CN114614925B - Energy efficiency optimization method in reconfigurable intelligent-surface-assisted millimeter wave non-orthogonal multiple access system - Google Patents
Energy efficiency optimization method in reconfigurable intelligent-surface-assisted millimeter wave non-orthogonal multiple access system Download PDFInfo
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Abstract
The invention discloses an energy efficiency optimization method in a millimeter wave non-orthogonal multiple access system assisted by a reconfigurable intelligent surface, which aims at maximizing energy efficiency, jointly optimizes transmission power of a user, hybrid beam forming of a base station and passive beam forming of the reconfigurable intelligent surface, and provides a high-efficiency energy efficiency optimization algorithm based on alternate optimization, so as to obtain a suboptimal joint resource allocation design method; the combined optimization method provided by the invention is effective and can realize high energy efficiency.
Description
Technical field:
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 a Hybrid Beamforming (HBF) -based RIS-assisted mmWave-NOMA system.
The background technology is as follows:
with the rapid development of mobile communication, the shortage of spectrum resources presents a great challenge to the prior art. mmWave has a large number of idle frequency bands available for use, and can alleviate the problem of frequency spectrum resource shortage. In addition, mmWave communications can support high data rates due to the large bandwidth available.
In addition, the NOMA technology actively introduces interference information at a transmitting end, and correctly decodes signals of different users through serial interference elimination at a receiving end, so that higher frequency spectrum efficiency can be obtained. Meanwhile, energy efficiency is a key index of future green communication, and in such a background, research on an energy efficiency optimization scheme of the mmWave-NOMA system is necessary.
Although the mmWave band is rich in spectral resources, the mmWave signal experiences a more significant path loss over its band than the path loss of the propagating signal over the low band. For this reason, by deploying a large antenna array, the array diversity gain is enhanced, which is a method for compensating for high path loss in an mmWave communication system. However, the high directivity makes mmWave communication easy to be blocked, and particularly in indoor or densely populated environments, a very small obstacle such as a person's arm effectively blocks the link. RIS, an emerging technology, can address 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 extending over the outermost plane to interact with the incoming signal. The inner layer typically employs copper plates 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 may also be implemented by an intelligent controller. The RIS can control each element to independently adjust the amplitude and/or phase of an incident signal and cooperatively realize passive beam forming, thereby improving the performance of a communication system and the coverage area and connectivity of a base station. 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 comprises the following steps:
aiming at the 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 user power distribution, 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, which can obtain a better energy efficiency optimization scheme with polynomial time complexity.
The invention adopts the technical scheme that: an energy efficiency optimization method in an HBF-based RIS-assisted mmWave-NOMA system comprises the following steps:
step S1: establishing HBF-based RIS-assisted mmWave-NOMA system composed of two single-antenna users, an RIS and a mmWave base station, which adopts HBF architecture and is provided with N antennas and N RF Radio frequency link, N low noise amplifiers and NN RF A phase shifter, and each antenna passing through a low noise amplifier and N RF The phase shifters are connected to the radio frequency link; assuming one data stream, the HBF of the base station comprises an Analog Beamforming (ABF) matrixDigital beamforming vector +.>PIS consists of M reflective elements whose reflection phase vector +.>Wherein θ is m ∈[0，2π]Base station to RIS channel +.>Channel between RIS and user k>Channel of base station up to user k +.>Modeling as a millimeter wave channel;
step S2: the user k received signal may be expressed as:
wherein p is k Representing the transmission power of user k, x k Signals representing user k, n k Representing a complex gaussian white noise and,obeying the mean value to be 0 and the variance to be sigma 2 Is used for the distribution of the gaussian distribution of (c),representing a base station to RIS, RIS to user k cascade channel, the system energy efficiency optimization problem is modeled as follows according to NOMA protocol, taking the channel gain descending order as an example
Wherein the method comprises the steps ofP C ＝P BB +N RF P RF +NN RF P PS +NP LNA Representing the power consumption of a fixed circuit, P BB ，P RF ，P PS ，P LNA The power consumption of the baseband, the power consumption of the radio frequency link, the power consumption of the phase shifter and the power consumption of the low noise amplifier are respectively defined as the set +.>Xi represents the power amplifier coefficient, C 1 Representing a minimum rate constraint, r k Representing minimum transmission rate, C 2 For maximum power constraint, P max Indicating maximum transmit power, C 3 For normal mode constraint of ABF matrix, C 4 Normal mode constraint representing PBF vector, C 5 Decoding conditions for serial interference cancellation;
step S3: the optimization problem in step S2 belongs to a non-convex split-planning problem, introducing an auxiliary variable p=p 1 +p 2 The original problem is equivalent to:
wherein the method comprises the steps ofUsing an Alternating Optimization (AO) algorithmDecomposing the problem into beam forming sub-problems and power allocation sub-problems:
given P, the auxiliary variable w=ad is introduced,the beam forming problem is that by adopting a penalty function method
Wherein ρ is (l) The penalty coefficient is the penalty coefficient in the first iteration of the penalty function method;
given HBF and PBF, the power allocation sub-problem is
Wherein the method comprises the steps of
Step S4: aiming at the beam forming sub-problem 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 introduced 1 ，t 2 ，w＝Ad，Obtaining { u } through penalty function method and SCA algorithm k The w optimization problem is that
Wherein the method comprises the steps ofI.e. the value of the SCA algorithm at the q-1 th iteration, the convex problem described above can be solved by means of a convex optimization tool, resulting in a solution +.>When { u } is fixed k When w, A, θ }, solving the sub-problem of d can be expressed as:
deriving the objective function and making the derivative be 0, the optimal solution of the problem can be obtained asFix { u } k Let a= [ a ] in w, d, θ ] 1 ，...，a N ] H The solution of A can be obtained by adopting an MM algorithm;
wherein the method comprises the steps ofRepresentation->Phase of-> Representation->Is the maximum eigenvalue of (2);
fix { u } k Let u=θ at w, a, d } * Solving the PBF sub-problem of RIS as
Wherein the method comprises the steps ofSolving the above problem by adopting RMO, wherein the Euclidean gradient and the Riemann gradient of the objective function are as follows:
wherein ". Alpha.indicates Hadamard product, the solution of the PBF sub-problem is
Wherein delta (s-1) ，u (s-1) The step size and the value of u at the s-1 th iteration are respectively represented;
step S5: aiming at the power distribution sub-problem in the step S3, solving according to a Lambert W functionThe available power allocation solution is
Wherein: Ω=ap C /ξ-b。
The invention has the following beneficial effects: the energy efficiency optimization method in the RIS-assisted mmWave-NOMA system based on the HBF 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 converts the problem into a beam forming sub-problem and a power distribution sub-problem which are easier to solve, and provides an energy efficiency optimization algorithm of an AO algorithm, a penalty function method, SCA, MM and RMO algorithm, which can converge to a feasible suboptimal solution, and finally, an effective energy efficiency optimization scheme is obtained.
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 scheme and the other two comparison schemes according to the embodiment of the present invention.
Fig. 4 is a simulation graph of the PBF scheme and the other two optimization schemes proposed in the embodiment of the present invention.
The specific embodiment is as follows:
the invention is further described below with reference to the accompanying drawings.
1. System model
The system model involved in the RIS-assisted mmWave-NOMA system based on HBF of the invention is shown in figure 1, the system consists of two single-antenna users, an RIS and a mmWave base station, the base station adopts HBF architecture and is provided with N antennas and N RF Radio frequency link, N low noise amplifiers and NN RF A phase shifter, and each antenna passing through a low noise amplifier and N RF The phase shifters are connected to the radio frequency link; assuming one data stream, the HBF of the base station comprises an Analog Beamforming (ABF) matrixDigital beamforming vector +.>RIS is composed of M reflective elements, whose reflective phase vectorsWherein θ is m ∈[0，2π]Base station to RIS channel +.>Channel between RIS and user k>Channel of base station up to user k +.>Modeled as milliA meter wave channel;
2. modeling and solving process of energy efficiency optimization problem
In order to improve the energy efficiency of the system, a corresponding maximized energy efficiency optimization problem is established, wherein the optimization target is to maximize the energy efficiency of all users, and the specific optimization problem is expressed as follows:
wherein the method comprises the steps ofXi represents the power amplifier coefficient, P C ＝P BB +N RF P RF +NN RF P PS +NP LNA Representing the power consumption of a fixed circuit, P BB ，P RF ，P PS ，P LNA The power consumption of the baseband, the power consumption of the radio frequency link, the power consumption of the phase shifter and the power consumption of the low noise amplifier are respectively defined as the set +.>C 1 Representing a minimum rate constraint, r k Representing minimum transmission rate, C 2 For maximum power constraint, P max Indicating maximum transmit power, C 3 For normal mode constraint of ABF matrix, C 4 Normal mode constraint representing PBF vector, C 5 For decoding conditions of serial interference cancellation, an auxiliary variable p=p is introduced 1 +p 2 The original problem is equivalent to:
wherein the method comprises the steps ofThe problem is decomposed into beam forming sub-problems and power allocation sub-problems using an Alternating Optimization (AO) algorithm:
given P, introduce auxiliary variablesw＝Ad，The beam forming problem is that by adopting a penalty function method
Wherein ρ is (l) The penalty coefficient is the penalty coefficient in the first iteration of the penalty function method; given HBF and PBF, the power allocation sub-problem is
Wherein the method comprises the steps of
For the beam forming sub-problem, the AO algorithm is used to decompose the problem into four sub-problems: given { A, d, θ }, an auxiliary variable t is introduced 1 ，t 2 ，w＝Ad，Obtaining { u } through penalty function method and SCA algorithm k The w optimization problem is that
Wherein the method comprises the steps ofI.e. the value of the SCA algorithm at the q-1 th iteration, the convex problem described above can be solved by means of a convex optimization tool, resulting in a solution +.>When { u } is fixed k When w, A, θ }, solving the sub-problem of d can be expressed as:
deriving the objective function and making the derivative be 0, the optimal solution of the problem can be obtained asFix { u } k Let a= [ a ] in w, d, θ ] 1 ，...，a N ] H The solution of A can be obtained by adopting an MM algorithm;
wherein the method comprises the steps ofRepresentation->Phase of-> Representation->Is the maximum eigenvalue of (2);
fix { u } k Let u=θ at w, a, d } * Solving the PBF sub-problem of RIS as
Wherein the method comprises the steps ofSolving the above problem by adopting RMO, wherein the Euclidean gradient and the Riemann gradient of the objective function are as follows:
wherein ". Alpha.indicates Hadamard product, the solution of the PBF sub-problem is
Wherein delta (s-1) ，u (s-1) The step size and the value of u at the s-1 th iteration are respectively represented;
solving the power distribution sub-problem according to the Lambert W functionThe available power allocation solution is
Wherein: Ω=ap C /ξ-b。
In summary, the invention provides an energy efficiency optimization algorithm based on the AO algorithm, the penalty function method, the SCA algorithm, the MM algorithm and the RMO algorithm, and the energy efficiency of the algorithm provided by the invention is verified through Matlab simulation, wherein the base station and the RIS are respectively positioned at (0 m,0 m) and (80 m,5 m). All users are evenly distributed in a range with (150 m,0 m) 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:
FIG. 2 compares the energy efficiency performance of the proposed energy efficiency optimization scheme with the other two comparison schemes, wherein"NOMA-based scheme" means the energy efficiency optimization scheme proposed by the present invention; "FPA NOMA-based scheme" means that the base station power is divided by the maximum transmit power, i.e., p 1 ＝p 2 ＝P max /2."TDMA-based scheme" means that Time Division Multiple Access (TDMA) technology is employed to maximize energy efficiency, wherein each user is allocated by an equal time slot. As can be seen from comparing the curves of "NOMA-based scheme" and "FPANOMA-based scheme", when P max When smaller, the performance of both algorithms follows P max Increased with an increase in (a), and has the same energy efficiency performance, namely P max 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. However when P max When increasing, the algorithm provided by the invention tends to stabilize, and the 'FPA NOMA-based scheme' gradually decreases. "FPA NOMA-based scheme" increases the rate at the expense of more power consumption, while the rate increases to a lesser extent than the overall power consumption, and therefore energy efficiency is instead reduced; the NOMA-based scheme does not sacrifice more power to boost the rate, thus stabilizing the performance. Furthermore, comparing the curves of "NOMA-based scheme" and "TDMA-based scheme" it is known that using NOMA can achieve higher energy efficiency than orthogonal multiple access.
The performance of the RIS-mmWave-NOMA system under different PBF optimization algorithms proposed by the present invention is compared in FIG. 3. In the OFDMA scheme, a "PSO PBF" using a particle swarm algorithm, a "Random PBF" based on a Random phase, and an algorithm "Designed PBF" given by the present invention are included. As can be seen from fig. 3, the PBF algorithm adopted in the present invention can achieve EE performance similar to that of the PSO algorithm, and has lower complexity. In addition, both performance is superior to "Random PBF" because the PBF of "Random PBF" is randomly generated and not optimized, and the above results also illustrate the effectiveness of the PBF algorithm presented in the present invention.
In summary, the energy efficiency method provided by the invention can effectively improve the energy efficiency performance of the RIS-assisted mmWave-NOMA system, and meanwhile, the method has simpler implementation steps, which fully illustrates the effectiveness of the energy efficiency optimization method in the RIS-assisted mmWave-NOMA system based on the HBF.
The foregoing is merely a preferred embodiment of the invention, and it should be noted that modifications could be made by those skilled in the art without departing from the principles of the invention, which modifications would also be considered to be within the scope of the invention.
Claims (1)
1. An energy efficiency optimization method in a millimeter wave mmWave non-orthogonal multiple access NOMA system of a reconfigurable intelligent surface auxiliary RIS is characterized by comprising the following steps of: the method comprises the following steps:
step S1: establishing RIS-assisted mmWave-NOMA system based on mixed beam forming HBF, the system is composed of two single antenna users, one RIS and one mmWave base station, the base station adopts HBF architecture and is provided with N antennas and N RF Radio frequency link, N low noise amplifiers and NxN RF A phase shifter, and each antenna passing through a low noise amplifier and N RF The phase shifters are connected to the radio frequency link; assuming one data stream, the HBF of the base station comprises an analog beamforming ABF matrixDigital beamforming vector +.>RIS consists of M reflective elements, which passively beamform PBF vectorsThe corresponding PBF matrix is->Wherein θ is m ∈[0，2π]Base station to RIS channel +.>Channel between RIS and user k>Channel with base station up to user kModeling as a millimeter wave channel;
step S2: establishing a system energy efficiency optimization problem, the user k received signal can be expressed as:
wherein p is k Representing the transmission power of user k, x k Signals representing user k, n k Representing complex Gaussian white noise, obeying a mean value of 0 and a variance of sigma 2 Is used for the distribution of the gaussian distribution of (c),representing the cascade channel from the base station to the RIS, from the RIS to the user k, taking the descending order of channel gain as an example according to the NOMA protocol, the system energy efficiency optimization problem is modeled as follows:
wherein the method comprises the steps ofP C ＝P BB +N RF ×P RF +(N×N RF )P PS +N×P LNA Representing the power consumption of a fixed circuit, P BB ，P RF ，P PS ，P LNA The power consumption of the baseband, the power consumption of the radio frequency link, the power consumption of the phase shifter and the power consumption of the low noise amplifier are respectively defined as the set +.>ζ represents the power amplifier coefficient, and the optimization variable is the transmission power { p }, of the user 1 ，p 2 HBF { a, d } of base station and PBF vector θ, C of RIS 1 Representing a minimum rate constraint, r k Representing minimum transmission rate, C 2 For maximum power constraint, P max Indicating maximum transmit power, C 3 For normal mode constraint of ABF matrix, C 4 Normal mode constraint representing PBF vector, C 5 Decoding conditions for serial interference cancellation;
step S3: the optimization problem in the step S2 belongs to a non-convex split planning problem, and the problem is decomposed into a beam forming sub-problem of fixed power allocation and a power allocation sub-problem of fixed beam forming by using an alternating optimization AO algorithm;
step S4: aiming at the beam forming sub-problem in the step S3, an auxiliary variable { u } is introduced by a penalty function method k W, (k=1, 2), the AO algorithm is used to decompose the problem into four sub-problems: given { A, d, θ } solve { u } k Sub-problem of w, using penalty function and successive convex approximation SCA algorithm and by means of convex optimization tool to obtain { u } k Suboptimal solution for w, given u k Solving a sub-problem of the digital beam forming vector d by w, A, theta, obtaining an optimal solution of the digital beam forming vector d by deriving an unconstrained convex optimization problem, and giving { u } k Solving the sub-problem of the analog beamforming matrix A by w, d, theta, obtaining the sub-optimal solution of the analog beamforming matrix A by utilizing an optimization minimization MM algorithm, and giving { u } k Solving the sub-problem of the PBF vector theta by w, A, d, and obtaining the sub-optimal solution of the PBF vector theta by utilizing a Riemann manifold optimization algorithm;
step S5: aiming at the problem of the power allocation sub-step S3, a closed solution is given by adopting a lambertian function, and power allocation is obtained.
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