Beamforming method and system for massive MIMO-NOMA system in low-orbit satellite communication scenario

Abstract

The application discloses a beam forming method and system of a large-scale MIMO-NOMA system in a low-orbit satellite communication scene, clusters users based on the spatial angles of the users, and performs power distribution by adopting a fractional power distribution method; the user clustering result and the power distribution result are subjected to beam forming vector optimization, a weighted sum of SLNR of each cluster and SINR of each user in the cluster is maximized as an optimization target, a multi-target beam forming vector optimization problem is established; an alternating direction multiplier method is used for solving, and a beam forming vector is output; or a beam forming scheme using statistical channel information is adopted, a weighted sum of average signal-to-leakage-and-noise ratio and average signal-to-interference-and-noise ratio is maximized as an optimization target, the alternating direction multiplier method is used for solving, and a beam forming vector is output. The application solves the technical problem of maximum SLNR and SINR in the large-scale MIMO-NOMA system, and effectively improves the sum rate performance of the system.

Description

Beamforming Method and System for Large-Scale MIMO-NOMA Systems in Low-Earth Orbit Satellite Communication Scenarios Technical Field

[0001] This invention belongs to the field of beamforming technology in low-Earth orbit satellite communication systems, specifically relating to a beamforming method and system for a large-scale MIMO-NOMA system in low-Earth orbit satellite communication scenarios. Background Technology

[0002] Faced with a severe shortage of wireless spectrum resources and the demands of high bandwidth, massive connectivity, and high reliability in future wireless communication systems, how to further improve spectrum utilization is an urgent problem that mobile communication systems and their evolution must solve. In orthogonal multiple access (OMA) technology, only one user resides in each time slot or frequency band, and users utilize mutually orthogonal resources, effectively suppressing inter-user interference. However, this leads to low spectrum efficiency. Therefore, non-orthogonal multiple access (NOMA) technology has been extensively studied to improve spectrum efficiency. NOMA schemes mainly include power domain NOMA and sparse code multiple access (SCMA). The NOMA discussed in this invention is a power domain NOMA technology where user signals are superimposed in the power domain. Combining multiple-input multiple-output (MIMO) technology with power domain NOMA technology can simultaneously utilize the degrees of freedom in both the spatial and power domains to improve the system's spectrum efficiency, and is considered a key candidate physical layer solution for future terrestrial mobile communication and low-Earth orbit satellite communication systems.

[0003] Currently, the application of this technology in terrestrial communication networks is relatively widespread and mature. However, due to the limited coverage of terrestrial cellular networks, in sparsely populated areas such as remote mountainous regions, deserts, and oceans, terminal devices need to access the internet at high cost or may even be unable to do so. Therefore, satellite communication systems have received increasing attention due to their superior coverage capabilities. The future 6G network will be an integrated air-space-ground-sea network, in which satellite communication systems will occupy a crucial position. Compared to geosynchronous Earth Orbit (GEO) satellites, LEO satellites have lower costs and relatively lower path loss and transmission latency, making LEO (Low Earth Orbit) satellite communication systems a focus of attention for many researchers. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a beamforming method and system for large-scale MIMO-NOMA systems in low-Earth orbit satellite communication scenarios, which addresses the shortcomings of the prior art and effectively improves the sum rate performance of the system.

[0005] The present invention adopts the following technical solution:

[0006] A beamforming method for large-scale MIMO-NOMA systems in low-Earth orbit satellite communication scenarios includes the following steps:

[0007] S1. Based on the spatial perspective of each user, user clustering is performed to obtain the user clustering results. Then, the power allocation method is used to perform power allocation to obtain the power allocation results.

[0008] S2. Perform beamforming vector optimization on the user clustering results and power allocation results obtained in step S1. The optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster. With the transmit power as the constraint, a multi-objective beamforming vector optimization problem is established.

[0009] S3. Solve the multi-objective beamforming vector optimization problem obtained in step S2 using the alternating direction multiplier method. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector. S4. Optimize the beamforming vector of the user clustering and power allocation results obtained in step S1. Use a beamforming scheme with statistical channel information. The optimization objective is to maximize the weighted sum of the average signal-to-noise ratio and the average signal-to-interference-plus-noise ratio. The constraint is the transmit power constraint.

[0010] S5. Solve the multi-objective beamforming vector optimization problem obtained in step S4 using the alternating direction multiplier method. Input statistical channel state information and superimposed NOMA signals, and output the beamforming vector.

[0011] Specifically, in step S1, power allocation is performed using a fractional power allocation method, and the power p allocated to the k-th user in the m-th cluster is... m,k for:

[0012]

[0013] Among them, h m,k / n m,k μ represents the channel quality of the k-th user in the m-th cluster. FTPA K is the attenuation factor. m Let P be the number of users in the m-th cluster. m Let be the transmission power of the m-th cluster.

[0014] Specifically, in step S2, the multi-objective beamforming vector optimization problem is as follows:

[0015]

[0016] st||w m || 2 =1

[0017] Among them, w m SLNR represents the beamforming vector of the m-th cluster. m K represents the signal-to-leakage-to-noise ratio of the m-th cluster, γ0 represents the weighting factor corresponding to the signal-to-leakage-to-noise ratio of the m-th cluster, and K m SINR represents the number of users in the m-th cluster. m,n γ represents the signal-to-interference-plus-noise ratio (SIR) of the nth user in the mth cluster. n This represents the weighting factor corresponding to the signal-to-interference-plus-noise ratio (SIN / N) of the nth user in the cluster.

[0018] Furthermore, the optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of all users within the cluster.

[0019]

[0020]

[0021] Where, α m,n P represents the power allocation factor for the nth user in the mth cluster. m h represents the transmission power of the m-th cluster. m,n M represents the channel vector between the satellite and the nth user in the m-th cluster. b σ represents the total number of beams. 2 P is the noise power. j Let be the power of the j-th cluster beam. Let be the beamforming vector of the m-th cluster beam, and I be the identity matrix.

[0022] Specifically, in step S3, an auxiliary variable z is added. m Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function. Gradient descent and corresponding approximate equivalents are then used to obtain the iterative update formula for the optimization variables until the iteration stopping condition is met, i.e., the original error r is reached. (k) With dual error s (k) The number of iterations is less than the set value or reaches the pre-set maximum number of iterations.

[0023] Furthermore, the original error r (k) With dual error s (k) Specifically:

[0024]

[0025]

[0026] Where ε and ζ are both very small numbers, As an auxiliary variable, Let be the beamforming vector of the m-th cluster in the k-th iteration.

[0027] Specifically, in step S4, the optimization problem with maximizing the weighted sum of SLNR and SINR as the optimization objective and transmit power as the constraint is expressed as:

[0028]

[0029] st||w m ||=1

[0030] Where, γ n γm is the weighted value of the average signal-to-interference-plus-noise ratio (SIR) for the nth user in the mth cluster, γ0 is the weighted value of the average SIR for the mth cluster, and wm is the weighted value of the average SIR for the nth user in the mth cluster. m Let be the beamforming vector of the m-th cluster beam.

[0031] Furthermore, the optimization objective is to maximize the weighted sum of the signal-to-leakage-to-noise ratio and the signal-to-interference-to-noise ratio, specifically:

[0032]

[0033]

[0034] Among them, ASLNR m Let m be the average signal-to-noise ratio of users within the m-th beam. K is the conjugate transpose of the m-th beamforming vector. m Let α be the number of users within the m-th beam. m,i Let μ be the power allocation factor for the i-th user within the m-th beam. m,i v represents the channel gain for the i-th user within the m-th beam. m,i M is the channel direction vector of the m-th beam and the i-th user. b Where σ is the beam number, P is the noise standard deviation, and σ is the noise standard deviation. m Let I be the power of the m-th beam, and I be the identity array. ASINR m,n P represents the average signal-to-interference-plus-noise ratio (SIR) of the nth user within the mth beam. j Let be the power of the j-th beam.

[0035] Specifically, in step S5, an auxiliary variable z is added. m Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function L(w). m ,z m Then, through gradient descent and corresponding approximate equivalence, the iterative update formula of the optimization variables is obtained until the iteration stopping condition is met, that is, the original error and dual error are less than the set value or the maximum number of iterations set in advance is reached.

[0036] Secondly, embodiments of the present invention provide a beamforming system for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario, comprising:

[0037] The clustering module performs user clustering based on the spatial perspective of each user, obtains the user clustering results, and uses the fractional power allocation method to perform power allocation, obtains the power allocation results;

[0038] The first optimization module performs beamforming vector optimization on the user clustering results and power allocation results obtained by the clustering module. The optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster. With the transmit power as a constraint, a multi-objective beamforming vector optimization problem is established.

[0039] The first shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the first optimization module. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector.

[0040] The second optimization module performs beamforming vector optimization on the user clustering results and power allocation results obtained by the clustering module. It adopts a beamforming scheme based on statistical channel information. The optimization objective is to maximize the weighted sum of the average signal-to-noise ratio and the average signal-to-interference-plus-noise ratio, and the constraint is the transmit power constraint.

[0041] The second shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the second optimization module. It takes statistical channel state information and superimposed NOMA signals as input and outputs the beamforming vector.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] This paper proposes a beamforming method for large-scale MIMO-NOMA systems in low-Earth orbit (LEO) satellite communication scenarios. The method focuses on maximizing the weighted sum of SLNR and SINR, with transmit power as a constraint, and solves the problem using the ADMM algorithm, suitable for solving large-scale distributed optimization problems. Furthermore, addressing the issues of outdated channel state information and difficulty in obtaining instantaneous CSI in LEO satellite communication scenarios, this paper proposes utilizing slower-changing statistical channel state information to generate beamforming vectors in LEO MIMO-NOMA systems, which also reduces computational overhead.

[0044] Furthermore, considering the computational complexity of large-scale MIMO-NOMA systems, a fractional power allocation method that compromises between complexity and performance is adopted for power allocation, and a user clustering method based on user perspective, which has higher reliability and feasibility, is adopted for user clustering.

[0045] Furthermore, a multi-objective beamforming vector optimization problem is established with the weighted sum maximization of signal-to-leakage-to-noise ratio and signal-to-interference-to-noise ratio as the optimization objective and transmit power constraint as the constraint condition, in order to reduce inter-cluster interference and improve system and rate performance.

[0046] Furthermore, based on the established optimization problem, the definitions of SLNR and SINR for each user within the cluster are given.

[0047] Furthermore, by adding auxiliary variables, we can optimize variables from multiple directions and improve efficiency.

[0048] Furthermore, we define dual error and primal error, and introduce a stopping condition for iteration: the variable and the auxiliary variable converge infinitely close.

[0049] Furthermore, considering that the instantaneous channel state information used in S1 and S2 is not easy to obtain accurately in practice, statistical channel state information, which changes more slowly and is easier to obtain, is introduced. An optimization problem is established with the weighted sum of the average signal-to-noise ratio of each beam and the average signal-to-interference-plus-noise ratio of each user as the optimization objective and the transmit power constraint as the constraint condition, so as to reduce inter-beam interference and improve the feasibility of the scheme.

[0050] Furthermore, based on the established optimization problem and statistical channel state information, the definitions of average SLNR and average SINR of each user within the cluster are given.

[0051] Furthermore, by adding auxiliary variables and optimizing them from multiple directions, we can improve the efficiency of solving optimization problems based on statistical channel state information.

[0052] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0053] In summary, this invention addresses the large-scale MIMO-NOMA system in low-Earth orbit (LEO) satellite communication scenarios by proposing an optimization problem based on maximizing the weighted sum of SLNR and SINR with transmit power as a constraint, and solving it using the ADMM algorithm, which is suitable for solving large-scale distributed optimization problems. Furthermore, to address the issues of outdated channel state information and difficulty in obtaining instantaneous CSI in LEO satellite communication scenarios, this invention proposes utilizing slower-changing statistical channel state information to generate beamforming vectors in LEO satellite communication MIMO-NOMA systems, which can also reduce computational overhead.

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0055] Figure 1 shows a model diagram of a MIMO-NOMA system in a low-Earth orbit satellite communication scenario.

[0056] Figure 2 is a comparison of the sum rate performance of the proposed scheme and different beamforming schemes;

[0057] Figure 3 is a comparison of the sum rate performance of the proposed scheme with that of strong and weak users under different beamforming schemes.

[0058] Figure 4 shows the sum rate performance of the proposed scheme as a function of antenna size under the same weights.

[0059] Figure 5 shows the sum rate performance of the proposed scheme and various beamforming schemes under different antenna sizes;

[0060] Figure 6 shows the system and rate diagrams of the proposed scheme and various beamforming schemes under perfect CSI and imperfect CSI.

[0061] Figure 7 shows the sum rate performance of the proposed scheme and various beamforming schemes under different numbers of users;

[0062] Figure 8 shows the sum rate performance of the proposed scheme and various beamforming schemes under different user selection ranges.

[0063] Figure 9 shows a comparison of the signal-to-interference-plus-noise ratio (SINR) of the proposed scheme and various beamforming schemes.

[0064] Figure 10 shows the sum rate performance of the proposed WSSSM scheme based on iCSI and sCSI, respectively;

[0065] Figure 11 is a comparison of the sum rate performance of the proposed scheme and different BF schemes based on iCSI and sCSI. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0068] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0069] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this document generally indicates that the preceding and following objects have an "or" relationship.

[0070] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0071] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0072] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0073] Extending massively multi-input multiple-output (MIMO) technology to low-Earth orbit (LEO) satellite communication systems enables satellites to implement flexible beamforming, helping to fully exploit the system's spatial degrees of freedom and significantly improving the spectral and power efficiency of LEO satellite communication systems. Furthermore, introducing power-domain NoMedal-Multi-Action (NOMA) technology into LEO multi-beam satellite systems employing massively multi-input multiple-output (MIMO) naturally creates a massively multi-input multiple-output (MIMO-NOMA) transmission structure. At this point, designing the beamforming (BF) scheme by fully integrating the characteristics of the wireless channel between the satellite and the ground, as well as the NOMA transceiver structure, becomes a key problem to be solved in LEO satellite communication systems. Beam design requires LEO satellites to obtain downlink channel state information (CSI). Considering the long distance and relatively high mobility between the satellite and the user, in FDD systems, channel information must be fed back through ground terminals, which cannot guarantee that the satellite (i.e., the transmitter) will obtain timely and accurate CSI. Therefore, in LEO satellite communication systems, it is necessary to design the transmit beam under the condition of slowly changing statistical CSI.

[0074] Please refer to Figure 1. This invention discloses a beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario. In the downlink transmission link of the system, the transmitting end mainly includes user clustering, power allocation, and beamforming modules, and includes the following steps:

[0075] S1. In the user clustering module, user clustering is performed based on the spatial angle of each user. The user clustering results obtained in step S1 are used to perform power allocation using the fractional power allocation method.

[0076] Similar to terrestrial communication networks, two users need to share the same beam. Therefore, the stronger the correlation between two users within the same cluster, the better the effect of sharing the same beam. In low-Earth orbit (LEO) satellite communication systems, the channel model between the satellite and the user considers both large-scale fading and small-scale fading. Because the distance between the satellite and the user is relatively large, the distance difference between users within the same cluster and the satellite is very small, and their large-scale fading can be approximately equal. Therefore, the impact of free path loss is also approximately the same. Thus, unlike terrestrial communication networks, the channel gain difference between users within the same cluster is very small in LEO satellite communication scenarios, so user grouping mainly relies on the user's spatial angle.

[0077] In summary, this invention employs a user grouping method based on the user's perspective, selecting users who are as close as possible to form a cluster.

[0078] Based on a MIMO-NOMA system model in a single LEO satellite communication scenario, user clustering is first performed according to the user's spatial perspective. Considering that multi-beam LEO satellites are equipped with M=M... x ×M y A uniform planar array (UPA) consisting of M antennas, where M x and M y These represent the number of antennas along the x-axis and y-axis, respectively. Let the altitude of the LEO satellite above the ground be h. Within the coverage area of ​​the low-Earth orbit satellite beam, there are L randomly distributed single-antenna users, and these L users are assigned to M... b There are 3 beams, with full frequency reuse (FFR) between beams; a power-domain NOMA transmission structure is used within each cluster, and users within the same cluster share the same beam; the number of users in the m-th beam is denoted as K. m Furthermore, assuming the user's location is stationary within the considered interval, the channel model between the nth user in the mth beam and the LEO satellite is expressed as:

[0079]

[0080] in, v mn f represents the channel gain, Doppler shift, minimum delay of multipath propagation, and array direction vector of the nth user in the mth beam, respectively. c The carrier frequency is used. Channel modeling considers both large-scale and small-scale fading, and channel gain is also considered. It follows the Ricean fading factor of κ. mn Power is The Rice distribution is defined as:

[0081]

[0082] Among them, G s and G mn These represent the satellite antenna gain and the antenna gain of the nth user in the m-th beam, respectively; d mn It is the distance between the satellite and the nth user of the m-th beam, where c is the speed of light, and δ mn The Rice factor is represented as κ. mn Rice decay, multipath number L u .

[0083] v mn Guided by array vectors in the x-axis and y-axis directions and Rewritten as:

[0084]

[0085] in, a x and a y θ represents the antenna spacing along the x-axis and y-axis. mn and φ mn These are the vertical and horizontal angles at which the nth user in the mth beam departs. Indicates the Kronecker product, therefore and It is information relevant from the user's perspective.

[0086] The channel gain ranking results for users in the m-th beam are as follows:

[0087]

[0088] Therefore, the power allocation result is:

[0089]

[0090] The receiver performs SIC decoding. After Doppler frequency shift and time delay compensation, the nth user in the m-th beam obtains the received signal y. mn :

[0091]

[0092] in, This is the Doppler frequency shift and time delay compensation factor; w m (m=1,...,M b ) is the beamforming vector of the m-th beam; α m,nIt is the power allocation factor for the nth user in the mth beam; P m n is the transmission power of the m-th cluster; m,n It is additive white Gaussian noise; It is the equivalent channel of the nth user in the mth beam after compensation.

[0093] Power allocation is performed using a fractional power allocation method. Let the signal transmission power of the m-th cluster be P. m Then the power allocated to the k-th user in the m-th cluster is:

[0094]

[0095] Among them, h m,k / n m,k This represents the channel quality of the k-th user in the m-th cluster; when μ FTPA When μ = 0, each user in the system is allocated the same amount of power; FTPA As the value of increases, the power allocated to users with poor channel conditions will increase accordingly. In low-Earth orbit satellite communication scenarios, the distance between the satellite and the user is very far, so the channel gain difference among users in the same cluster is very small, and the power allocated to each user in the same cluster is very similar.

[0096] S2. With the goal of maximizing the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster, and with transmit power as a constraint, a multi-objective beamforming vector optimization problem is established.

[0097] With the optimization objective of maximizing the SLNR of each cluster and the weighted sum of the SINR of all users within the cluster, and with transmit power as a constraint, the optimization problem is as follows:

[0098]

[0099] Among them, w m SLNR represents the beamforming vector of the m-th cluster. m K represents the signal-to-leakage-to-noise ratio of the m-th cluster, γ0 represents the weighting factor corresponding to the signal-to-leakage-to-noise ratio of the m-th cluster, and K m SINR represents the number of users in the m-th cluster. m,n γ represents the signal-to-interference-plus-noise ratio (SIR) of the nth user in the mth cluster. n (n=1,...,K m ) represents the weighting factor corresponding to the signal-to-interference-plus-noise ratio of the nth user in the cluster, specifically:

[0100]

[0101]

[0102] Where, α m,n P represents the power allocation factor for the nth user in the mth cluster. m h represents the transmission power of the m-th cluster. m,n M represents the channel vector between the satellite and the nth user in the m-th cluster. b σ represents the total number of beams. 2 This represents noise power.

[0103] S3. Solve the multi-objective beamforming vector optimization problem obtained in step S2 using the alternating direction multiplier method. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector.

[0104] The alternating direction multiplier method, suitable for solving large-scale distributed problems, is employed to solve the joint optimization problem. First, an auxiliary variable z is introduced. m Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function. Then, the iterative update formula of the optimization variable is obtained through gradient descent and the corresponding approximate equivalence until the iteration stopping condition is met, that is, the original error and the dual error are less than a very small value or the maximum number of iterations set in advance is reached.

[0105] Add auxiliary variable z m The original optimization problem is expressed as:

[0106]

[0107] Solving the optimization problem of the above equation, the optimization objective of equation (1.5) is expanded to obtain:

[0108]

[0109] Simplified and rewritten as:

[0110]

[0111] in, C 2,n It is a constant given that the BF vectors of other clusters are known.

[0112]

[0113]

[0114] Combining the Lagrange multiplier method and the penalty function method, the corresponding augmented Lagrange function is obtained as follows:

[0115]

[0116] Where λ is the Lagrange factor (dual factor) and ρ is the penalty parameter.

[0117] The steps to obtain the ADMM update are as follows:

[0118]

[0119]

[0120]

[0121] Equations (1.7) and (1.8) can be expanded as follows:

[0122]

[0123]

[0124] First, update the variable z. m Substituting equation (1.4) into equation (1.11), we get:

[0125]

[0126] The objective function contains a second-order fractional programming term and a quadratic regularization term, making it impossible to solve directly using the generalized Rayleigh entropy. This affects the yield of z. m The analytical expression is unfavorable. Based on the idea that "the larger the quotient of two variables, the larger their difference," we use subtraction to approximate division here, and then rearrange the expression for z. m The gradient is used to obtain its update formula.

[0127] Equation (1.12) is transformed into:

[0128]

[0129]

[0130]

[0131] get:

[0132]

[0133] make Get z m The updated formula is:

[0134]

[0135] Solve for w m The updated version.

[0136] Similarly, from equations (1.3) and (1.15), we obtain:

[0137]

[0138]

[0139] Therefore, w m The updated formula is:

[0140]

[0141] The condition for stopping iterative optimization is reaching the maximum number of iterations or the original residual r. (k) and dual residual s (k) All are less than a very small number (k in the upper right corner indicates the k-th iteration), and the iteration process is convergent, as detailed below:

[0142]

[0143]

[0144] In this case, ε and ζ are both very small numbers.

[0145] S4. A beamforming scheme based on statistical channel information is adopted, with the optimization objective being to maximize the weighted sum of the signal-to-leakage-to-noise ratio and the signal-to-interference-to-noise ratio, and the constraint being the transmit power constraint.

[0146] To address the difficulty of obtaining instantaneous channel information in low-Earth orbit satellite communication scenarios, a beamforming scheme based on statistical channel information that changes slowly and is easily obtained with high precision is proposed. The statistical information used in this invention includes the channel direction vector v. mn and channel gain The statistical characteristics of the instantaneous channel gain can be seen from the channel model. It follows the Ricean fading factor of κ. mn Power is The Ricean distribution, therefore the power μ mn It can be used as channel gain. Based on the statistical characteristics, the average SLNR (ASLNR) of the m-th beam and the average SINR (ASINR) of strong and weak users within the beam are obtained, similar to equations (1.3) and (1.4), and are defined as follows:

[0147]

[0148]

[0149] Where, α m,n P represents the power allocation factor for the nth user in the mth cluster. m This represents the transmission power of the m-th cluster. v represents the channel gain between the satellite and the nth user in the m-th cluster. m,n M represents the array direction vector between the satellite and the nth user in the m-th cluster. b σ represents the total number of beams. 2 This represents noise power.

[0150] The optimization problem with maximizing the weighted sum of SLNR and SINR as the objective and transmit power as the constraint is expressed as:

[0151]

[0152] S5. Use the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained in step S4. The input is statistical channel state information and superimposed NOMA signal, and the output is beamforming vector.

[0153] In step S3, the alternating direction multiplier method, suitable for solving large-scale distributed problems, is used to solve the joint optimization problem. First, an auxiliary variable z is added. m Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function. Then, the iterative update formula of the optimization variable is obtained through gradient descent and the corresponding approximate equivalence until the iteration stopping condition is met, that is, the original error and the dual error are less than a very small value or the maximum number of iterations set in advance is reached.

[0154] Add auxiliary variable z m The optimization problem (1.29) is transformed into

[0155]

[0156] Substituting equations (1.27) and (1.28) into the above equation, and simplifying it, we can obtain...

[0157]

[0158] in, C' 2,n It is a constant given that the BF vectors of other clusters are known.

[0159]

[0160]

[0161] The corresponding augmented Lagrangian function is obtained from equation (1.30):

[0162]

[0163] The augmented Lagrangian function incorporates first- and second-order regularization terms related to the constraints, where λ is the Lagrange multiplier and ρ is the penalty parameter. Using the ADMM algorithm, the update steps for each variable are as follows:

[0164]

[0165]

[0166]

[0167] Update each variable

[0168] First, update variable z according to equation (1.35). m For variable z m The update is similar to equation (1.17), obtained from equation (1.28).

[0169]

[0170]

[0171]

[0172] get

[0173]

[0174] make Get z m The updated version:

[0175]

[0176]

[0177]

[0178] The gradient is obtained from equation (1.43).

[0179]

[0180] make Get w m The updated version:

[0181]

[0182] Repeat the above steps until the maximum number of iterations is reached or the iteration stopping conditions of equations (1.25) and (1.26) are met, at which point the iterative update process stops.

[0183] In another embodiment of the present invention, a beamforming system for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario is provided. This system can be used to implement the beamforming method for the large-scale MIMO-NOMA system in the low-Earth orbit satellite communication scenario. Specifically, the beamforming system for the large-scale MIMO-NOMA system in the low-Earth orbit satellite communication scenario includes a clustering module, a first optimization module, a first shaping module, a second optimization module, and a second shaping module.

[0184] The clustering module performs user clustering based on the spatial perspective of each user, obtains the user clustering results, and uses the fractional power allocation method to perform power allocation, obtains the power allocation results.

[0185] The first optimization module performs beamforming vector optimization on the user clustering results and power allocation results obtained by the clustering module. The optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster. With the transmit power as a constraint, a multi-objective beamforming vector optimization problem is established.

[0186] The first shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the first optimization module. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector.

[0187] The second optimization module performs beamforming vector optimization on the user clustering results and power allocation results obtained by the clustering module. It adopts a beamforming scheme based on statistical channel information. The optimization objective is to maximize the weighted sum of the average signal-to-noise ratio and the average signal-to-interference-plus-noise ratio, and the constraint is the transmit power constraint.

[0188] The second shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the second optimization module. It takes statistical channel state information and superimposed NOMA signals as input and outputs the beamforming vector.

[0189] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0190] Consider a MIMO-NOMA scenario under a single low-Earth orbit satellite communication system. In this scenario, the beamforming scheme for the MIMO-NOMA system in the low-Earth orbit satellite communication scenario proposed in this invention is used. Detailed simulation parameters are shown in Table 1.

[0191] Table 1 Simulation Parameters

[0192]

[0193] In the instantaneous channel information section, the free path loss (large-scale fading) of each user adopts the assumption of free path loss normalization, i.e., in equation (1.28).

[0194]

[0195] Comparison of options:

[0196] Comparison Scheme 1: Fractional power allocation is adopted, user clustering uses the method in S1, and the beamforming module adopts the ZF beamforming scheme;

[0197] Comparison Scheme 2: Fractional power allocation is adopted, user clustering adopts the method in S1, and the beamforming module adopts the MMSE beamforming scheme.

[0198] Comparison Scheme 3: Fractional power allocation is adopted, user clustering adopts the method in S1, and the beamforming module adopts the SLNR beamforming scheme.

[0199] Please refer to Figure 2. With L = 64 users and M = 8*8 antennas, the transmit power P on each antenna... s With a signal-to-noise ratio (SNR) of 30 dBm and weights γ0 = 1, γ1 = 5, and γ2 = 85, the sum rate performance of different beamforming schemes as a function of SNR was simulated and observed. The results are shown in Figure 2. The proposed scheme is labeled "WSSSM" (Weighted Sum of SLNR and SINR Maximization) in the figure. It can be seen that the proposed scheme has a significant advantage in sum rate performance compared to other beamforming schemes, and can further improve the sum rate.

[0200] Please refer to Figure 3. Under the same simulation parameter settings, further observe the sum rate performance of strong and weak users under each BF scheme. The results are shown in Figure 3. It can be seen that under the proposed scheme WSSSM, the sum rate performance of strong users has an absolute advantage, while the performance of weak users is slightly worse than that of the SLNR precoding scheme. However, overall, the proposed scheme has a significant improvement in sum rate performance.

[0201] Please refer to Figure 4. For the same set of weights (γ0=1, γ1=1, γ2=85), with a fixed total power, the simulation results show the sum rate performance of the proposed scheme under different antenna array sizes. As can be seen, under the same set of weights, the system sum rate increases with the increase of the antenna array size because more antennas bring greater antenna gain. The same weights do not affect the overall performance increasing with the number of antennas.

[0202] Please refer to Figure 5. Under the same simulation settings as Figure 4, the sum rate performance of each beamforming scheme under different numbers of antennas is compared. The results are shown in Figure 5. Increasing the number of antennas brings corresponding antenna gain, which helps the generated beam to be better aligned with the target user cluster. Therefore, the sum rate performance of each beamforming scheme increases with the increase of the number of antennas. It can be seen that the sum rate performance of the proposed scheme is also more advantageous compared with other schemes.

[0203] Please refer to Figure 6. With L = 64 users and M = 8*8 antennas, the transmit power P on each antenna... sWith a parameter setting of 30dBm, the impact of imperfect CSI on the system and rate performance using different beamforming schemes was simulated and observed, and the results are shown in Figure 6. Although it is reasonable to assume that the user's spatial angle is known based on relevant literature, imperfect CSI can still occur in real-world scenarios. The vertical and horizontal angles of the user's departure angle respectively follow... and Where Δθ=0° and Δφ=0° represent perfect CSI. It can be seen that the sum rate performance of the MMSE and SLNR beamforming schemes is significantly affected by imperfect CSI, while the proposed scheme is least affected, indicating that the proposed scheme also has good robustness to imperfect CSI.

[0204] Please refer to Figure 7. With antenna count M = 8*8 and signal-to-noise ratio (SNR) = 10dB, simulations were performed to observe the system sum rate performance of each beamforming scheme as a function of the number of users. The results are shown in Figure 7. These users were all selected from a user set of the same size (100 users), and the number of users per cluster was fixed at 2. With the number of antennas and users per cluster remaining constant, an increase in the number of users means an increase in the number of beams. The increasingly dense beams in the same space inevitably lead to more severe inter-beam interference (IBI). As can be seen from the figure, the sum rate performance of MMSE and SLNR beamforming shows a decreasing trend, indicating that the gain from an increase in the number of users cannot compensate for the adverse effects of increased IBI on the sum rate. Especially for the MMSE beamforming scheme, the sharp increase in IBI leads to a rapid performance degradation.

[0205] Please refer to Figure 8. With M = 8*8 antennas, the transmit power P on each antenna... s Under a simulation setting of 30dBm, the changes in system performance and rate under different user selection ranges for different beamforming schemes were observed, and the results are shown in Figure 8. Specifically, "64 / 100" in the figure indicates that the 64 users served by the system were selected from a user set of 100, and "64 / 64" means that the 64 users were randomly generated and then grouped according to the same user clustering strategy. As can be seen from Figure 8, for SLNR and MMSE beamforming schemes, selecting users from a larger user set yields better performance, especially for the MMSE beamforming scheme; however, for the proposed scheme, there is no significant impact. This is mainly because the proposed scheme considers the channel state information of both strong and weak users, while the MMSE beamforming scheme only generates the BF vector based on the channel of strong users. Selecting from a larger user set means that more closely matched user pairs can be selected, therefore MMSE is most affected by the user selection range.

[0206] Please refer to Figure 9. With M = 8*8 antennas, the transmit power P on each antenna...s Under a simulation setting of 30dBm, the signal-to-interference-plus-noise ratio (SIR) of users under different BF schemes was observed to examine the receiver performance. The results are shown in Figure 9. As can be seen from Figures 2 and 9, the proposed WSSSM scheme has significant advantages over other comparative schemes in terms of system performance, data rate, and SIR.

[0207] Please refer to Figure 10. With the parameters of L=64 users divided into 32 clusters and M=8*8 antennas, simulations were performed to observe the changes in the sum-rate performance of beamforming schemes based on statistical channel information and instantaneous channel state information as a function of the transmit power of each antenna. The results are shown in Figure 10. It can be seen that the sum-rate performance of the beamforming scheme based on statistical channel information is very close to that based on instantaneous channel state information. This means that using sCSI can significantly reduce computational overhead at the cost of a slight performance loss, thus solving the practical problem of channel obsolescence in LEO satellite communication systems.

[0208] Please refer to Figure 11. Under the same simulation parameter settings as Figure 10, the simulation observes the variation of the sum rate with the transmit power of each antenna under different beamforming schemes in sCSI and iCSI. The results are shown in Figure 11. It can be seen that the sum rate performance of the ZF and MMSE beamforming schemes based on sCSI and iCSI differs relatively greatly. Compared with other schemes, the proposed WSSSM scheme can achieve higher sum rate performance, and the sum rate performance based on sCSI and iCSI is very similar. This means that the scheme proposed in this chapter for generating BF vectors based on statistical channel information has certain effectiveness and feasibility.

[0209] In summary, this invention provides a beamforming method and system for large-scale MIMO-NOMA systems in low-Earth orbit (LEO) satellite communication scenarios. For LEO satellite communication systems, it proposes an optimization problem based on maximizing the weighted sum of SLNR and SINR with transmit power as a constraint, and solves it using the ADMM algorithm, suitable for solving large-scale distributed optimization problems. Furthermore, addressing the issues of outdated channel state information and difficulty in obtaining instantaneous CSI in LEO satellite communication scenarios, it proposes using slower-changing statistical channel state information to generate beamforming vectors in LEO satellite communication MIMO-NOMA systems, which also reduces computational overhead.

[0210] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A beamforming method for large-scale MIMO-NOMA systems in low-Earth orbit satellite communication scenarios, characterized in that, Includes the following steps: S1. Based on the spatial perspective of each user, user clustering is performed to obtain the user clustering results. Power allocation is then performed using a fractional power allocation method to obtain the power allocation results. The fractional power allocation method is then used to allocate power. Cluster No. Power allocated to each user for: in, Indicates the first Cluster No. Channel quality for individual users As the attenuation factor, For the first Number of users in the cluster For the first S2. Perform beamforming vector optimization on the user clustering results and power allocation results obtained in step S1. The optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster. With the transmit power as a constraint, a multi-objective beamforming vector optimization problem is established. The multi-objective beamforming vector optimization problem is as follows: in, Representing the Cluster beamforming vector, Representing the The signal-to-noise ratio of the cluster. Representing the The weighting factor corresponding to the cluster signal-to-noise ratio. Representing the Number of users in the cluster Representing the Cluster No. Signal-to-interference-plus-noise ratio per user Represents the first of the clusters S3. Solve the multi-objective beamforming vector optimization problem obtained in step S2 using the alternating direction multiplier method. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector. S4. Optimize the beamforming vector of the user clustering and power allocation results obtained in step S1. The beamforming scheme of statistical channel information is adopted. The optimization objective is to maximize the weighted sum of the average signal leakage noise ratio and the average signal interference noise ratio. The constraint condition is the transmit power constraint. S5. Solve the multi-objective beamforming vector optimization problem obtained in step S4 using the alternating direction multiplier method. The input is the statistical channel state information and the superimposed NOMA signal, and the output is the beamforming vector.

2. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 1, characterized in that, The optimization objective is to maximize the weighted sum of the SLNR of each cluster and the SINR of all users within the cluster. in, Indicates the first Cluster No. Power allocation factor for each user Indicates the first Cluster transmit power, Indicates satellite and the first Cluster No. Channel vectors between users Represents the total number of beams. For noise power, For the first Cluster beam power, For the first The beamforming vector of a cluster beam. It is a unit array.

3. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 1, characterized in that, In step S3, add auxiliary variables. Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function. Gradient descent and corresponding approximate equivalents are then used to obtain the iterative update formula for the optimization variables until the iteration stopping condition, i.e., the original error, is met. With dual error The number of iterations is less than the set value or reaches the pre-set maximum number of iterations.

4. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 3, characterized in that, Original error With dual error Specifically: in, and They are all very small numbers. As an auxiliary variable, For the first In the nth iteration The beamforming vector of the cluster.

5. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 1, characterized in that, In step S4, the optimization problem with maximizing the weighted sum of SLNR and SINR as the optimization objective and transmit power as the constraint is expressed as: in, For the first Cluster No. The weighted average signal-to-interference-plus-noise ratio for each user. For the first The weighted average signal-to-noise ratio of the cluster. For the first The beamforming vector of a cluster beam. For the first Average signal-to-noise ratio of users within a beam For the first Within the first beam Average signal-to-interference-plus-noise ratio per user.

6. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 5, characterized in that, The optimization objective is to maximize the weighted sum of the signal-to-leakage-to-noise ratio and the signal-to-interference-plus-noise ratio, specifically: in, For the first Average signal-to-noise ratio of users within a beam For the first The conjugate transpose of beamforming vectors For the first Number of users within a beam For the first Within the first beam Power allocation factor for each user For the first Within the first beam Channel gain for each user For the first The first beam Channel direction vector for each user For the number of beams, The standard deviation of noise. For the first The power of each beam As a unit array, For the first Within the first beam Average signal-to-interference-plus-noise ratio per user For the first The power of each beam.

7. The beamforming method for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario according to claim 1, characterized in that, In step S5, add auxiliary variables. Then, the Lagrange multiplier method and the penalty function method are combined to obtain the augmented Lagrange function. Then, through gradient descent and corresponding approximate equivalence, the iterative update formula of the optimization variables is obtained until the iteration stopping condition is met, that is, the original error and dual error are less than the set value or the maximum number of iterations set in advance is reached.

8. A beamforming system for a large-scale MIMO-NOMA system in a low-Earth orbit satellite communication scenario, characterized in that, include: The clustering module performs user clustering based on the spatial perspective of each user, obtains the user clustering results, and then performs power allocation using a fractional power allocation method. Cluster No. Power allocated to each user for: in, Indicates the first Cluster No. Channel quality for individual users As the attenuation factor, For the first Number of users in the cluster For the first The transmit power of the cluster; the first optimization module performs beamforming vector optimization on the user clustering results and power allocation results obtained by the clustering module, with the goal of maximizing the weighted sum of the SLNR of each cluster and the SINR of each user within the cluster, and with transmit power as a constraint, to establish a multi-objective beamforming vector optimization problem, which is specifically as follows: in, Representing the Cluster beamforming vector, Representing the The signal-to-noise ratio of the cluster. Representing the The weighting factor corresponding to the cluster signal-to-noise ratio. Representing the Number of users in the cluster Representing the Cluster No. Signal-to-interference-plus-noise ratio per user Represents the first of the clusters The first shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the first optimization module. The input is the channel matrix and the superimposed NOMA signal, and the output is the beamforming vector. The second optimization module optimizes the user clustering results and power allocation results obtained by the clustering module. It adopts a beamforming scheme based on statistical channel information. The optimization objective is to maximize the weighted sum of the average signal leakage noise ratio and the average signal interference noise ratio. The constraint is the transmit power constraint. The second shaping module uses the alternating direction multiplier method to solve the multi-objective beamforming vector optimization problem obtained by the second optimization module. The input is statistical channel state information and the superimposed NOMA signal, and the output is the beamforming vector.

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