that the final solution strictly meets the interference threshold requirements, achieving an effective balance between algorithm complexity and performance.

[0032] The final output of step 130 is the optimized satellite launch precoding matrix, which can optimally improve the communication quality of satellite users (achieving the set performance indicators) while strictly protecting the ground network from excessive interference (meeting interference power constraints) and complying with the satellite's own energy limitations (meeting power constraints).

[0033] Step 140: Process the signal according to the precoding matrix and send it to the satellite user terminal.

[0034] The signal processing can be achieved by the satellite's baseband processing unit constructing a symbol vector from the data symbol stream to be sent to the satellite user terminal, and then multiplying this symbol vector with the precoding matrix to obtain the transmitted signal vector after beamforming processing.

[0035] The processed signal vector undergoes radio frequency processing such as digital-to-analog conversion, up-conversion, and power amplification before being fed to a large-scale antenna array (e.g., a uniform planar array) onboard the satellite. The signal components radiated by each antenna element collectively form a transmit beam with specific spatial directivity and energy distribution. This beam pattern is a direct spatial representation of the precoding matrix, designed to enhance the signal strength directed at the target satellite user while actively avoiding or suppressing energy radiation to ground user areas, thereby achieving step interference suppression.

[0036] In this embodiment, modeling and optimization are performed using readily available and slowly changing network-side information, such as satellite-side statistical channel information and ground base station location information. This eliminates the need for precise real-time iCSI interaction between satellite and ground systems, significantly reducing reliance on cross-system coordination protocols and data sharing mechanisms, minimizing massive signaling overhead, and enhancing the independence and flexibility of system deployment. By introducing an integral model based on the statistical characteristics of user spatial distribution, the interference impact of satellites on a large number of discrete ground users is transformed into continuous integral calculation over the base station coverage area, allowing for a more accurate description of aggregated interference in large-scale user scenarios. The precoding design, constrained by both interference power thresholds and satellite transmit power, supports optimization targeting different communication performance indicators, such as maximizing the weighted sum rate or minimizing the mean square error. For high-throughput scenarios, iterative optimization algorithms can be used to approximate the performance upper limit, while for low-complexity real-time requirements, closed-form solutions can be obtained combined with rapid parameter adjustment strategies, providing flexible and robust interference suppression methods for different service scenarios and resource conditions.

[0037] Figure 2 This illustration shows a flowchart of another interference suppression method for a satellite-ground integrated network provided by an embodiment of this application. This method can be executed by an electronic device, which may include a server and / or terminal devices. In other words, the method can be executed by software or hardware installed on the server and / or terminal devices, and includes the following steps: Step 210: Obtain statistical channel information of the satellite user terminal and network-side information provided by the ground network side, wherein the network-side information includes the location information of the ground base station.

[0038] Step 210 can be found above. Figure 1 The specific description of step 110 in the illustrated embodiment can achieve the same technical effect, and will not be repeated here to avoid repetition.

[0039] Step 220, based on step 120 of the above embodiment, based on the location information of the ground base station and the spatial distribution statistical characteristics of the ground user terminals within its coverage area, a statistical interference integral model is constructed to characterize the average interference power of satellite transmitted signals to ground user terminals. The method of this embodiment may further include the following specific steps: Based on the spatial distribution probability density function of the ground user terminal, the statistical interference channel matrix is ​​obtained by integrating the coverage area of ​​the ground base station.

[0040] The statistical interference channel matrix can be a mathematical representation obtained by aggregating the interference effects of satellites on a large number of randomly distributed ground users through statistical integration. Specifically, the coverage area of ​​the ground base station is used as the integration domain, which is usually centered on the base station and bounded by its coverage radius. The spatial distribution probability density function of the ground user terminals is used as the integration weight, which describes the statistical probability of a user appearing at different locations within the base station coverage area (e.g., uniform distribution, Gaussian distribution, etc.). Within the base station coverage area, for each possible location, the statistical contribution of the satellite interference channel to the user at that location (i.e., the kernel function) is calculated. This kernel function integrates physical factors such as the outer product of the array response vector determined by the satellite antenna array geometry, free space path loss, and antenna gain. Subsequently, this kernel function is multiplied by the probability of the user appearing at that location (i.e., the spatial distribution probability density function) to obtain the weighted contribution of that location to the overall interference statistics. Finally, this weighted contribution is double-integrated over the entire coverage area, and the integration result is each element of the statistical interference channel matrix.

[0041] This step describes user distribution from a continuous probabilistic and statistical perspective, avoiding the errors and randomness that may arise from modeling based on discrete user samples. Although integration is involved, its integrand and integration domain are well-defined, allowing for efficient computation using numerical integration methods. Furthermore, once established, the model can be reused as long as the statistical characteristics of the user distribution remain relatively unchanged, eliminating the need for frequent updates. The entire process relies entirely on statistical characteristics (distribution function) and slowly varying information (base station location, path loss model), without requiring real-time instantaneous channel state information from any ground users, thus addressing the challenge of cross-system signaling sharing.

[0042] Step 230: Under the condition of satisfying the interference power constraint and satellite transmission power constraint of the statistical interference integral model, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving.

[0043] Step 240: Process the signal according to the precoding matrix and send it to the satellite user terminal.

[0044] Steps 230 and 240 can be found above. Figure 1 The specific descriptions of steps 130 and 140 in the illustrated embodiment are provided, and they achieve the same technical effect. To avoid repetition, they will not be repeated here.

[0045] In this embodiment, by introducing the probability density function of user spatial distribution and integrating it over the entire base station coverage area, the interference situation of massive, randomly distributed ground users can be continuously statistically analyzed. This avoids the random errors and information gaps that may exist in traditional models based on discrete sampling or approximate modeling of typical users, making the interference assessment results more statistically representative. The modeling process relies only on slowly varying statistical information and static or semi-static network information, without needing to obtain real-time instantaneous channel state information of ground users. This solves the problems of difficulty in obtaining high-precision CSI and large shared signaling overhead caused by high dynamics and long latency between satellite and ground systems, enhancing feasibility.

[0046] In yet another exemplary embodiment, the integrand in the integral operation includes: an outer product matrix composed of satellite antenna array response vectors, a free-space path loss and antenna gain term from the satellite to the ground user terminal, and the spatial distribution probability density function.

[0047] The integrand in the integral operation can specifically include the following three core elements: The outer product matrix formed by the response vectors of the satellite antenna array is used to reflect the spatial structural characteristics of a large-scale antenna array, determine the radiation directionality of the signal in three-dimensional space, and is a mathematical representation of the spatial directivity of interference.

[0048] The free-space path loss and antenna gain term from satellite to ground user terminal reflects the power attenuation of the signal during the propagation process of the satellite-to-ground link and the gain characteristics of the transmitting and receiving antennas themselves, which together determine the power intensity of the interference signal.

[0049] The spatial distribution probability density function is used as a statistical weight to combine the physical impact of the disturbance with the probability of the actual distribution of ground users, thus transforming the model from a deterministic description to a statistical description.

[0050] In this embodiment, by clarifying and integrating the above three elements, a more refined and complete mathematical characterization of the statistical characteristics of satellite-to-ground interference can be achieved. These three elements correspond to the spatial directionality, power intensity, and statistical distribution of the interference, respectively, and can be used to describe the process of interference effects from generation and propagation to statistical aggregation, ensuring the physical interpretability of the model. Compared with models that use simplified path loss or ignore user distribution, the integral model in this embodiment can more accurately reflect the actual impact of the spatial selective attenuation of satellite beams and the non-uniform distribution of users on the aggregated interference statistics, thus providing a more reliable constraint basis for subsequent precoding optimization.

[0051] In some embodiments, see Figure 3 The diagram illustrates a downlink scenario of spectrum sharing in a satellite-to-ground network, involving one satellite and... Each ground-based BS serves and User terminals have overlapping coverage areas at the edges. Both terrestrial and satellite communication systems share sub-6 GHz spectrum for downlink transmission to meet 3GPP requirements. Communication links include end-to-end wireless connections established for transmitting user data (e.g., voice, text, video, control signaling), while inference links include wireless connections for acquiring, estimating, or sensing environmental state information. In schemes relying on perfect instantaneous CSI, a high-quality feedback link from the terrestrial user to the satellite (or to the processing center) is required to transmit CSI. This type of link can be considered an inference link, its sole purpose being to allow the satellite to sense or infer accurate channel conditions. This embodiment eliminates or greatly simplifies the reliance on such demanding links, eliminating the need for terrestrial users to feed back instantaneous CSI via inference links. Instead, it utilizes statistical CSI (slowly varying information) and network-side information (e.g., base station location), which can be obtained through background configuration, low-speed feedback, or database queries. This helps reduce the quality, real-time, and overhead requirements of inference links.

[0052] Channel and signal models Consider a low-Earth orbit satellite equipped with a large-scale uniform planar array (UPA), which consists of... It consists of several antennas, among which... and They represent along shaft and Number of antennas along the axis. Channel modeling method based on ray tracing, satellite terminal. In time and frequency The spatial channel response vector can be modeled as:

[0053] in, This represents the downlink channel gain for low-Earth orbit satellites. Due to the line-of-sight propagation characteristics of satellite communication, we assume a channel gain of... It follows a Rice distribution, and its Rice factor is And the power meets Specifically, The real and imaginary parts are independently and identically distributed with mean . variance is It follows a real-valued Gaussian distribution. Furthermore, This indicates the Doppler frequency shift caused by satellite motion, while Indicates the first The minimum propagation delay of each satellite UT. The array response vector can be expressed as: .like Figure 3 As shown, channel space angle and These represent UT relative to UPA. shaft and The direction cosine on the axis. Wherein, For satellite to the number The elevation angle of the satellite UT. It is the azimuth angle. and They represent in shaft and The direction vector on the axis is expressed as follows:

[0054] in, Indicates that adjacent antenna elements are in shaft and Spacing on the axis. In ITSN, satellites and... Each terrestrial base station (BS) shares spectrum to provide communication services to its corresponding ground-based terminal (UT). Since satellites typically supplement terrestrial communication systems, when a terminal is in an area where satellite and terrestrial networks overlap, it can preferentially access the terrestrial network over the satellite network. This indicates that satellite UTs are usually located outside the coverage area of ​​terrestrial BSs, therefore interference from terrestrial BSs to satellite UTs is negligible. Signal received by a satellite UT It can be represented as:

[0055] in, For beamforming vectors, Indicates that the satellite sent to the first The symbol for a satellite UT. Represents additive noise, following a complex Gaussian distribution. For the sake of simplicity, the received signals from all satellite UTs are combined as follows:

[0056] The channel matrix is ​​represented as follows: The beamforming matrix is Furthermore, the symbol matrix Represents the symbols transmitted by the satellite and satisfies While spectrum sharing between satellite and terrestrial networks can improve spectrum utilization, inter-system interference can degrade overall performance. Effective interference suppression in the overlapping coverage areas of ITSNs is crucial for efficient spectrum sharing. To simplify the analysis, interference between terrestrial base stations (BSs) is ignored, and the focus is on satellite interference to terrestrial ground stations (UTs). The average interference power for each terrestrial UT can be expressed as:

[0057] in, This represents the satellite-to-ground UT channel matrix based on iCSI. To ensure the reliability of ground communication, this interference should be minimized and constrained to a set threshold. under.

[0058] Statistical channel information for robust beamforming and interference models Benefiting from the large-scale antenna arrays of satellite equipment, beamforming technology is used to reduce interference in ITSN systems. Traditional beamforming designs typically rely on the availability of iCSI, but obtaining accurate iCSI is usually impractical due to long propagation delays, significant Doppler shifts, and limited pilot overhead. Furthermore, frequent updates to the beamforming vector based on iCSI require continuous adjustments. and This presents significant challenges in the practical implementation of satellite payloads. Therefore, satellite beamforming design is employed using statistical channel state information (sCSI) to meet the requirements of ITSN systems, including:

[0059] In ITSN systems, these parameters are assumed to change slowly. The average interference power can be further expressed statistically as follows:

[0060] in, Since the number of ground-based touchpoints (UTs) affected by interference is large, obtaining the sCSI of all UTs would still incur significant pilot overhead. Therefore, the sum of all discrete ground-based UT channels is transformed into an integral of the user distribution within the ground-based base station (BS) coverage area. This integral is expressed as:

[0061] in, and These are the ground base stations (BS) and the number of unmanned aerial vehicles (UTs) per BS. and .in, and These are the transmit gain and receive gain of a single antenna, respectively. It is the probability density function of the user distribution. Given the th Polar coordinates of a ground BS UT and Representing angular and radial positions respectively, the propagation distance between the satellite and the UT can be calculated using the following formula:

[0062] in, Indicates the satellite's altitude. Indicates the first The polar angle of a ground BS, It is the first The distance from the ground base station (BS) to the satellite's nadir point is then calculated. The Middle The value of an element is represented as:

[0063] The index of an element is determined by the following expression: The indexes are arranged in the following order:

[0064] Channel space angle from The calculation yielded the following result. It is the coverage radius of the satellite, making Therefore, the statistical interference channel term is obtained. The integral form of which Each element can be re-represented as:

[0065] The integral form of this statistical interference model reduces the dependence of satellite and ground UT on iCSI, thereby alleviating the need for significant pilot overhead, delay, and computational complexity.

[0066] In some embodiments, based on step 130 of the above embodiments, with the goal of optimizing the communication performance indicators of the satellite user terminal, the following may be included: constructing the communication performance indicators based on the statistical channel information of the satellite user terminal.

[0067] In yet another exemplary embodiment, based on step 130 of the above embodiment, and with the interference power constraint and satellite transmit power constraint of the statistical interference integral model as conditions, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving. The method of this embodiment may further include the following specific steps: The objective of optimizing the communication performance indicators of the satellite user terminal includes maximizing the weighted sum rate of the satellite communication user terminal.

[0068] In this embodiment, the optimization objective is defined as maximizing the weighted sum rate to improve the overall spectral efficiency and capacity of the satellite communication system in the space-ground integrated network. The weighted sum rate is a core indicator for measuring the total data throughput of a multi-user system. Precoding optimization with this objective directly addresses the fundamental need for extremely high data rates and system capacity, and is suitable for high-traffic service scenarios such as video backhaul, broadband access, and high-throughput satellite services. By assigning different weighting factors to different satellite user terminals, this embodiment can flexibly reflect user priorities, service requirements, or service level agreements. It can prioritize the rate of high-weight users (e.g., VIP users, emergency services) during optimization, thereby achieving intelligent and differentiated scheduling of network resources and improving service quality and user satisfaction. With a large-scale satellite antenna array configuration, precoding design aimed at maximizing the weighted sum rate can collaboratively optimize beams pointing to multiple users, intelligently utilizing spatial channel differences between users. While suppressing interference between users, it enables parallel transmission for multiple users, helping to improve the utilization efficiency of spectrum resources.

[0069] In yet another exemplary embodiment, based on step 130 of the above embodiment, and with the interference power constraint and satellite transmit power constraint of the statistical interference integral model as conditions, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving. The method of this embodiment may further include the following specific steps: Initialize the precoding matrix; based on the current precoding matrix, update the auxiliary variables; fix the auxiliary variables, solve the convex optimization problem with the weighted sum rate lower bound as the objective and the interference power constraint and the satellite transmit power constraint as the conditions, and update the precoding matrix; alternately iterate the steps of updating the auxiliary variables and solving the convex optimization problem until the convergence condition is met.

[0070] Specifically, the precoding matrix at the satellite transmitter is initialized. Initialization can be based on a simple beamforming method (e.g., Maximum Ratio Transmission (MRT)) or random initialization. Simultaneously, an iteration counter, convergence threshold, and maximum iteration count are set. Based on the precoding matrix obtained through iteration, a set of auxiliary variables is updated according to predetermined rules. These auxiliary variables are introduced using mathematical tools such as multidimensional complex quadratic transformations, and their purpose is to decouple complex fractional terms (e.g., signal-to-interference-plus-noise ratio, SINR) in the original objective function. For the problem of maximizing the weighted sum rate, the optimal values ​​of the auxiliary variables usually have closed-form solutions. The auxiliary variables are then fixed to the updated values ​​from the previous steps. At this point, the original problem of maximizing the weighted sum rate (or its equivalent after transformation) is transformed into an optimization problem about the precoding matrix. After fixing the auxiliary variables, this problem is convex with respect to the precoding matrix, and its objective function is typically a tight lower bound of the weighted sum rate, simultaneously constrained by interference power constraints and total power constraints. This convex problem can be efficiently solved using optimization algorithms (e.g., interior-point methods) to obtain the updated precoding matrix. The algorithm calculates the objective function value for the current iteration (e.g., an estimate of the weighted sum rate) and compares it with the value from the previous iteration. If the increment of the objective function value is less than a preset convergence threshold, or the number of iterations reaches the maximum number of iterations, the algorithm terminates and outputs the current precoded matrix as the optimal solution. Otherwise, a new round of alternating optimization begins.

[0071] In this embodiment, by introducing auxiliary variables and applying mathematical transformations, the originally difficult-to-solve non-convex weighted sum rate maximization problem is decomposed into a series of convex optimization problems with respect to the auxiliary variables and the precoding matrix, respectively. Each subproblem has an efficient and stable numerical solution, ensuring the algorithm's feasibility. This alternating optimization algorithm exhibits monotonically convergent characteristics, meaning that each iteration guarantees that the objective function value (lower bound of the weighted sum rate) does not decrease and eventually converges to a stable point, ensuring the algorithm's reliability. In each iteration, the algorithm strictly considers and satisfies interference power constraints and transmit power constraints. The final converged precoding matrix not only effectively improves the weighted sum rate of the satellite system but also ensures that interference to the ground network is controlled below the threshold and conforms to the satellite's power budget, achieving simultaneous optimization of performance and constraints.

[0072] In some embodiments, beamforming is avoided by maximizing interference and rate, and the specific steps are as follows: Problem Derivation First, a beamforming scheme is designed to maximize the weighted sum rate (WSR) while ensuring that the average satellite-to-ground interference (UT) remains within a threshold. The optimization problem can be described as follows:

[0073] in, Indicates the antenna power budget. Indicates the first The weights of each satellite UT. It can be proven that problem (15) is equivalent to problem (16), that is, the global optimal solutions of the two problems are the same.

[0074]

[0075] Among them, the definition and , where represents the channel matrix ignoring phase information. Problem (16) remains a non-convex optimization problem, which presents a challenge in obtaining the global optimum.

[0076] Alternating Optimization Algorithm Based on MCQT According to Jensen's inequality, the objective function in problem (16), ergodicity and rate, has the following lower bound constraint:

[0077] Among them, the definition and Therefore, the direct maximization problem of ergodic sums and rates is reformulated as the maximization problem of its lower bound. Since this problem is a standard concave-convex multi-ratio fractional programming problem, it is solved by applying the multidimensional complex quadratic transformation (MCQT). This transformation decouples the numerator and denominator of each SINR through MCQT decoupling. Thus, the original weighted sum rate problem (15) is transformed into:

[0078] in, Let the auxiliary variable be an example, and its objective function be as follows:

[0079] This question relates to optimization variables. and It is convex. Based on this transformation, an alternating optimization algorithm is proposed to solve this problem. Specifically, when the matrix... When the constraint is fixed, the problem becomes an unconstrained convex optimization problem, i.e. This is the optimal point. By using gradient To obtain by setting it to zero:

[0080] With fixed auxiliary variables In this case, the original optimization problem can be transformed into:

[0081] The problem described above is a convex problem, which can be solved using general convex optimization algorithms, such as the interior point method. and The optimization is performed alternately until convergence. This process is summarized in the following table, "Algorithm 1: Satellite Interference Avoidance Beamforming Algorithm Based on WSR-MCQT".

[0082]

[0083] Interference avoidance algorithm based on WMMSE because The large dimensionality of the problem (21) still leads to high computational complexity. Therefore, in this section, an iterative algorithm is proposed, which is derived from the equivalence between the WSR problem and the Weighted Minimum Mean Square Error (WMMSE) problem. The algorithm uses the KKT conditions of the WMMSE problem to simplify the solution process, thereby reducing the computational complexity. Definition and The WMMSE problem can then be expressed as:

[0084] It is equivalent to problem (18), that is, the global optimal solution of both. They are the same. Mean squared error It can be represented as:

[0085] In fixed and In this case, The optimal value can be obtained by... right To determine this, set the derivative to zero:

[0086] at this time, The value can be calculated as:

[0087] When the KKT conditions for both problems are satisfied, an equivalence relationship can be established between the WSR and WMMSE problems. By making their Lagrangian gradients equal, an equivalence relationship can be established for a given WSR problem. and Derive the optimal mean square error weights :

[0088] Then, fix the vector and The optimization problem then simplifies to:

[0089] Its Lagrange function can be derived as:

[0090] in, and These are Lagrange multipliers. (Through...) It can The closed-form iterative expression is expressed as:

[0091] Among them, it means And define the matrix as well as By substituting this expression into problem (27), it can be simplified to the following about and Optimization issues:

[0092] Although the problem is nonconvex, its low-dimensional optimization variables can be solved efficiently using traditional iterative algorithms. Then, by... and Substituting back into formula (29), we can obtain The results and process are summarized in the table below, "Algorithm 2: Satellite Interference Avoidance Beamforming Algorithm Based on WSR-WMMSE Equivalent".

[0093]

[0094] In yet another exemplary embodiment, based on step 130 of the above embodiment, and with the interference power constraint and satellite transmit power constraint of the statistical interference integral model as conditions, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving. The method of this embodiment may further include the following specific steps: The goal of optimizing the communication performance indicators of the satellite user terminal includes minimizing the mean square error of the satellite communication user terminal.

[0095] In this embodiment, the optimization objective is set as minimizing the mean square error of the satellite communication user terminal, so as to minimize the mean square error between the signal recovered by the satellite user at the receiving end and the original transmitted signal, thereby improving the demodulation performance and reliability of the link.

[0096] The objective function for minimizing the mean square error (MSE) is directly related to the receiver's demodulation performance (e.g., bit error rate). Optimizing precoding to minimize MSE improves signal reception quality for satellite users and reduces the risk of bit errors. This approach is particularly suitable for services with high reliability requirements, such as critical command transmission, high-precision sensor data backhaul, or real-time control signaling. Compared to the weighted sum rate maximization problem, the precoding optimization problem based on the MMSE criterion is generally mathematically more user-friendly. In many scenarios, especially after appropriate transformations (e.g., introducing penalty functions to handle interference constraints), the optimal precoding matrix can be derived into a closed-form solution, avoiding complex iterative optimization processes and reducing the complexity and time delay of online computation. This is beneficial for meeting the stringent real-time processing requirements of the system. MMSE precoding design often forms a joint optimal or near-optimal transceiver design with a linear receiver (e.g., an MMSE receiver). This reduces the complexity requirements for user terminals, making them easier to implement in practical satellite user equipment and improving the practicality and terminal compatibility of the solution.

[0097] In yet another exemplary embodiment, based on step 130 of the above embodiment, and with the interference power constraint and satellite transmit power constraint of the statistical interference integral model as conditions, and with the goal of optimizing the communication performance index of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving. The method of this embodiment may further include the following specific steps: The interference power constraint is introduced into the mean square error objective function as a penalty term to construct an unconstrained optimization problem; the unconstrained optimization problem is solved to obtain a closed-form solution of the precoding matrix with the penalty factor as a parameter; the penalty factor is adjusted so that the actual interference power calculated based on the closed-form solution of the precoding matrix meets the preset interference power threshold.

[0098] Specifically, an unconstrained optimization problem with a penalty term is constructed, incorporating the constraint on statistical interference power from the original problem into the mean square error objective function as a penalty term. Solving the unconstrained problem yields a closed-form solution with the penalty factor as a parameter. For the transformed problem, considering only the total power constraint or after appropriate processing (e.g., introducing the Lagrange multiplier method to handle power constraints), a closed-form expression for the optimal precoding matrix can be derived. This expression explicitly depends on the penalty factor, the statistical channel information of the satellite users, the noise power, and the total satellite power. The penalty factor is adjusted to satisfy the interference threshold. Since the closed-form solution is a function of the penalty factor, its corresponding actual interference power also changes. Therefore, a one-dimensional search process (e.g., an efficient bisection method) can be used to find the penalty factor that makes the actual interference power satisfy the preset threshold. Substituting the penalty factor into the closed-form solution yields the optimal precoding matrix that simultaneously satisfies both interference and power constraints.

[0099] In this implementation, a single closed-form matrix operation and a fast one-dimensional search for a single variable avoid large-scale iterative optimization, resulting in a significantly lower computational burden than the weighted sum rate maximization algorithm. This makes it highly suitable for onboard processing units or real-time systems with stringent requirements for computational resources and processing latency. The penalty factor directly adjusts the relationship between satellite user reception quality and ground interference suppression. Through a bisection search, the penalty factor that satisfies the strict interference threshold can be precisely found, ensuring that the constraints are strictly satisfied while optimizing MSE performance as much as possible under these constraints. The optimal pre-coded closed-form solution has a clear mathematical form, making it easy to program and implement in a digital signal processor. Its structure is similar to classic regularized zero-forcing or MMSE beamforming, facilitating engineers' understanding and integration into existing systems.

[0100] In some embodiments, closed-loop interference avoidance beamforming based on MMSE is implemented through the following steps: For traditional linear beamforming designs, MMSE can serve as another important design criterion, aiming to improve the demodulation performance at the receiver, and the MMSE problem typically has a closed-form solution. This embodiment involves the MMSE problem under the same constraints as the WSR problem.

[0101] Problem Derivation The interference avoidance beamforming optimization problem based on the MMSE criterion can be formulated as follows:

[0102] ,in, This represents phase compensation for receiver delay and Doppler shift. Compared to the difficulty of phase compensation at the transmitter, the receiver can accurately estimate the phase error based on the downlink pilot signal to assist in compensation. To simplify the problem, a penalty function method is used to mitigate interference. Specifically, a penalty term is introduced into the objective function. This transforms the problem into a power-constrained convex optimization problem. Here, Let represent the penalty factor. For ease of derivation, let represent... Therefore, the optimization problem can be rewritten as:

[0103] The optimal solution to this problem is derived as follows:

[0104] in, And assume that the noise power of all satellite UTs is .also, Normalize the power. When and All are identity matrices, and are set to... as well as When the beamforming matrix in formula (29) is reduced to the closed MMSE beamforming matrix in formula (33), the beamforming matrix in formula (29) can be reduced to the closed MMSE beamforming matrix in formula (33).

[0105] Optimal Closed Beamforming Based on Interference Threshold parameter The choice of is crucial because it effectively reflects the trade-off between mean square error performance and interference management capability. Specifically, for formula (33) The closed-form solution, total disturbance right The derivative is negative:

[0106] because The larger the value, the greater the interference power. The smaller the value, the lower the average interference threshold. At a specific signal-to-noise ratio, a suitable method can be used to determine the appropriate signal-to-noise ratio. Value. Although the bisection method requires iterative calculation of the beamforming matrix, it can be used to predict interference avoidance beamforming when performing interference avoidance beamforming within continuous time slots or beamforming cycles. The changes significantly reduce the execution frequency of the bisection method. This method makes the beamforming scheme approximately a closed-loop computation, thereby reducing computational complexity. The algorithm summary is shown in Table 3, "Algorithm 3: Satellite Interference Avoidance Beamforming Algorithm Based on MMSE".

[0107]

[0108] In yet another exemplary embodiment, the method of this embodiment may further include the following specific steps: The interference channel between the satellite and the ground user terminal in the statistical interference integral model is approximated as the interference channel between the satellite and ground base stations in various locations.

[0109] Specifically, the interference channel of satellites to a large number of randomly distributed ground user terminals in the statistical interference integral model can be approximated as the interference channel of satellites to a limited number of fixed-location ground base stations. Considering that in a satellite-ground converged network, the coverage area of ​​a ground base station (typically hundreds of meters to several kilometers) is much smaller than the coverage area of ​​a satellite beam (typically tens to hundreds of kilometers), and users are usually distributed around their serving base stations, it can be approximated that the aggregate interference of a satellite to all users served by a ground base station mainly depends on the geometric relationship and channel characteristics between the satellite and the base station, while the statistical impact of the user's specific location within the cell on the aggregate interference is secondary. As long as the virtual interference power caused by the satellite's transmitted signal to the locations of various ground base stations is controlled, the average interference to real users within its coverage area will also be effectively suppressed.

[0110] In this embodiment, the modeling complexity is reduced from being related to the number and distribution of users to being related only to the number of base stations through interference approximation, resulting in an order-of-magnitude improvement in computational efficiency. The approximated model no longer requires the potentially difficult-to-obtain statistical information of the spatial distribution probability density function of ground users as input; it only requires the location information of ground base stations and the average number of users, making model construction simpler and more robust. The approximation operation itself does not introduce the requirement for instantaneous CSI of ground users; all calculations are still based on the statistical CSI from satellite to base station location (e.g., path loss, array response). Due to the lightweight computation and stable input information, this approximation model can quickly respond to network topology changes and easily scale to ultra-large-scale terrestrial network scenarios without incurring computational burden, thus enhancing the feasibility and scalability of the solution in real-world dynamic network environments.

[0111] In some embodiments, the interference approximation in beamforming design involves the following steps: Approximate interference at base station location In the above scheme, interference avoidance beamforming depends on the integral term. However, the computation of this integral term is substantial, and it is difficult to obtain real-time distribution information of ground users. To address these issues, ground B location information is used to approximate the result. This eliminates the dependence on ground user distribution integration, significantly reducing the overall computational complexity of the beamforming scheme. Typically, the coverage area of ​​a ground-based BS cell is significantly smaller than the size of a satellite beam. Therefore, the interference channel from the satellite to the ground-based UT is approximated as the channel from the satellite to the corresponding ground-based BS. Definition This indicates the channel from the satellite to the ground base station (BS), and The approximation can be expressed as: ,in This represents the number of UTs for each ground-based BS. The original average interference power constraint can be approximated as:

[0112] The other steps remain unchanged, but formula (29) needs to be modified as follows:

[0113] Similarly, the original closed-form solution in formula (33) needs to be modified as follows:

[0114] Approximate Interference Error Analysis Considering that this approximation may introduce errors that could affect performance, the factors influencing the approximation error were further analyzed. Assume a ground user located at a single ground base station (BS) at a sub-satellite point has a radius of [missing information - likely a distance in terrestrial base station radius]. The internal distribution follows a uniform pattern, and the user density is... Squared error matrix Statistical expressions in integral form Its approximate value The error between them, its first Each element is calculated using the following formula:

[0115] Among them, the definition as well as Utilizing the properties of the first kind of Bessel functions The integral can be simplified to:

[0116] matrix about The gradient is given as:

[0117] The following inequality can be derived:

[0118] Considering The gradient satisfies the following inequality:

[0119] See Figure 4 Interference approximation mean square error vs. (User density) ),also, Figure 4 The simulation results presented in the paper verify the ground BS radius. The monotonic relationship between the approximation error and the carrier frequency, which varies with different carrier frequencies. and user density The results were verified. Specifically, the approximate mean square error of a single ground base station (BS) located at the nadir point was simulated. The results show that as the radius of the ground BS increases... and user density As the carrier frequency increases, the mean square error increases; and as the carrier frequency increases... As the value increases, the mean square error decreases. Furthermore, when the position of the ground UT completely coincides with the corresponding ground BS, there is... At this time, the approximate term and Exactly the same. By using approximate The computational complexity associated with this term is significantly reduced, with the complexity order decreasing from [previous order]. Reduce to ,in, and These are the radii of the ground base stations. and polar angle The number of discrete samples.

[0120] In this embodiment, the Monte Carlo method is used to evaluate the proposed scheme. Consider a broadband low-Earth orbit satellite communication system, where the Rice factor of all UT channels is set to... The radius of the ground BS is 500 meters. Calculate:

[0121] in, Boltzmann's constant, Standard temperature For system bandwidth, noise power along with Changes. The configurations of the remaining satellite systems are shown in the table below.

[0122]

[0123] For the above embodiments, simulation verification and analysis were performed. The specific steps are as follows: Performance verification of the interference avoidance beamforming algorithm: This study verifies the effectiveness of the proposed satellite interference avoidance beamforming algorithm and compares it with the following schemes: MRT, ZF, MMSE, and WMMSE (baseline): four common linear beamforming methods.

[0124] WQTIA: Satellite interference avoidance beamforming based on WSR-MCQT.

[0125] WWEIA: Satellite interference avoidance beamforming based on WSR-WMMSE equivalence.

[0126] MMSEIA: MMSE-based satellite interference avoidance beamforming.

[0127] Set the number of satellite users Number of ground base stations Number of single-ground BS users Interference power threshold .

[0128] See Figure 5 Satellite beam diagram (red star: satellite UTs, green circle: ground UTs). Figure 5 The image shows beammaps generated by different beamforming schemes. A comparison of these schemes reveals that the MMSEIA scheme has lower interference power at the ground user terminal (green circle position) compared to the MMSE scheme, proving the effectiveness of interference avoidance.

[0129] See Figure 6 In the comparison of satellite throughput, rate, and SNR, the total throughput of the MMSEIA scheme is close to that of the MMSE scheme, demonstrating its effectiveness in maintaining throughput. Furthermore, the WWEIA and WQTIA schemes outperform MMSE and approach its performance. These two iterative algorithms significantly improve the total throughput, while the closed-form solution of MMSEIA has lower computational complexity.

[0130] See Figure 7 The diagram illustrates the average interference power. Three interference avoidance beamforming schemes, MMSEIA, WWEIA, and WQTIA, successfully achieved the interference threshold. This demonstrates the effectiveness of their interference management.

[0131] See Figure 8 The diagram illustrates the convergence of satellites and rates. For the iterative algorithms WWEIA and WQTIA, their convergence performance in terms of total satellite throughput is shown. The proposed WWEIA and WQTIA schemes converge rapidly in terms of total satellite throughput within the specified number of iterations. The results are validated under different signal-to-noise ratios, demonstrating the consistent convergence performance of these algorithms. Furthermore, compared to the WQTIA scheme, WWEIA requires more iterations to converge.

[0132] The impact of interference threshold on the number of satellite UTs, such as Figure 9 As shown, when the signal-to-noise ratio At that time, the total throughput of both the MMSE and WMMSE schemes remained unchanged. However, with the interference threshold... The overall satellite throughput of the MMSEIA and WWEIA protocols decreased. Specifically, when... At that time, and Compared to the previous scenario, the total throughput of these three algorithms decreased by approximately .

[0133] See Figure 10 The diagram illustrates the relationship between average interference power and interference threshold. The average interference power remains constant for both the MMSE and WMMSE schemes, while it varies with the interference threshold. The average interference power of the MMSEIA, WWEIA, and WQTIA schemes is adaptively reduced.

[0134] See Figure 11 A diagram illustrating the relationship between satellites, their rates, and the number of satellite UTs is provided, demonstrating the impact of different numbers of satellite UTs on the proposed interference avoidance beamforming scheme, while keeping the number of ground BSs and ground UTs constant. Examples are given for the low-complexity MMSEIA and WWEIA systems. Figure 11 The total throughput of satellites increases with the number of satellite UTs. It increases with the increase of. However, with As the growth rate increases, the rate of growth gradually slows down. At that point, MMSEIA's total satellite throughput stabilized and remained almost unchanged thereafter. It's worth noting that MMSEIA's performance in total satellite throughput is close to that of MMSE, while WWEIA's performance is close to that of WMMSE.

[0135] The verification of the interference approximation further validates the beamforming design performance after applying the interference approximation. This is based on the integral interference term of sCSI from satellite to ground UT. Approximately the corresponding satellite-to-ground (BS) channel, denoted as This approximation process is also known as Ground Position Aided (PA).

[0136] The ground BS radius is fixed as The proposed schemes MMSEIA-PA, WWEIA-PA, and WQTIA-PA were compared with the original interference-avoidance beamforming schemes MMSEIA, WWEIA, and WQTIA. Figure 12 In this study, the sum-rate performance of the approximate scheme is consistent with that of the original scheme. For example... Figure 13 As shown, the results indicate that all three PA schemes in All reached the interference threshold. This demonstrates the effectiveness of the approximation method in interference management. The proposed PA method reduces computational complexity while maintaining effective interference management and satellite and rate performance, highlighting the practical advantages of the PA scheme in ITSN systems.

[0137] In yet another exemplary embodiment, the method is performed by an on-board processing unit of a low-Earth orbit satellite or by a cloud processing platform that is communicatively connected to the satellite.

[0138] The on-board processing mode allows all steps of this method (including interference model construction and precoding matrix solution) to be completed directly within the satellite's on-board processing unit, provided the satellite platform has sufficient computing power, storage resources, and energy supply. In this mode, the satellite only needs to receive or store necessary network-side information (such as ground base station locations) and satellite user statistical channel information via a satellite-to-ground link (e.g., a feeder link) to autonomously complete the calculations and directly apply the resulting precoding matrix to its digital beamformer. This mode offers advantages such as extremely low decision-making and execution latency and independence from continuous air-to-ground backhaul links, making it suitable for scenarios with extremely high real-time requirements or limited backhaul links.

[0139] The cloud processing mode takes into account the limited onboard computing resources of some satellites (especially early or low-cost satellites). This method can also be deployed on a cloud processing platform connected to the satellite via a high-speed, reliable link (such as an inter-satellite link or a feeder link). In this mode, the satellite uploads the required raw or preprocessed information (such as user measurement reports and its own status) to the cloud. The cloud platform centrally runs the method, completing complex modeling and optimization calculations, and finally sends the calculated precoded matrix back to the satellite for execution. This mode can fully utilize the powerful parallel computing capabilities and flexible algorithm update capabilities of ground-based cloud computing centers, handling more complex models and larger-scale networks while reducing the burden on satellite payloads.

[0140] Corresponding to the interference suppression processing method for satellite-ground fusion networks provided in the above embodiments, based on the same technical concept, this application also provides an interference suppression processing device for satellite-ground fusion networks. See Figure 14 The device 400 includes an information acquisition module 410, an interference modeling module 420, a precoding solution module 430, and a signal processing module 440.

[0141] The information acquisition module 410 is used to acquire statistical channel information of the satellite user terminal and network-side information provided by the ground network side, including the location information of the ground base station; the interference modeling module 420 is used to construct a statistical interference integral model to characterize the average interference power of the satellite transmitted signal to the ground user terminal based on the location information of the ground base station and the spatial distribution statistical characteristics of the ground user terminals within its coverage area; the precoding solution module 430 is used to solve for the precoding matrix of the satellite transmitter by satisfying the interference power constraints and satellite transmission power constraints of the statistical interference integral model and optimizing the communication performance index of the satellite user terminal; and the signal processing module 440 is used to process the signal according to the precoding matrix and send it to the satellite user terminal.

[0142] It should be noted that the interference suppression processing device for satellite-ground fusion network provided in this application embodiment and the interference suppression processing method for satellite-ground fusion network provided in this application embodiment are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned interference suppression processing method for satellite-ground fusion network, and the repeated parts will not be described again.

[0143] The interference suppression method and apparatus for satellite-ground integrated networks provided in this application, compared to traditional interference modeling methods that often rely on sharing precise CSI between satellite and ground systems, utilize ground user distribution information to construct an interference modeling mechanism that does not require sharing CSI. This significantly improves the system's feasibility and network independence. This application employs a distributed integral approach to continuously model the interference impact of satellites on ground-based ground units (UTs), providing a more accurate interference description framework suitable for scenarios with large-scale, densely deployed users in satellite-ground systems. Furthermore, to reduce the computational complexity of the integral model, this application introduces an approximate modeling scheme based on ground base station locations, effectively simplifying the integral calculation process. This is suitable for complex network deployments and real-time dynamic interference assessment, improving modeling efficiency and scalability.

[0144] The interference suppression method and apparatus for satellite-ground fusion networks provided in this application, with its robust precoding design, effectively designs transmit beams based solely on statistical CSI, compared to existing patents that rely on precise channel information. This enhances the adaptability of the precoding scheme under uncertain or difficult-to-obtain channel conditions. The precoding design simultaneously introduces two key constraints: interference threshold and transmit power, and proposes corresponding optimization strategies to improve resource utilization efficiency. This application's embodiments are based on a multi-criteria precoding framework design, constructing a dual-criteria optimization framework: (i) an iterative scheme aiming to maximize the weighted sum rate, suitable for high-throughput scenarios; and (ii) a closed-loop scheme aiming to minimize the mean square error, suitable for low-complexity real-time requirements. The bisection method flexibly controls interference constraints, achieving a balance between performance and complexity. The precoding strategy proposed in this application, without relying on real-time CSI, can be widely adapted to diverse satellite-ground fusion scenarios, exhibiting higher engineering feasibility and future expansion potential.

[0145] Corresponding to the interference suppression processing method for the satellite-to-ground fusion network provided in the above embodiments, based on the same technical concept, this application also provides an electronic device for performing the above-described method. Figure 15 To illustrate the structure of an electronic device according to various embodiments of this application, as shown in the following diagrams... Figure 15As shown. Electronic device 500 can vary considerably due to differences in configuration or performance, and may include one or more processors 510 and memory 520. Memory 520 may store one or more application programs or data. Memory 520 may be temporary or persistent storage. The application programs stored in memory 520 may include one or more modules (not shown), each module may include a series of computer-executable instructions for the electronic device. Furthermore, processor 510 may be configured to communicate with memory 520 and execute the series of computer-executable instructions stored in memory 520 on the electronic device.

[0146] This application also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, which, when executed by a computer, implement the steps of the interference suppression processing method for the satellite-ground fusion network as described above.

[0147] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, apparatus, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0148] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems, devices), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0149] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0150] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0151] In a typical configuration, an electronic device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0152] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0153] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0154] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0155] Those skilled in the art will understand that embodiments of this application can be provided as methods, apparatus, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0156] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for interference suppression in a satellite-ground fusion network, characterized in that, The method includes the following steps: The system acquires statistical channel information from satellite user terminals and network-side information provided by the ground network, including the location information of ground base stations. Based on the location information of ground base stations and the spatial distribution statistical characteristics of ground user terminals within their coverage areas, a statistical interference integral model is constructed to characterize the average interference power of satellite transmitted signals to ground user terminals. To satisfy the interference power constraints and satellite transmit power constraints of the statistical interference integral model, and with the goal of optimizing the communication performance indicators of the satellite user terminal, the precoding matrix of the satellite transmitter is obtained by solving the problem. The signal is processed according to the precoding matrix and then sent to the satellite user terminal.

2. The method according to claim 1, characterized in that, The step of constructing a statistical interference integral model to characterize the average interference power of satellite-transmitted signals to ground user terminals, based on the location information of ground base stations and the spatial distribution statistical characteristics of ground user terminals within their coverage areas, includes the following steps: Based on the spatial distribution probability density function of the ground user terminal, the statistical interference channel matrix is ​​obtained by integrating the coverage area of ​​the ground base station.

3. The method according to claim 2, characterized in that, The integrand in the integral operation includes: the outer product matrix composed of the satellite antenna array response vector, the free space path loss and antenna gain term from the satellite to the ground user terminal, and the spatial distribution probability density function.

4. The method according to claim 1, characterized in that, The objective of optimizing the communication performance indicators of the satellite user terminal includes maximizing the weighted sum rate of the satellite communication user terminal.

5. The method according to claim 4, characterized in that, The process of obtaining the precoding matrix of the satellite transmitter by satisfying the interference power constraints and satellite transmit power constraints of the statistical interference integral model, with the objective of optimizing the communication performance indicators of the satellite user terminal, includes the following steps: Initialize the precoding matrix; Update the auxiliary variables based on the current precoding matrix; With the auxiliary variables fixed, solve a convex optimization problem with the weighted sum rate lower bound as the objective and the interference power constraint and the satellite transmit power constraint as the conditions, and update the precoding matrix; The steps of updating the auxiliary variables and solving the convex optimization problem are performed alternately and iteratively until the convergence condition is met.

6. The method according to claim 1, characterized in that, The objective of optimizing the communication performance indicators of the satellite user terminal includes minimizing the mean square error of the satellite communication user terminal.

7. The method according to claim 6, characterized in that, The process of obtaining the precoding matrix of the satellite transmitter by satisfying the interference power constraints and satellite transmit power constraints of the statistical interference integral model, with the objective of optimizing the communication performance indicators of the satellite user terminal, includes the following steps: The interference power constraint is introduced into the mean square error objective function in the form of a penalty term to construct an unconstrained optimization problem. Solving the unconstrained optimization problem yields a closed-form solution to the precoding matrix with a penalty factor as a parameter; The penalty factor is adjusted so that the actual interference power calculated from the closed-form solution of the precoding matrix meets the preset interference power threshold.

8. The method according to claim 1, characterized in that, It also includes the following steps: The interference channel between the satellite and the ground user terminal in the statistical interference integral model is approximated as the interference channel between the satellite and ground base stations in various locations.

9. The method according to any one of claims 1 to 8, characterized in that, The method is executed by the on-board processing unit of the low-Earth orbit satellite or by a cloud processing platform that is in communication with the satellite.

10. An interference suppression processing device for a satellite-ground fusion network, characterized in that, The device includes the following: The information acquisition module is used to acquire statistical channel information of satellite user terminals and network-side information provided by the ground network side, wherein the network-side information includes the location information of ground base stations; The interference modeling module is used to construct a statistical interference integral model to characterize the average interference power of satellite-transmitted signals to ground user terminals based on the location information of ground base stations and the spatial distribution statistical characteristics of ground user terminals within their coverage area. The precoding solution module is used to solve for the precoding matrix of the satellite transmitter by satisfying the interference power constraints and satellite transmit power constraints of the statistical interference integral model and optimizing the communication performance index of the satellite user terminal. as well as The signal processing module is used to process the signal according to the precoding matrix and send it to the satellite user terminal.

11. An electronic device, characterized in that, It includes a processor, a memory, a program or instructions stored in the memory and executable on the processor, wherein the program or instructions, when executed by the processor, implement the steps of the method as described in any one of claims 1 to 8.

12. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions that, when executed by a computer, implement the steps of the method as described in any one of claims 1 to 8.

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