CN109962727B - Hybrid beam forming and non-orthogonal multiple access transmission method for air-to-air communication - Google Patents
Hybrid beam forming and non-orthogonal multiple access transmission method for air-to-air communication Download PDFInfo
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- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
- H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
- H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
- H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B7/00—Radio transmission systems, i.e. using radiation field
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- H04B7/15—Active relay systems
- H04B7/185—Space-based or airborne stations; Stations for satellite systems
- H04B7/18502—Airborne stations
- H04B7/18506—Communications with or from aircraft, i.e. aeronautical mobile service
Abstract
The invention discloses a hybrid beam forming and non-orthogonal multiple access transmission method for air-space communication, which adopts hybrid beam forming and non-orthogonal multiple access technology aiming at a downlink transmission system for air-space communication and belongs to the technical field of air-space communication. The method comprises the steps of constructing a communication scene of a ground base station and the unmanned aerial vehicles, grouping the unmanned aerial vehicles according to channel response vectors, and jointly designing mixed beam forming and power distribution, so that the aim of maximizing the sum of multi-space-based rate and multi-user reachable rate under the constraint of the lowest reachable rate is fulfilled; the number of the unmanned aerial vehicles can be increased in multiples under the same time-frequency resource, and the frequency spectrum efficiency is effectively improved.
Description
Technical Field
The invention belongs to the technical field of space-air communication, and particularly relates to a space-air communication hybrid beam forming and non-orthogonal multiple access transmission method.
Background
With the rapid development of mobile communication technology, ground infrastructure is continuously improved, the supported data transmission rate is gradually increased, the transmission rate of fifth-generation mobile communication is increased by at least more than 10 times compared with the transmission rate of the previous-generation technology, the data service is increased by 1000 times, and the number of internet equipment is increased by more than 100 times. However, a bottleneck in the development of mobile communication is coverage, and at present, mobile communication can only cover land areas with high population density, and cannot cover remote areas, mountains, forests, deserts, oceans and the like. One solution to the coverage holes of these ground base stations is to use satellite coverage, however, since the satellite orbit is usually high, the distance attenuation of the signal is serious, the transmission rate of the satellite communication is limited, and the problem of high time delay is also accompanied, and the satellite communication cost is high, which becomes an obstacle to further development.
In order to take coverage capability and transmission rate into consideration, air-to-air communication becomes a new development direction and is also valued by countries in the world. Compared with the satellite orbit, the near space and the low-altitude space are closer to the ground, so that the defect of the satellite communication time delay problem can be greatly overcome; on the other hand, the air flying vehicle has flexible mobility, can realize flexible deployment and coverage, and effectively supplements the service for the ground base station coverage blind area. In addition, the air-facing aircraft can also complete various tasks such as detection, monitoring, aerial photography, remote sensing, disaster early warning and the like, so that the labor cost is reduced, the operation efficiency is improved, and the air-facing aircraft is more important to real-time control and communication of the aircraft.
Although the operating distance of the air-bound communication is greatly reduced compared with that of a satellite, the communication distance is still far compared with that of a ground base station, even can reach dozens of kilometers to hundreds of kilometers, and in order to improve the communication speed, a higher frequency band, such as a millimeter wave frequency band (30-300GHz), can be adopted. Because the distance attenuation of the high-frequency signals is serious, a large-scale array antenna can be adopted for directional communication, and because the wavelength of the millimeter wave signals is shorter, the millimeter wave signals can be carried in a smaller area and simultaneously assisted with a beam forming technology, so that the channel gain is improved. At present, the mainstream beam forming technology is divided into two types, one type is a digital beam forming technology, a multi-radio frequency multi-antenna structure is adopted, multi-channel signals are transmitted/received through multi-channel radio frequency, and the digital beam forming has higher flexibility and communication capacity, but the radio frequency cost and power consumption are higher, so that the digital beam forming technology is difficult to be practically applied; the other is an analog beam forming technology, a plurality of antennas are connected by only adopting a single radio frequency, the phase of a signal is changed through a phase converter, and higher array gain is obtained in a specific direction. In order to realize the compromise between the communication cost and the speed, a hybrid beam forming structure can be adopted, a small number of radio frequencies are used for connecting a plurality of antennas, and beam forming is decomposed into low-dimensional digital beam forming and high-dimensional analog beam forming, so that space division multiple access is realized.
Taking the ground base station to transmit to a plurality of unmanned aerial vehicles as an example, as the number of unmanned aerial vehicles increases, space division multiple access under analog beam forming cannot guarantee that all unmanned aerial vehicles are accessed, in order to further improve the spectrum efficiency and the communication rate, a non-orthogonal multiple access technology can be adopted, multiple signals are transmitted in a superposition mode in the same time frequency, and are distinguished in a power domain. The receiving end adopts the serial interference elimination technology, and each way signal is decoded in proper order, just so can improve unmanned aerial vehicle's access quantity manyfold. However, due to the problems of mutual signal interference and occasional multi-resource variation, the adoption of hybrid beamforming and non-orthogonal multiple access techniques in the air-space communication still faces great difficulty.
Disclosure of Invention
The invention provides a method for maximizing the total capacity of a system by adopting a hybrid beam forming and non-orthogonal multiple access technology in the air-space communication through optimizing design grouping, hybrid beam forming and power distribution.
The method of the invention is applicable to the scene: 1. the ground base station serves a plurality of low-altitude unmanned downlink transmissions; 2. the ground base station transmits downlink to a plurality of temporary empty base stations; 3. downlink transmission of the temporary empty base station to a ground user; 4. and the temporary base station transmits downlink to a plurality of low-altitude unmanned machines. The transmission mechanism of each scene is similar, and the following description is only made for scene 1.
The invention provides a hybrid beam forming and non-orthogonal multiple access transmission method for air-space communication, which comprises the following specific steps:
step one, aiming at a downlink temporary air non-orthogonal multiple access communication system, a channel between a ground base station and an unmanned aerial vehicle is modeled.
And step two, dividing the K unmanned aerial vehicles into M groups according to the channel gain and the channel correlation.
And step three, the ground base station superposes and transmits the power normalization signals sent by each group of unmanned aerial vehicles, and the power normalization signals are received by each unmanned aerial vehicle through beam forming, channel response and antenna noise.
And step four, determining the signal decoding sequence of each group of unmanned aerial vehicles.
And step five, calculating the reachable rate of the unmanned aerial vehicle.
Step six, constructing an objective function: and when the sum of the reachable rates of all the unmanned aerial vehicles reaches the maximum, designing constraint conditions to be met by power distribution and beam forming of the joint transceiving end.
And step seven, solving the power distribution under the fixed mixed beam forming.
And step eight, fixing the analog beam forming matrix, and solving the digital beam forming matrix by adopting a zero forcing method.
And step nine, simulating beam forming, namely substituting the power distribution and the digital beam forming matrix obtained in the step seven and the step eight into the target function in the step six, and finally obtaining a simulated beam forming matrix.
The invention has the advantages that:
1. a hybrid beam forming and non-orthogonal multiple access transmission method for air-to-air communication provides a low-complexity unmanned aerial vehicle grouping method;
2. a hybrid beam forming and non-orthogonal multiple access transmission method for air-air communication proposes that unmanned aerial vehicles in the same group are accessed by non-orthogonal multiple access, and unmanned aerial vehicles in different groups are accessed by orthogonal multiple access;
3. a hybrid beam forming and non-orthogonal multiple access transmission method for air-space communication jointly designs hybrid beam forming and power distribution, and has lower computational complexity;
4. a hybrid beam forming and non-orthogonal multiple access transmission method for air-to-air communication can improve the number of unmanned aerial vehicles to be accessed in a multiplied mode under the same time-frequency resource, and effectively improves the frequency spectrum efficiency.
Drawings
Fig. 1 is a schematic diagram of an antenna structure of a transmitting end of a hybrid beamforming and non-orthogonal multiple access system for air-space communication according to the present invention;
fig. 2 is a flow chart of a hybrid beamforming and non-orthogonal multiple access transmission method for space-time communication according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The invention provides a hybrid beam forming and non-orthogonal multiple access transmission method for air-space communication, which comprises the following specific steps:
step one, aiming at a downlink temporary air non-orthogonal multiple access communication system, a channel between a ground base station and an unmanned aerial vehicle is modeled.
Ground base station in same time domain, frequency domain and code domain resourceConnect K long-range single antenna unmanned aerial vehicle in the piece, name unmanned aerial vehicle 1, unmanned aerial vehicle 2, … …, unmanned aerial vehicle K respectively. A millimeter wave hybrid beam forming structure is adopted for directional communication at a ground base station, as shown in fig. 1, the number of antennas carried by the ground base station is N, the number of radio frequencies is M, and K is>M; the radio frequency and the antenna are in a full-communication structure, and each antenna is controlled by a power amplifier and a phase converter respectively. Channel response vector h between ground base station and unmanned aerial vehiclekComprises the following steps:
wherein K is 1,2 …, K; lambda [ alpha ]k,lComplex coefficient, Ω, representing the l-th path of drone kk,lCosine value L representing emission angle of first path of unmanned aerial vehicle k at ground base stationkRepresents the total number of multipath components of unmanned plane k, and a (-) represents the function of the orientation vector, and the expression is:
step two, dividing the K unmanned aerial vehicles into M groups according to the channel gain and the channel correlation, wherein the specific mode is as follows:
201. calculating the channel gain h of each UAVk||2;
202. Calculating channel correlation coefficients between droneshiAnd hjRespectively are the channel response vectors of the ground base station and unmanned aerial vehicle i and unmanned aerial vehicle j.
203. Randomly selecting M unmanned aerial vehicles as representatives to be distributed into M groups;
204. the other unmanned aerial vehicles select the unmanned aerial vehicle representative with the largest channel correlation coefficient to be classified into the same group;
205. each group of drones reselects the drone with the largest channel gain as a representative, and the step 204 is repeated until the packet is not sent any moreAnd (4) changing, and recording the set of all groups of unmanned planes as Gm,1≤m≤M}。
Thirdly, the ground base station superposes and transmits the power normalization signals sent by each group of unmanned aerial vehicles, and the power normalization signals are received by each unmanned aerial vehicle after beam forming, channel response and antenna noise in sequence;
the received signal expression of the nth drone of the mth group is:
wherein h ism,nIs the channel response vector of the mth group nth drone and the ground base station,an analog beamforming matrix is represented and,representing a digital beamforming matrix, P ═ diag { P }1,p2,…,pMDenotes a power allocation matrix, in whichFor power normalization of the signal, um,nIs a power of σ2White gaussian noise.Andrepresenting N × M and M × M complex matrix spaces, respectivelymAnd | represents the number of the unmanned aerial vehicles in the mth group, and M is 1,2, … and M.
Step four, determining the signal decoding sequence of each group of unmanned aerial vehicles, and gaining each group of unmanned aerial vehicles according to effective channelsOrdering, wherein wmFor the mth column of the hybrid beamforming matrix W ═ AD, assume the effective signals of any set of dronesChannel gain is ordered asThe lower the effective channel gain, the higher the decoding priority.
And step five, calculating the reachable rate of the unmanned aerial vehicle. Each unmanned aerial vehicle takes other unmanned aerial vehicle signals as interference, serial interference elimination is carried out on the unmanned aerial vehicle signals of the same group, and the received signal reachable rate R of the nth unmanned aerial vehicle of the mth groupm,nComprises the following steps:
wherein p ism,nRepresents the nth unmanned aerial vehicle signal emission power of the mth group, | GiI represents the number of unmanned planes in the ith group, pi,qRepresenting the signal transmission power of the ith group of qth drones.
And step six, when the sum of the achievable rates of all the adjacent empty base stations reaches the maximum, designing constraint conditions to be met by power distribution and beam forming of the joint transceiving end.
The sum of the achievable rates is maximized, i.e., the objective function, as follows:
the constraints to be satisfied are as follows:
wherein r ism,nRepresents the minimum reachable rate constraint of the nth unmanned plane in the mth group, P is the maximum transmitting power of the ground base station, [ AD ]]:,mRepresents the mth column of the matrix;
step seven, solving the power distribution of the fixed mixed beam forming and defining the inter-group power distribution variableThe problem in the case of fixed beamforming translates into:
the method for solving the problem is as follows:
702. Calculating power distribution in each group:
703. fixing the inter-group interference, solving the problem of inter-group power distribution by adopting a water injection algorithm to obtain new inter-group power distribution { P }mRepeat step 702 until convergence.
Step eight, fixing the analog beam forming matrix, and solving the digital beam forming matrix by adopting a zero forcing method; the specific method comprises the following steps:
801. selecting the unmanned aerial vehicle with the highest effective channel gain in each group as the representative of the group to obtain an equivalent channel matrix as follows:
802. computing a digital beamforming matrix using a zero forcing methodWhereinRepresenting a generalized inverse matrix;
Step nine, simulating beam forming, namely substituting the power distribution and the digital beam forming matrix obtained in the step seven and the step eight into the target function in the step six, so that the target function can be solved as a simulated beam forming problem by adopting a particle swarm algorithm based on boundary compression, and the specific method comprises the following steps:
902. Randomly initializing the position x of I particles within a search spacel=AlAnd an initial velocity vl;
Wherein A islAnalog wave representing the first particleBeamforming matrix, each AlAre all N × M dimensional matrices vlRepresenting the motion speed of the analog beamforming matrix of the ith particle; 1,2, …, I;
903. finding the local optimum position p of each current particlebest,lAnd global optimal position gbest;
904. For each iteration loop, T is from 1 to T, which represents the maximum number of iterations. Calculating an inertia factor and an inner boundary of a search space;
wherein ω ismaxRepresenting the maximum value of the inertia factor, omegaminRepresenting the minimum value of the inertia factor;
905. update the velocity and position of each component of each particle:
[vl]i,j=ω[vl]i,j+c1rand()*([pbest,l]i,j-[xl]i,j)+c2rand()*([gbest]i,j-[xl]i,j)
[xl]i,j=[xl]i,j+[vl]i,j
wherein, c1As a cognitive factor, c2For social factors, rand () represents a uniformly distributed random number between 0 and 1, pbest,lDenotes the local optimum position, g, experienced by the l-th particlebestRepresenting the global optimal positions experienced by all particles; [ x ] ofl]i,jThe ith row and the jth column of the ith particle current position matrix are represented; [ v ] ofl]i,jAnd the ith row and the jth column of the ith particle current motion speed matrix are represented.
906. For particles beyond the inner/outer boundary of the search space, directly compressing the particles onto the inner/outer boundary;
907. Allocating the power in the seventh and eighth stepSubstituting the digital beam forming matrix D into the target function in the sixth step to obtain the value of a fitness function R (x), wherein R (x) represents the sum of the achievable rates under the current analog beam forming;
908. updating the local optimum position p of each particlebest,lAnd global optimal position gbest;
909. Obtaining the analog beam forming matrix A after all the loop iterations are finished*=gbest。
Claims (5)
1. A hybrid beam forming and non-orthogonal multiple access transmission method for air-to-air communication is characterized in that: the method comprises the following steps of,
the method comprises the following steps that firstly, a channel between a ground base station and an unmanned aerial vehicle is modeled aiming at a downlink temporary space non-orthogonal multiple access communication system;
dividing K unmanned aerial vehicles into M groups according to the channel gain and the channel correlation; k is the number of the remote single-antenna unmanned aerial vehicles connected in the same time domain, frequency domain and code domain resource block by the ground base station; the value of M is the radio frequency number; the second step comprises the following specific steps:
201. calculating the channel gain h of each UAVk||2;k=1,2…,K;
202. Calculating channel correlation coefficients between droneshiAnd hjRespectively are channel response vectors of the ground base station, the unmanned aerial vehicle i and the unmanned aerial vehicle j; 1,2 …, K; j ═ 1,2 …, K;
203. randomly selecting M unmanned aerial vehicles as representatives to be distributed into M groups;
204. the other unmanned aerial vehicles select the unmanned aerial vehicle representative with the largest channel correlation coefficient to be classified into the same group;
205. reselecting the unmanned aerial vehicle with the largest channel gain as a representative unmanned aerial vehicle in each group, repeating the step 204 until the grouping does not change any more, and recording the set of unmanned aerial vehicles in each group as Gm,1≤m≤M};
Thirdly, the ground base station superposes and transmits the power normalization signals sent by each group of unmanned aerial vehicles, and the power normalization signals are received by each unmanned aerial vehicle through beam forming, channel response and antenna noise;
step four, determining the signal decoding sequence of each group of unmanned aerial vehicles;
step five, calculating the reachable rate of the unmanned aerial vehicle; in the fifth step, the reachable rate of the unmanned aerial vehicle is calculated, and the received signal reachable rate R of the nth unmanned aerial vehicle in the mth groupm,nComprises the following steps:
wherein p ism,nRepresents the nth unmanned aerial vehicle signal emission power of the mth group, | GiI represents the number of unmanned planes in the ith group, pi,qRepresenting the signal transmission power of the ith group of qth drones; h ism,nIs the channel response vector of the mth group nth unmanned aerial vehicle and the ground base station; w is amIs the mth column of the hybrid beamforming matrix; p is a radical ofm,jIs the firstm groups of jth unmanned aerial vehicle signal emission power; w is aiIs the ith column of the hybrid beamforming matrix; sigma2Represents the power of white gaussian noise;
step six, constructing an objective function: when the sum of the reachable rates of all unmanned aerial vehicles reaches the maximum, designing constraint conditions to be met by power distribution and beam forming of a joint receiving and transmitting end; in the sixth step, the sum of the reachable rates reaches the maximum, that is, the objective function, as follows:
the constraints to be satisfied are as follows:
wherein r ism,nRepresents the minimum reachable rate constraint of the nth unmanned plane in the mth group, P is the maximum transmitting power of the ground base station, [ AD ]]:,mThe mth column of the matrix AD; a represents an analog beamforming matrix, D represents a digital beamforming matrix, | GmL represents the number of the unmanned aerial vehicles in the mth group, and M is 1,2, … and M; rm,nReachable rate of received signal, p, for the nth drone of the mth groupm,nRepresenting the mth group nth drone signal transmission power; n is a ground base stationCarrying the number of the antennas;
solving power distribution of fixed mixed beam forming; in the seventh step, an intergroup power distribution variable is definedThe power allocation problem under fixed beamforming translates into:
the method for solving the power distribution problem under the fixed beam forming condition is as follows:
702. Calculating power distribution in each group:
703. fixing the inter-group interference, solving the problem of inter-group power distribution by adopting a water injection algorithm to obtain new inter-group power distribution { P }mRepeating the steps 702-703 until convergence; w is aiIs prepared by mixingIn the ith column of the composite wave beam forming matrix, R is the sum of the achievable rates, PiA variable is allocated to the inter-group power,allocating power for the mth group of 1 st drone signal transmissions,allocating power for the mth group nth drone signal transmission,distributing power for the mth group qth unmanned aerial vehicle signal transmission;
step eight, fixing the analog beam forming matrix, and solving the digital beam forming matrix by adopting a zero forcing method;
and step nine, simulating beam forming, namely substituting the power distribution and the digital beam forming matrix obtained in the step seven and the step eight into the target function in the step six, and finally obtaining a simulated beam forming matrix.
2. The hybrid beamforming and non-orthogonal multiple access transmission method for space-critical communication according to claim 1, wherein: the channel modeling between the ground base station and the unmanned aerial vehicle in the step one refers to establishing a channel response vector h between the ground base station and the unmanned aerial vehiclekComprises the following steps:
wherein K is 1,2 …, K; lambda [ alpha ]k,lComplex coefficient, Ω, representing the l-th path of drone kk,lCosine value L representing emission angle of first path of unmanned aerial vehicle k at ground base stationkRepresents the total number of multipath components of unmanned plane k, and a (-) represents the function of the orientation vector, and the expression is:
n is the number of the ground base station carrying antennas, and K is the number of the ground base station connecting the remote single-antenna unmanned aerial vehicles in the same time domain, frequency domain and code domain resource block.
3. The hybrid beamforming and non-orthogonal multiple access transmission method for space-critical communication according to claim 1, wherein: in step three, the signal received by the unmanned aerial vehicle has the expression:
wherein, ym,nA received signal for an mth group nth drone; h ism,nIs the channel response vector of the mth group nth drone and the ground base station,an analog beamforming matrix is represented and,representing a digital beamforming matrix, P ═ diag { P }1,p2,…,pMDenotes a power allocation matrix, in which In order to normalize the signal for the power,denotes the Mth group | GMPower normalization signals of | unmanned aerial vehicles; u. ofm,nIs a power of σ2White gaussian noise of (1);andrepresenting N × M and M × M complex matrix spaces, respectivelymAnd | represents the number of the unmanned aerial vehicles in the mth group, and M is 1,2, … and M.
4. The hybrid beamforming and non-orthogonal multiple access transmission method for space-critical communication according to claim 1, wherein: the eighth step is as follows:
801. selecting the unmanned aerial vehicle with the highest effective channel gain of each group as a representative of the group, wherein the obtained equivalent channel matrix is as follows:
802. computing a digital beamforming matrix using a zero forcing methodWhereinRepresenting a generalized inverse matrix;
5. The hybrid beamforming and non-orthogonal multiple access transmission method for space-critical communication according to claim 1, wherein: the ninth step is as follows:
901. the search space for defining the analog beamforming matrix isWherein [ A ]]i,jAn ith row and a jth column representing an analog beamforming matrix; n is the number of antennas carried by the ground base station;
902. randomly initializing the position x of I particles within a search spacel=AlAnd an initial velocity vl;
Wherein A islAn analog beamforming matrix representing the l-th particle, each AlAre all N × M dimensional matrices vlRepresenting the motion speed of the analog beamforming matrix of the ith particle; 1,2, …, I;
903. finding the local optimum position p of each current particlebest,lAnd global optimal position gbest;
904. For each iteration cycle, T is from 1 to T, and T represents the maximum iteration number; calculating an inertia factor and an inner boundary of a search space;
wherein ω ismaxRepresenting the maximum value of the inertia factor, omegaminRepresenting the minimum value of the inertia factor;
905. update the velocity and position of each component of each particle:
[vl]i,j=ω[vl]i,j+c1rand()*([pbest,l]i,j-[xl]i,j)+c2rand()*([gbest]i,j-[xl]i,j)
[xl]i,j=[xl]i,j+[vl]i,j
wherein, c1As a cognitive factor, c2For social factors, rand () represents a uniformly distributed random number between 0 and 1, pbest,lDenotes the local optimum position, g, experienced by the l-th particlebestRepresenting the global optimal positions experienced by all particles; [ x ] ofl]i,jThe ith row and the jth column of the ith particle current position matrix are represented; [ v ] ofl]i,jThe ith row and the jth column of the ith particle current motion speed matrix are represented; [ p ]best,l]i,jIth row and jth column, [ g ] representing the locally optimal position experienced by the ith particlebest]i,jRow i, column j representing the global optimal positions experienced by all particles;
906. for particles beyond the inner boundary or the outer boundary of the search space, directly compressing the particles onto the inner boundary and the outer boundary;
i.e. if | [ x | ]l]i,jIf | is less than d, takeIf it is notThen getIf | [ p ]best,l]i,jIf | is less than d, take
907. Allocating the power in the seventh and eighth stepAnd a digital beamforming matrix D*Substituting the target function in the sixth step to obtain the value of a fitness function R (x), wherein R (x) represents the sum of the achievable rates under the current analog beam forming;
908. updating the local optimum position p of each particlebest,lAnd global optimal position gbest;
909. Obtaining the analog beam forming matrix A after all the loop iterations are finished*=gbest。
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