CN110611526A

CN110611526A - Millimeter wave hybrid analog/digital beam forming method based on improved Riemann manifold optimization

Info

Publication number: CN110611526A
Application number: CN201910892182.0A
Authority: CN
Inventors: 陈俊飞; 易辉跃; 许晖; 张武雄; 裴俊
Original assignee: Shanghai Institute of Microsystem and Information Technology of CAS; Shanghai Research Center for Wireless Communications
Current assignee: Shanghai Institute of Microsystem and Information Technology of CAS; Shanghai Research Center for Wireless Communications
Priority date: 2019-09-20
Filing date: 2019-09-20
Publication date: 2019-12-24

Abstract

The invention discloses a millimeter wave mixed analog/digital beam forming method based on improved Riemann manifold optimization, which comprises the following steps: projecting the conjugate gradient to a tangent space to obtain a Riemann gradient; searching points in a tangential space along the Riemann gradient, determining a step length by utilizing a Wolfe-Powell criterion, and backtracking the search points to the Riemann manifold; and when the stopping condition is met, obtaining an analog beam forming matrix and a digital beam forming matrix through calculation. The invention reduces the algorithm complexity and avoids the problem of missing minimum points in the searching process, thereby greatly reducing the calculation time and the bit error rate, and solving the problems that the hybrid beam forming can not achieve the full digital beam forming spectrum efficiency and the algorithm complexity is overhigh.

Description

Millimeter wave hybrid analog/digital beam forming method based on improved Riemann manifold optimization

Technical Field

The invention relates to a beam forming method, in particular to a hybrid analog/digital beam forming method based on improved Riemannian manifold optimization and used in a millimeter wave communication system, and belongs to the technical field of millimeter wave communication.

Background

Currently, the fifth generation mobile communication network (5G) has started to enter the commercialization phase. Millimeter wave (mmWave) communication, one of the key technologies of 5G, can solve the problem of insufficient bandwidth of the current mobile communication system, and is generally considered as the most potential technical direction in 5G.

In millimeter wave communication systems, large signal attenuation is overcome by means of narrow Beam and beamforming (Beam forming) in massive MIMO (multiple input multiple output) technology. To compensate for the severe path loss and penetration loss of the millimeter wave band, it is necessary to use large-scale antenna arrays at the transmitting end and the receiving end to obtain complementary link budgets. The large-scale antenna array can be combined with a beam forming technology to improve channel gain, so that the problem of millimeter wave high loss is solved. The beam forming can act on the transmitting end and the receiving end simultaneously, and forms a fixed pointed beam by controlling the phase of the array elements in the antenna array, thereby effectively improving the signal-to-noise ratio and inhibiting the interference between networks. However, the large increase in the number of antennas leads to non-trivial practical constraints. For example, conventional MIMO processing is typically implemented at baseband, which can control the phase and amplitude of the signal. However, digital processing requires dedicated baseband and radio frequency hardware to be configured for each antenna element. Unfortunately, due to the high cost and high power consumption of millimeter wave hybrid signal processing hardware, such an all-digital architecture is not currently available, forcing millimeter wave communication systems to rely heavily on analog or radio frequency processing.

A Hybrid Beamforming (HBF) architecture combines a low-dimensional baseband digital beamforming matrix with a high-dimensional analog beamforming matrix implemented with a phase shifter, which can significantly reduce the number of Radio Frequency (RF) chains while ensuring sufficient beamforming gain. Compared with the traditional full-digital beamforming, the difficulty of hybrid beamforming is that besides the difficulty of joint optimization of the four beamforming variables of transmission and reception analog beamforming and digital beamforming, the problem has high non-convexity and is difficult to solve due to the existence of phase shifters and the constant modulus constraint of analog beamforming. In the prior art, a common method for solving the problem is to decouple the original problem into sub-problems of digital and analog beam forming, and then to solve constant modulus constraints in the sub-problems in a centralized manner. Among them, an effective and widely used approach is to consider hybrid beamforming design as a matrix factorization problem, minimizing the euclidean distance between the all-digital beamforming matrix and the hybrid beamforming matrix. However, in general, the existing methods still have the problems of high computational complexity and the like, and the practical application is severely limited.

Disclosure of Invention

In view of the deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a hybrid analog/digital beamforming method based on improved riemann manifold optimization for use in a millimeter wave communication system.

In order to achieve the purpose, the invention adopts the following technical scheme:

according to an embodiment of the invention, a millimeter wave hybrid analog/digital beam forming method based on improved Riemannian manifold optimization is provided, which comprises the following steps:

projecting the conjugate gradient to a tangent space to obtain a Riemann gradient; searching points in a tangential space along the Riemann gradient, determining a step length by utilizing a Wolfe-Powell criterion, and backtracking the search points to the Riemann manifold; and when the stopping condition is met, obtaining an analog beam forming matrix and a digital beam forming matrix through calculation.

Wherein preferably, the conjugate gradient J (FRF (i)) is calculated according to the formula:

wherein, F_RFFor the purpose of simulating the beamforming matrix,is N_s×N_sThe dimension-unit matrix is a matrix of the dimension units,for transmit power constraints, i is the number of iterations, H₁＝H^HW_RFW_BBWherein W is_RFFor receiving analog combining matrices, W_BBThe matrix is merged for the received numbers.

Preferably, the Riemann gradient is obtained by projecting the conjugate gradient onto a tangential space according to the following formula:

wherein the content of the first and second substances,i is the number of iterations.

Preferably, the iterative search direction and search step are determined by using a linear search algorithm based on the Wolfe-Powell criterion.

Preferably, the Wolfe-Powell criterion is:

wherein x is_kIs the current point, α_kIs an independent variable, d_kIn order to be in the descending direction,taylor expansion as a function, g_kIs the directional derivative.

Preferably, the mean square error MSE is used as an objective function of the hybrid precoding design.

Preferably, the search points are traced back to the riemann manifold, and the mean square error MSE is calculated as follows:

wherein the content of the first and second substances,beta is an element (0,1) as a scale factor, and W is equal to W_RFW_BBFor the receive beamforming matrix, H is the channel matrix, F is the transmit beamforming matrix, s is the signal vector, n is the noise vector,is N_s×N_sAn identity matrix of dimensions.

Preferably, the stop condition is:

calculating the relative difference between the MSEs of the two iterations, namely delta MSE (i +1) ═ MSE (i +1) -MSE (i) |, if the delta MSE (i +1) is smaller than a preset value, ending the iteration to obtain the analog beam forming matrix

Preferably, the optimized digital beamforming matrix is calculated according to the following formula

Compared with the prior art, the improved linear search method can reduce the error rate of Riemannian manifold optimization, thereby improving the spectrum efficiency. The linear search is based on the Wolfe-Powell criterion, and the condition that the minimum value point is excluded from a feasible interval when the Armijo-Goldstein criterion is adopted in the existing Riemann manifold optimization can be avoided, so that the error rate is reduced, and the spectrum efficiency is improved. On the other hand, the improved Riemannian manifold optimization algorithm can reduce the complexity of the algorithm and greatly reduce the calculation time. The relative difference between the MSEs of the two iterations of the linear search stopping condition based on the Wolfe-Powell criterion can be set to be larger than that of the original linear search, and still can obtain the performance which is the same as or even better than that of the original algorithm, so that the iteration times can be reduced, the complexity of the algorithm is reduced, and the calculation time is shortened.

Drawings

Fig. 1 is a schematic structural diagram of a millimeter wave communication system for implementing the hybrid analog/digital beamforming method provided in the present invention;

FIG. 2 is a schematic structural diagram of a Riemannian manifold;

FIG. 3 is a graph comparing the spectral efficiency of the method of the present invention with other related methods;

fig. 4 is a graph comparing BER (bit error rate) index of the method provided by the present invention with other related methods.

Detailed Description

The technical contents of the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.

As mentioned above, the conventional MIMO technology employs an all-digital beamforming scheme, and each antenna element requires special baseband and radio frequency hardware, including a low noise amplifier, a down converter, analog-to-digital/digital-to-analog conversion, etc., which causes high cost and high power consumption. When the number of base station antennas is very large, it is difficult to assign a separate Radio Frequency (RF) chain for each antenna. In order to solve the above problems, the millimeter wave communication system needs to perform special analog or radio frequency processing, i.e. analog beamforming applies constant modulus constraints using phase shifters, but this results in analog beamforming having poorer performance than all-digital beamforming. To this end, near digital beamforming performance is achieved in massive MIMO by deploying limited radio frequency chains through a Hybrid Beamforming (HBF) architecture. Where digital signal processing may be implemented using a microprocessor at baseband frequencies and analog signal processing may be implemented using a phase shifter at radio frequencies.

In the prior art, although the hybrid beam forming technology is used, the problem of high computational complexity exists. Therefore, the hybrid analog/digital beam forming method provided by the invention decouples the original problem into the sub-problem of hybrid pre-coding and merging, focuses on solving the normal mode constraint of the sub-problem, and uses the improved linear search algorithm to carry out Riemann manifold optimization, thereby reducing the algorithm complexity and avoiding the problem of missing minimum points in the search process, greatly reducing the calculation time and the error rate, and solving the problems that the hybrid beam forming can not achieve the full digital beam forming spectrum efficiency and the algorithm complexity is too high. The specific steps of the hybrid analog/digital beamforming method are described in detail below.

Fig. 1 is a schematic structural diagram of a millimeter wave communication system for implementing the hybrid analog/digital beamforming method provided by the present invention. In the embodiment shown in fig. 1, it is assumed that the number of antennas at the transmitting end is N_tThe number of receiving end antennas is N_rBoth the transmitting end and the receiving end are equipped with N_RFA Radio Frequency (RF) chain, and satisfies N_r≥N_RF≥N_sAnd N_t≥N_RF≥N_sOf (3) is performed. The number of data streams to be transmitted is N_sThe data stream being N_sA x 1-dimensional vector, after being processed by a digital precoder, enters N of a transmitting end_RFProcessing with a Radio Frequency (RF) chain to form N_RF×N_sDimensional digital beam forming matrix F_BBThen sent to an analog precoder, N being achieved by using a phase shifter_t×N_RFDimension simulation beam forming matrix F_RFAnd generating a radio frequency signal to be transmitted. Wherein the normalized transmit power is constrained toThe radio frequency signal is transmitted by a transmitting terminal antenna, is received by a receiving terminal antenna, firstly enters an analog combiner, and then passes through N positioned at the receiving terminal respectively_RFAfter being processed by a Radio Frequency (RF) chain, the processed signal enters a digital combiner for subsequent processing and is output externally.

The millimeter wave propagation channel is a channel model based on geometry, and each channel model comprises N_clA cluster, each cluster including N_rayAnd (4) rays. In the embodiment shown in FIG. 1, consider a millimeter wave communication system with a uniform planar array (UPS) with half-wave spacing at both the transmitting and receiving ends, N_r×N_tThe channel matrix of the dimension can be expressed as:

α_ilrepresents the gain of the ith ray in the ith cluster, assuming α_ilIs an i.i.d. random variable following a complex Gaussian distribution, and the normalization factor gamma satisfies Andrepresenting receive and transmit array response vectors, in whichAndrepresenting the horizontal azimuth and elevation of arrival and departure, the array response vector corresponding to the ith ray in the ith cluster in the uniform planar array can be represented as:

wherein d is the antenna spacing, λ is the signal wavelength, p is 0, Y-1, q is 0, Z-1 is the coordinates of the antenna unit on the Y and Z axes, and the size of the antenna array is N is Y × Z.

Suppose N_sThe x 1-dimensional transmission signal vector is s, and the transmission signal after baseband digital beamforming and transmit-side analog beamforming can be represented as:

x＝F_RFF_BBs

the transmitted signal after baseband digital precoding and transmit-side analog beamforming can be represented as:

similar to the hybrid beamforming at the transmitting end, the receiving end consists of an N_r×N_RFAnalog combiner W of dimension_RFAnd one N_RF×N_sDigital combiner W of dimension_BBThe received signal may be expressed as:

where ρ is the average received power and n is the additive noise vector that follows the same independent distribution. Channel State Information (CSI) is known at both the transmitter and the receiver, and accurate CSI can be obtained by receiver channel estimation and transmitter channel estimation using efficient feedback techniques.

The inventor considers that the Mean Square Error (MSE) is another important measurement factor besides the spectrum efficiency based on the intensive study of the prior art. One direct motivation for considering MSE is: practical millimeter wave communication systems are typically constrained by a particular modulation and coding scheme, rather than gaussian codes, and MSE is therefore a direct performance indicator characterizing transmission reliability. In addition, related studies have shown that variables of MSE, such as sum-MSE, minmax MSE, modified MSE, weighted MSE, and the like, are related to other important performance indicators, such as signal-to-noise ratio (SINR) and Symbol Error Rate (SER). Therefore, MSE is of great significance as another optimization target for Hybrid Beamforming (HBF). In addition, precoding designs based on the minimum mse (mmse) criterion may also achieve better spectral efficiency.

On this basis, in the embodiment of the present invention, a Mean Square Error (MSE) is used as a performance index and an optimization target of the hybrid precoding design, and is expressed as:

wherein, β is a scale factor, y is a receiving signal, s is a sending signal, and is obtained by combining with a receiving signal expression:

in combination with the transmit power constraint and the constant modulus constraint of the phase shifter, the optimization problem can be written as:

the advantage of taking MSE as the objective function is:

1. the problem of the combined receiving and transmitting hybrid beam forming is decoupled into a sub-problem of the combination of hybrid precoding and receiving, and better precoding optimization performance is realized by considering the noise effect;

2. the fading factor helps to handle the total transmit power constraint, simplifying the precoding optimization process.

Next, the design scheme adopted by the transmitting end is first explained.

As shown in fig. 2, the riemann manifold is a differential manifold in which the tangential space of each point p defines a dot product and its value varies smoothly with p. The tangent space TxM at a given point x on manifold M consists of the tangent vector ξ of curve γ passing through point x. The manifold M is provided with a symmetric positive second-order covariant tensor field, i.e. an positive quadratic form in the tangential space of each point. The distance between a computed point and a point in euclidean space may be calculated using a modulo operation of the vector. In the riemann manifold, the points on the manifold are mapped to the tangent space, and then the distance is calculated by the defined dot product on the tangent space.

The rich geometry of the Riemannian manifold makes it possible to define the gradient of the cost function. More importantly, the optimization on the riemann manifold is locally similar to the optimization on euclidean space with smooth constraints. The Riemann manifold has an inner product defined on the tangent space TxM, referred to as the Riemann metric, which allows for the measurement of distances and angles on the manifold. In particular, it is possible to use calculus on the riemann manifold of the riemann metric.

In the prior art, it is proposed to define a riemann manifold for the analog beamforming matrix under consideration of the constant modulus constraint, and iteratively update the optimization variables in the riemann gradient direction to obtain a locally optimal analog beamforming matrix. But this method still has the defect of high computational complexity. Aiming at the problem, the invention provides a method for obtaining an analog beam forming matrix and a digital beam forming matrix by calculating when a stopping condition is met by projecting a conjugate gradient on a Euclidean space to a tangential space to obtain a Riemann gradient, searching points in the tangential space along the Riemann gradient, determining a step length by using a Wolfe-Powell criterion, tracing back the searched points to a manifold and obtaining the analog beam forming matrix and the digital beam forming matrix. This is explained in more detail below.

And at the transmitting end, the design is carried out by adopting a Riemann manifold optimization mode. Specifically, the precoder at the transmitting end is fixed, and the baseband precoding matrix is decomposed into F_BB＝βF_U，F_UIs a non-normalized baseband precoder. The optimization problem can be rewritten as:

wherein H₁＝H^HW_RFW_BB. First fix F_RFSolving for F_UAnd beta, and then taking the obtained result as F_RFIs derived, and finally, the objective function is further optimized through constant modulus constraint to optimize F_RF. Due to the limitation of the transmit power, there must be an optimal solution in the case of maximum total transmit power. β can be expressed as:f was obtained by KKT Conditions (Karush-Kuhn-Tucker Conditions)_BBIs expressed in a closed form, and then the Mean Square Error (MSE) is obtained as F_RFThe closed form expression of the function has high challenge to the optimization of the analog precoder, so that the beta is generally set as1.

According to the KKT condition, F_UThe closed-form solution of (c) can be expressed as:

finish solving F_UAnd β, the equation for computing MSE, can be simplified as:

wherein, F_RFIn order to simulate the beam-forming matrix,is N_sThe dimension-unit matrix is a matrix of the dimension units,for transmit power constraints, i is the number of iterations, H₁＝H^HW_RFW_BBWherein W is_RFFor receiving analog combining matrices, W_BBThe matrix is merged for the received numbers.

The optimization problem can be rewritten as:

in consideration of constant modulus constraint, is F_RFDefining a riemann manifold and iteratively updating the optimization variables in the direction of the riemann gradient (i.e. the projection of the conjugate gradient in euclidean space onto a point tangential space on the riemann manifold), in a similar manner to the projection of the euclidean gradient descent algorithm, but it is difficult to find the conjugate gradient in euclidean space, and thus the corresponding riemann gradient.

Definition ofThen

In one embodiment of the invention, the hybrid analog/digital beamforming method based on the improved Riemannian manifold optimization comprises the following steps:

step 1: constructing an optimization problem according to equation (11):

step 2: initializing FRF (0), wherein the iteration number is represented by a number in parentheses after the FRF;

and step 3: the conjugate gradient J (frf (i)) is calculated according to equation (10):

and 4, step 4: calculating FRF (i +1) using manifold optimization algorithm

(1) Projecting the conjugate gradient onto the tangent space according to equation (13) yields a riemann gradient:

(2) and searching points in a tangential space along the Riemann gradient, and determining an iterative search direction and search step length by using a linear search algorithm based on the Wolfe-Powell criterion. Then, the search points are traced back to the riemann manifold, and the Mean Square Error (MSE) in equation (6) is calculated as follows:

wherein, beta belongs to (0,1) as a scale factor, and W is equal to W_RFW_BBFor the receive beamforming matrix, H is the channel matrix, F is the transmit beamforming matrix, s is the signal vector, n is the noise vector,is N_s×N_sAn identity matrix of dimensions.

(3) Judging whether a stop condition is met:

calculating the relative difference between the MSEs of the two iterations, Δ MSE (i +1) ═ MSE (i +1) -MSE (i) |, if Δ MSE (i +1) is less than 10^－5And then ending the iteration to obtain the analog beam forming matrix

And 5: computing an optimized digital beamforming matrix according to equation (9)

In this way, an optimal analog beamforming matrix can be obtainedAnd a digital beamforming matrix

The linear search algorithm based on the Wolfe-Powell criterion used in step 4 is specifically described below:

from an initial point x₀Initially, then an iteration direction d is generated_kIn this direction, a step size alpha is selected₀The next point is x₀+α₀d_kUntil the best is foundHas the advantages of simple process and low cost. There are two key steps in this process, the first being the calculation of the iteration direction d_kThe second step is to select the appropriate step size in this direction.

The first step of generating an iteration direction d_kIs where the different optimization methods differ, but the most essential requirement is that it must be the direction of fall, i.e., (x)_k)^Td_k＜0，▽f(x_k) Is x_kThe gradient direction of (a);

the second step is a linear search, also comprising two key parts: one is the stopping condition and the other is the step size selection algorithm. The stopping condition is satisfied to ensure that the optimization algorithm can converge normally.

In the article "Hybrid Beamforming for Millimeter Wave Systems Using the MMSE Criterion", published in IEEEtransactions on Communications, vol.67, No.5, pp. 3693-. Namely:

1. the objective function value is sufficiently reduced;

2. the one-dimensional search step cannot be too small.

The basic idea is to move a larger estimated step size in the search direction and then iteratively reduce the step size until the step size results in a function f (x)_k+α_kd_k) Relative to the current function value f (x)_k) Until the degree of reduction is greater than a preset desired value.

The expression is as follows:

wherein rho is more than 0 and less than 0.5

Where α is_kFor the argument, the function is subjected to taylor expansion:

removing high-order infinity, known(this is to ensure d_kIs an essential condition for the descending direction), and 0 < ρ < 0.5, so the right side of the equation of (15) is a ratio f (x)_k) A small number ensures that the function value is decreasing.

Because 0 < rho < 0.5 andtherefore, the right side of equation (16) is smaller than the right side of equation (15) if the step size α is larger_kIf the value is too small, the inequality sign approach is not true, and the formula (16) ensures that the search step cannot be too small.

The above two constraints just limit the minimum point to a range satisfying the conditions. However, the use of the Armijo-Goldstein criterion may result in exclusion of true minima and may not function well. To this end, in one embodiment of the invention, the Wolfe-Powell criterion is employed to solve the problem.

The specific contents of the Wolfe-Powell criterion are as follows:

(18) The formula is the same as the formula (15) of the Armijo-Goldstein criterion, and the formula (19) is understood to mean that the slope of the tangent at the acceptable point is ≧ a times the initial slope. Since σ ∈ (ρ,1), the slope of the tangent line of the point where α ═ 0 is larger than the slope of the corresponding point in the Armijo-Goldstein criterion, the minimum value can be limited to a range that satisfies the condition.

The computational complexity of the hybrid analog/digital beamforming method provided by the present invention is analyzed below. In the present invention, since the transmission precoder and the reception combiner can be solved in the same process, the complexity analysis is performed by taking the transmission precoder as an example. Because the complexity of the digital precoders of all hybrid beamforming algorithms is the same, the computation complexity is much lower than that of the analog precoders, and therefore only the analog precoders are computed during computation.

1. Conjugate gradient calculation:

according toTotal complexity ofWhereinIs two N_RF×N_RFTransposing of the matrix.

2. Orthogonal projection and shrinkage:

the essence of orthogonal projection is the Hadamard process, two 2N_antN_RFThe product of the matrices; complexity of the shrinkage is N_antN_RF。

3. Linear search:

to ensure convergence, the complexity of the backtracking search using Armijo isWhereinIs two N_RF×N_RFTransposing of the matrix. The complexity of the search using the Wolfe-Powell criterion is

Representation of the total complexity:

representing the number of inner iterations and the number of outer iterations as N_inAnd N_outThe total complexity of the Riemann manifold can be expressed asThe total complexity of the hybrid analog/digital beamforming method provided by the present invention can be expressed as

Next, the algorithm performance of the hybrid analog/digital beamforming method provided by the present invention is further evaluated through simulation experiments. In the simulation experiment, 64 transmitting and 64 receiving antenna structures are used, the number of data streams is 2, the number of radio frequency chains is 2, comparison algorithms include a traditional SVD algorithm (adopting full digital beam forming and regarded as the optimal performance of the system), a weighted mmse algorithm, an OMP algorithm, a riemann manifold algorithm and the hybrid analog/digital beam forming method, and the performance of the algorithms is evaluated by using two indexes, namely spectral efficiency and BER (bit error rate), shown in fig. 3 and 4 respectively.

And (3) comparing the running time:

riemann manifold algorithm:

time has elapsed 0.115061 seconds.

Time has elapsed 0.053016 seconds.

Time has elapsed 0.096704 seconds.

Time has elapsed 0.056353 seconds.

Time has elapsed 0.092447 seconds.

current SNR：－15

Time has elapsed 0.023249 seconds.

Time has elapsed 0.093643 seconds.

Time has elapsed 0.024938 seconds.

Time has elapsed 0.031092 seconds.

Time has elapsed 0.024545 seconds.

current SNR：5

SNR-15, total time: 0.413581, respectively;

SNR is 5, total time: 0.197467

The hybrid analog/digital beam forming method comprises the following steps:

time has elapsed 0.111720 seconds.

Time has elapsed 0.067059 seconds.

Time has elapsed 0.057417 seconds.

Time has elapsed 0.078851 seconds.

Time has elapsed 0.057422 seconds.

current SNR：－15

Time has elapsed 0.030229 seconds.

Time has elapsed 0.030140 seconds.

Time has elapsed 0.022335 seconds.

Time has elapsed 0.022822 seconds.

Time has elapsed 0.029468 seconds.

current SNR：5

SNR-15, total time: 0.366;

SNR is 5, total time: 0.134994

Compared with the Riemann manifold algorithm used in the prior art, the hybrid analog/digital beam forming method reduces 11.53% when the SNR is-15 and reduces 31.64% when the SNR is 5. Therefore, the linear search algorithm based on the Wolfe-Powell criterion can greatly reduce the calculation complexity. The required computation time is also reduced to a large extent compared to algorithms commonly used in the prior art.

The millimeter wave hybrid analog/digital beam forming method based on the improved riemann manifold optimization provided by the invention is explained in detail above. Any obvious modifications to the invention, which would occur to those skilled in the art, without departing from the true spirit of the invention, would constitute a violation of the patent rights of the invention and would carry a corresponding legal responsibility.

Claims

1. A millimeter wave hybrid analog/digital beam forming method based on improved Riemannian manifold optimization is characterized by comprising the following steps:

2. The millimeter wave hybrid analog-to-digital beamforming method according to claim 1, wherein the conjugate gradient J (frf (i)) is calculated according to the following formula:

wherein, F_RFFor the purpose of simulating the beamforming matrix,is N_sThe dimension-unit matrix is a matrix of the dimension units,for transmit power constraints, i is the number of iterations, H₁＝H^HW_RFW_BBWherein W is_RFFor receiving analog combining matrices, W_BBThe matrix is merged for the received numbers.

3. The millimeter wave hybrid analog-to-digital beamforming method according to claim 2 wherein the Riemann gradient is obtained by projecting the conjugate gradient onto the tangential space according to the following equation:

4. The millimeter wave hybrid analog-to-digital beamforming method according to claim 1, wherein:

and determining the iterative search direction and search step length by utilizing a linear search algorithm based on the Wolfe-Powell criterion.

5. The millimeter wave hybrid analog-to-digital beamforming method according to claim 1 wherein the Wolfe-Powell criterion is:

6. The millimeter wave hybrid analog-to-digital beamforming method according to claim 1, wherein:

the mean square error MSE is taken as the objective function of the hybrid precoding design.

7. The millimeter wave hybrid analog/digital beamforming method according to claim 6 wherein the search points are traced back to the Riemann manifold, and the mean square error MSE is calculated as follows:

8. The millimeter wave hybrid analog-to-digital beamforming method according to claim 7, wherein the stop condition is:

9. The millimeter wave hybrid analog-to-digital beamforming method according to claim 8, wherein:

the predetermined value is 10^－5。

10. The millimeter wave hybrid analog-to-digital beamforming method of claim 9, wherein the optimized digital beamforming matrix is calculated according to the following formula