CN113258985B - Energy efficiency optimization method for single-station multi-satellite MIMO (multiple input multiple output) upper injection system - Google Patents

Energy efficiency optimization method for single-station multi-satellite MIMO (multiple input multiple output) upper injection system Download PDF

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CN113258985B
CN113258985B CN202110502017.7A CN202110502017A CN113258985B CN 113258985 B CN113258985 B CN 113258985B CN 202110502017 A CN202110502017 A CN 202110502017A CN 113258985 B CN113258985 B CN 113258985B
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satellite
energy efficiency
power
injection system
mimo
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CN113258985A (en
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唐成凯
蔚保国
张娟
张怡
陈沛林
张玲玲
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Northwestern Polytechnical University
CETC 54 Research Institute
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CETC 54 Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/1851—Systems using a satellite or space-based relay
    • H04B7/18513—Transmission in a satellite or space-based system
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

A method for optimizing energy efficiency of a single-station multi-satellite MIMO upward injection system includes the steps of firstly carrying out mathematical modeling on an energy efficiency optimization problem of the single-station multi-satellite MIMO upward injection system under the limit of QOS and total transmitting power of each satellite, then converting a target function in a fraction form into a target function in a reduction form easy to solve by utilizing the property of fraction optimization, and then solving the dual problem through knowledge of convex optimization to obtain a mathematical expression of a power distribution matrix.

Description

Energy efficiency optimization method for single-station multi-satellite MIMO (multiple input multiple output) upper injection system
Technical Field
The invention relates to an energy efficiency optimization method under multi-user MIMO (multiple input multiple output) represented by low-orbit satellites, in particular to an energy efficiency optimization method based on a single-base-station multi-satellite MIMO upward injection model.
Background
With the development of communication technology, people have higher and higher requirements on data transmission rate. Low Earth Orbit (LEOS) is an important part of air-space-ground-sea integrated communication due to its advantages of short communication delay, high data transmission rate, etc., and is close to the ground.
In low earth orbit satellite communication systems, power allocation techniques are an integral part thereof. The simplest scheme of the power allocation technique is to perform Water-Filling (WF) power allocation on different satellites according to Channel State Information (CSI) to maximize the transmission rate. The WF is a classical power allocation algorithm, and can allocate more power to the satellite with good channel state according to the obtained CSI information, and allocate less power to the satellite with poor channel state. However, WF has the disadvantages that the water injection line is selected more complicated, the calculation amount is too large, and the WF is not suitable for the high-speed low-time slot transmission requirement of the low-orbit satellite communication system.
The power allocation technique can be mainly divided into a capacity maximization algorithm and an energy efficiency maximization algorithm according to the purpose. The capacity maximization algorithm mainly aims to improve the data transmission rate and maximize the system capacity. However, with the rapid increase of energy consumption, the existing energy sources are increasingly tense, the conventional power allocation technology for seeking channel capacity maximization cannot meet the requirement of current green communication, and more researchers begin to focus on energy efficiency maximization algorithms. The core idea of the energy efficiency maximization algorithm is to maximize the data transmission rate through an optimization theory under the requirements of limited transmission power and minimum data transmission rate.
At present, many energy efficiency maximization algorithms suitable for terrestrial communication have been proposed, these algorithms can implement fast and flexible power allocation according to channel quality, and some algorithms also introduce knowledge of optimization theory, so as to jointly optimize the number of antennas, user selection and power allocation. However, in an actual satellite communication system, due to the influence of the atmospheric environment, a channel has the characteristics of large interference, low signal-to-noise ratio and the like. The channel conditions in practical application scenarios are more complex than in terrestrial mobile communications. Meanwhile, the satellite has high running speed and short visible time, and the complexity of the algorithm cannot be too high. The improvement of the calculation difficulty and the requirement on the algorithm complexity are difficult to be considered, and the design difficulty of the algorithm is continuously increased.
Disclosure of Invention
Aiming at the problems that the existing energy efficiency optimization algorithm mostly stays in the research stage of terrestrial mobile communication and is difficult to be practically applied to a complex satellite communication system, the invention researches a single-station multi-satellite MIMO upward injection system energy efficiency optimization algorithm.
The method fully considers the power consumption of the system, deduces and obtains an energy efficiency function of the MIMO system adopting Block Diagonalization (BD) pre-coding, performs mathematical modeling on the energy efficiency optimization problem of the single-station multi-satellite MIMO upward injection system under the limitation of Quality of service (QoS) and total transmission power of each satellite, performs problem transformation by using a fraction optimization theory, obtains a mathematical expression of a power distribution matrix by solving a dual problem, and effectively solves the problem of difficulty in solving the energy efficiency optimization problem under the constraint condition. In addition, in the process of updating the power distribution matrix, the Dinkelbach method is adopted to accelerate the convergence of the algorithm and improve the practicability of the algorithm.
The technical scheme of the invention is as follows:
the energy efficiency optimization method for the single-station multi-satellite MIMO upward injection system comprises the following steps:
step 1: performing total modeling on the power of the single-station multi-satellite MIMO upward injection system to obtain an energy efficiency function of the system, and determining an energy efficiency optimization problem under the limitation of the service quality and the total transmitting power of each satellite according to the energy efficiency function of the system;
step 2: the method comprises the steps of solving the energy efficiency optimization problem of the single-station multi-satellite MIMO upper injection system by adopting a Dinkelbach method, and iterating by adopting a dual-rise method in the Dinkelbach method.
Further, the energy efficiency optimization problem of the single-station multi-satellite MIMO uplink injection system determined in step 1 is as follows:
Figure BDA0003056766750000021
wherein p is kl Is the power distribution matrix P of satellite k k K, K is the number of satellites, and the base station transmits L to the satellite K k A sub-stream, η is the reciprocal of the system power amplifier coefficient, P others Other power than transmit power; c (P) isThe system channel capacity after coding; Θ is a set consisting of power allocation policies that satisfy the following constraints:
Figure BDA0003056766750000031
R k is the transmission rate, R, of the signal up-fill to the kth satellite min Is the minimum transmission rate requirement, P, for the signal to be injected max For the total maximum transmit power, C1 and C2 limit the maximum and minimum transmit power for each user, respectively, and C3 guarantees the minimum transmission rate for each satellite.
Further, R min ＝4Gbps，P max ＝30dBm，p min ＝0。
Further, P others ＝NP cir +P ac,bw W+NP sp,bw W+P r ，NP cir Representing the power consumption of the circuit in relation to the number of transmitting antennas, P ac,bw W denotes the circuit power consumption in relation to the system bandwidth, NP sp,bw W denotes the power consumption of the circuit, P, related to both the number of transmit antennas and the system bandwidth r Representing a fixed power consumption.
Further, in the single-station multi-satellite MIMO uplink injection system, a BD precoding algorithm is adopted to obtain the system channel capacity C (P) after precoding.
In a further aspect of the present invention,
Figure BDA0003056766750000032
wherein phi kl Is Λ k,eff The first diagonal element of (a) is,
Figure BDA0003056766750000033
is the variance of Gaussian noise, Λ k,eff Is L k ×L k Diagonal matrix of dimensions, through equivalent channel H to satellite k k,eff Carrying out SVD decomposition to obtain:
Figure BDA0003056766750000034
U k,eff is M k ×M k The left singular matrix of the dimension is,
Figure BDA0003056766750000035
is L k ×L k Right singular matrix of dimensions.
Further, when the Dinkelbach method is adopted in the step 2 to solve the energy efficiency optimization problem of the single-station multi-satellite MIMO uplink injection system, the solving process of the power distribution matrix is divided into two processes, namely initialization and cycle iteration:
firstly, initializing a power distribution matrix and a Lagrange multiplier, determining an iteration step length and a convergence ending condition, and giving the limitation of the maximum transmitting power and the lowest transmission rate of each user;
and after initialization is completed, iterative solution of the power distribution matrix is carried out, wherein the problem is converted into inner layer iteration and outer layer iteration through a dual-rise method.
Further, the solving process of the power distribution matrix specifically includes:
step 2.1: given an initial power allocation matrix P * ＝P 0 Initializing the optimization factor q * Initializing Lagrange multipliers lambda, gamma and mu, giving an iteration step length alpha and a loop termination condition epsilon;
step 2.2: converting an energy efficiency optimization objective function from a fractional form to a subtractive form
Figure BDA0003056766750000041
Wherein the optimization factor
Figure BDA0003056766750000042
Thereby converting the energy efficiency optimization problem into
Figure BDA0003056766750000043
Step 2.3: performing outer layer iteration and updating a power distribution matrix:
fixing q in the transformed energy efficiency optimization problem formula obtained in step 2.2, one can obtain information about p kl Function of, memory
Figure BDA0003056766750000044
f in relation to p kl Is a concave function, and the original problem is converted into a convex optimization problem; the lagrange function of the objective function is:
Figure BDA0003056766750000045
wherein λ, μ k More than or equal to 0, corresponding to Lagrange multipliers of constraint conditions C1 and C3 respectively, and corresponding dual problems are
Figure BDA0003056766750000046
For the three-variable problem of the Lagrange multiplier and the power distribution matrix, the optimal transmission power needs to meet the requirement of the KKT condition
Figure BDA0003056766750000051
Thus, the optimum transmit power is
Figure BDA0003056766750000052
Wherein] + Indicating taking a non-negative value, using
Figure BDA0003056766750000053
Combine to obtain P * ；
Step 2.4: inner layer iteration, updating Lagrange multiplier:
the lagrangian multiplier is updated in iterations by the sub-gradient descent method:
Figure BDA0003056766750000054
Figure BDA0003056766750000055
where t is the number of iterations, α t Is the iteration step size;
step 2.5: after inner-layer iteration and outer-layer iteration are completed through a dual-rise method, whether an algorithm convergence condition is reached is judged:
Figure BDA0003056766750000056
and if the loop ending condition is reached, outputting the power distribution matrix, otherwise, returning to the step 2.2 to continue the execution.
Further, the iteration step size
Figure BDA0003056766750000057
Advantageous effects
The energy efficiency optimization model of the single-station multi-satellite MIMO upward injection system is established, the updated calculation formula of the power distribution matrix under the limit of the QOS and the total transmitting power of each satellite is deduced and perfected, and the energy efficiency optimization algorithm design of the single-station multi-satellite MIMO upward injection system is realized.
The Dinkelbach method is adopted, so that the reasonable power distribution can be still carried out within the limited injection time under the conditions of high satellite operation speed and short visible time, and the energy efficiency of the system is effectively improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a diagram of a model of a single-station multi-satellite MIMO uplink injection system.
The system comprises a base station and K satellites, wherein the base station simultaneously injects signals to the K satellites in the same frequency band, the base station is provided with N transmitting antennas, and L (K = 1.. Multidot., K) is transmitted to the satellites K k Sub-data stream, satellite k configuration M k A receiving antenna. Arrows indicate transmission links between transmitting antennas and receiving antennas, a MIMO communication system is formed between the base station and each satellite through a plurality of transmitting antennas and receiving antennas, and a multi-user MIMO communication system is formed between the base station and K satellites.
Fig. 2 is a data transmission block diagram of a single-station multi-satellite MIMO uplink injection system.
Wherein
Figure BDA0003056766750000061
For signals transmitted by base stations to satellite k, P k A matrix is assigned to the power of the satellite k,
Figure BDA0003056766750000062
the precoding matrix of the satellite k is mainly used for eliminating the co-channel interference among the satellites, the data received by each satellite comprises signals sent by a base station to the satellite and signals sent by the base station to other satellites, and the co-channel interference can be eliminated by designing a reasonable precoding matrix.
Figure BDA0003056766750000063
Is the channel matrix between the base station and the satellite k,
Figure BDA0003056766750000064
is gaussian noise. After power distribution and precoding, the K data streams are transmitted simultaneously through N transmitting antennas of the base station and are received by different satellites respectively through channel matrixes of the different satellites. Finally, the product is processedRecovering a data stream by receiving a matrix
Figure BDA0003056766750000065
FIG. 3 is a schematic diagram of the Dinkelbach algorithm.
The Dinkelbach algorithm is to solve the problem that the shape is r = ∑ v [ i =]*x[i]/∑c[j]*x[i](i =1,2,3.. N) for the purpose of solving the largest R (i.e., R in the figure). Taking any one of r, F (r) = ∑ v [ i ] on the X axis]*x[i]-r*∑c[i]*x[i]If there is at least one straight line F (r)>0, indicating that at least one further line intersects the X-axis to the right of it, then this r must not be a maximum, the true maximum being to the right of it. Find F (r) max The line is then moved r above the intercept of the line, (see FIG. 3, find the current F (r) max The straight line on which R is moved above R4), R can be found finally.
Detailed Description
The invention aims to provide an energy efficiency optimization method of a single-station multi-satellite MIMO upward injection system, which has the advantages of low calculation complexity and high convergence speed and can effectively solve the energy efficiency optimization method under multi-user MIMO represented by low-earth orbit satellites.
The energy efficiency optimization method of the single-station multi-satellite MIMO upward injection system provided by the invention combines the advantages of rapid convergence and low complexity of a dual-ascending method of a Dinkelbach method. According to the invention, firstly, under the limit of QOS and total emission power of each satellite, mathematical modeling is carried out on the energy efficiency optimization problem of the single-station multi-satellite MIMO annotating system, then the objective function in the form of fraction is converted into the objective function in the form of reduction which is easy to solve by using the property of fraction optimization, and then the dual problem is solved through the knowledge of convex optimization, so that the mathematical expression of the power distribution matrix is obtained, the problem that the energy efficiency optimization problem under the constraint condition is difficult to solve is effectively solved, and the practicability of the algorithm is improved.
BD (B) precoding algorithm
In a single-station Multi-satellite MIMO uplink transmission system, in order to ensure that signals between satellites do not interfere with each other, a precoding technology is required to be adopted at a transmitting end to suppress Multi-User Interference (MUI). Aiming at the problem of MUI elimination, the invention adopts a BD pre-coding algorithm, thereby effectively inhibiting MUI and improving the data transmission quality of the system. The flow of the BD pre-coding algorithm will be further described below.
The BD algorithm is a common precoding technology in an MU-MIMO system, and achieves the purpose of eliminating multi-user interference in a multi-user MIMO downlink mainly through a Singular Value Decomposition (SVD) method. The linear precoding and receive filter matrices can be obtained by the BD algorithm, which is mainly divided into two steps.
Step 1: and finding a precoding matrix which can eliminate the interference of other users, and forming a block channel of each user through the precoding matrix. Interference due to a base station transmitting signals to multiple satellites simultaneously is eliminated by mapping the signal of each satellite to the channel nulls of all other satellites.
Definition of
Figure BDA0003056766750000071
Channel joint matrix for all other satellites (K satellites in total), H k-1 A channel matrix representing the k-1 th satellite; for is to
Figure BDA0003056766750000072
Performing (Singular Value Decomposition, SVD) Singular Value Decomposition, including
Figure BDA0003056766750000073
Wherein
Figure BDA0003056766750000074
And
Figure BDA0003056766750000075
are respectively
Figure BDA0003056766750000076
Left singularity ofA matrix and a non-zero matrix of singular values,
Figure BDA0003056766750000077
and
Figure BDA0003056766750000078
by
Figure BDA00030567667500000713
Respectively correspond to
Figure BDA00030567667500000710
The non-zero singular values and the zero singular values of,
Figure BDA00030567667500000711
the column vector of (1) constitutes
Figure BDA00030567667500000714
The orthonormal basis of null space is then
Figure BDA0003056766750000081
From
Figure BDA0003056766750000082
Get L k Design the precoder with individual column vectors, L k Number of data streams transmitted by base station to satellite k, order
Figure BDA0003056766750000083
Is provided with
Figure BDA0003056766750000084
Since L is transmitted from the base station to the satellite k k The data streams, to ensure interference cancellation,
Figure BDA0003056766750000085
should at least have L k A column vector, so that the number of data streams and the number of transceiving antennas per satellite should be satisfied
Figure BDA0003056766750000086
So far, a precoding matrix B capable of eliminating other satellite interference is found k 。
And 2, step: the channel of each satellite is decomposed into independent parallel sub-channels, and optimization processing of each sub-channel is performed. Definition H keff ＝H k B k Is the equivalent channel of satellite k, pair H keff Performing SVD decomposition of
Figure BDA0003056766750000087
Wherein U is k,eff Is M k ×M k The left singular matrix of the dimension is,
Figure BDA0003056766750000088
is L k ×L k Right singular matrix of dimension, Λ k,eff Is L k ×L k A diagonal matrix of dimensions whose diagonal elements are non-zero singular values, whereby each user block channel is decomposed into a plurality of sub-channels. Then the BD precoding matrix for satellite k is
Figure BDA0003056766750000089
Wherein P is k Is the satellite k power allocation matrix, which is the term to be solved.
The receiving filter matrix of each satellite can be obtained through the second step of operation
Figure BDA00030567667500000810
The signal received by satellite k is
Figure BDA00030567667500000811
Wherein
Figure BDA00030567667500000812
Is equivalent noise. s k For data transmitted by the base station to the kth satellite, n k Is the reception noise of the kth satellite.
The system channel capacity after adopting BD precoding is
Figure BDA0003056766750000091
Where W is the bandwidth of the system,
Figure BDA0003056766750000092
φ kl is Λ k,eff The first diagonal element of (1), p kl Is P k The ith diagonal element of (1). I is a unit array;
Figure BDA0003056766750000093
is the gaussian noise variance.
Energy efficiency optimization method for (II) single-station multi-satellite MIMO upward injection system
To optimize the energy efficiency of a system, accurate modeling of the power of the system is required in addition to the system capacity. The power consumption of the system includes both the transmission power and the power consumption of the transceiver end circuitry associated with the signal processor, power amplifier, analog-to-digital converter, etc. The total power of the system can therefore be expressed as:
P total ＝ηP T +NP cir +P ac,bw W+NP sp,bw W+P r (9)
wherein
Figure BDA0003056766750000094
Representing signal transmission power (unknown term), NP cir Representing the power consumption of the circuit in relation to the number of transmitting antennas, P ac,bw W denotes the circuit power consumption in relation to the system bandwidth, NP sp,bw W denotes sum hairCircuit power consumption, P, related to both the number of antennas and the system bandwidth r Representing the fixed power consumption, and η is the inverse of the power amplifier coefficient.
Figure BDA0003056766750000095
P others ＝NP cir +P ac,bw W+NP sp,bw W+P r Representing other powers than the transmit power (considered known quantities), and since the goal is to optimize the transmit power, variations in other powers do not affect the subsequent derivation and can be considered as a whole.
Based on the above analysis, the energy efficiency optimization problem of the single-station multi-satellite MIMO uplink injection system can be expressed as follows:
Figure BDA0003056766750000101
where Θ is the set consisting of power allocation policies that satisfy the following constraints:
Figure BDA0003056766750000102
wherein R is min Is the minimum transmission rate requirement for the signal to be injected. C1 and C2 limit the maximum and minimum transmit power of each user, respectively, and C3 guarantees the minimum transmission rate of each satellite. P max Is the total maximum transmit power.
The application scene of the upper note of the low-orbit satellite signal is mainly considered, and the orbit height of the low-orbit satellite signal is 200-2000 km. Considering the problems of long injection path and short satellite visible time on satellite signals, the setting of constraint parameters is different from terrestrial communication, and R is set min ＝4Gbps，P max =30dBm. Since the system energy efficiency function is an increasing and then decreasing curve with increasing power, p min Must be less than the power corresponding to the energy efficiency maximum point, for convenience, p min Is generally set to 0, although with increased iterationTimes, but no occurrence of p min A situation where the setting is too large and the optimum point is missed.
The method comprises the steps of solving the energy efficiency optimization problem of the single-station multi-satellite MIMO upper injection system by adopting a Dinkelbach method, and iterating by adopting a dual-rise method in the Dinkelbach method.
In the energy efficiency optimization method of the single-station multi-satellite MIMO upward injection system, the solving process of the power distribution matrix can be mainly divided into two processes of initialization and cyclic iteration. Firstly, initializing a power distribution matrix and a Lagrange multiplier, determining an iteration step length and a convergence ending condition, and giving the limitation of the maximum transmitting power and the lowest transmission rate of each user. And after the initialization is finished, the iterative solution of the power distribution matrix is carried out, the problem can be converted into inner-layer iteration and outer-layer iteration through a dual-rise method, and the power distribution matrix is updated according to a formula in the outer-layer iteration. Updating Lagrange multiplier lambda, mu by a sub-gradient descent method in inner layer iteration k . And when the algorithm convergence condition is judged to be reached, the loop is ended.
The specific operation is as follows:
step 1: given an initial power allocation matrix P * ＝P 0 In practical applications, the initial power allocation matrix is usually given empirically, which is beneficial to speed up the convergence of the algorithm. Initializing an optimization factor q * =0, initializing lagrange multiplier λ =0, γ =0, μ =0, given iteration step α = α 0 And determining the updating speed of the Lagrange multiplier, wherein a cycle termination condition epsilon =0.01 is given, wherein the size of epsilon influences the accuracy of the algorithm, if epsilon is too large, the result of power distribution often cannot reach the optimal value of energy efficiency, if epsilon is too small, the convergence speed of the algorithm is reduced, power distribution and information can not be realized within the visible time of the satellite, and the actual size needs to be dynamically adjusted according to the requirement in the application.
Step 2: the fractional form is converted to a reduced form and the optimization factor is updated according to an iterative formula. Because the energy efficiency optimization problem is a constrained fractional optimization problem and is not easy to directly solve, the invention firstly converts the fractional form into a subtractive form which is easy to solve and then applies the knowledge of convex optimization to solve. According to the property of the fraction planning, the objective function of the energy efficiency optimization problem can be converted into:
Figure BDA0003056766750000111
wherein
Figure BDA0003056766750000112
The iteration updates the optimization factor q by the formula (14) * Where k denotes the kth satellite and l denotes the l data stream. The power optimization problem is converted into:
Figure BDA0003056766750000113
and step 3: and performing outer layer iteration and updating the power distribution matrix. By fixing q in equation (15), one can obtain information about p kl Function of (2), memory
Figure BDA0003056766750000114
It is apparent that f is related to p kl Is a concave function and the original problem is transformed into a convex optimization problem. Since the constraint C2 only needs to ensure that the power is not negative, negative values can be rounded off when the optimal power is finally taken. The lagrangian function of the objective function is:
Figure BDA0003056766750000121
wherein λ, μ k More than or equal to 0, corresponding to Lagrange multipliers of constraint conditions C1 and C3 respectively. (15) Is that
Figure BDA0003056766750000122
The three-variable problem is about Lagrange multipliers and power distribution matrixes, and according to KKT (Karush-Kuhn-Tucker) conditions, optimal transmitting power needs to meet the requirement of
Figure BDA0003056766750000123
Thus, the optimum transmit power is
Figure BDA0003056766750000124
Wherein] + Indicating a non-negative value. By using
Figure BDA0003056766750000125
Combine to obtain P * 。
And 4, step 4: and (5) iterating the inner layer, and updating the Lagrange multiplier.
And updating the Lagrange multiplier in the iteration through a sub-gradient descent method in the iteration:
Figure BDA0003056766750000126
Figure BDA0003056766750000127
where t is the number of iterations, α t Is the iteration step size, where set
Figure BDA0003056766750000128
The step size is reduced as the number of iterations increases, thereby ensuring convergence of the algorithm, where α is a small constant.
And 5: after inner-layer iteration and outer-layer iteration are completed through a dual-rise method, whether an algorithm convergence condition is reached is judged:
Figure BDA0003056766750000129
and if the cycle end condition is met, outputting the power distribution matrix, otherwise, returning to the step 2 to continue execution.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (6)

1. A single-station multi-satellite MIMO upward injection system energy efficiency optimization method is characterized by comprising the following steps: the method comprises the following steps:
step 1: performing total modeling on the power of the single-station multi-satellite MIMO upward injection system to obtain an energy efficiency function of the system, and determining an energy efficiency optimization problem under the limitation of the service quality and the total transmitting power of each satellite according to the energy efficiency function of the system;
the energy efficiency optimization problem of the single-station multi-satellite MIMO upward injection system is determined as follows:
Figure FDA0003951600230000011
wherein p is kl Is the power distribution matrix P of satellite k k K, K is the number of satellites, and the base station transmits L to the satellite K k A sub-stream, η is the reciprocal of the system power amplifier coefficient, P others Other power than transmit power; c (P) is the system channel capacity after precoding and is obtained by adopting a BD precoding algorithm; Θ is a set consisting of power allocation policies that satisfy the following constraints:
Figure FDA0003951600230000012
R k is the transmission rate, R, of the signal up-fill to the kth satellite min Is the minimum transmission rate requirement, P, for the signal to be injected max For the total maximum transmission power, C1 and C2 limit the maximum and minimum transmission power of each user, respectively, and C3 ensures the minimum transmission rate of each satellite;
the system channel capacity C (P) after precoding obtained by adopting a BD precoding algorithm is as follows:
Figure FDA0003951600230000013
where W is the system bandwidth, φ kl Is Λ k,eff The first diagonal element of (a) is,
Figure FDA0003951600230000014
is a Gaussian noise variance, Λ k,eff Is L k ×L k Diagonal matrix of dimensions, through equivalent channel H to satellite k k,eff Carrying out SVD decomposition to obtain:
Figure FDA0003951600230000015
U k,eff is M k ×M k The left singular matrix of the dimension is,
Figure FDA0003951600230000016
is L k ×L k A right singular matrix of dimensions;
and 2, step: the method comprises the steps of solving the energy efficiency optimization problem of the single-station multi-satellite MIMO upper injection system by adopting a Dinkelbach method, and iterating by adopting a dual-rise method in the Dinkelbach method.
2. The method for optimizing the energy efficiency of the single-station multi-satellite MIMO upward injection system according to claim 1, wherein the method comprises the following steps: r is min ＝4Gbps，P max ＝30dBm，p min ＝0。
3. The method for optimizing the energy efficiency of the single-station multi-satellite MIMO upward injection system according to claim 1, wherein the method comprises the following steps: p others ＝NP cir +P ac,bw W+NP sp,bw W+P r ，NP cir Representing the power consumption of the circuit in relation to the number of transmitting antennas, P ac,bw W denotes the circuit power consumption in relation to the system bandwidth, NP sp,bw W denotes the power consumption of the circuit, P, related to both the number of transmitting antennas and the system bandwidth r Representing a fixed power consumption.
4. The energy efficiency optimization method of the single-station multi-satellite MIMO upward injection system according to claim 1, characterized in that: when the Dinkelbach method is adopted in the step 2 to solve the energy efficiency optimization problem of the single-station multi-satellite MIMO uplink injection system, the solving process of the power distribution matrix is divided into two processes of initialization and circular iteration:
firstly, initializing a power distribution matrix and a Lagrange multiplier, determining an iteration step length and a convergence ending condition, and giving the limitation of the maximum transmitting power and the lowest transmission rate of each user;
and after the initialization is finished, carrying out iterative solution on the power distribution matrix, wherein the problem is converted into inner layer iteration and outer layer iteration through a dual-rise method.
5. The method for optimizing the energy efficiency of the single-station multi-satellite MIMO upward injection system according to claim 4, characterized in that: the solving process of the power distribution matrix specifically comprises the following steps:
step 2.1: given an initial power allocation matrix P * ＝P 0 Initializing the optimization factor q * Initializing Lagrange multipliers lambda, gamma and mu, giving an iteration step length alpha and a loop termination condition epsilon;
step 2.2: converting an energy efficiency optimization objective function from a fractional form to a subtractive form
Figure FDA0003951600230000021
Wherein the optimization factor
Figure FDA0003951600230000022
Thereby converting the energy efficiency optimization problem into
Figure FDA0003951600230000031
Step 2.3: performing outer layer iteration, and updating a power distribution matrix:
fixing q in the transformed energy efficiency optimization problem formula obtained in step 2.2, one can obtain information about p kl Function of, memory
Figure FDA0003951600230000032
f in relation to p kl Is a concave function, and the original problem is converted into a convex optimization problem; the lagrange function of the objective function is:
Figure FDA0003951600230000033
wherein λ, μ k More than or equal to 0, corresponding to Lagrange multipliers of constraint conditions C1 and C3 respectively, and corresponding dual problems are
Figure FDA0003951600230000034
For the three-variable problem of the Lagrange multiplier and the power distribution matrix, the optimal transmission power needs to meet the requirement of the KKT condition
Figure FDA0003951600230000035
Thus, the optimum transmit power is
Figure FDA0003951600230000036
Wherein] + Indicating taking a non-negative value, using
Figure FDA0003951600230000037
Combine to obtain P * ；
Step 2.4: inner layer iteration, updating Lagrange multiplier:
the lagrangian multiplier is updated in iterations by the sub-gradient descent method:
Figure FDA0003951600230000038
Figure FDA0003951600230000041
where t is the number of iterations, α t Is the iteration step size;
step 2.5: after inner-layer iteration and outer-layer iteration are completed through a dual-rise method, whether an algorithm convergence condition is reached is judged:
Figure FDA0003951600230000042
and if the cycle end condition is met, outputting the power distribution matrix, otherwise, returning to the step 2.2 to continue execution.
6. The energy efficiency optimization method for the single-station multi-satellite MIMO upward injection system according to claim 5, characterized in that: iteration step size
Figure FDA0003951600230000043
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