CN106850028B - Combined beam forming method based on SWIPT system - Google Patents

Combined beam forming method based on SWIPT system Download PDF

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CN106850028B
CN106850028B CN201710094650.0A CN201710094650A CN106850028B CN 106850028 B CN106850028 B CN 106850028B CN 201710094650 A CN201710094650 A CN 201710094650A CN 106850028 B CN106850028 B CN 106850028B
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energy
information
beam forming
time slot
value
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CN106850028A (en
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徐玉滨
王云
马琳
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Harbin Institute of Technology
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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
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0802—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using antenna selection

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Abstract

In order to solve the problem that the information transmission rate and the energy collection rate in the SWIPT system are low, the invention provides a combined beam forming method based on the SWIPT system, and belongs to the field of wireless energy-carrying communication. The method comprises the following steps: the method comprises the following steps: the sending end simultaneously sends mutually independent information beam forming vectors and energy wave velocity forming vectors; step two: the receiving end receives information and collects energy, and comprises an information receiving time slot and an energy receiving time slot: in the information receiving time slot, the information beam forming vector is utilized to align the specific user to the information resource, thereby realizing the error-free transmission of the information; in the energy receiving time slot, the energy beam forming vector is utilized to align the energy resource for a specific user, and the interference between the users is taken as the source of energy collection. The invention realizes the independent control of information transmission and energy transmission, increases the energy received by the energy collecting end, and reasonably utilizes the interference among users to obtain a better R-E curve.

Description

Combined beam forming method based on SWIPT system
Technical Field
The invention belongs to the field of wireless energy-carrying communication, and particularly relates to a combined beam forming method based on an SWIPT system.
Background
With the development of scientific strategies, people are always dedicated to searching a new energy source instead of relying on natural resources such as wind energy and solar energy. In practical application systems, for some small devices, such as sensor nodes, smart phones, artificial intelligence hearts, etc., it is difficult to design an energy collection circuit to charge the small devices with solar energy and wind energy so as to maintain stable operation for a long time. To overcome this practical problem, a new energy source, i.e., a Radio Frequency (RF) signal, is being sought. In a wireless communication system in the conventional sense, a radio frequency signal plays a role of transmitting information, but now, it appears that the radio frequency signal can carry not only information but also energy. Therefore, the receiving end can collect the radio frequency signal as energy to be used as an energy source of the receiving end, so that the service life of the communication network is prolonged. Therefore, the receiving end not only can demodulate information, but also can collect energy simultaneously through the design of the receiving circuit.
The concept of SWIPT (Wireless energy-carrying communication system, Simultaneous Wireless Information and PowerTransfer) is first proposed by l.r.varsheney in 2008, and indicates that the SWIPT strategy not only responds to the call for green communication but also can prolong the service life of the energy-limited Wireless communication network, and then the SWIPT also researches the problem of the compromise between the Information transmission rate and the energy transmission rate in the SWIPT system based on a SISO (single Input single Output) flat fading channel, namely a so-called R-E curve, which can clearly express the utilization conditions of two resources, namely Information and energy, in the SWIPT system, if the utilization rate of the Information resources is improved, the Information rate is increased, and if the utilization rate of the energy resources is improved, the electric energy collection amount is increased. In addition, the energy collection efficiency is not high due to the power dissipation of the free space and the low conversion efficiency of the energy conversion circuit, and the existence of the energy collection end affects the information transmission rate of the communication system. Therefore, domestic and foreign communication scholars pay extensive attention and research to the problems of insufficient electric energy collection amount and how to optimally compromise the R-E curve.
The Beam Forming (BF) strategy plays a positive role in optimizing R-E, and the strategy can increase the signal strength output in the antenna array direction, and reduce the strength of interference signals, thereby improving the reachable information rate of the communication network. The research of the beam forming strategy in the SWIPT system is divided into the following four aspects, namely the research of the beam forming strategy under different channels, the research of the beam forming strategy under different Receiver strategies, the research of the beam forming strategy under different optimization targets and the research of the joint beam forming strategy under the condition that an Information Receiver (IR) and an Energy Receiver (ER) are not shared.
However, the above research on the beamforming strategy is single and is limited to simple changes of the system model, the receiving strategy or the optimization target. The fact that a better R-E curve can be obtained by changes in the system model, the reception strategy or the optimization objective cannot be denied, but the study of the beamforming strategy does not propose some innovation points in combination with the characteristics of the SWIPT system itself. For example, two resources, namely information and energy, exist in the SWIPT system, but the conventional wireless communication system only has one component of the information resource, and for the application of the beam forming strategy in the SWIPT system, the difference between the information resource and the energy resource is still considered. Therefore, the R-E curve using conventional beamforming strategies may not be optimal.
In a conventional wireless communication system, a radio frequency signal plays a role in transferring information, and since the radio frequency signal itself can also carry energy, a wireless communication system using the radio frequency signal as a medium can carry out information transmission and electric energy transmission, and the communication system with the dual functions is called a wireless energy-carrying communication system, namely an SWIPT system.
In a multi-antenna SWIPT system, a traditional beam forming strategy has been widely applied, and the strategy can increase the strength of a useful signal in the direction of an antenna array and reduce the strength of an interference signal so as to realize directional transmission of information and energy. However, the conventional beamforming strategy only adopts one beamforming vector, and does not consider the difference between an information component and an Energy component in the SWIPT system, and ignores the fact that interference between users can also be used as Energy, so that resources in the system are not reasonably utilized, and the Energy and power received by the Energy collection end are too little, so that an information-Rate (R-Energy, R-E) curve does not achieve a good effect.
Disclosure of Invention
The invention aims to solve the problem that the information transmission rate and the energy collection rate in an SWIPT system are slow, and provides a combined beam forming method based on the SWIPT system.
The invention discloses a combined beam forming method based on an SWIPT system, which comprises the following steps:
the method comprises the following steps: the sending end simultaneously sends mutually independent information beam forming vectors and energy wave velocity forming vectors;
step two: the receiving end receives information and collects energy, and comprises an information receiving time slot and an energy receiving time slot:
in the information receiving time slot, the information beam forming vector is utilized to align the specific user to the information resource, thereby realizing the error-free transmission of the information;
in the energy receiving time slot, the energy beam forming vector is utilized to align the energy resource for a specific user, and the interference between the users is taken as the source of energy collection.
Preferably, the second step includes:
according to the information receiving time slot and the energy receiving time slot, an objective function is established:
Figure BDA0001229815440000021
constraint of the objective function:
Figure BDA0001229815440000031
wherein v iskForming a vector for an information beam of a kth user at a sending end;
m is the number of users;
wkforming a vector for an energy beam of a kth user at a sending end;
α is the time slot division ratio, W is the transmission channel bandwidth;
Figure BDA0001229815440000032
is hkConjugate transpose of (i), hkA channel gain matrix for a kth user;
Figure BDA0001229815440000033
antenna noise power for the kth user; zetakEnergy conversion efficiency for the kth user; gamma raykThe minimum signal-to-interference-and-noise ratio threshold of the kth user in the information receiving time slot; e.g. of the typekA minimum collected energy threshold for the kth user of the energy receiving time slot;
solving an optimal solution for the parameters in the established objective function;
and receiving information and collecting energy by using the objective function of solving the optimal solution.
Preferably, the optimal solution of the parameters in the established model is:
and solving the optimal solution of the parameters in the objective function by using a Lagrange relaxation method.
Preferably, the method for solving the optimal solution for the parameters in the objective function by using the lagrangian relaxation method comprises the following steps:
and converting the established objective function into the following functions by utilizing a Lagrange relaxation method:
Figure BDA0001229815440000034
and
Figure BDA0001229815440000035
Figure BDA0001229815440000036
Lk() Is a Lagrangian function, and lambda is a Lagrangian multiplier;
the constraint conditions of the converted objective function are as follows:
Figure BDA0001229815440000041
and solving the optimal value of the converted objective function.
Preferably, the information beamforming vector vkOptimum value of (2)
Figure BDA0001229815440000042
Comprises the following steps:
Figure BDA0001229815440000043
wherein the content of the first and second substances,
Figure BDA0001229815440000044
Φkrepresenting information beamforming vectors vkThe domain of (3); n is a radical oftIndicating the number of transmit antennas at the transmit end.
Preferably, the energy beam forming vector wkOptimum value of (2)
Figure BDA0001229815440000045
Comprises the following steps:
Figure BDA0001229815440000046
Figure BDA0001229815440000047
Figure BDA0001229815440000048
Figure BDA0001229815440000049
according to L ═ A-1Λ, obtaining
Figure BDA00012298154400000410
Figure BDA00012298154400000411
Is composed of
Figure BDA00012298154400000412
The orthonormal basis of (a);
Ntindicating the number of transmit antennas at the transmit end.
Preferably, said optimum value of α
Figure BDA00012298154400000413
α initial value of αstartα Final value of αendUsing the formula
Figure BDA00012298154400000414
The value of α is updated when satisfied
Figure BDA0001229815440000051
The α value at time is the optimal value of α
Figure BDA0001229815440000052
Preferably, the optimum value of λ
Figure BDA0001229815440000053
The upper bound of the Lagrange multiplier is λmaxThe lower bound of the Lagrange multiplier is λminUsing the formula
Figure BDA0001229815440000054
Updating the value of lambda when P is satisfiedm-α|vk|2-|wk|2+α|wk|2The value of λ at 0 is the optimum value of said λ
Figure BDA0001229815440000055
Wherein
Figure BDA0001229815440000056
P is the maximum transmit power threshold of the transmitting end.
The features mentioned above can be combined in various suitable ways or replaced by equivalent features as long as the object of the invention is achieved.
The invention has the advantages that in order to realize independent control of information transfer and energy transfer, increase the energy received by an energy collection end and reasonably utilize the interference among users to obtain a better R-E curve, the invention provides a combined beam forming method based on an SWIPT system, and the method extends a single beam forming vector to two independent beam forming vectors. In the information receiving stage, the information beam forming vector is utilized to align the specific user to the information resource, and at the moment, in order to eliminate the user interference and realize the error-free transmission of the information, the orthogonal relation exists between the information beam forming vector and the channel gain; in the energy receiving stage, the energy beam forming vector is used to align the energy resource for a specific user, and considering that the interference between users can be used as the source of energy collection and there is no interference factor for energy receiving, the orthogonal relation between the energy beam forming vector and the channel gain is not necessarily satisfied. The invention obtains a maximum solving problem containing inequality constraint through mathematical modeling, and can solve the problem by utilizing a Lagrange multiplier method. Finally, simulation experiments show that the strategy provided by the invention can optimize the R-E curve.
Drawings
Fig. 1 is a schematic diagram of a SWIPT system model established in an embodiment.
Fig. 2 is a schematic diagram of a general beamforming method and a TS receiving mode in an embodiment.
Fig. 3 is a schematic diagram of a joint beamforming method and a TS receiving mode according to the present invention in an embodiment.
Fig. 4 is an R-E curve obtained by respectively simulating a general beam forming method and a combined beam forming method according to the present invention in the specific embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
In this embodiment, a joint beam forming method based on an SWIPT system includes the following steps:
the method comprises the following steps: the sending end simultaneously sends mutually independent information beam forming vectors and energy wave velocity forming vectors;
step two: the receiving end receives information and collects energy, and comprises an information receiving time slot and an energy receiving time slot:
in the information receiving time slot, the information beam forming vector is utilized to align the specific user to the information resource, thereby realizing the error-free transmission of the information;
in the energy receiving time slot, the energy beam forming vector is utilized to align the energy resource for a specific user, and the interference between the users is taken as the source of energy collection.
In the information receiving time slot, the information beam forming vector is utilized to align the specific user to the information resource, and at the moment, in order to eliminate the user interference and realize the error-free transmission of the information, the orthogonal relation exists between the information beam forming vector and the channel gain; in the energy receiving time slot, the energy beam forming vector is used for aligning the energy resource for a specific user, and considering that the interference between users can be used as the source of energy collection and the interference is not existed for the energy receiving, the orthogonal relation between the energy beam forming vector and the channel gain is not needed to be satisfied. Under the condition that the same information rate can be achieved, the electric energy collection amount of the system is improved to a certain extent, so that an optimal R-E curve is obtained, and the problems of low information transmission rate and low energy collection rate in an SWIPT system are solved.
In a preferred embodiment, step two includes:
step two, firstly: according to the information receiving time slot and the energy receiving time slot, an objective function is established:
Figure BDA0001229815440000061
constraint of the objective function:
Figure BDA0001229815440000071
wherein v iskForming a vector for an information beam of a kth user at a sending end;
m is the number of users;
wkforming a vector for an energy beam of a kth user at a sending end;
α is the time slot division ratio, W is the transmission channel bandwidth;
Figure BDA0001229815440000072
is hkConjugate transpose of (i), hkA channel gain matrix for a kth user;
Figure BDA0001229815440000073
antenna noise power for the kth user; zetakEnergy conversion efficiency for the kth user; gamma raykThe minimum signal-to-interference-and-noise ratio threshold of the kth user in the information receiving time slot; e.g. of the typekA minimum collected energy threshold for the kth user of the energy receiving time slot;
step two: solving an optimal solution for the parameters in the established objective function;
step two and step three: and receiving information and collecting energy by using the objective function of solving the optimal solution.
In the embodiment, the system and the rate are taken as optimization targets, the minimum signal-to-interference-and-noise ratio of the information receiver and the minimum collected energy of the energy receiver are taken as limiting conditions, so that the joint optimization of the proportion of the transmitting beam forming vector and the receiving TS is realized, and an objective function is established. In addition, in order to save communication resources, certain limitations need to be made on the transmission power of the base station.
In a preferred embodiment, in the second step, the method for solving the optimal solution for the parameters in the established model comprises the following steps:
and solving the optimal solution of the parameters in the objective function by using a Lagrange relaxation method.
The target function established above has more constraint conditions, and in order to solve the optimal parameters in the target function, the constraint conditions are absorbed into the target function, so that some constraints are reduced, and the difficulty in solving the problem is greatly reduced.
In a preferred embodiment, the method for solving the optimal solution for the parameters in the objective function by using the lagrangian relaxation method comprises the following steps:
and converting the established objective function into the following functions by utilizing a Lagrange relaxation method:
Figure BDA0001229815440000074
and
Figure BDA0001229815440000075
Figure BDA0001229815440000076
Lk() Is a Lagrangian function, and lambda is a Lagrangian multiplier;
the constraint conditions of the converted objective function are as follows:
Figure BDA0001229815440000081
and solving the optimal value of the converted objective function.
The embodiment specifically provides a target function and constraint conditions simplified by using a Lagrange relaxation method.
In a preferred embodiment, the information beamforming vector vkOptimum value of (2)
Figure BDA0001229815440000082
Comprises the following steps:
Figure BDA0001229815440000083
wherein the content of the first and second substances,
Figure BDA0001229815440000084
Φkrepresenting information beamforming vectors vkThe domain of (3); n is a radical oftIndicating the number of transmit antennas at the transmit end.
In the preferred embodiment, the energy beam forming vector wkOptimum value of (2)
Figure BDA0001229815440000085
Comprises the following steps:
Figure BDA0001229815440000086
Figure BDA0001229815440000087
Figure BDA0001229815440000088
Figure BDA0001229815440000089
according to L ═ A-1Λ, obtaining
Figure BDA00012298154400000810
Figure BDA00012298154400000811
Is composed of
Figure BDA00012298154400000812
The orthonormal basis of (a);
Ntindicating the number of transmit antennas at the transmit end.
Preferably, α is the optimum value
Figure BDA00012298154400000813
α initial value of αstartα Final value of αendUsing the formula
Figure BDA0001229815440000091
The value of α is updated when satisfied
Figure BDA0001229815440000092
The α value at time is the optimal value of α
Figure BDA0001229815440000093
In a preferred embodiment, the optimum value of λ
Figure BDA0001229815440000094
The upper bound of the Lagrange multiplier is λmaxThe lower bound of the Lagrange multiplier is λminUsing the formula
Figure BDA0001229815440000095
Updating the value of lambda when P is satisfiedm-α|vk|2-|wk|2+α|wk|2The value of λ at 0 is the optimum value of said λ
Figure BDA0001229815440000096
Wherein
Figure BDA0001229815440000097
P is the maximum transmit power threshold of the transmitting end.
The embodiment mode respectively gives the following embodiments of the joint beam forming method and the common beam forming method based on the SWIPT system, and gives the performance comparison simulation effect:
firstly, establishing a SWIPT system model:
the SWIPT system is composed of a base station and M users. Base station side is provided with NtThe user side is provided with 1 antenna respectively. Considering only the case of downlink information transmission and energy collection, a schematic diagram of a SWIPT system model is shown in fig. 1.
The transmitting end respectively adopts a common beam forming method and the combined beam forming method of the invention to carry out precoding processing on the transmitted information, aiming at carrying out comparison and embodying the advantages of the invention. The receiving end adopts a TS mode, namely, signals received by the receiving end are collected by the energy collecting end or are used for demodulating information by the information demodulating end. At this time, the embodiment performs slot division on a normalized time unit, and the normalized time unit is divided into 2 slots: time slot 1 and time slot 2, and time slot 1 and time slot 2 at the receiving end are respectively an information receiving time slot and an energy receiving time slot. In the information receiving time slot, the user demodulates the information; in the energy receiving time slot, the user performs energy collection.
Fig. 2 shows a schematic diagram of a general beamforming method and a TS receiving mode, and fig. 3 shows a schematic diagram of a combined beamforming method and a TS receiving mode according to the present invention.
As can be seen from fig. 2 and 3, the transmitting end of the conventional beamforming method only transmits the information beamforming vector, whereas the joint beamforming method of the present invention needs to transmit the information beamforming vector and the energy beamforming vector.
Secondly, the receiving end describes the mathematical problem formed in the information receiving time slot and the energy receiving time slot:
at the receiving end, the information receiving is carried out by the user in the information receiving time slot, and the information signals sent by the base station end after the weighting of the beam forming vector in the common beam forming method and the combined beam forming method of the invention are as follows:
Figure BDA0001229815440000101
wherein M is the number of users; v. ofkIs NtA beam-forming vector of x 1,
Figure BDA0001229815440000102
skthe information of the kth user follows circular symmetry complex Gaussian distribution, the mean value is 0, and the variance is 1.
The information signal received by the kth user is:
Figure BDA0001229815440000103
wherein h iskFor the k user NtA channel gain matrix of x 1; the superscript H represents the conjugate transpose of the matrix; n iskThe antenna noise at the receiving end of the kth user follows the circular symmetry complex Gaussian distribution, the mean value is zero, and the variance is
Figure BDA0001229815440000104
In order to suppress interference between users and achieve error-free transmission of information, the relationship between the beamforming vector and the channel gain matrix can be utilized, that is:
Figure BDA0001229815440000105
then, in the case of no user interference, the information signal received by the kth user is:
Figure BDA0001229815440000106
the signal-to-interference-and-noise ratio of the information receiving end can be expressed as:
Figure BDA0001229815440000107
wherein the content of the first and second substances,
Figure BDA0001229815440000108
is the noise power of the antenna.
According to shannon's theorem, the maximum average information rate of a received signal is:
Figure BDA0001229815440000109
where W is the transmission channel bandwidth and α is the time slot division ratio for information demodulation.
In summary, the maximum average sum information rate of all K users in the SWIPT system is:
Figure BDA00012298154400001010
energy collection is carried out on users in energy receiving time slots, and energy signals sent by base station ends of a common beam forming method and a combined beam forming method after beam forming vector weighting are respectively as follows:
Figure BDA0001229815440000111
Figure BDA0001229815440000112
wherein M is the number of users; v. ofkIs NtA beam-forming vector of x 1,
Figure BDA0001229815440000113
wkis NtA beam-forming vector of x 1,
Figure BDA0001229815440000114
skthe information of the kth user follows circular symmetry complex Gaussian distribution, the mean value is 0, and the variance is 1.
The energy signals received by the kth user of the common beam forming method and the joint beam forming method are respectively as follows:
Figure BDA0001229815440000115
Figure BDA0001229815440000116
wherein h iskFor the k user NtA channel gain matrix of x 1; the superscript H represents the conjugate transpose of the matrix; n iskThe antenna noise at the receiving end of the kth user follows the circular symmetry complex Gaussian distribution, the mean value is zero, and the variance is
Figure BDA0001229815440000117
In the common beam forming method, because the same beam forming vector is used to control information and energy simultaneously, interference between users in the second stage is also eliminated, and the joint beam forming method can collect the interference between users as energy, so that energy signals received by the kth user in the common beam forming method and the joint beam forming method are respectively:
Figure BDA0001229815440000118
Figure BDA0001229815440000119
because of the square sum relationship between the signal and the power, the energy collected by the kth user in the energy receiving time slot of the common beam forming method and the joint beam forming method is respectively
Figure BDA00012298154400001110
Figure BDA00012298154400001111
Wherein the content of the first and second substances,
Figure BDA00012298154400001112
noise power of antenna, time for energy collection, 1- αkTo energy conversion efficiency.
In unit time, the total transmission power of the SWIPT systems of the common beam forming method and the combined beam forming method is respectively as follows:
Figure BDA0001229815440000121
Figure BDA0001229815440000122
for the research of the beam forming technology in the SWIPT system, the purpose of the embodiment is to realize the increase of the system and the speed and the collection electric quantity through the directional transmission of information and energy. Since the SWIPT system can realize wireless communication and wireless charging at the same time, the importance of the wireless communication and the wireless charging needs to be objectively measured to determine the final optimization target. In a SWIPT system, the information transfer is ultimately serviced regardless of the amount of power collected. Therefore, under the condition that the information receiver and the energy receiver can work normally, the larger the system and the speed are, the better the performance of the SWIPT system is. Therefore, the joint optimization of the ratio of the transmitting beam forming vector and the receiving TS is realized by taking the system and the rate as optimization targets and taking the minimum signal-to-interference-and-noise ratio of the information receiver and the minimum collected energy of the energy receiver as limiting conditions. In addition, in order to save communication resources, certain limitations need to be made on the transmission power of the base station. The problem of applying the common beamforming method and the joint beamforming method of the present invention is thus described as equation (18) and equation (19), respectively:
Figure BDA0001229815440000123
Figure BDA0001229815440000131
thirdly, describing and solving the formed mathematical problem:
mathematical problem solving for common beam forming method
Observing the formula (18), finding that the beam forming vectors of each user in the base station transmission power constraint are coupled together, in order to reduce the original problem into M simple subproblems, firstly absorbing the-d) of the formula (18) into the objective function (a) by using a lagrangian relaxation technology, and obtaining a generalized lagrangian function:
Figure BDA0001229815440000132
wherein the lambda is more than or equal to 0,
Figure BDA0001229815440000133
to obtain
Figure BDA0001229815440000134
In order to establish the relationship between the generalized Lagrange function and the original objective function, the generalized Lagrange function is obtained by the formula (20)
Figure BDA0001229815440000135
Substituting equation (21) into equation (18) yields a new problem equivalent to the original problem:
Figure BDA0001229815440000136
equation (22) is still a problem with the most-valued solution of complex inequality constraints, if the optimal value of the objective function λ, L ({ v } v), is solved firstkH, λ, α) contain a large number of unknowns and are inconvenient to solve, therefore, consider solving the original problem by solving the lagrange dual problem of equation (22), i.e., exchanging the order of the two most-valued solutions
Figure BDA0001229815440000141
Order to
Figure BDA0001229815440000142
At this time, the original problem becomes two most-valued solving problems, one is solving
Figure BDA0001229815440000143
The other is to solve
Figure BDA0001229815440000144
First, solve for
Figure BDA0001229815440000145
Simple mathematical transformation is performed on the formula (20) to
Figure BDA0001229815440000146
Equation (20) can be decomposed into M independent uncorrelated subforms:
Figure BDA0001229815440000147
wherein, the kth sub-formula can be expressed as:
Figure BDA0001229815440000148
because the M sub-equations are independent of each other, so:
Figure BDA0001229815440000149
a new problem can be derived from equation (26):
Figure BDA00012298154400001410
objective function Lk({vk}, λ, α) is divided into three cases, namely, the case where the objective function has an extreme point and the extreme point is in the defined domain, the case where the objective function has the maximum value at the extreme point, the case where the objective function has an extreme point but the extreme point is not in the defined domain, the case where the objective function has the maximum value at the boundary, and the case where the objective function does not have an extreme point, the case where the objective function also has the maximum value at the boundary.
First, the objective function L is judgedk({vkH, λ, α) when an extremum exists, the multivariate objective function LkThe partial derivatives of the respective orders ({ vk }, λ, α) must satisfy both
Figure BDA0001229815440000151
And
Figure BDA0001229815440000152
first, solve for
Figure BDA0001229815440000153
Assuming λ and α are known quantities, this is a derivation process for vectors, and this embodiment applies to the following mathematical knowledge
Figure BDA0001229815440000154
According to the above formula, the derivation of formula (27-a) can be:
Figure BDA0001229815440000155
v at the extreme pointkSatisfy the requirement of
Figure BDA0001229815440000156
From equation (28):
Figure BDA0001229815440000157
h in formula (29)kAnd vkThe relation of (a) is complicated and v cannot be determinedkIt is proposed separately, if the two can be combined, the solution can be simplified, the two sides of the equation are simultaneously left-multiplied
Figure BDA0001229815440000158
Obtaining:
Figure BDA0001229815440000159
order to
Figure BDA00012298154400001510
Wherein G iskFor complex constants, equation (30) is simplified to:
Figure BDA00012298154400001511
vkcontaining NtThe unknowns, v cannot be solved by only one equation of equation (31)kExact numerical value, which is sought with respect to vkTo jointly pair v with other equations ofkAnd (6) solving. For equations (27-c), (31) and
Figure BDA00012298154400001512
the combination is carried out, so that:
Figure BDA00012298154400001513
order to
Figure BDA00012298154400001514
Obtaining:
Figure BDA0001229815440000161
the formula (33-b) is a matrix equation in which,
Figure BDA0001229815440000162
the base solution of formula (33-b) therefore contains an orthonormal basis. For the matrix equation, the embodiment directly solves the matrix equation by using the library function in matlab to obtain the standard orthogonal basis of the matrix equation
Figure BDA0001229815440000163
The solution of equation (33-b) is then:
Figure BDA0001229815440000164
wherein l is any non-zero real number,
Figure BDA0001229815440000165
if the target function has the extreme point, the extreme point v'kThe following are also satisfied:
Figure BDA0001229815440000166
to solve the specific value of l, the present embodiment is based on the formula (33-a)
Figure BDA0001229815440000167
From the above formula, one can obtain:
Figure BDA0001229815440000168
wherein, α should satisfy:
Figure BDA0001229815440000169
v is obtained from the formula (35)kOf extreme point v'kComprises the following steps:
Figure BDA00012298154400001610
l can be obtained from the formula (39)k({vk}, λ, α) about variable vkOf extreme point v'kAnd then judging the extreme point v 'by combining the formula (27-b) and the formula (27-c)'kWhether within the definition domain, vkOf domain ΨkCan be expressed as:
Figure BDA00012298154400001611
if v isk′∈ΨkThen L can be determinedk({vk}, λ, α) takes the maximum value, v, at the extreme pointkOptimum value of (2)
Figure BDA00012298154400001612
Can be expressed as
Figure BDA0001229815440000171
If it is not
Figure BDA0001229815440000172
Because L isk({vkH, λ, α) are about vkIs increasing and decreasing, so Lk({vk}, λ, α) takes a maximum value at the lower boundary, vkLower boundary value v ofk"can be expressed as:
Figure BDA0001229815440000173
at this time, vkBoundary value v ofk"also satisfies the formula (33-b), i.e.:
Figure BDA0001229815440000174
substituting equation (42) into equation (43) yields:
Figure BDA0001229815440000175
carrying out formula transformation to obtain:
Figure BDA0001229815440000176
thus, vkOptimum value of (2)
Figure BDA0001229815440000177
Can be expressed as:
Figure BDA0001229815440000178
among them, α must satisfy:
Figure BDA0001229815440000179
in summary, the beamforming vector vkOptimum value of (2)
Figure BDA00012298154400001710
Can be expressed as:
Figure BDA00012298154400001711
then, the optimal value of α is solved, α has a definite value range, that is, 0< α <1, which can be obtained from the formula (22) and the formula (31):
α≥max(Θ1，Θ2)＝Θmax(49)
thus, the value range of α can be expressed as:
Figure BDA0001229815440000181
determining α whether there is an extreme point, and obtaining the deviation of α for equation (25), assuming v iskAnd λ is a known quantity, given as:
Figure BDA0001229815440000182
to solve for the optimal value of α, let
Figure BDA0001229815440000183
Obtaining:
Figure BDA0001229815440000184
due to the fact that
Figure BDA0001229815440000185
And is
Figure BDA0001229815440000186
Therefore, it is not only easy to use
Figure BDA0001229815440000187
Equation (52) has no solution, i.e., α has no extreme point, Lk({vk}, λ, α) is an increasing function with respect to α, thus, α takes the optimum value at the upper boundary, as given by equation (18-b):
Figure BDA0001229815440000188
the formula (50) is combined to obtain:
Figure BDA0001229815440000189
therefore, the optimum value of α
Figure BDA00012298154400001810
Comprises the following steps:
Figure BDA00012298154400001811
the second most-valued problem is then solved, i.e.
Figure BDA00012298154400001812
Wherein the content of the first and second substances,
Figure BDA00012298154400001813
at this time, there are three cases in which g (λ) takes the minimum value, one is that the objective function has an extreme point, and the extreme point is in the defined domain, and at this time, the objective function takes the maximum value at the extreme point; secondly, the target function has extreme points, but the extreme points are not in the definition domain, and the target function obtains the maximum value at the boundary; thirdly, the objective function has no extreme point, and the objective function also has the maximum value at the boundary. In the present embodiment, λ is not clearly defined, and therefore if λ has the maximum value, it is inevitably at the extreme value point.
Firstly, judging whether an extremum exists in g (lambda), and solving the derivative of g (lambda) with respect to lambda to obtain:
Figure BDA00012298154400001814
the derivative at the extreme point is zero, so:
Pm＝|vk|2(57)
g (λ) can take a minimum value when equation (57) is satisfied, but a specific value of λ cannot be found. Thus, the present embodiment solves for the problem by using the dichotomy, which is an iterative method with fast convergence, and the optimal value of λ can be obtained by combining equation (41)
Figure BDA0001229815440000199
The concrete process of the dichotomy solution is as follows: with provision for Lagrange multipliersUpper bound of lambdamaxAnd a lower bound λminUsing the formula
Figure BDA0001229815440000191
The value of λ is updated so that the optimum value of λ is the value of λ for which the formula (57) holds
Figure BDA0001229815440000192
(II) solving a mathematical problem of the joint beam forming method:
firstly, absorbing the formula (19-d) into an objective function by utilizing a Lagrangian relaxation technology to obtain a generalized Lagrangian function:
Figure BDA0001229815440000193
wherein lambda is more than or equal to 0, as can be seen from the formula (58),
Figure BDA0001229815440000194
therefore, the first and second electrodes are formed on the substrate,
Figure BDA0001229815440000195
obtaining:
Figure BDA0001229815440000196
substituting equation (59) into equation (19) results in a new problem equivalent to equation (19):
Figure BDA0001229815440000197
equation (60) is still a complex inequality constrained extremum solving problem, considering the lagrangian dual problem by solving equation (60) to solve the original problem, namely:
Figure BDA0001229815440000198
order to
Figure BDA0001229815440000201
At this time, the original problem becomes two most-valued solving problems, one is solving
Figure BDA0001229815440000202
The other is to solve
Figure BDA0001229815440000203
First, solve for
Figure BDA0001229815440000204
Order to
Figure BDA0001229815440000205
A simple mathematical transformation of equation (28) yields:
Figure BDA0001229815440000206
equation (62) can be decomposed into M independent uncorrelated subforms. Wherein, the kth sub-formula can be expressed as:
Figure BDA0001229815440000207
since the above M sub-expressions are independent of each other, they can be obtained from the formula (32) and the formula (33):
Figure BDA0001229815440000208
next, a new problem can be obtained by transforming the formula (60-b) and the formula (60-c), and substituting the formula (60-d) into the formula (60-b), and then combining the formula (64):
Figure BDA0001229815440000209
objective function Lk({vk},{wk}, lambda, α) can be divided into three casesFirstly, an extreme point exists in the objective function, and the extreme point is in a defined domain, and the objective function obtains a maximum value at the extreme point; secondly, the target function has extreme points, but the extreme points are not in the definition domain, and the target function obtains the maximum value at the boundary; thirdly, the objective function has no extreme point, and the objective function also has the maximum value at the boundary.
First, the objective function L is judgedk({vk},{wkH, λ, α) when an extremum exists, the multivariate objective function Lk({vk},{wkThe partial derivatives of the respective orders of (i) }, λ, α) must satisfy simultaneously
Figure BDA00012298154400002010
Figure BDA0001229815440000211
And
Figure BDA0001229815440000212
first, solve for
Figure BDA0001229815440000213
The solving process is similar to the solving of the mathematical problem of the common beamforming method. Finally get vkOf extreme point v'kComprises the following steps:
Figure BDA0001229815440000214
then, the formula (65-b) is combined to judge whether the extreme point is in the defined domain, vkThe domain of definition of (a) may be expressed as:
Figure BDA0001229815440000215
if v at the extreme pointk′∈ΦkThen L can be determinedk({vk},{wk}, λ, α) takes the maximum value at the extreme point, vkOptimum value of (2)
Figure BDA0001229815440000216
Comprises the following steps:
Figure BDA0001229815440000217
if at the extreme point
Figure BDA0001229815440000218
Lk({vk},{wkH, λ, α) are about vkIs increasing and decreasing, so Lk({vk},{wk}, λ, α) takes a maximum value at the lower boundary, vkLower boundary value v ofk"can be expressed as:
Figure BDA0001229815440000219
vk"is similar to the solving of mathematical problems in the ordinary beam forming method, and v is obtainedkBoundary value v ofk"is:
Figure BDA00012298154400002110
at this time, vkOptimum value of (2)
Figure BDA00012298154400002111
Comprises the following steps:
Figure BDA00012298154400002112
in summary, the information beamforming vector vkOptimum value of (2)
Figure BDA00012298154400002113
Can be expressed as:
Figure BDA00012298154400002114
followed bySolving for wkFor simplifying the expression of the formula (65), let gk＝|vk|2，
Figure BDA00012298154400002115
Wherein, by solving above, gkAnd bkAre all known quantities, in which case equation (65) may be equivalent to:
Figure BDA0001229815440000221
wherein the objective function can be expressed as:
Figure BDA0001229815440000222
from the formula (73-c), wkDefinition domain I ofkCan be expressed as:
Figure BDA0001229815440000223
therefore, the formula (73) can be rewritten as
Figure BDA0001229815440000224
Wherein the content of the first and second substances,
Figure BDA0001229815440000225
Ψk(wk) The maximum point can be divided into three conditions, namely, the target function has an extreme point, and the extreme point is in a defined domain, and the target function obtains the maximum value at the extreme point; secondly, the target function has extreme points, but the extreme points are not in the definition domain, and the target function obtains the maximum value at the boundary; thirdly, the objective function has no extreme point, and the objective function also has the maximum value at the boundary.
First determine Ψk(wk) Whether the extreme point of (2) exists. To psik(wk) To findIs derived from
Figure BDA0001229815440000226
Let us assume Ψk(wk) Exist to solve for wkAccording to the Ferman theorem, order
Figure BDA0001229815440000227
From equation (77):
2(α-1)λwk＝0 (78)
solving the equation (78) to obtain wkEither 0 or α -1, apparently, is not true, so Ψk(wk) The most valued point belongs to the third case. The objective function obtainable from equation (76) is with respect to wkIs a decreasing function of so wkThe maximum value is obtained at the lower boundary, and w is obtained from the formula (75)kHas a domain of IkIts lower boundary I _ LkCan be expressed as
Figure BDA0001229815440000231
When equation (80) is satisfied:
Figure BDA0001229815440000232
since with respect to wkHas less constraints, so that its value is broader, and the formulas (79) and (80) are wkOne, but not the only, value that satisfies the domain of definition.
Equation (79) comprises a matrix equation
Figure BDA0001229815440000233
Wherein the content of the first and second substances,
Figure BDA0001229815440000234
so that the basic solution system of the equation contains Nt-1 orthonormal basis. For the matrix equation, the embodiment can directly perform the matrix equation by using the library function in matlabSolving to obtain N t1 orthonormal radicals, each being
Figure BDA0001229815440000235
Equation of
Figure BDA0001229815440000236
Solution of (2)
Figure BDA0001229815440000237
Is composed of
Figure BDA0001229815440000238
Wherein the content of the first and second substances,
Figure BDA0001229815440000239
any non-zero real number.
Order to
Figure BDA00012298154400002310
Obtained from the formula (81)
Figure BDA00012298154400002311
Since the vectors in the base solution system are orthogonal to each other, equation (82) can be rewritten as
Figure BDA0001229815440000241
Writing the formula (83) into a matrix form to obtain
AL＝Λ (84)
Wherein the content of the first and second substances,
Figure BDA0001229815440000242
Figure BDA0001229815440000243
Λ＝[Λ1 2,…,Λk-1 2,Λk+1 2,…,ΛM 2]H∈C(M-1)×1(87)
a and Λ are both known quantities, and A is a square matrix, the solution of equation (84) is
L＝A-1Λ (88)
Then, the root number of the element in the vector L is set and a positive value is taken to obtain
Figure BDA0001229815440000244
In summary, wkOptimum value of (2)
Figure BDA0001229815440000245
Is composed of
Figure BDA0001229815440000246
Wherein the content of the first and second substances,
Figure BDA0001229815440000247
and
Figure BDA0001229815440000248
which can be derived from matlab library functions and equations (88), respectively.
Then, the optimal value of α is solved, α has a definite value range, namely 0< α <1, which can be obtained from the formula (80)
Figure BDA0001229815440000249
In summary, the value range of α can be expressed as
Figure BDA00012298154400002410
Judging α whether there is an extreme point, and calculating the deviation of α in formula (63) to obtain
Figure BDA0001229815440000251
To solve for the optimal value of α, let
Figure BDA0001229815440000252
To obtain
Figure BDA0001229815440000253
When equation (93) is satisfied, the objective function takes the maximum value, but the specific value of α cannot be obtained, and therefore, the present embodiment solves the problem by the dichotomy, assuming that the initial value of α is αstartα Final value of αendUsing the formula
Figure BDA0001229815440000254
The value α is updated so that α satisfying equation (93) is the optimum value of α
Figure BDA0001229815440000255
The second most-valued problem is then solved, i.e.
Figure BDA0001229815440000256
Wherein the content of the first and second substances,
Figure BDA0001229815440000257
the g (lambda) is the minimum value, and the three conditions are the same, namely, an extreme point exists in the objective function, the extreme point is in a defined domain, and the maximum value is obtained by the objective function at the extreme point; secondly, the target function has extreme points, but the extreme points are not in the definition domain, and the target function obtains the maximum value at the boundary; thirdly, the objective function has no extreme point, and the objective function also has the maximum value at the boundary. In the present embodiment, λ is not clearly defined, and therefore if λ has the maximum value, it is inevitably at the extreme value point.
First solving the derivative of g (lambda) with respect to lambda
Figure BDA0001229815440000258
Then, according to the Ferman's theorem, the derivative at the extreme point is zero, so
Pm-α|vk|2-|wk|2+α|wk|2＝0 (95)
When equation (95) is satisfied, g (λ) can take a minimum value, but a specific value of λ cannot be found. The bisection method is also utilized for solving, and the upper bound lambda of the Lagrange multiplier is setmaxAnd a lower bound λminUsing the formula
Figure BDA0001229815440000259
The value of λ is updated so that the value of λ satisfying equation (79) is the optimum value of λ
Figure BDA00012298154400002510
Fourthly, the method comprises the following steps: performance comparison simulation
It can be seen from the formula that the user average and information rate expressions are the same when the common beam forming method and the joint beam forming method of the present invention are used, but the common beam forming method uses the same beam forming vector vkThe information and energy are controlled, so that the inter-user interference can be used as an energy source in an energy receiving time slot, but the energy collecting end only collects the energy contained in the self user information due to the control of zero forcing beam forming. The joint beamforming method of the present invention uses two beamforming vectors vkAnd wkThe information and the energy are respectively controlled, so that the user interference can be removed in the information receiving time slot, and more energy can be collected in the energy receiving time slot, which is the advantage of the invention.
Suppose that the base station in the MISO SWIPT system is provided with NtThe receiving end of the root antenna is provided with M users. And the transmitting terminal adopts beam forming to directionally transmit the user information. The invention respectively adopts a beam forming strategy and a combined beam forming strategy to carry out alignment transmission on user information, and in order to completely eliminate the interference between users, the embodiment makes NtM. In order to reduce the complexity of the calculation, it is assumed that each parameter of each user is the same, i.e. the signal to interference plus noise ratio threshold γ of each user is the samekNoise power of antenna
Figure BDA0001229815440000261
User energy conversion efficiency ζkAnd the energy threshold e of the userkAre equal, i.e. gammak＝γ，
Figure BDA0001229815440000262
ζk＝ζ，ekE. The simulation parameter settings are shown in table 1.
TABLE 1 simulation parameters
Figure BDA0001229815440000263
As can be seen from fig. 4, as the SWIPT system and rate increase, the energy collected by the SWIPT system decreases because the transmit power threshold P is constant, the more for information demodulation, the less for energy collection. When the SWIPT system and the speed are equal, the energy collected by applying the combined beam forming method of the invention is more than that collected by applying the common beam forming method, because in the energy time slot, the combined beam forming method of the invention is controlled by the independent energy beam forming vector, the redundant user interference is collected as the energy, and the common beam forming method eliminates the interference among the users in the energy collecting time slot, but the energy collection is not necessary at all. When the collected energy is the same, the SWIPT system and the rate applying the joint beam forming method are larger than those applying the ordinary beam forming method, because when the same energy is collected, the energy time slot occupied by the joint beam forming method due to the collection of the redundant user interference is smaller, more time slots are left for information reception, and therefore the SWIPT system and the rate are larger.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It is to be understood that features described in different dependent claims and in this embodiment may be combined in ways other than those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (7)

1. A joint beamforming method based on a SWIPT system, the method comprising the steps of:
the method comprises the following steps: the sending end simultaneously sends mutually independent information beam forming vectors and energy wave velocity forming vectors;
step two: the receiving end receives information and collects energy, and comprises an information receiving time slot and an energy receiving time slot:
in the information receiving time slot, the information beam forming vector is utilized to align the specific user to the information resource, thereby realizing the error-free transmission of the information;
in the energy receiving time slot, the energy beam forming vector is utilized to align specific users to the energy resources, and the interference between the users is taken as the source of energy collection;
the second step is characterized by comprising the following steps:
according to the information receiving time slot and the energy receiving time slot, an objective function is established:
Figure FDA0002444705860000011
constraint of the objective function:
Figure FDA0002444705860000012
wherein v iskForming a vector for an information beam of a kth user at a sending end;
m is the number of users;
wkforming a vector for an energy beam of a kth user at a sending end;
α is the time slot division ratio, W is the transmission channel bandwidth;
Figure FDA0002444705860000013
is hkConjugate transpose of (i), hkA channel gain matrix for a kth user;
Figure FDA0002444705860000014
antenna noise power for the kth user; zetakEnergy conversion efficiency for the kth user; gamma raykThe minimum signal-to-interference-and-noise ratio threshold of the kth user in the information receiving time slot; e.g. of the typekA minimum collected energy threshold for the kth user of the energy receiving time slot;
solving an optimal solution for the parameters in the established objective function;
receiving information and collecting energy by using the objective function which obtains the optimal solution;
p is the maximum transmit power threshold of the transmitting end.
2. The joint beam forming method based on the SWIPT system as claimed in claim 1, wherein the optimal solution for the parameters in establishing the objective function is:
and solving the optimal solution of the parameters in the objective function by using a Lagrange relaxation method.
3. The joint beam forming method based on the SWIPT system as claimed in claim 2, wherein the method for solving the optimal solution for the parameters in the objective function by using the Lagrangian relaxation method comprises the following steps:
and converting the established objective function into the following functions by utilizing a Lagrange relaxation method:
Figure FDA0002444705860000021
and
Figure FDA0002444705860000022
Figure FDA0002444705860000023
Lk() Is a Lagrangian function, and lambda is a Lagrangian multiplier;
the constraint conditions of the converted objective function are as follows:
Figure FDA0002444705860000024
and solving the optimal value of the converted objective function.
4. The joint beamforming method based on a SWIPT system according to claim 3,
information beamforming vector vkOptimum value of (2)
Figure FDA0002444705860000025
Comprises the following steps:
Figure FDA0002444705860000026
wherein the content of the first and second substances,
Figure FDA0002444705860000027
Φkrepresenting information beamforming vectors vkThe domain of (3); n is a radical oftIndicating the number of transmit antennas at the transmit end.
5. The joint beamforming method based on a SWIPT system according to claim 3,
energy beam forming vector wkOptimum value of (2)
Figure FDA0002444705860000028
Comprises the following steps:
Figure FDA0002444705860000029
Figure FDA0002444705860000031
Λ＝[Λ1 2,…,Λk-1 2,Λk+1 2,…,ΛM 2]H∈C(M-1)×1
Figure FDA0002444705860000032
according to L ═ A-1Λ, obtaining
Figure FDA0002444705860000033
Figure FDA0002444705860000034
Is composed of
Figure FDA0002444705860000035
The orthonormal basis of (a);
Ntindicating the number of transmit antennas at the transmit end.
6. The SWIPT system based joint beamforming method according to claim 3, wherein the optimal value of α is
Figure FDA0002444705860000036
α initial value of αstartα Final value of αendUsing the formula
Figure FDA0002444705860000037
The value of α is updated when satisfied
Figure FDA0002444705860000038
The α value at time is the optimal value of α
Figure FDA0002444705860000039
7. A SWIPT system based joint beamforming method according to claim 3, wherein the optimal value of λ
Figure FDA00024447058600000310
The upper bound of the Lagrange multiplier is λmaxThe lower bound of the Lagrange multiplier is λminUsing the formula
Figure FDA00024447058600000311
Updating the value of lambda when P is satisfiedm-α|vk|2-|wk|2+α|wk|2The value of λ at 0 is the optimum value of said λ
Figure FDA00024447058600000312
Wherein
Figure FDA00024447058600000313
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《基于时隙分配的无线携能通信接收机算法研究》;冯雨晴;《中国优秀硕士学位论文全文数据库(信息科技辑)》;20170215(第02期);I136-214 *

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