An IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters

Abstract

The present invention discloses an IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, including: S1, establishing a joint beamforming optimization problem model of an IRS-assisted millimeter-wave system; S2, decoupling the joint design of IRS reflection beamforming and hybrid beamforming at the transceiver end; S3, proposing an iterative algorithm based on cross entropy to solve the optimal IRS reflection beamforming matrix according to the constraints of the discrete phase shifter; S4, based on the optimal IRS reflection beamforming matrix, designing a hybrid beamforming matrix by adopting an alternating minimization strategy. The present invention adopts the above-mentioned IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, which can improve the spectral efficiency of the system while reducing the hardware cost and power consumption of the phase shifter.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters. Background Art

[0002] Millimeter waves have richer spectrum resources and can provide data transmission rates of gigabits per second for current and future wireless networks. Compared with signals below 6 GHz, millimeter wave signals experience severe path loss and atmospheric attenuation, but their shorter wavelength allows the deployment of large-scale antenna arrays, which in turn produces higher beamforming gain and compensates for severe transmission losses. However, highly directional millimeter wave beams are more susceptible to obstacles, resulting in interruptions in communication links. To solve this problem, intelligent reflecting surface (IRS) technology has been introduced into millimeter wave communication systems. This technology can reflect the incident signal from the base station to the desired direction by intelligently controlling the coefficients of each element, thereby reducing the probability of link blocking. On the other hand, since the production of IRS does not use any RF link, it is also low-cost and energy-saving. Based on this, IRS-assisted millimeter wave communication systems have received widespread attention from academia and industry.

[0003] At present, a key problem facing IRS-assisted millimeter wave communication systems is the joint beamforming design of IRS and transceiver. In existing work, Chandan Pradhan et al. proposed a gradient projection method in Hybrid Precoding Design for Reconfigurable Intelligent Surface Aided mmWave Communication Systems published in the IEEE wireless communications letters in 2020, and used the minimum mean square error to design the beamforming problem; Peilan Wang et al. proposed a design algorithm based on manifold optimization (MO) in Joint Transceiver and Large Intelligent Surface Design for Massive MIMO mmWave Systems published in the IEEE Transactions on Wireless Communications in 2021 to improve the system spectrum efficiency; SH Hong et al. designed the IRS reflection matrix and hybrid beamforming matrix based on the sparse scattering structure and large-scale characteristics of the millimeter wave channel in Hybrid Beamforming for Intelligent Reflecting Surface Aided Millimeter Wave MIMO Systems published in the IEEE Transactions on Wireless Communications in 2022. In the above work, IRS reflection beamforming and transceiver beamforming are both realized by continuous phase shifters, but due to their high hardware cost and power consumption, they are difficult to implement in practice. Summary of the invention

[0004] The purpose of the present invention is to provide an IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, aiming to solve the high cost and high energy consumption problems brought by continuous phase shifters, while maximizing the spectral efficiency of the system.

[0005] To achieve the above object, the present invention provides an IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, comprising the following steps:

[0006] S1. Establish the joint beamforming optimization problem model of IRS-assisted millimeter wave system;

[0007] S2, decoupling the joint design of IRS reflective beamforming and transceiver hybrid beamforming;

[0008] S3. According to the constraints of discrete phase shifters, an iterative algorithm based on cross entropy is proposed to solve the optimal IRS reflection beamforming matrix;

[0009] S4. Based on the optimal IRS reflection beamforming matrix, the hybrid beamforming matrix is ​​designed by adopting an alternating minimization strategy.

[0010] Preferably, in step S1, the joint beamforming optimization problem is modeled as:

[0011]

[0012] In the formula, F BB and F RF denote the digital precoding matrix and the analog precoding matrix respectively, W BB and W RF are digital combination matrix and analog combination matrix respectively, [F RF ] i,j Denotes the matrix F RF The element in the i-th row and j-th column, [W RF ] i,j Represents the matrix W RF The element in row i and column j of ; is additive white Gaussian noise, σ 2 is the noise power, I represents the unit matrix, represents the equivalent channel matrix between the base station BS and the user UE, where G is the channel matrix between the base station BS and the IRS, and R is the channel matrix between the IRS and the user UE. is the reflection beamforming matrix, M is the number of reflection units, and the reflection coefficient is the mth diagonal element of Φ, θ m ∈0,2π represents the corresponding phase shift, and the constraint of the transmission power ρ is Due to the hardware constraints of discrete phase shifters with Q-bit resolution, the transmitter analog beamforming matrix F RF , the receiving end simulates the beamforming matrix W RF Each element in the reflection beamforming matrix Φ must be restricted to the set In

[0013]

[0014] In the formula, Q represents the resolution of the phase shifter, symbol Q IRS , Q BS and Q UE They represent the resolutions of the phase shifters at the IRS, base station BS and user UE respectively.

[0015] Preferably, in step S2, the joint design of IRS reflection beamforming and transceiver hybrid beamforming is decoupled, and the specific process is as follows:

[0016] For now, we will not consider F RF and W RF The hybrid beamforming matrix (F RF F BB / W RF W BB ) is regarded as a beamforming matrix (F / W) of a purely digital structure, then formula (1) is simplified to:

[0017]

[0018] It is worth noting that when Φ is known, the optimal F and W are obtained by H e The singular value decomposition of is obtained, that is, and W opt =U1, where H e =U∑V H , is a submatrix of the unitary matrix V, is a submatrix of the unitary matrix U, is a submatrix of ∑, N s represents the number of data flows, and then, by using the alternating minimization strategy, we obtain a value close to F opt / W opt The hybrid beamforming matrix (F RF F BB / W RF W BB ); On the other hand, the obtained F opt and W opt Substituting into formula (3), we obtain the optimization problem of the IRS reflection beamforming matrix Φ:

[0019]

[0020] In the formula, is a function of Φ.

[0021] Preferably, in step S3, according to the constraints of the discrete phase shifter, an iterative algorithm based on cross entropy is proposed to solve the optimal IRS reflection beamforming matrix:

[0022] In the iterative algorithm based on cross entropy, set u m,q Represents the reflection coefficient Select Collection The probability parameter of the qth element in , and u m,q satisfy And initialize the probability parameters Afterwards, in the i-th iteration, according to the probability distribution Generate X candidate reflection beamforming matrices At this time, formula (4) can be rewritten as

[0023]

[0024] Then, based on Calculate X And in descending order Arrange it, that is:

[0025]

[0026] Then, select the first X elite The corresponding larger The value of Φ [x] As elite samples; based on the probability distribution of these elite samples, the probability parameters are updated by minimizing the cross entropy for:

[0027]

[0028] in, Represents the generation of Φ [x] The probability of is:

[0029]

[0030] In the formula, Representing a collection The qth element in When true, the indicator function otherwise The Lagrangian coefficient Introducing formula (8), we get:

[0031]

[0032] About the above Find the first-order derivative and set the result to zero, and we get:

[0033]

[0034] Put formula (10) in Adding the cases together, we get Then we get:

[0035]

[0036] Finally, the above process is repeated until the maximum number of iterations I is reached, at which point the optimal IRS reflection beamforming matrix is ​​obtained with a probability close to 1.

[0037] Preferably, in step S4, based on the optimal IRS reflection beamforming matrix, a hybrid beamforming matrix is ​​designed by adopting an alternating minimization strategy:

[0038] For the optimal IRS reflective beamforming matrix Φ ＊ , find H e =RΦ ＊ G=U ＊ ∑ ＊ (V ＊ ) H , and Then, the optimization problem of the hybrid beamforming matrix at the transmitting and receiving ends is expressed as

[0039]

[0040]

[0041] The above formula (12) and formula (13) belong to the same problem model, so they are both solved using the existing alternating minimization strategy to obtain the approximately optimal F RF , F BB , W RF and W BB .

[0042] Therefore, the present invention adopts the above-mentioned IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, and its technical effects are as follows:

[0043] (1) In the discrete phase shifter scenario, a joint beamforming problem model for an IRS-assisted millimeter-wave system can be formed.

[0044] (2) The proposed cross-entropy based iterative algorithm is used to solve the IRS reflection beamforming problem and obtain the optimal solution with a probability close to 1.

[0045] (3) Based on the constraints of the discrete phase shifter, the IRS reflection beamforming and the transmit and receive beamforming are jointly optimized, which can reduce the hardware cost and energy consumption while maximizing the system spectrum efficiency.

[0046] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a system model diagram of IRS-assisted millimeter wave communication;

[0048] Figure 2 It is a simulation result diagram of the number of iterations and spectral efficiency;

[0049] Figure 3 It is a schematic diagram of simulation comparison of transmission power and spectrum efficiency. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0051] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0052] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the main idea or essential features of the present invention. Therefore, from all points of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0053] In addition, it should be understood that although this specification is described according to the implementation modes, not every implementation mode includes only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation modes that can be understood by those skilled in the art. These other implementation modes are also covered within the protection scope of the present invention.

[0054] It should also be understood that the specific embodiments described above are only used to explain the present invention, and the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, which should be covered by the protection scope of the present invention / invention.

[0055] Technologies, methods, and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0056] The disclosed contents of the prior art documents cited in the present specification are incorporated into the present invention by reference in their entirety and are therefore part of the disclosure of the present invention.

[0057] Embodiment 1

[0058] The embodiment of the present invention adopts an IRS-assisted millimeter wave communication system under a hybrid beamforming architecture, wherein the base station BS is equipped with N tAntenna RF chains, the user UE is equipped with N r Antenna RF chains, the base station BS and the user UE achieve N with the assistance of an IRS s Communication of data streams, such as Figure 1 shown.

[0059] In order to solve the problem of high hardware cost and power consumption of phase shifters in millimeter wave communication systems, the present invention provides an IRS-assisted millimeter wave joint beamforming method based on discrete phase shifters, comprising the following steps:

[0060] S1. Establishing the joint beamforming optimization problem model for IRS-assisted millimeter wave system

[0061] The joint beamforming optimization problem is modeled as:

[0062]

[0063] In the formula, F BB and F RF denote the digital precoding matrix and the analog precoding matrix respectively, W BB and W RF are digital combination matrix and analog combination matrix respectively, F RFi,j Denotes the matrix F RF The element in the i-th row and j-th column, [W RF ] i,j Represents the matrix W RF The element in row i and column j of ; is additive white Gaussian noise, σ 2 is the noise power, I represents the unit matrix, represents the equivalent channel matrix between the base station BS and the user UE, where G is the channel matrix between the base station BS and the IRS, and R is the channel matrix between the IRS and the user UE. is the reflection beamforming matrix, M is the number of reflection units, and the reflection coefficient is the mth diagonal element of Φ, θ m ∈0,2π represents the corresponding phase shift, and the constraint of the transmission power ρ is Due to the hardware constraints of discrete phase shifters with Q-bit resolution, the transmitter analog beamforming matrix F RF , the receiving end simulates the beamforming matrix W RF Each element in the reflection beamforming matrix Φ must be restricted to the set In

[0064]

[0065] In the formula, Q represents the resolution of the phase shifter, symbol Q IRS , Q BS and Q UE They represent the resolutions of the phase shifters at the IRS, base station BS and user UE respectively.

[0066] S2. Decoupling the joint design of IRS reflective beamforming and transceiver hybrid beamforming

[0067] For now, we will not consider F RF and W RF The hybrid beamforming matrix (F RF F BB / W RF W BB ) is regarded as a beamforming matrix (F / W) of a purely digital structure, then formula (1) is simplified to:

[0068]

[0069] It is worth noting that when Φ is known, the optimal F and W are obtained by H e The singular value decomposition of is obtained, that is, and W opt =U1, where H e =U∑V H , is a submatrix of the unitary matrix V, is a submatrix of the unitary matrix U, is a submatrix of ∑, N s represents the number of data flows, and then, by using the alternating minimization strategy, we obtain a value close to F opt / W opt The hybrid beamforming matrix (F RF F BB / W RF W BB ); On the other hand, the obtained F opt and W opt Substituting into formula (3), we obtain the optimization problem of the IRS reflection beamforming matrix Φ:

[0070]

[0071] In the formula, is a function of Φ.

[0072] S3. According to the constraints of discrete phase shifters, an iterative algorithm based on cross entropy is proposed to solve the optimal IRS reflection beamforming matrix.

[0073] In the iterative algorithm based on cross entropy, set u m,q Represents the reflection coefficient Select Collection The probability parameter of the qth element in , and u m,q satisfy And initialize the probability parameters Afterwards, in the i-th iteration, according to the probability distribution Generate X candidate reflection beamforming matrices At this time, formula (4) can be rewritten as

[0074]

[0075] Then, based on Calculate X And in descending order Arrange it, that is:

[0076]

[0077] Then, select the first X elite The corresponding larger The value of Φ [x] As elite samples; based on the probability distribution of these elite samples, the probability parameters are updated by minimizing the cross entropy for:

[0078]

[0079] in, Represents the generation of Φ [x] The probability of is:

[0080]

[0081] In the formula, Representing a collection The qth element in When true, the indicator function otherwise The Lagrangian coefficient Introducing formula (8), we get:

[0082]

[0083] About the above Find the first-order derivative and set the result to zero, and we get:

[0084]

[0085] Put formula (10) in Adding the cases together, we get Then we get:

[0086]

[0087] Finally, the above process is repeated until the maximum number of iterations I is reached, at which point the optimal IRS reflection beamforming matrix is ​​obtained with a probability close to 1.

[0088] S4. Based on the optimal IRS reflective beamforming matrix, the hybrid beamforming matrix is ​​designed by adopting an alternating minimization strategy.

[0089] For the optimal IRS reflective beamforming matrix Φ ＊ , find H e =RΦ ＊ G=U ＊ ∑ ＊ (V ＊ ) H , and Then, the optimization problem of the hybrid beamforming matrix at the transmitting and receiving ends is expressed as

[0090]

[0091]

[0092] The above formula (12) and formula (13) belong to the same problem model, so they are both solved using the existing alternating minimization strategy to obtain the approximately optimal F RF , F BB , W RF and W BB .

[0093] Embodiment 2

[0094] The design method of the first embodiment is adopted to design the model for simulation experiment. The details are as follows:

[0095] (1) Simulation conditions

[0096] The present invention adopts a three-dimensional model, in which the IRS at (0,148m,10m) is equipped with The base station BS located at (2m, 0, 10m) is equipped with N antennas. t =64 antennas in a uniform linear array, with N user UEs at (5m, 150m, 1.8m) r = a uniform linear array of 64 antennas. In addition, the number of RF chains at the base station BS and the user UE is The number of data streams is N s =4. The noise power is σ 2 =-90dBm. The phase shifter resolution corresponding to the analog beamforming at the base station BS is Q BS=5, the phase shifter resolution corresponding to the analog beamforming at the user UE is Q UE =5.

[0097] (2) Simulation content and conclusions

[0098] In order to evaluate the convergence of the method of the present invention, IRS =1,ρ=50dBm and X elite Under the condition of X = 0.2, Figure 2 The relationship between the spectral efficiency and the number of iterations I and the number of candidate matrices X is shown. It can be seen that when X is small, the increase of X will significantly improve the spectral efficiency, and when X is large enough, the spectral efficiency will tend to be stable. In addition, the method of the present invention tends to converge with the increase of the number of iterations I. In order to ensure the effectiveness of the method of the present invention, X=150 and I=30 are set. In addition, Figure 3 The relationship between spectrum efficiency and transmit power ρ is shown. Comparison Algorithm 1 is the algorithm mentioned in the paper “Joint Transceiver and Large Intelligent Surface Design for Massive MIMO mmWave Systems”, and Comparison Algorithm 2 is an algorithm based on random phase design of IRS beamforming. It can be seen that when Q IRS =2, the performance of the method of the present invention is significantly better than the other two comparison algorithms, and can be slightly higher than Q IRS The performance of Algorithm 1 is compared with that of =∞.

[0099] Therefore, the present invention adopts the above-mentioned IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, aiming to solve the high cost and high energy consumption problems brought by continuous phase shifters, while maximizing the spectrum efficiency of the system.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. An IRS-assisted millimeter-wave joint beamforming method based on discrete phase shifters, characterized in that: The following steps are involved: S1. Establish the joint beamforming optimization problem model of IRS-assisted millimeter wave system; The joint beamforming optimization problem is modeled as: In the formula, F BB and F RF denote the digital precoding matrix and the analog precoding matrix respectively, W BB and W RF are digital combination matrix and analog combination matrix respectively, [F RF ] i,j Denotes the matrix F RF The element in the i-th row and j-th column, [W RF ] i,j Represents the matrix W RF The element in row i and column j of ; is additive white Gaussian noise, σ 2 is the noise power, I represents the unit matrix, represents the equivalent channel matrix between the base station BS and the user UE, where G is the channel matrix between the base station BS and the IRS, and R is the channel matrix between the IRS and the user UE. is the reflection beamforming matrix, M is the number of reflection units, and the reflection coefficient is the mth diagonal element of Φ, θ m ∈(0,2π) represents the corresponding phase shift, and the constraint of the transmission power ρ is Due to the hardware constraints of discrete phase shifters with Q-bit resolution, the transmitter analog beamforming matrix F RF , the receiving end simulates the beamforming matrix W RF Each element in the reflection beamforming matrix Φ must be restricted to the set In In the formula, Q represents the resolution of the phase shifter, symbol Q IRS , Q BS and Q UE Respectively represent the resolution of the phase shifter at the IRS, base station BS and user UE; S2. Decouple the joint design of IRS reflection beamforming and transceiver hybrid beamforming. The specific process is as follows: For now, we will not consider F RF and W RF The hybrid beamforming matrix (F RF F BB / W RF W BB ) is regarded as a beamforming matrix (F / W) of a purely digital structure, then formula (1) is simplified to: It is worth noting that when Φ is known, the optimal F and W are obtained by H e The singular value decomposition of is obtained, that is, and W opt =U1, where H e =U∑V H , is a submatrix of the unitary matrix V, is a submatrix of the unitary matrix U, is a submatrix of ∑, N s represents the number of data flows, and then, by using the alternating minimization strategy, we obtain a value close to F opt / W opt The hybrid beamforming matrix F RF F BB / W RF W BB On the other hand, the obtained F opt and W opt Substituting into formula (3), we obtain the optimization problem of the IRS reflection beamforming matrix Φ: In the formula, is a function of Φ; S3. According to the constraints of discrete phase shifters, an iterative algorithm based on cross entropy is proposed to solve the optimal IRS reflection beamforming matrix; In the iterative algorithm based on cross entropy, set u m,q Represents the reflection coefficient Select Collection The probability parameter of the qth element in , and u m,q satisfy And initialize the probability parameters Afterwards, in the i-th iteration, according to the probability distribution Generate X candidate reflection beamforming matrices At this time, formula (4) can be rewritten as Then, based on Calculate X And in descending order Arrange it, that is: Then, select the first X elite The corresponding larger The value of Φ [x] As an elite sample; Based on the probability distribution of these elite samples, the probability parameters are updated by minimizing the cross entropy for: in, Represents the generation of Φ [x] The probability of is: In the formula, Representing a collection The qth element in When true, the indicator function otherwise The Lagrangian coefficient Introducing formula (8), we get: About the above Find the first-order derivative and set the result to zero, and we get: Put formula (10) in Adding the cases together, we get Then we get: Finally, the above process is repeated until the maximum number of iterations I is reached, at which point the optimal IRS reflection beamforming matrix is ​​obtained with a probability close to 1; S4. Based on the optimal IRS reflection beamforming matrix, the hybrid beamforming matrix is ​​designed by adopting an alternating minimization strategy: For the optimal IRS reflective beamforming matrix Φ ＊ , find H e =RΦ ＊ G=U ＊ ∑ ＊ (V ＊ ) H , and Then, the optimization problem of the hybrid beamforming matrix at the transmitting and receiving ends is expressed as The above formula (12) and formula (13) belong to the same problem model, so they are both solved using the existing alternating minimization strategy to obtain the approximately optimal F RF , F BB , W RF and W BB .

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