CN114614925A - Reconfigurable intelligent surface assisted energy efficiency optimization method in millimeter wave non-orthogonal multiple access system - Google Patents

Reconfigurable intelligent surface assisted energy efficiency optimization method in millimeter wave non-orthogonal multiple access system Download PDF

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CN114614925A
CN114614925A CN202210234895.XA CN202210234895A CN114614925A CN 114614925 A CN114614925 A CN 114614925A CN 202210234895 A CN202210234895 A CN 202210234895A CN 114614925 A CN114614925 A CN 114614925A
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虞湘宾
黄旭
杨承弘
蔡嘉丽
党小宇
黎宁
陈小敏
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
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    • H—ELECTRICITY
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming

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Abstract

The invention discloses an energy efficiency optimization method in a reconfigurable intelligent surface assisted millimeter wave non-orthogonal multiple access system, which aims at maximizing energy efficiency, jointly optimizes the transmission power of a user, the mixed beam forming of a base station and the passive beam forming of a reconfigurable intelligent surface, provides a high-efficiency energy efficiency optimization algorithm based on alternative optimization, and can obtain a suboptimal joint resource allocation design method; the joint optimization method provided by the invention is effective and can realize high energy efficiency.

Description

Reconfigurable intelligent surface assisted energy efficiency optimization method in millimeter wave non-orthogonal multiple access system
The technical field is as follows:
the invention belongs to the field of mobile communication, relates to a resource allocation method of a mobile communication system, and particularly relates to an energy efficiency optimization method in an RIS (RIS) assisted mmWave-NOMA (weighted average-mean-average) system based on Hybrid Beam Forming (HBF).
Background art:
with the rapid development of mobile communications, the shortage of spectrum resources has brought about a great challenge to the prior art. mmWave has a large number of idle frequency bands for use, and can alleviate the problem of shortage of spectrum resources. Furthermore, mmWave communication is able to support high data rates due to the large available bandwidth.
In addition, the NOMA technology actively introduces interference information at a sending end, and correctly decodes signals of different users at a receiving end through serial interference elimination, so that higher spectral efficiency can be obtained. Meanwhile, energy efficiency is a key index of future green communication, and under the background, research on an energy efficiency optimization scheme of the mmWave-NOMA system is necessary.
While the mmWave band is rich in spectral resources, mmWave signals experience more significant path loss over their band than the path loss of a propagating signal over a low band. Therefore, the method for compensating the high path loss in the mmWave communication system is a method for enhancing the diversity gain of the array by deploying a large-scale antenna array. However, the high directivity makes mmWave communications susceptible to being blocked, especially in indoor or densely populated environments, where a very small obstruction, such as one's arm, would effectively block the link. RIS, an emerging technology, can solve this problem by expanding the communication range, achieving higher beamforming gain and EE. The RIS has a three-layer architecture and an intelligent controller with a large number of low-cost passive reflective elements distributed throughout the outermost plane to interact with the incident signal. The inner layer is usually a copper plate to minimize energy leakage during RIS reflection. The innermost layer is a control circuit board which is responsible for exciting the reflecting element and adjusting the reflecting amplitude and/or phase of the reflecting element in real time. In addition, the link between the base station and the RIS can also be implemented by an intelligent controller. The RIS can control each element to independently adjust the amplitude and/or the phase of an incident signal, and realize passive beam forming in a coordinated mode, so that the performance of a communication system is improved, and the coverage area and the connectivity of a base station are improved. Based on the above discussion, the invention researches an energy efficiency optimization method in an RIS-assisted mmWave-NOMA system based on HBF, and the method is oriented to high-energy-efficiency large-scale connection and green communication in the RIS-assisted mmWave-NOMA system.
The invention content is as follows:
aiming at an RIS-assisted mmWave-NOMA system, in order to improve the energy efficiency of the system, the invention maximizes the energy efficiency of all users, jointly optimizes the power distribution of the users, the HBF of a base station and the PBF of the RIS, and provides an energy efficiency optimization method in the RIS-assisted mmWave-NOMA system based on the HBF, so that a better energy efficiency optimization scheme can be obtained with polynomial time complexity.
The technical scheme adopted by the invention is as follows: an HBF-based RIS-assisted medium energy efficiency optimization method in an mmWave-NOMA system comprises the following steps:
step S1: establishing HBF-based RIS-assisted mmWave-NOMA system, wherein the system comprises two single-antenna users, an RIS and an mmWave base station, and the base station adopts HBF architecture and is provided with N antennas and N base stationsRFStrip radio frequency link, N low noise amplifiers and NNRFA phase shifter, each antenna passing through a low noise amplifier and NRFA phase shifter connected to the radio frequency link; assuming one data stream, the HBF of the base station includes an Analog Beamforming (ABF) matrix
Figure BSA0000268264210000021
And digital beamforming vectors
Figure BSA0000268264210000022
PIS is composed of M reflecting elements, the reflecting phase vector of which
Figure BSA0000268264210000023
Wherein theta ism∈[0，2π]Base station to RIS channel
Figure BSA0000268264210000024
Channel between RIS and user k
Figure BSA0000268264210000025
And base station directed to user k channel
Figure BSA0000268264210000026
Modeling as a millimeter wave channel;
step S2: the user k received signal can be expressed as:
Figure BSA0000268264210000027
wherein p iskRepresenting the transmission power, x, of user kkSignals representing user k, nkRepresenting complex white Gaussian noise, obeying a mean of 0 and a variance of σ2The distribution of the gaussian component of (a) is,
Figure BSA0000268264210000028
representing the cascade channels from the base station to the RIS and from the RIS to the user k, according to the NOMA protocol, taking the descending order of the channel gain as an example, the system energy efficiency optimization problem is modeled as
Figure BSA0000268264210000029
Wherein
Figure BSA0000268264210000031
PC＝PBB+NRFPRF+NNRFPPS+NPLNARepresenting fixed circuit power consumption, PBB，PRF，PPS，PLNADefining sets of baseband power consumption, radio frequency link power consumption, phase shifter power consumption and low noise amplifier power consumption respectively
Figure BSA0000268264210000032
Xi denotes the power amplifier coefficient, C1Represents a minimum rate constraint, rkIndicates the minimum transmission rate, C2For maximum power constraint, PmaxDenotes the maximum transmission power, C3Being a normal mode constraint of the ABF matrix, C4Normal-mode constraints, C, representing PBF vectors5A decoding condition for successive interference cancellation;
step S3: the optimization problem in step S2 belongs to a non-convex fractional programming problem, and an auxiliary variable P is introduced1+p2The original problem is equivalent to：
Figure BSA0000268264210000033
Wherein
Figure BSA0000268264210000034
The problem is decomposed into a beamforming sub-problem and a power allocation sub-problem using an Alternating Optimization (AO) algorithm:
given P, an auxiliary variable w is introduced as Ad,
Figure BSA0000268264210000035
using a penalty function method, the beamforming problem is
Figure BSA0000268264210000036
Where ρ is(l)The penalty coefficient is obtained when the first iteration is carried out by the penalty function method;
given HBF and PBF, the power allocation sub-problem is
Figure BSA0000268264210000037
Wherein
Figure BSA0000268264210000038
Step S4: aiming at the sub-problem of beam shaping in the step S3, the problem is decomposed into four sub-problems by adopting an AO algorithm: given { A, d, θ }, an auxiliary variable t is introduced1，t2，w＝Ad，
Figure BSA0000268264210000039
By means of penalty function method, SCA algorithm to obtain the relation { ukW optimization problem of
Figure BSA0000268264210000041
Wherein
Figure BSA0000268264210000042
Namely the value of the SCA algorithm in the q-1 iteration, the convex problem can be solved by means of a convex optimization tool to obtain a solution
Figure BSA0000268264210000043
When fixed { ukW, A, θ, the sub-problem to solve for d can be expressed as:
Figure BSA0000268264210000044
the objective function is derived and the derivative is made to be 0, the optimal solution to the problem is obtained as
Figure BSA0000268264210000045
Fixed { u }kW, d, θ }, let A ═ a1，...，aN]HBy adopting the MM algorithm, the solution of A can be obtained;
Figure BSA0000268264210000046
wherein
Figure BSA0000268264210000047
To represent
Figure BSA0000268264210000048
The phase of (a) is determined,
Figure BSA0000268264210000049
Figure BSA00002682642100000410
to represent
Figure BSA00002682642100000411
The maximum eigenvalue of (d);
fixed { ukWhen w, A, d } is equal to θ*Solving the PBF subproblem of the RIS as
Figure BSA00002682642100000412
Wherein
Figure BSA00002682642100000413
The above problem is solved using RMO, and the euclidean and riemann gradients of the objective function are:
Figure BSA00002682642100000414
wherein [ ] indicates a Hadamard product, the solution of the PBF sub-problem is
Figure BSA00002682642100000415
Wherein delta(s-1)，u(s-1)Respectively representing the step length and the value of u in the s-1 th iteration;
step S5: solving the power distribution subproblem in the step S3 according to a Lambert W function
Figure BSA0000268264210000051
The available power allocation is solved as
Figure BSA0000268264210000052
Wherein: omega ═ aPC/ξ-b。
The invention has the following beneficial effects: the energy efficiency optimization method in the HBF-based RIS-assisted mmWave-NOMA system has polynomial time complexity and can effectively improve the energy efficiency of the system. The method fully considers the internal structure of the original optimization problem, firstly alternately optimizes and equivalently converts the problem into a beamforming subproblem and a power distribution subproblem which are easier to solve, provides an energy efficiency optimization algorithm of an AO algorithm, a penalty function method, an SCA, an MM and an RMO algorithm, can converge to a feasible suboptimal solution, and finally obtains an effective energy efficiency optimization scheme.
Description of the drawings:
FIG. 1 is a flow chart of a system in an embodiment of the invention.
FIG. 2 is a diagram of a system in an embodiment of the invention.
Fig. 3 is a simulation graph of the energy efficiency optimization proposed in the embodiment of the present invention and two other comparison schemes.
Fig. 4 is a simulation graph of the proposed PBF scheme and two other optimization schemes in an embodiment of the present invention.
The specific implementation mode is as follows:
the invention will be further described with reference to the accompanying drawings.
First, system model
The system model related in the RIS-assisted mmWave-NOMA system based on HBF is shown in figure 1, and the system consists of two single-antenna users, one RIS and one mmWave base station, wherein the base station adopts HBF architecture and is provided with N antennas and N antennasRFStrip radio frequency link, N low noise amplifiers and NNRFA phase shifter, each antenna passing through a low noise amplifier and NRFA phase shifter connected to the radio frequency link; assuming one data stream, the HBF of the base station includes an Analog Beamforming (ABF) matrix
Figure BSA0000268264210000053
And digital beamforming vectors
Figure BSA0000268264210000054
The RIS consists of M reflecting elements, the reflecting phase vector of which
Figure BSA0000268264210000061
Wherein theta ism∈[0，2π]Base station to RIS channel
Figure BSA0000268264210000062
Channel between RIS and user k
Figure BSA0000268264210000063
And base station directed to user k channel
Figure BSA0000268264210000064
Modeling as a millimeter wave channel;
second, energy efficiency optimization problem modeling and solving process
In order to improve the energy efficiency of the system, a corresponding maximum energy efficiency optimization problem is established, the optimization target of the maximum energy efficiency optimization problem is to maximize the energy efficiency of all users, and the specific optimization problem is expressed as follows:
Figure BSA0000268264210000065
wherein
Figure BSA0000268264210000066
Xi denotes the power amplifier coefficient, PC＝PBB+NRFPRF+NNRFPPS+NPLNARepresenting fixed circuit power consumption, PBB，PRF，PPS，PLNADefining sets of baseband power consumption, radio frequency link power consumption, phase shifter power consumption and low noise amplifier power consumption respectively
Figure BSA0000268264210000067
C1Represents a minimum rate constraint, rkIndicates the minimum transmission rate, C2For maximum power constraint, PmaxDenotes the maximum transmission power, C3Being a normal mode constraint of the ABF matrix, C4Normal-mode constraints, C, representing PBF vectors5For decoding conditions of successive interference cancellation, an auxiliary variable P ═ P is introduced1+p2The original problem is equivalent to:
Figure BSA0000268264210000068
wherein
Figure BSA0000268264210000069
The problem is decomposed into a beamforming sub-problem and a power allocation sub-problem using an Alternating Optimization (AO) algorithm:
given P, an auxiliary variable w is introduced as Ad,
Figure BSA00002682642100000610
using a penalty function method, the beamforming problem is
Figure BSA0000268264210000071
Where ρ is(l)The penalty coefficient is obtained when the first iteration is carried out by the penalty function method; given HBF and PBF, the power allocation sub-problem is
Figure BSA0000268264210000072
Wherein
Figure BSA0000268264210000073
Aiming at the sub-problem of beam forming, the problem is decomposed into four sub-problems by adopting an AO algorithm: given { A, d, θ }, introduce an auxiliary variable t1，t2，w＝Ad，
Figure BSA0000268264210000074
By means of penalty function method, SCA algorithm to obtain the relation { ukW optimization problem of
Figure BSA0000268264210000075
Wherein
Figure BSA0000268264210000076
I.e. the value of the SCA algorithm at the q-1 iterationThe convex problem can be solved by means of a convex optimization tool to obtain a solution
Figure BSA0000268264210000077
When fixed { ukW, A, θ, the sub-problem to solve d can be expressed as:
Figure BSA0000268264210000078
the objective function is derived and the derivative is made 0, the optimal solution of the problem can be obtained as
Figure BSA0000268264210000079
Fixed { u }kW, d, θ }, let A ═ a1，...，aN]HBy adopting the MM algorithm, the solution of A can be obtained;
Figure BSA00002682642100000710
wherein
Figure BSA00002682642100000711
To represent
Figure BSA00002682642100000712
The phase of (a) is determined,
Figure BSA00002682642100000713
Figure BSA0000268264210000081
to represent
Figure BSA0000268264210000082
The maximum eigenvalue of (c);
fixed { ukW, A, d, let u equal theta*Solving the PBF subproblem of the RIS as
Figure BSA0000268264210000083
Wherein
Figure BSA0000268264210000084
The above problem is solved using RMO, and the euclidean and riemann gradients of the objective function are:
Figure BSA0000268264210000085
wherein [ ] indicates a Hadamard product, then the resolution of the PBF sub-problem is
Figure BSA0000268264210000086
Wherein delta(s-1)，u(s-1)Respectively representing the step length and the value of u in the s-1 th iteration;
aiming at the power distribution subproblem, solving according to a Lambert W function
Figure BSA0000268264210000087
Available power allocation solution as
Figure BSA0000268264210000088
Wherein: omega ═ aPC/ξ-b。
In summary, the present invention provides an energy efficiency optimization algorithm based on AO algorithm, penalty function method, SCA, MM and RMO algorithm, and the energy efficiency of the algorithm proposed by the present invention is verified by Matlab simulation, wherein the base station and the RIS are located at (0m, 0m) and (80m, 5m), respectively. All users are uniformly distributed in a range which takes (150m, 0m) as a center and 5m as a radius, the carrier frequency of the base station is 28GHz, and default parameter settings are listed in the following table:
Figure BSA0000268264210000089
Figure BSA0000268264210000091
FIG. 2 compares the energy efficiency performance of the energy efficiency optimization scheme proposed by the present invention with two other comparison schemes, wherein "NOMA-based scheme" represents the energy efficiency optimization scheme proposed by the present invention; "FPA NOMA-based scheme" means that the base station power is equally divided by the maximum transmission power, i.e. p1＝p2＝Pmax/2. "TDMA-based scheme" means that Time Division Multiple Access (TDMA) technology is employed to maximize energy efficiency, with each user allocated in equal time slots. Comparing the curves of "NOMA-based scheme" and "FPANOMA-based scheme" shows that when P is equal to PmaxWhen smaller, the performance of both algorithms follows PmaxAnd has the same energy efficiency performance, i.e., PmaxWhen smaller, the power allocation strategy is the same for both algorithms. This is because the power values allocated by both schemes are limited by the maximum power constraint, and thus the same power allocation is obtained, thereby achieving the same energy efficiency. When P howevermaxWhen the number of the algorithms is increased, the algorithm provided by the invention tends to be stable, and the FPA NOMA-based scheme is gradually decreased. "FPA NOMA-based scheme" increases the rate at the cost of consuming more power, and the rate is increased to a lesser extent than the total power consumption, so the energy efficiency is decreased; while the NOMA-based scheme does not sacrifice more power to increase the speed, thereby stabilizing the performance. In addition, comparing the curves of "NOMA-based scheme" and "TDMA-based scheme" shows that higher energy efficiency can be achieved with NOMA compared to orthogonal multiple access.
FIG. 3 shows the RIS-mmWave-NOMA system energy efficiency performance under different PBF optimization algorithms proposed by the present invention. In the OFDMA scheme, the "PSO PBF" using the particle swarm algorithm, the "Random PBF" based on the Random phase, and the algorithm "Designed PBF" given in the present invention are included. As can be seen from fig. 3, the PBF algorithm employed in the present invention can achieve EE performance similar to that of the PSO algorithm, and has lower complexity. In addition, both performances are superior to the Random PBF, because the PBF of the Random PBF is randomly generated and is not optimized, and the results also show the effectiveness of the PBF algorithm provided by the invention.
In conclusion, the energy efficiency method provided by the invention can effectively improve the energy efficiency performance of the RIS-assisted mmWave-NOMA system, and the steps for realizing the method are simple, so that the effectiveness of the energy efficiency optimization method in the RIS-assisted mmWave-NOMA system based on the HBF provided by the invention is fully demonstrated.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (1)

1. A method for optimizing energy efficiency in a millimeter wave mmWave non-orthogonal multiple access (NOMA) system of a reconfigurable intelligent surface assisted RIS is characterized by comprising the following steps: the method comprises the following steps:
step S1: establishing a RIS-assisted mmWave-NOMA system based on hybrid beam forming HBF, wherein the system consists of two single-antenna users, an RIS and an mmWave base station, and the base station adopts HBF architecture and is provided with N antennas and N base stationsRFStrip radio frequency link, N low noise amplifiers and NNRFA phase shifter, each antenna passing through a low noise amplifier and NRFA phase shifter connected to the radio frequency link; assuming one data stream, the HBF of the base station includes an analog beamforming ABF matrix
Figure FSA0000268264200000011
And digital beamforming vectors
Figure FSA0000268264200000012
The RIS consists of M reflecting elements, the reflecting phase vector of which
Figure FSA0000268264200000013
Corresponding reflection phase matrix is
Figure FSA0000268264200000014
Wherein theta ism∈[0，2π]Base station to RIS channel
Figure FSA0000268264200000015
Channel between RIS and user k
Figure FSA0000268264200000016
And base station directed to user k channel
Figure FSA0000268264200000017
Modeling as a millimeter wave channel;
step S2: establishing a system energy efficiency optimization problem with the optimization goal of maximizing the energy efficiency of all users
Figure FSA0000268264200000018
Optimizing variables to the transmission power of the user p1，p2The optimization constraints are the minimum rate constraint and the maximum power constraint of a user, the normal mode constraint of an ABF matrix, the normal mode constraint of a PBF vector and the decoding conditions of serial interference elimination; wherein R is1And R2Achievable rates for user 1 and user 2, ξ represents the power amplifier coefficient, PCExpressed as fixed circuit power consumption;
step S3: the optimization problem in step S2 belongs to a non-convex fractional programming problem, and the problem is decomposed into a beamforming subproblem of fixed power distribution and a power distribution subproblem of fixed beamforming using an alternating optimization AO algorithm;
step S4: for the sub-problem of beam shaping in step S3, an auxiliary variable { u } is introduced by a penalty function methodkW, the problem is decomposed into four subproblems by adopting an AO algorithm: given { A, d, θ } solution { u }kW.given { u }, a sub-problemkW, A, θ solve the sub-problem of the digital beamforming vector d, given { u }kCalculation of w, d, thetaSolving the sub-problem of the analog beamforming matrix A and given { u }kW, A, d solving the sub-problem of the PBF vector theta, and respectively solving by utilizing a sequential convex approximation SCA, a derivation, an optimization minimization algorithm and a Riemann manifold optimization algorithm;
step S5: and aiming at the power allocation sub-problem in the step S3, a closed-form solution is given by adopting a Lambert function, and power allocation is obtained.
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