CN113938183B - Communication resource allocation method based on non-orthogonal multiple access under multi-beam satellite system - Google Patents
Communication resource allocation method based on non-orthogonal multiple access under multi-beam satellite system Download PDFInfo
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Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a communication resource allocation method based on non-orthogonal multiple access under a multi-beam satellite system, which comprises the steps of constructing an objective function model of multi-beam satellite communication resource allocation, obtaining an optimal resource allocation scheme by solving the model, firstly executing a grouping algorithm on users to obtain user grouping sets in the process of solving the objective function model, and then executing power allocation on each group of users; the user grouping algorithm adopted by the invention can ensure fairness among users, reduce the number of time slot groups, increase the service frequency of a single time slot and reduce the resource waste of wave beams; and the transmission rate of the whole system is effectively improved by a power distribution algorithm on the premise of meeting the minimum service quality of each user according to the grouped situation.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a communication resource allocation method based on non-orthogonal multiple access under a multi-beam satellite system.
Background
With the increasing development of mobile communication services, the explosive growth of mobile data volume and the high standard requirements for communication service quality and coverage range, satellite communication, and particularly multi-beam satellite communication, are increasingly gaining attention. The non-orthogonal multiple access (NOMA) technology can realize multiplexing of multiple users in the same time-frequency domain, has higher spectral efficiency and better fairness, so that NOMA is introduced into a multi-beam satellite communication system, power domain resources can be more fully utilized, the transmission rate of the system and the number of service users are improved, and powerful guarantee is provided for realizing extremely high spectral efficiency. However, in this case, interference between beams and other users in the beams is unavoidable in the multi-beam satellite communication system.
To reduce the impact of interference, it is generally necessary to group multiple users according to a certain criterion, and on this basis, the transmitting end performs joint preprocessing to reduce the interference between beams, i.e. precoding. Meanwhile, the receiving end adopts a serial interference elimination technology to eliminate user interference in wave beams, so that proper power distribution proportion can ensure correct demodulation of users and promote the transmission rate of the whole system in order to reduce noise interference suffered by users which are decoded preferentially and interference brought by users which are not decoded.
Disclosure of Invention
In order to effectively improve the transmission rate of the whole system, the invention provides a communication resource allocation method based on non-orthogonal multiple access under a multi-beam satellite system, which comprises the steps of constructing an objective function model of multi-beam satellite communication resource allocation, obtaining an optimal resource allocation scheme by solving the model, firstly executing a grouping algorithm on users to obtain user grouping sets in the process of solving the objective function model, and then executing power allocation on each group of users; the objective function model of the multi-beam satellite communication resource allocation is expressed as:
s.t.C1:
C2:
C3:
C4:
C5:
wherein G is t Representing a user grouping set;representing the transmission power of the ith user in the nth beam of the time slot t; t is the total time slot number; n is the total beam number; />Representing the signal-to-interference-and-noise ratio of a strong user receiving end; />Representing the signal-to-interference-and-noise ratio of a weak user receiving end; />User i, representing beam n service in time slot t>Indicating that the user belongs to the t-th slot,the value of i indicates the type of user, i indicates a strong user when i=1, and i=2 indicates a weak user when i=2, indicating that the user does not belong to the t-th slot; p represents the total transmitting power of the transmitting end; />Representing the transmission rate of user i served by beam n in time slot t; r is R min Indicating a minimum transmission rate.
Further, in the process of solving the objective function, firstly, a grouping algorithm is executed on multiple users to obtain a user grouping set, and the method specifically comprises the following steps:
step 101, initializing parameters including the total number of users K total Beam number N, user setNumber of time slot group T, number of users K contained in single time slot t =2×n, set of time slots>User grouping set
Step 102, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 103, otherwise executing step 104;
step 103, initializing each user group according to user group selection criteria, and distributing the first user of each group;
step 104, judging whether the user set is an empty set, if not, executing step 105, otherwise, executing step 106;
step 105, according to the channel correlation, putting the selected proper user into the corresponding time slot group, and if the length of the time slot group is greater than or equal to the length of the user contained in a single time slot, reallocating a new time slot;
step 106, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 107, otherwise executing step 111;
step 107, judging whether the number of users is the user in the corresponding time slot, if yes, executing step 108, otherwise executing step 110;
step 108, forming clusters of the selected proper users according to the channel gain difference, and determining strong and weak users according to the channel gain of a single user;
step 109, updating the current user grouping set and the time slot group set, changing the number of users, and executing step 107;
step 110, adding 1 to the time slot number, and executing step 106;
step 111, outputting the final user grouping set.
Further, in step 103, the criteria for initializing the user group to select the first user is that the channel vector norm is taken to be the largest, and the channel vector norm calculation includes:
in step 105, the selection user criteria is that the user with the largest channel vector norm and the users in each time slot group respectively calculate the channel correlation coefficient, and the users are put into the time slot group with the smallest channel correlation coefficient, and the channel gain calculation includes:
in step 108, the criterion for selecting suitable users to cluster is that the channel gain difference is calculated between every two users in each time slot group, the two users with large channel gain difference form a cluster, and the channel gain difference calculation includes:
d (i,j) ＝||h i |-|h j ||；
wherein,representing the channel gain of user k; />The channel gain of user i at time slot t is shown; h is a i Channel gain, which represents user i>
Further, when power distribution is performed on each group of users after user grouping, the objective function model may be equivalently represented as T power distribution sub-problems, which are expressed as:
further, in order to solve the T power allocation sub-problems, the numerator and denominator after the sub-problems are divided are transformed, and the power allocation sub-problems are reconstructed based on the properties of the exponential function and the logarithmic function, which is expressed as:
C6:
C7:
C8:
wherein m is n 、y n 、u n 、v n For the numerator and denominator corresponding to the nth wave beam after the power distribution sub-problem is dividedA relaxation variable obtained by transformation; y is n By noise power->Decision, denoted->m is the same asWith x in the relaxation variable in the beam n Is expressed as m= [ m ] 1 ,...,m N ] T The method comprises the steps of carrying out a first treatment on the surface of the u is u in the relaxation variables in all beams n Is denoted as u= [ u ] 1 ,...,u N ] T The method comprises the steps of carrying out a first treatment on the surface of the v is the value of v in the relaxation variables in all beams n Is expressed as v= [ v ] 1 ,...,v N ] T ；/>Representing the transmission power of a strong user under the nth beam of the t time slot; />The channel gain for the strong user served by beam n at time slot t; w (w) n Representing the nth column of the ZF precoding matrix generated by all users under t time slots; />Representing the transmission power of the weak user under the nth beam of the t time slot; />Representing the channel gain of the weak user served by beam n at time slot t.
Further, the inter-beam interference is eliminated by zero-forcing the precoding matrix, so that the satellite transmits the signal x via the beam n n Expressed as:
wherein w is n Representing the nth column of the zero forcing precoding matrix generated by all users at time slot t,representing the transmission power of the kth user in the nth beam, the transmission data is expressed as +.>And satisfy->
Further, if the strong user eliminates the intra-cluster interference according to the serial interference elimination technology, the signal-to-interference-and-noise ratio of the receiving end of the strong userExpressed as:
signal-to-interference-and-noise ratio of weak user receiving endExpressed as:
wherein,representing the noise power.
Further, the power allocation sub-problem is divided into a numerator and a denominatorExpressed as:
further, the constraint condition C8 is converted into a convex constraint, namely, a first-order Taylor expansion approximation method is adopted to convert the constraint condition C8 into:
wherein,is a point of linearization. -
Compared with the prior art, the method has the advantages that the fairness among users can be guaranteed by adopting the user grouping algorithm, the number of time slot groups is reduced, the service frequency of a single time slot is increased, and the resource waste of wave beams is reduced. The transmission rate of the whole system is effectively improved by a power distribution algorithm on the premise of meeting the minimum service quality of each user according to the grouped situation.
Drawings
Fig. 1 is a flow chart of resource allocation for a multi-beam satellite communication system of the present invention;
fig. 2 is a system model diagram of a multi-beam satellite communication system of the present invention;
fig. 3 is a flow chart of a user grouping method of the multi-beam satellite communication system of the present invention;
fig. 4 is a flow chart of a power allocation algorithm of the multi-beam satellite communication system of the present invention;
FIG. 5 is a comparison of the transmission rate of the system at different transmit powers for the present invention with the prior art scheme;
fig. 6 is a comparison of the transmission rates of the present invention with a prior art scheme under a single set of time slots;
fig. 7 is a comparison of the number of time slot groups for different numbers of users for the present invention with the prior art scheme.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
In this embodiment, a process of constructing an objective function model for multi-beam satellite communication resource allocation will be specifically described.
The invention is suitable for the high-flux multi-beam satellite communication scene, and the system mechanism is shown in figure 2. In the forward link of the system, a single-wideband multi-beam satellite is K total The individual users provide services and the full frequency multiplexing mode is adopted to improve the spectrum efficiency.
Let K be total The individual users are evenly distributed among N beams generated by the satellite, and each beam is evenly servedAnd the individual users. To serve multiple users simultaneously, multibeam satellites employ both time division multiple access (time division multiple access, TDMA) and non-orthogonal multiple access techniques. The system provides services for a plurality of users simultaneously in units of frames through a TDMA technology, each frame comprises T time slots, and each beam under each time slot selects one user cluster for data transmission through a NOMA technology. The number of user clusters served by the NOMA technology may be greater than or equal to two, and it is assumed herein that there are two users in each user cluster in the same time slot of each beam, and the strong users are divided according to the magnitude of the user channel gain.
At the t-th time slot, from K total Selecting K from among the users t (K t =2n) users. To ensure fairness of user service, each user under all beams of all slots has and only has a chance to be served once, a set of slots t= {1,2, &..once, T }, total set of users is definedThe user group under each time slot is G t Therefore there are
Since the high-flux multi-beam satellite communication system mostly adopts the Ku/Ka frequency band, the satellite channel model is built by taking the influence of path propagation loss, multi-beam antenna gain and rainfall attenuation on the system performance into consideration. The channel gain for satellite versus ground arbitrary user k is expressed as:
wherein h is k Channel gain for satellite and ground arbitrary user k; b max The free space loss is represented by the path propagation loss and noise, expressed as:
wherein lambda is the carrier wavelength, d 0 Represents the distance from the satellite to the beam center of the beam corresponding to the ground user terminal, d represents the distance from the user to the beam center, κ is the Boltzmann constant, T R Is the receiver noise temperature, B W Is the noise bandwidth.
Among the various atmospheric effects, the influence of rain fade is most severe, and the corresponding rain fade vector Φ is expressed as:
wherein, rain attenuation gain xi dB (units dB) obeys log-normal distribution, i.ePhi is a phase vector that is uniformly distributed over [0,2 pi ].
The gain of the multi-beam antenna is mainly dependent on the antenna beam gain of the satellite and the user position, the antenna beam gain g of user k k Expressed as g k ＝{g k,1 ,g k,2 ,...,g k,n ,...,g k,N Beam gain g at antenna n for user k }, then k,n Expressed as:
where u= 2.07123sin (θ k,n )/sin(θ k,3dB )，J 1 ,J 3 Bessel functions of a first order first type and a third order first type respectively; θ k,3dB Representing the 3dB angle of the beam where the user k is positioned, and the included angle between the kth user and the center of the nth beam is represented by theta k,n A representation; g max Indicating the maximum satellite antenna gain.
At the t-th time slot, suppose K is selected in total t Individual users forming user group G t There is
Wherein,representing the strong and weak users served simultaneously by beam n in time slot t. In this time slot, the signal is receivedThe expression is as follows:
wherein y is n,1 Representing the received signal of a strong user in the nth beam, y n,2 Representing the received signal of the weak user in the nth beam,is satellite and user group G under t time slot t Channel matrix between>Is the transmission signal of the satellite at time t slots, < >>Representing a mean value of 0, variance +.>Additive white gaussian noise of (c).
To mitigate inter-beam interference caused by channel matrix, the satellite transmits signal x by zero-forcing (ZF) precoding matrix to eliminate inter-beam interference n Can be expressed as:
wherein,represents the nth column of the ZF precoding matrix generated by all users in the t time slot, ++>Representing the transmission power of the kth user in the nth beam, for transmitting data>Is expressed and meets
Since the precoding matrix is generated according to the channel gain vector of the strong user, the inter-beam interference of the strong user can be completely eliminated. While strong users can cancel intra-cluster interference according to the serial interference cancellation (successive interference cancellation, SIC) technique. Therefore, the signal received by the strong user at the receiving end in the time slot is:
and weak users cannot eliminate inter-beam interference and intra-cluster interference, the signals received at the receiving end are:
therefore, the signal-to-interference-and-noise ratios (signal to interference plus noise ratio, SINR) of the strong and weak user receiving ends are respectively:
the user transmission rate of the nth beam at the t time slot can be obtained by the shannon formulaThe method comprises the following steps:
then user group G at time t t Is a transmission rate of a transmission systemRepresented as
Then the satellite has a total transmission rate R through the TDMA service total Represented as
Wherein maximizing the system transmission rate is maximizing the user group transmission rate per slot, which is selected by K for a single slot t Determined by the individual user. And K is selected per slot t The individual users are not identical. The power allocation may be performed for users under each slot to maximize the system transmission rate. The resource allocation problem of the multi-beam satellite communication system can be solved by optimizing the user group G t Inter-group user powerAn optimized objective function of the following resource allocation problem is established.
Where C1 represents the number of users per slot and only 2N, C2 represents that each user can be divided into only one slot, C3 represents that the power available to the user per slot is not negative, C4 represents the total power constraint per slot, C5 represents the minimum quality of service constraint per user,indicating that the user belongs to the t-th time slot, < > and>indicating that the user does not belong to the t-th slot.
Example 2
The objective function model of the multi-beam satellite communication resource allocation proposed in embodiment 1 is a non-convex problem that is difficult to solve directly. For this purpose, it is proposed to perform a grouping algorithm on multiple users and then perform a power allocation algorithm on users in each slot to obtain a sub-optimal solution. The present embodiment proposes a grouping algorithm for multiple users.
Clustering-based NOMA user grouping. The flow chart of the user grouping method designed by the method is shown in fig. 3, and comprises the following steps:
step 1, constructing a multi-beam satellite communication system, initializing system parameters including the total number of users K total Beam number N, user setNumber of time slot group T, number of users K contained in single time slot t Time slot group set =2×nUser group set +.>
Step 2, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 3, otherwise, executing step 4;
step 3, circularly calculating the user setEach user channel vector norm in (a) and selecting user u with the largest norm value k I.e.
As each group G' t And G' t ＝G′ t ∪{u k }，Until T is equal to T, the initialization of the time slot group is finished;
step 4,Judging user setIf the set is empty, executing the step 5 if the set is not empty, otherwise executing the step 6;
step 5, collectingUser u with the largest channel vector norm k According to a channel correlation coefficient calculation formula:
calculating user u respectively k With each time slot group G' t The channel correlation coefficient of the inner user obtains 1 channel correlation coefficient matrix C' and users u k And placing the time slots into a time slot group corresponding to the minimum element in the matrix. If the time slot group length is greater than or equal to the number of users contained in a single time slot, reallocating a new time slot;
step 6, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 7, otherwise executing step 11;
step 7, judging whether the number of users is the user in the corresponding time slot, if so, executing step 8, otherwise, executing step 10;
step 8, according to a calculation formula of the channel gain difference:
computing group of time slots G' t User u i And user u j (j∈{i+1,...,K t Channel gain difference { d }) between i,j }→D i At set D i Maximum value is taken, user u i And user u j Dividing into the same cluster, defining strong and weak users according to the gain of a single user channel, K t For K total Is written in the middle of (2);
step 9, updating the current user group set G t ＝G t ∪{u i ,u j Sum of time slot group set G' t ＝G′ t \{u i ,u j -performing step 7;
step 10, adding 1 to the time slot number, and executing step 6;
step 11, outputting the final user grouping set G t 。
Example 2
The present embodiment proposes a method of performing power allocation for each group of users by calculating after grouping the users. The iterative power allocation algorithm for maximizing the transmission rate of the system according to this embodiment, as shown in fig. 4, specifically includes:
after user grouping is finished, power distribution is performed based on the maximization of the transmission rate of the system, and the objective function can be equivalently solved as T power distribution sub-problems, namely:
although the constraint conditions are all raised strips, the objective function is a multivariable coupling and non-convex optimization problem, and can not be directly solved. Firstly, the denominator of the objective function after the general division is subjected to variable substitution as follows:
by utilizing the properties of exponential and logarithmic functions, the objective function can be written asWherein m is n ,u n ,v n Is a relaxation variable and yn is determined by noise power +.>Constant of decision, i.e.)>Thus by relaxing the variable m= [ m ] 1 ,...,m N ] T ，u＝[u 1 ,...,u N ] T ,v＝[v 1 ,...,v N ] T The objective function can be reconstructed as:
since C8 is a non-convex constraint, it needs to be transformed into a convex constraint to solve the objective function using the convex optimization problem. Thus for C8, a first order taylor expansion approximation method is employed.
By initialisationObtaining an initial feasible point +.>And (3) for the initial value of the transmitting power of the strong user under the beam n of the t time slot, when the difference value of the transmission rates obtained by two adjacent iterations is smaller than a set threshold value or reaches the maximum iteration number, the iteration is ended, and the maximum transmission rate is returned. Constraint C8 may be approximated at each iteration.
Each wave beam is respectively iterated, and N iterations are carried out to obtainDenoted as-> Is a point of linearization. By the above transformation, the non-convex constraint C8 is converted into a convex constraint, so far the objective function and the constraint condition have been converted into a convex function. The objective function may be re-expressed as:
the above problem can be solved using standard mathematical optimization tools such as CVX.
Example 4
In this example, simulation experiments were performed based on the theories provided in examples 1 to 3.
In the present embodiment, the multi-beam satellite communication system is composed of a single multi-beam GEO satellite equipped with n=16 beams, and the coverage areas of the multiple beams constitute the entire coverage area of the satellite. And each beam simultaneously serves k=2 users using the power domain NOMA technique in a single slot.
The invention provides an algorithm and an existing multi-antenna downlink orthogonal grouping algorithm (multiple antenna downlink clustering, MADOC) scheme for simulation contrast verification experiment: wherein MADOC algorithm trades off user service fairness against system transmission rate so its packet threshold ε takes 0.3 and 0.35, respectively. The satellite carrier frequency is 20GHz, the user link bandwidth B is 500MHz, the user antenna gain is 41.7dBi, the ground user receiving quality factor G/T is 17.68dB/K, and the Boltzmann constant kappa=1.38X10-23) J/K, by κB W T R Normalizing the noise power, and varianceThe overall transmission rate of the system is defined as follows:
fig. 5 compares the total transmission rate performance of the proposed algorithm with MADOC algorithm-epsilon=0.3 and MADOC algorithm-epsilon=0.35 at different satellite transmission powers. Let the total number of users K total Total slot number t=10, =320. As can be seen from fig. 5, as the satellite transmission power increases, the overall transmission rate of the system increases, wherein the algorithm system keeps the overall transmission rate at the highest level. The invention not only maximizes the number of service users on the time slot group and improves the fairness of user service, but also considers the power distribution among users and maximizes the transmission rate of the system as much as possible on the premise of ensuring the minimum user service quality.
Fig. 6 compares the transmission rate of each time slot group between the proposed algorithm of the present invention and MADOC algorithm-epsilon=0.3 and MADOC algorithm-epsilon=0.35 for a single time slot group, and in this picture, three histograms in each of the 1-10 time slot group numbers are MADOC algorithm-epsilon=0.35, proposed algorithm of the present invention and MADOC algorithm-epsilon=0.3 in order from left to right. Because the algorithm adds the power domain NOMA technology to increase the number of users served by a single wave beam in the same time slot, the transmission rate calculation of the MADOC algorithm in a single time slot group is that the summation and the average are carried out among adjacent time slot groups. As can be seen from fig. 6, the transmission rate of the algorithm under any time slot group is always higher than that of the MADOC algorithm, whether the grouping threshold of the MADOC algorithm is 0.3 or 0.35.
Fig. 7 compares the proposed algorithm with MADOC algorithm-epsilon=0.3 and MADOC algorithm-epsilon=0.35 for time slot sets with different total numbers of users. As can be seen from fig. 7, as the total number of users increases, the number of time slot groups used in each algorithm increases, but the present invention proposes that the number of time slot groups used in the algorithm is the smallest. Since the more slot groups, the lower the service frequency of a single slot group, the fewer the number of slot groups should be, the better in order to increase the service frequency of each slot group. The invention provides an algorithm which can ensure that the number of time slot groups is minimized under the condition of total number of users, and the number of service users of each time slot group is maximized.
The simulation result shows that the user service fairness is better, the number of user time slot groups is further reduced on the basis of MADOC algorithm, the number of service users of a single time slot group is increased, the spectrum utilization rate of the system is improved, and the transmission rate of the system is improved to some extent.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (7)
1. The communication resource allocation method based on non-orthogonal multiple access under the multi-beam satellite system is characterized in that an optimal resource allocation scheme is obtained by constructing an objective function model of multi-beam satellite communication resource allocation and solving the model, a grouping algorithm is firstly executed on users to obtain a user grouping set in the process of solving the objective function model, and then power allocation is executed on each group of users; the objective function model of the multi-beam satellite communication resource allocation is expressed as:
constraint C1:
C2:
C3:
C4:
C5:
wherein G is t Representing a user grouping set;representing the transmission power of the ith user in the nth beam of the time slot t; t is the total time slot number; n is the total beam number; />Representing the signal-to-interference-and-noise ratio of a strong user receiving end; />Representing the signal-to-interference-and-noise ratio of a weak user receiving end; />User i, representing beam n service in time slot t>Indicating that the user belongs to the t-th time slot, < > and>the value of i indicates the type of user, i indicates a strong user when i=1, and i=2 indicates a weak user when i=2, indicating that the user does not belong to the t-th slot; p represents the total transmitting power of the transmitting end; />Representing the transmission rate of user i served by beam n in time slot t; r is R min Representing a minimum transmission rate;
in the process of solving the objective function, firstly, a grouping algorithm is executed on multiple users to obtain a user grouping set, and the method specifically comprises the following steps:
step 101, initializing parameters including the total number of users K total Beam number N, user setThe number of users K is contained in a single time slot t =2×n, set of time slots>User group set +.>
Step 102, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 103, otherwise executing step 104;
step 103, initializing each user group according to user group selection criteria, and distributing the first user of each group;
step 104, judging whether the user set is an empty set, if not, executing step 105, otherwise, executing step 106;
step 105, according to the channel correlation, putting the selected proper user into the corresponding time slot group, and if the length of the time slot group is greater than or equal to the length of the user contained in a single time slot, reallocating a new time slot;
step 106, judging whether the time slot number is less than or equal to the time slot group number, if yes, executing step 107, otherwise executing step 111;
step 107, judging whether the number of users is the user in the corresponding time slot, if yes, executing step 108, otherwise executing step 110;
step 108, forming clusters of the selected proper users according to the channel gain difference, and determining strong and weak users according to the channel gain of a single user;
step 109, updating the current user grouping set and the time slot group set, changing the number of users, and executing step 107;
step 110, adding 1 to the time slot number, and executing step 106;
step 111, outputting the final user grouping set.
2. The method for allocating communication resources based on non-orthogonal multiple access in a multi-beam satellite system according to claim 1, wherein in step 103, the criteria for initializing the user group to select the first user is the user with the largest channel vector norm, and the calculating the channel vector norm comprises:
in step 105, the selection user criteria is that the user with the largest channel vector norm and the users in each time slot group respectively calculate the channel correlation coefficient, and the users are put into the time slot group with the smallest channel correlation coefficient, and the channel gain calculation includes:
in step 108, the criterion for selecting suitable users to cluster is that the channel gain difference is calculated between every two users in each time slot group, the two users with large channel gain difference form a cluster, and the channel gain difference calculation includes:
wherein,representing user u k Channel gain of (a); />Representing user u at time slot t i Channel gain of (a); />Representing user u at time slot t j Is of (1)Channel gain; />
3. The method for allocating communication resources based on non-orthogonal multiple access in a multi-beam satellite system according to claim 1, wherein when performing power allocation for each group of users after user grouping, the objective function model can be equivalently expressed as T power allocation sub-problems, which are expressed as:
constraint conditions: c3, C4, C5.
4. A method for allocating communication resources based on non-orthogonal multiple access in a multi-beam satellite system according to claim 3, wherein, in order to solve T power allocation sub-problems, the numerator and denominator after the sub-problems are divided are transformed, and the power allocation sub-problems are reconstructed based on the properties of an exponential function and a logarithmic function, which is expressed as:
constraint conditions: c3, C4, C5
C6:
C7:
C8:
Wherein m is n 、y n 、u n 、v n To power pairThe numerator and denominator corresponding to the nth wave beam after the sub-problem division is allocatedA relaxation variable obtained by transformation; y is n By noise power->Decision, denoted->m is m in the relaxation variables in all beams n Is expressed as m= [ m ] 1 ,...,m N ] T The method comprises the steps of carrying out a first treatment on the surface of the u is u in the relaxation variables in all beams n Is denoted as u= [ u ] 1 ,...,u N ] T The method comprises the steps of carrying out a first treatment on the surface of the v is the value of v in the relaxation variables in all beams n Is expressed as v= [ v ] 1 ,...,v N ] T ；/>Representing the transmission power of a strong user under the nth beam of the t time slot; />The channel gain for the strong user served by beam n at time slot t; w (w) n Representing the nth column of the ZF precoding matrix generated by all users under t time slots; />Representing the transmission power of the weak user under the nth beam of the t time slot; />The channel gain for the weak user served by beam n at time slot t; x is x k Representing the transmission signal in the kth beam.
5. The method for non-orthogonal multiple access based communication resource allocation in a multi-beam satellite system according to claim 4, wherein the zero forcing precoding matrix is usedTo eliminate the interference between beams, so that the satellite transmits the signal x through the beam n n Expressed as:
wherein w is n Representing the nth column of the zero forcing precoding matrix generated by all users at time slot t,representing the transmission power of the kth user in the nth beam, the transmission data is expressed as +.>And satisfy->
6. The method for allocating communication resources based on non-orthogonal multiple access in a multi-beam satellite system according to claim 5, wherein the strong user eliminates intra-cluster interference according to a serial interference cancellation technique, and the signal-to-interference-and-noise ratio of the receiving end of the strong userExpressed as:
signal-to-interference-and-noise ratio of weak user receiving endExpressed as:
wherein,representing the noise power.
7. The method for allocating communication resources based on non-orthogonal multiple access in a multi-beam satellite system according to claim 4, wherein the constraint C8 is converted into a convex constraint, that is, the constraint C8 is converted into:
wherein,is a point of linearization.
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