CN113032932B - Intelligent reflecting surface phase shift matrix design method - Google Patents
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Abstract
The invention relates to a design method of an intelligent reflecting surface phase shift matrix, which comprises the following steps of (1) introducing a positive scalar quantity delta for expressing the equivalent relation of amplitude values between a direct path signal and a reflected path signal; (2) And designing an IRS optimal phase shift matrix solving criterion based on a least square method according to the equivalence relation. The method for solving the IRS optimal phase shift matrix has application universality, the solving result is only related to the channel state information and is not related to the IRS scene and the optimization problem, and the IRS optimal phase shift matrix can be designed according to the method as long as the channel state information can be accurately estimated.
Description
Technical Field
The invention belongs to the field of wireless communication, and relates to a design method of an intelligent reflecting surface phase shift matrix.
Background
With the rapid development of mobile communication technology and internet of things technology, the number of mobile devices and internet of things devices is increased explosively, and accordingly, spectrum resources are increasingly tense. An Intelligent Reflection Surface (IRS) is a new technology, and it is not only expected to solve the problem of the surge of the number of wireless communication devices in the future, but also can reduce the energy consumption of the wireless internet of things system. In addition, the most important advantage of the wireless communication system based on the IRS enhancement is that it can greatly increase the channel capacity of the user without occupying additional spectrum resources.
The IRS consists of a microcontroller (Micro-Controller) and a series of Passive Reflecting Elements (Passive Reflecting Elements). The microcontroller performs the necessary computational and control functions, such as Channel State Information (CSI) estimation or controlling switching circuits in the passive array elements to change the phase of the reflected signal. The passive reflection array element is composed of a subsurface (metassurface) and a switch circuit. Subsurface is a new material with special electromagnetic properties that can be programmably controlled for the phase of the reflected signal, thereby achieving beam steering and beamforming. In essence, the IRS changes the phase of the multipath signal by controlling the switching circuit of the passive reflection array element to improve the multipath diversity gain between the AP and the user, thereby improving the signal-to-noise ratio of the user.
Therefore, the key to improve the channel capacity of the wireless communication system based on the IRS is: and setting reasonable reflection signal phase shift for each reflection array element of the IRS, so that multipath signals passing through different reflection array elements of the IRS are superposed in phase at a user receiver, and a user obtains the maximum diversity gain.
Documents [1] and [2] represent the mainstream method for solving the optimal phase shift in the current IRS research, that is, taking the phase shift matrix of the IRS array element as one of the optimized variables, so as to achieve the optimization target of maximizing the signal-to-noise ratio of the user receiver or minimizing the AP transmission power. Meanwhile, the beamforming vector of the AP can be used as an optimization variable to form a multivariable combined optimization problem together with the IRS array element phase shift matrix. Generally, the beamforming of the AP and the phase shift matrix of the IRS are multiplicatively coupled, which makes the proposed optimization problem generally non-convex, which is to be solved by converting the non-convex problem into a convex problem through relaxation, approximation or alternative optimization.
The optimal phase shift matrix solving methods based on the optimization problem proposed in documents [1] and [2] generally have excellent performance, but the methods are not very versatile, and on one hand, if the proposed optimization problem cannot be converted from a non-convex optimization problem to a convex problem, this means that the proposed optimization problem is not solvable, the optimal phase shift of the IRS cannot be solved, and whether the non-convex optimization can be converted to the convex optimization problem depends on the optimization experience of researchers. On the other hand, not only is the non-convex problem generally difficult to transform into a convex problem, but also the solution process of non-convex optimization is usually tedious, for example: by using an iterative method, the complexity of calculation cannot be guaranteed; with the alternating optimization method, the multiple optimization variables make it difficult for the optimization results to converge. Therefore, the method for solving the IRS optimal phase shift matrix does not have universality.
[1]Q.Wu and R.Zhang,“Intelligent reflecting surface enhanced wirelessnetwork:Joint active and passive beamforming design,”in Proc.
2018IEEE Global CommunicationsConference(GLOBECOM),Abu Dhabi,United Arab Emirates,United Arab Emirates,Dec.2018.
[2]C.Huang,G.C.Alexandropoulos,A.Zappone,M.Debbah,andC.Yuen,“Energy efficient multi-user miso communication using lowresolution large intelligent surfaces,”in Proc.2018 IEEE GlobecomWorkshops(GC Wkshps),Abu Dhabi,United Arab Emirates,UnitedArab Emirates,Dec.2018.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a method for designing an intelligent reflecting surface phase shift matrix, which is not only suitable for an IRS-based wireless communication system, but also can be used for solving an optimal IRS phase shift matrix in various scenes such as wireless energy transmission, wireless energy carrying communication, unmanned aerial vehicle-based wireless communication and the like; meanwhile, the method can be independently solved from the optimization problem, so that the difficulty of transformation of the optimization problem from non-convex optimization to convex optimization is reduced; the method provided by the invention has the advantages of low algorithm complexity and low time cost.
The technical scheme for solving the problems is as follows: a design method of an intelligent reflecting surface phase shift matrix is characterized by comprising the following steps:
1) Introducing a positive scalar delta, and writing an equivalent relation delta g = h Θ f between a direct path signal and a reflected path signal;
2) Designing a least square method to solve an optimal IRS phase shift matrix method according to the characteristic that delta g = h theta f is an underdetermined equation, searching by a dichotomy to accelerate the searching speed,
s.t.‖θ k ‖ 2 ≤1
and when the objective function of the least square method obtains an optimal value 0 and the value of delta takes a maximum value in the feasible solution, the theta at the moment is the optimal IRS phase shift matrix to be solved.
Further, the method for solving the IRS optimal phase shift matrix based on the least square method comprises the following steps:
2.1 Obtaining necessary channel state information;
2.2 To initialize the maximum feasible upper bound of the positive scalar Δ, i.e., Δ max ；
2.3 Searching for a positive scalar quantity meeting the step 2) through a search algorithm;
2.4 Output the solved IRS optimal phase shift matrix.
Further, the step 2.1) acquires necessary channel state information, specifically:
and respectively estimating channel state information g, h and f between the AP and the user, between the AP and the IRS and between the IRS and the user according to the antenna numbers of the AP and the IRS.
Further, the step 2.3) of searching for the positive scalar quantity meeting the step 2) by using a search algorithm specifically includes:
2.3.1 ) initialize the search space Δ L ＝0，Δ U ＝Δ max L and U represent the lower and upper boundaries of the search interval, respectively;
2.3.2 Calculate median value Δ of search interval M ＝(Δ U +Δ L )/2；
2.3.3 Will Δ M Substituting into an optimized function expression of a least square method,
s.t.‖θ k ‖ 2 ≤1
solving the optimal value of the objective equation;
2.3.4 ) if the optimum value of the objective function of the least square method is 0, searching for the lower boundary Δ L ＝Δ M Maximum positive scalar Δ * ＝Δ M (ii) a If the optimal value of the minimum objective function is greater than 0, the upper bound Δ of the search is determined U ＝Δ M 。
Further, the solved IRS optimal phase shift matrix output in step 2.4) is specifically:
repeating the steps 2.3.2) -2.3.4) until the difference between the searched upper and lower boundaries is less than the preset valueError range of setting, i.e. Δ U -Δ L <E, outputting the optimal IRS phase shift matrix theta solved at the moment.
The invention has the advantages that:
(1) The method for solving the IRS optimal phase shift matrix has application universality, the solving result is only related to channel state information and is not related to an IRS scene and an optimization problem, and the IRS optimal phase shift matrix can be designed according to the method as long as the channel state information can be accurately estimated;
(2) The invention can independently solve the optimal phase shift of the IRS only by depending on the channel state information, can reduce the solving complexity of the optimization problem proposed according to the application scene, reduce the number of the optimization variables, simplify the influence of coupling among the optimization variables in the proposed optimization problem, reduce the difficulty of solving the optimization problem and ensure that the optimization solution is simpler and more convenient;
(3) The method is simple in calculation, the IRS phase shift matrix in the underdetermined equation can be solved directly through the least square method, the phase shift of each array element does not need to be calculated item by item, and the calculation complexity is low;
(4) The invention combines the proposed IRS optimal phase shift judgment criterion with dichotomy search, thereby greatly accelerating the solving speed of the IRS optimal phase shift.
Drawings
FIG. 1 is a least squares based optimal IRS phase shift matrix solution criteria performance analysis;
FIG. 2 is an IRS-based wireless communication system architecture;
fig. 3 is a flowchart of IRS optimal phase shift matrix solution.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention. Thus, the following detailed description of the embodiments of the present invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.
The method takes the intelligent reflecting surface phase shift matrix as a variable to be solved for the first time, judges the minimum value of an underdetermined equation in a feasible definition domain by a least square method according to the amplitude and phase relation between a direct path signal and a reflected path signal, and provides an IRS optimal phase shift matrix search criterion: (1) The optimal value of a target equation of a least square method for solving the underdetermined equation is 0, and (2) the amplitude ratio of the reflected path signal to the direct path signal is maximum. Therefore, the variable satisfying the two criteria is the IRS optimal phase shift matrix we are to solve.
Specifically, the method is based on the following technical means:
(1) Introducing a positive scalar Δ, writing an equivalence relation Δ g = h Θ f between the direct path signal and the reflected path signal.
(2) Designing a least square method to solve an optimal IRS phase shift matrix method according to the characteristic that delta g = h theta f is an underdetermined equation, searching by a dichotomy to accelerate the searching speed,
s.t.‖θ k ‖ 2 ≤1
and when the objective function of the least square method obtains an optimal value 0 and the value of delta takes a maximum value in the feasible solution, the theta at the moment is the optimal IRS phase shift matrix to be solved.
The following is the theoretical basis of the present invention:
(1) Channel modeling
The channels between the AP and the user, between the AP and the IRS, and between the IRS and the user are respectively defined as f belongs to C M×1 ，h∈C M×N And f ∈ C N×1 . Definition of θ = [ ] 1 ,…,θ N ]And
theta is a vector composed of phase factors, and theta is a matrix for describing the phase shift adjustment of the IRS on the reflected signal, where theta is n ∈[0,2π]. And p in Θ n ∈[0,1]Representing the reflection coefficient for the incident signal at the nth antenna of the IRS, in the present invention ρ n Is set to 1. Assuming that the AP is a uniform linear array, precoding the signal can be performed with a beamforming vector w ∈ C M×1 It is assumed that the signal s transmitted by the AP is a coherent signal of unit power.
In particular, in the present invention, M ≦ N is always true, i.e., the number of AP antennas is always smaller than the number of IRS elements. On one hand, this is because the IRS needs to ensure the multipath gain through a large number of reflection array elements; on the other hand, the cost of large-scale production and flexible deployment of the IRS array elements is low, the number of the IRS array elements can be easily increased and decreased, but the number of the AP antennas is usually fixed.
(2) Theoretical basis
Theorem 1: when the direct path and reflected path signals are in phase, the user receives the maximum signal power, which also means that there is a phase mismatch between the direct path and the reflected path signals
It holds that, therefore, the direct path and reflected path signal relationships can be written as,
Δg＝hΘf
wherein the content of the first and second substances,
is a positive scalar quantity.
Proof 1: when the phase shift matrix of the IRS array element is used as the optimization variable to maximize the received signal power of the user, the optimization problem is expressed as max θ ‖(g+hΘf) H w‖ 2 . The only thing that plays a role in the optimization is | (g + h Θ f) H ‖ 2 The method has the advantages of simple process,
wherein, the first and the second end of the pipe are connected with each other,
representing the phase difference between the direct path and reflected path signals, the above equation obtains the maximum value when α =0, i.e., the user obtains the maximum signal-to-noise ratio when the phases of the direct path and the reflected path are identical. Since the frequency of the signals of the direct path and the reflected path is the same, when the phases of the signals are equal, the magnitude relationship between the amplitudes thereof can be expressed by an equation, and then Δ g = h Θ f.
After the syndrome is confirmed.
However, it is still difficult to solve the optimal IRS phase shift according to the aforementioned rules, and on one hand, a search method is designed to determine Δ * On the other hand, to achieve fast solution of the underdetermined equations with domain constraints. The invention provides a thought for effectively solving the optimal IRS phase shift, and the implementation steps are specifically explained next, so that a person skilled in the art can solve the optimal IRS phase shift according to the thought and the steps provided by the invention on the basis of no creative labor.
The technical solution in the embodiment of the present application will be made clear and fully described below with reference to the drawings in the embodiment of the present application, wherein a search algorithm takes binary search as an example, and an IRS-based communication system should be composed of at least three parts, i.e., an AP, an IRS, and a user, as shown in fig. 1. Wherein the AP communicates with the IRS, and the IRS adjusts a reflection phase to control a reflection path signal and enhances the received signal power of the user; specifically, the method comprises the following steps:
2.1 Obtaining necessary channel state information; the method comprises the following specific steps:
and respectively estimating channel state information g, h and f between the AP and the user, between the AP and the IRS and between the IRS and the user according to the number of the antennas of the AP and the IRS.
2.2 Initialize the maximum feasible upper bound of the positive scalar Δ, i.e., Δ max . The maximum feasible upper bound of the positive scalar represents the proportion of the reflected path signal amplitude to the direct path signal amplitude.
The significance of introducing the presence of the positive scalar Δ is: on one hand, the relation between a direct path signal and a reflected path signal can be written into linearity, on the other hand, Δ gives a search target, and we want to search for a maximum Δ under the condition that an underdetermined equation Δ g = h Θ f is solved * Since the reflected path can now provide the maximum multipath gain for the user.
2.3 Searching for a positive scalar quantity satisfying step 2) by a search algorithm; the method specifically comprises the following steps:
2.3.1 ) initialize the search space Δ L ＝0，Δ U ＝Δ max L and U represent the lower and upper boundaries of the search interval, respectively.
2.3.2 Computing median value of search interval Δ M ＝(Δ U +Δ L )/2。
The step 3 and the step 4 are necessary initialization steps for binary search, and are not described again.
2.3.3 Will Δ M Substituting into an optimized function expression of a least square method,
s.t.‖θ k ‖ 2 ≤1
and solving the optimal value of the objective equation.
The steps areStep 2.3.3) is the core contribution of the present invention, giving an achievable method to directly solve the optimal IRS phase shift according to the phase, specifically, if the phase of the IRS can be arbitrarily valued, the formula Δ g = h Θ f must be solved, because the unknown number of the formula is more than the number of equations. But since the phase shift of each array element of IRS can only be taken at 0,2 pi]So Δ g = h Θ f is not a constant solution, but is limited by the power ratio between the reflected and the direct signal. When Δ M When the maximum value is too large, the optimal solution of the least square method target function is larger than 0, and the physical meaning means that: the direct path signal power at this time is greater than the maximum value that the reflected path signal can provide, i.e., is not physically realizable. Thus, there is a * The optimal value of the least square is 0, so that the physical realizability is ensured, and meanwhile delta * Again, is greater than all possible values of delta, which also ensures that the reflected signal power is maximized. Thus Δ * The corresponding variable Θ is the optimal phase shift matrix solution of IRS.
Therefore, in order to achieve said intended aim, the invention proposes an implementable technical solution, in particular: moving the expressions for both the reflected path signal and the direct path signal to one side of the equation and minimizing the two-norm of the equation is also the least squares form for solving the underdetermined equation. At the same time, | θ k ‖ 2 ≦ 1 means that the module of the adjustable phase per array element of the IRS is 1, i.e. the unit circle on the complex plane, which also guarantees the adjustable phase constraint of the IRS.
The method for solving the optimal IRS phase shift based on the least square method has the advantages that: (1) at a M Given, the least square method can directly and accurately solve the unknown variable theta corresponding to the optimal value of the underdetermined equation. (2) From the least squares expression, it can be found that the optimal IRS phase shift matrix is achieved when the direct path signal phase and the reflected path signal phase are made equal, which is consistent with our intended goal to be achieved.
2.3.4 ) if the optimal value of the objective function of the least square method is 0, searching for the lower boundary Δ L ＝Δ M Maximum positive scalar quantity delta * ＝Δ M (ii) a If the optimal value of the minimum objective function is larger than0, then the upper bound Δ of the search U ＝Δ M . The other cases are not changed.
2.4 Step 2.3.2) -2.3.4) are repeated until the difference between the searched upper and lower boundaries is smaller than the preset error range, i.e. delta U -Δ L <E, outputting the optimal IRS phase shift matrix theta solved at the moment.
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the above embodiment, and also comprises the technical scheme consisting of any combination of the above technical features, including but not limited to: a channel estimation and equalization mode, a solving mode of a least square method and the like.
And (3) verification:
the proposed method for solving the IRS optimal phase shift matrix is verified from two aspects: (1) IRS optimal phase shift matrix solution criterion feasibility verification; and (2) verifying dichotomy search performance.
(1) Feasibility verification of IRS optimal phase shift matrix solution criterion
As shown in FIG. 1, first we generate 100 discrete Δ ∈ (0, 1) and arrange them from small to large, and then substitute the 100 Δ values item by item into the following formula (the least square method solves the IRS optimal phase shift matrix criterion), to obtain the optimal value of the objective function,
s.t.‖θ k ‖ 2 ≤1
because the substituted delta values are different, the optimal value curve of the least square method objective function based on the search term by term can be drawn. From the observation of the term-by-term search curve we find: when the substituted delta value is small, the optimal value of the least squares method is 0, which also means that the underdetermined equation Δ g = h Θ f exists for the IRS optimal phase shift matrix Θ that makes the direct path signal amplitude equal to the reflected path signal amplitude. When the substituted delta value is larger, the optimal value of the least square method is larger than 0, which means that the reflected path signal power cannot be equal to the product of the direct signal power and the positive scalar delta no matter how the phase shift of the IRS is adjusted under the value range constraint condition of Θ in the physical sense.
Therefore, the simulation result is completely consistent with the proposed IRS optimal phase shift matrix solving criterion, (1) the least square method for solving the underdetermined equation is maintained to be the minimum value, and (2) the amplitude ratio of the reflected path signal to the direct path signal is the maximum.
(2) Dichotomy search performance verification
From the red trace in FIG. 1, we can find that when the bisection method is used to search for the maximum positive scalar Δ * Then, only 6 attempts are required to find the maximum amplitude ratio Δ of the reflected path signal to the direct path signal * =0.73, which is completely consistent with the result of the term-by-term search, and the operand is an exponential reduction.
Thus, Δ * The corresponding IRS phase shift matrix Θ is the optimal phase shift matrix of IRS.
The above description is only an embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes performed by the present invention or directly or indirectly applied to other related system fields are also included in the scope of the present invention.
Claims (2)
1. A method for designing an Intelligent Reflector (IRS) phase shift matrix is characterized by comprising the following steps:
1) Introducing a positive scalar delta, and writing an equivalent relation delta g = h Θ f between the direct path signal and the reflected path signal;
2) Designing a least square method to solve the optimal IRS phase shift matrix method according to the characteristic that delta g = h theta f is an underdetermined equation, searching by a dichotomy to accelerate the searching speed,
s.t.||θ k || 2 ≤1
when the objective function of the least square method obtains an optimal value of 0 and the value of delta takes a maximum value in a feasible solution, the theta at the moment is the optimal IRS phase shift matrix to be solved;
the method for solving the optimal IRS phase shift matrix based on the least square method comprises the following steps:
2.1 Obtaining necessary channel state information; the method specifically comprises the following steps:
respectively estimating channel state information g, h and f between the AP and the user, between the AP and the IRS and between the IRS and the user according to the antenna number of the AP and the IRS;
2.2 To initialize the maximum feasible upper bound of the positive scalar Δ, i.e., Δ max ；
2.3 Searching for the positive scalar quantity meeting the step 2) through a search algorithm, and specifically comprising the following steps:
2.3.1 ) initialization search space Δ L =0, Δ U ＝Δ max L and U represent the lower and upper boundaries of the search interval, respectively;
2.3.2 Calculate median value Δ of search interval M ＝(Δ U +Δ L )/2；
2.3.3 A is measured by M Substituting into the optimized function expression of the least square method,
s.t.||θ k || 2 ≤1
solving the optimal value of the objective equation;
2.3.4 ) if the optimum value of the objective function of the least square method is 0, searching for the lower boundary Δ L ＝Δ M Maximum positive scalar Δ * ＝Δ M (ii) a If the optimal value of the minimum objective function is greater than 0, the upper bound Δ of the search is determined U ＝Δ M ；
2.4 Output the solved optimal IRS phase shift matrix.
2. A method of designing an Intelligent Reflective Surface (IRS) phase shift matrix according to claim 1, characterized in that:
the step 2.4) outputs the solved IRS optimal phase shift matrix, which specifically includes:
repeating the steps 2.3.2) -2.3.4) until the difference between the upper boundary and the lower boundary is smaller than the preset error range, namely delta U -Δ L And e, outputting the optimal IRS phase shift matrix theta solved at the moment.
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