CN112653496B - Mixed precoding method of millimeter wave large-scale MIMO system - Google Patents

Abstract

The invention discloses a mixed pre-coding method of a millimeter wave large-scale MIMO system, which comprises the following steps: 1. channel modeling, determining a channel matrix H, performing singular value decomposition on the channel matrix to obtain an optimal unconstrained all-digital pre-coding matrix, 2, constructing a simulated pre-coding vector by adopting an alternative iteration method, 3, updating a residual matrix F by adopting a mode similar to matching tracking_resAnd 4, calculating a digital precoding matrix by adopting a least square method and carrying out normalization processing, and 5, obtaining an analog combination matrix and a digital combination matrix by adopting the same steps at a receiving end. The invention can obtain better spectrum efficiency close to the full-digital pre-coding method with relatively lower computation complexity, thereby obtaining the channel capacity close to the full-digital pre-coding and greatly saving the energy consumption of a radio frequency chain.

Description

Mixed precoding method of millimeter wave large-scale MIMO system

Technical Field

The invention belongs to the technical field of information and communication engineering, and particularly relates to hybrid precoding of a millimeter wave large-scale Multiple Input Multiple Output (MIMO) system.

Background

The explosive demand for capacity of wireless communication systems nowadays makes the traditional spectrum resources increasingly strained, and millimeter waves can provide rich frequency band resources and giga data rates, which are considered as the key technology of 5G (5 th-Generation). However, compared to current wireless communication systems, millimeter wave signals suffer from higher free space path loss due to the 10-fold increase in frequency. Fortunately, the reduction in wavelength allows the antenna to be smaller in size, allowing a large number of antennas to be packaged in the same space. The large array may implement beamforming gain to compensate for path loss. Furthermore, with large arrays, spectral efficiency can be improved by precoding. In a conventional MIMO system, each antenna needs to be equipped with a separate Radio Frequency (RF) chain, but in a millimeter wave massive MIMO system, if a conventional MIMO system is adopted, the hardware cost is increased dramatically by a large number of RF chains, and huge energy consumption is brought about. In order to solve this problem, a hybrid architecture combining a small number of rf chains and a large number of phase shifters is proposed, in which a transmission symbol is subjected to small-scale baseband precoding processing and then mapped to a transmission antenna after being subjected to large-scale analog precoding processing. The analog precoding section is constituted by a phase shifter which can adjust only the phase of the transmission signal. The hybrid architecture is divided into a partially connected architecture and a fully connected architecture according to the connection mode of the phase shifter and the radio frequency chain. Wherein the fully-connected hybrid architecture is capable of achieving near-all-digital precoding performance. Because the analog precoding is realized by the phase shifter, the elements of the analog precoding matrix are subjected to constant modulus constraint, the problem that the precoding matrix is solved in a non-convex mode by maximizing the spectrum efficiency is caused, and an optimal mixed precoding design scheme is difficult to obtain.

Disclosure of Invention

The invention aims to solve the problems to be solved in the mixed architecture precoding, and provides a mixed precoding method of a millimeter wave large-scale MIMO system, so that the better spectral efficiency close to a full-digital precoding method can be obtained with relatively low computational complexity, the channel capacity close to the full-digital precoding can be obtained, the energy consumption of a radio frequency chain is greatly saved, and the application of the mixed architecture in a wireless communication scene is realized.

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

the invention discloses a hybrid precoding method of a millimeter wave large-scale MIMO system, which is characterized by comprising the following steps of:

step S0: randomly generating a channel matrix H according to a narrow-band clustering channel model, and performing singular value decomposition on the channel matrix H to obtain a right unitary matrix V; at a sending end, taking the front N of the right unitary matrix V_sOptimal unconstrained all-digital precoding matrix formed by column vectors

Wherein N is_sIs the number of data streams sent;

step S1: constructing a first objective function and a limiting condition thereof as shown in formula (1):

in the formula (1), F_RFTo simulate a precoding matrix, F_BBIs a digital precoding matrix; (F)_RF)_m,nFor simulating a precoding matrix F_RFRow m and column n elements of (1); and F_RFThe modulus value of each element is 1, and the analog precoding matrix F is initialized randomly_RFDefines and initializes a residual matrix F_res＝F_optDefining and initializing an analog vector index n as 1;

step S2: constructing a simulation vector by adopting an alternate iteration method;

step S21: according to the first objective function, constructing a second objective function and a constraint condition thereof as shown in formula (2):

in equation (2), F is an analog precoding matrix F_RFOne of which simulates a vector and satisfies a corresponding constraint, f_mThe mth element representing the simulation vector f; the analog vector F may be considered as a residual matrix F_resA principal component of column space;

let the analog vector f be f ═ f_(m)+f_(-m)Wherein f is_(m)The m-th element of the vector is the same as the simulation vector f, and other elements are column vectors of zero; f. of_(-m)The m-th element of the simulation vector is zero, and other elements are column vectors which are the same as the simulation vector f;

defining an intermediate matrix F_{res_product}＝F_resF_res ^HInitializing an analog vector F to an analog precoding matrix F_RFDefining and initializing the iteration number i to 1;

step S22: initializing m to 1;

step S23: updating the column vector for the ith iteration using equation (3)

Obtaining the updated ith iteration column vector

In the formula (3), fⁱA simulation vector representing the ith iteration;

step S24: updating the simulation vector f of the ith iteration by using equation (4)ⁱObtaining a simulation vector f 'of the updated ith iteration'ⁱ：

In the formula (4), the reaction mixture is,

denotes f_(-m)Column vectors at the ith iteration;

step S25: assigning m +1 to m; and repeating steps S23 through S25 until m is N_tTo update the simulation vector f of the ith iterationⁱAll elements of (1), wherein, N_tIs the number of transmit antennas;

step S3: the updated simulation vector f 'of the ith iteration is subjected to equation (5)'ⁱNormalization is carried out to obtain a normalized analog vector f of the (i + 1) th iterationⁱ⁺¹：

In the formula (5), the reaction mixture is,

is Hadamard division, i.e. two vectors divided element by element, abs (f'ⁱ) Represents a pair of fⁱElement-by-element modulus taking;

step S4: i +1 is assigned to i, and the steps S22 to S4 are repeated until i is equal to i max; to obtain the final analog vector f^{i max}And assigns it to the analog precoding matrix F_RFThe nth column of (1);

step S5: obtaining an updated residual matrix F 'by equation (6)'_res：

F′_res＝F_res-F_weight (6)

In the formula (6), F_weightIs a residual matrix F_resAt the analog vector f^{i max}A matrix of components in a direction, and having:

in the formula (6), the reaction mixture is,

representing a residual matrix F_resAt the final analog vector f^{i max}The projection in the direction is that of the direction,

is kronecker product;

step S6: after N +1 is assigned to N, steps S2-S6 are repeated until N ═ N_RF，N_RFFor the number of radio frequency chains, thereby constructing N_RFCombining the analog vectors to form an analog precoding matrix F_RF；

Step S7: calculating a digital precoding matrix F using a least square method shown in equation (8)_BB：

In the formula (8), the reaction mixture is,

for simulating a precoding matrix F_RFThe pseudo-inverse of (1);

step S8: digital precoding matrix F using equation (9)_BBNormalizing to obtain a normalized digital precoding matrix F'_BB：

Step S9: at the receiving end, the first N of the channel matrix H_sA left singular vector constituting W_optAnd as an optimal unconstrained combination matrix, the optimal unconstrained all-digital pre-coding matrix F_optReplacement by the optimal unconstrained combining matrix W_optThus, according to the steps S1-S8, the simulation combination matrix W is obtained_RFAnd a normalized digital combined matrix W'_BB。

Compared with the prior art, the invention has the beneficial effects that:

1. the invention takes full-digital pre-coding as a target, constructs the analog pre-coding matrix by constructing the analog vectors one by one, so that the optimal unconstrained full-digital pre-coding matrix can be effectively represented by the constructed analog vectors linearly. By updating the residual matrix, the constructed analog vector is the main component of the column space of the residual matrix, the constant modulus constraint condition of analog precoding is met, and the spectral efficiency loss caused by artificially applying additional constraint conditions or adopting approximate derivation is overcome, so that the spectral efficiency close to the full-digital unconstrained precoding is brought, and the problem of high energy consumption of the full-digital precoding scheme is effectively solved. Simulation results show that the method can be superior to the existing method in terms of relatively low computational complexity, and can achieve the spectral efficiency close to the unconstrained full-digital precoding scheme.

2. In the step of constructing the analog vector, the analog vector to be solved is split into two complementary analog vectors, and each element in the analog vector to be solved is updated by adopting an alternate iteration method, so that the analog pre-coding vector meeting the constraint condition is effectively obtained, and meanwhile, the computation complexity is low.

3. In the process of constructing the analog precoding vectors one by one, the invention adopts a method similar to Matching Pursuit (MP) to update the residual error matrix, so that the optimal unconstrained all-digital precoding matrix can be linearly represented by the constructed analog precoding vectors, and the least square method is adopted to calculate the corresponding digital precoding matrix, thereby enabling F to be subjected to the calculation of the residual error matrix, and further enabling the optimization of the optimal unconstrained all-digital precoding matrix to be realized by the method of the Matching Pursuit (MP) and the method of the optimal unconstrained all-digital precoding matrix to be more convenient for the user to realize the optimization of the residual error matrix_RFF_BBApproximation F_optResulting in a spectral performance approaching that of all-digital precoding.

Drawings

FIG. 1 is a block diagram of a millimeter wave massive MIMO hybrid precoding system;

FIG. 2 is an overall flow chart of the practice of the present invention;

FIG. 3 is a flow chart of a design method for constructing a simulation vector implemented in accordance with the present invention;

FIG. 4 is a graph showing that_t＝36,N_rA graph of spectral efficiency versus SNR for different algorithms in a 16 antenna configuration;

FIG. 5 is a graph showing that_t＝100,N_rA graph of spectral efficiency versus SNR for different algorithms in a 36 antenna configuration;

fig. 6 is a graph comparing the spectral efficiency of different algorithms with the number of rf chains.

Detailed Description

The method aims at a millimeter wave large-scale MIMO full-connection hybrid architecture, adopts a narrow-band clustering channel model, a sending end and a receiving end are provided with Uniform Planar Array (UPA) antennas, the distance between the antennas is set to be half wavelength, and the azimuth angle and the pitch angle of an arrival angle and a departure angle are assumed to respectively obey 0,2p and pitch angle

The angle spread of the sending end and the receiving end is 7.5 degrees, all the flows are assumed to be distributed with equal power, and the simulation result is the average of the simulation results generated by 200 times of random channels. The number of iterations is 5, the system block diagram is shown in FIG. 1, the invention focuses on the transmissionThe design of analog and digital pre-coding matrix, and the method of the invention is also suitable for the design of analog and digital combined matrix of receiving end.

In this embodiment, a flow chart of a method for designing hybrid precoding to construct a simulation vector is shown in fig. 2, which is a method for constructing a simulation vector, and a simulation precoding matrix is designed based on the method, including the following steps:

step S0: assuming known channel state information, the millimeter wave massive MIMO system model is represented as:

in the formula (1), the reaction mixture is,

is the receiving symbol after the receiving end is combined with the matrix action, rho is the average receiving power,

is an analog combination matrix of a receiving end, the elements of which satisfy the constant modulus constraint,

is a digital combination matrix at the receiving end,

in order to be a matrix of channels,

is an analog matrix at the transmitting end, F_RFAnd F_BBNeed to satisfy power constraints

Satisfying a normalized power constraint for transmitting symbols

Is additive white Gaussian noise, obeys mean 0 and variance is sigma²Complex gaussian distribution.

Here, the Saleh-valencuela channel model is used, under which the channel matrix is represented as:

in the formula (2), N_clDenotes the number of scattering clusters, N_rayRepresenting the number of rays per scatter cluster. Alpha is alpha_ikRepresents the complex gain of the kth path of the ith cluster,

and

respectively representing antenna array response vectors at the receiving end and the transmitting end,

and

respectively the corresponding azimuth angles of the receiving end and the transmitting end,

and

is the corresponding pitch angle of the receiving end and the transmitting end. For a uniform planar array antenna, it is expressed as:

in the formula (3), λ is a carrier wavelength, d is an antenna pitch, and M and N are index values of the antenna in the horizontal and vertical directions, respectively.

The spectral efficiency is:

in the formula (4), the reaction mixture is,

is a noise covariance matrix.

Randomly generating a channel matrix H according to the channel model, and performing Singular Value Decomposition (SVD) on the channel matrix H to obtain a right unitary matrix V; at the transmitting end, the first N of the right unitary matrix V is taken_sOptimal unconstrained all-digital precoding matrix formed by column vectors

Wherein N is_sIs the number of data streams sent;

step S1: constructing a first objective function and a limiting condition thereof as shown in formula (5):

in the formula (5), F_RFTo simulate a precoding matrix, F_BBIs a digital precoding matrix; (F)_RF)_m,nFor simulating a precoding matrix F_RFRow m and column n elements of (1); and F_RFThe modulus value of each element is 1, and an analog precoding matrix F is initialized randomly_RFDefines and initializes a residual matrix F_res＝F_optDefining and initializing an analog vector index n as 1;

step S2: constructing a simulation vector by adopting an alternate iteration method; as shown in fig. 3.

Step S21: according to the first objective function, constructing a second objective function and a constraint condition thereof as shown in formula (6):

in equation (6), F is an analog precoding matrix F_RFOne of which simulates a vector and satisfies a corresponding constraint, f_mThe mth element representing the simulation vector f; the analog vector F can be regarded as a residual matrix F_resA principal component of column space;

let the analog vector f be f ═ f_(m)+f_(-m)Wherein f is_(m)The m-th element of the vector is the same as the simulation vector f, and other elements are column vectors of zero; f. of_(-m)The m-th element of the simulation vector is zero, and other elements are column vectors which are the same as the simulation vector f; then there are:

to solve equation (6), each element of f is optimized separately. At the solution of f_(m)When f is present_(-m)Is a constant. Thus, in equation (7), f is calculated_(m)When (F)_resF_res ^H)_m,mAnd f_(-m)HF_resF_resHf_(-m)Are all constants, so equation (6) is equivalent to equation (8):

thus, an intermediate matrix F is defined_{res_product}＝F_resF_res ^HInitializing an analog vector F to an analog precoding matrix F_RFDefining and initializing the iteration number i to 1;

step S22: initializing m to 1;

step S23: under the unit modulus constraint, the solution of equation (8) is:

in formula (8), angle ((F)_resF_res ^H)f_(-m) ⁱ) Is expressed as (F)_resF_res ^H)f_(-m) ⁱThe phase of (c). While formula (9) is equivalent to calculating f 'from formula (10)'_(m) ⁱ：

f′_(m) ⁱ＝(F_resF_res ^H)fⁱ-(F_resF_res ^H)f_(m) ⁱ (10)

Last to f'ⁱAnd (6) carrying out normalization.

Therefore, the column vector of the ith iteration is updated here using equation (11)

Obtaining the updated ith iteration column vector

In the formula (11), fⁱA simulation vector representing the ith iteration;

step S24: updating the simulation vector f of the ith iteration using equation (12)ⁱObtaining a simulation vector f 'of the updated ith iteration'ⁱ：

In the formula (12), the reaction mixture is,

denotes f_(-m)Column vectors at the ith iteration;

step S25: assigning m +1 to m; and repeat the stepsStep S23 to step S25, until m ═ N_tTo update the simulation vector f of the ith iterationⁱAll elements of (1), wherein, N_tIs the number of transmit antennas;

step S3: the updated simulation vector f 'of the ith iteration is subjected to equation (13)'ⁱNormalization is carried out to obtain a normalized analog vector f of the (i + 1) th iterationⁱ⁺¹：

In the formula (13), the reaction mixture is,

is Hadamard division, i.e. two vectors divided element by element, abs (f'ⁱ) Represents a pair of fⁱElement-by-element modulus taking;

step S4: i +1 is assigned to i, and the steps S22 to S4 are repeated until i is equal to i max; to obtain the final analog vector f^{i max}And assigns it to the analog precoding matrix F_RFThe nth column of (1);

step S5: obtaining an updated residual matrix F using equation (14)_r′_es：

F′_res＝F_res-F_weight (14)

In the formula (14), F_weightIs a residual matrix F_resAt the analog vector f^{i max}A matrix of components in a direction, and having:

in the formula (15), the reaction mixture is,

representing a residual matrix F_resAt the final analog vector f^{i max}The projection in the direction is that of the direction,

is kronecker product;

step S6: after N +1 is assigned to N, steps S2-S6 are repeated until N ═ N_RF，N_RFFor the number of radio frequency chains, thereby constructing N_RFCombining the analog vectors to form an analog precoding matrix F_RF；

Step S7: the digital precoding matrix F is calculated by the least square method shown in formula (16)_BB：

In the formula (16), the compound represented by the formula,

for simulating a precoding matrix F_RFThe pseudo-inverse of (1);

step S8: digital precoding matrix F using equation (17)_BBNormalizing to obtain a normalized digital precoding matrix F'_BB：

Step S9: at the receiving end, the first N of the channel matrix H_sA left singular vector constituting W_optAnd as the optimal non-constrained combination matrix, the optimal non-constrained all-digital pre-coding matrix F_optReplacement by the optimal unconstrained combining matrix W_optThus, according to the steps S1-S8, the simulation combination matrix W is obtained_RFAnd a normalized digital combined matrix W'_BB。

FIG. 4 shows spectral efficiencies of proposed Constructed Analog Vector (CAV) precoding method, MO-AltMin (modified Optimization-Optimization) precoding algorithm, OMP (orthogonal Matching pursuit) precoding algorithm, and optimal unconstrained precoding at N_RF＝N_sSimulation of signal-to-noise ratio in millimeter wave system under 4, 64 × 16 antenna configuration. It can be seen from the figure that the proposed CAV method performs better compared to the MO-AltMin algorithm and the OMP algorithm. For the classical OMP algorithm, it selects N from the array response set of the antenna_RFThe individual array response vectors are used to construct the analog precoding matrix, which results in a performance loss because it is selected from only a limited set of array response vectors, and it is not guaranteed that the selected array response vectors are the optimal analog vectors. Fig. 5 is a performance simulation of various algorithms in a millimeter wave system with a configuration of 100 × 36 antennas, and compared with fig. 4, the performance of all the algorithms is improved, and the proposed algorithms still have better performance than the MO-AltMin algorithm and the OMP algorithm.

Fig. 6 is a simulation of the spectral efficiency of each algorithm as a function of the number of rf chains, which is equal to the number of transmitted data streams, with a fixed signal-to-noise ratio of 0 dB. It can be seen from the figure that the proposed CAV algorithm is better than the other two algorithms in the whole range of variation of the radio frequency chain, and the performance difference between the performance of the proposed method and the optimal unconstrained precoding is stable, which means that F is a constraint of F_optThe constructed analog vector representation can be well realized.

Claims (1)

1. A mixed precoding method of a millimeter wave large-scale MIMO system is characterized by comprising the following steps:

step S0: randomly generating a channel matrix H according to a narrow-band clustering channel model, and performing singular value decomposition on the channel matrix H to obtain a right unitary matrix V; at a sending end, taking the front N of the right unitary matrix V_sOptimal unconstrained all-digital precoding matrix formed by column vectors

Wherein N is_sIs the number of data streams sent;

step S1: constructing a first objective function and a limiting condition thereof as shown in formula (1):

in the formula (1), F_RFTo simulate a precoding matrix, F_BBIs a digital precoding matrix; (F)_RF)_m,nFor simulating a precoding matrix F_RFRow m and column n elements of (1); and F_RFThe modulus value of each element is 1, and the analog precoding matrix F is initialized randomly_RFDefines and initializes a residual matrix F_res＝F_optDefining and initializing an analog vector index n as 1;

step S2: constructing a simulation vector by adopting an alternate iteration method;

step S21: according to the first objective function, constructing a second objective function and a constraint condition thereof as shown in formula (2):

in equation (2), F is an analog precoding matrix F_RFOne of which simulates a vector and satisfies a corresponding constraint, f_mThe mth element representing the simulation vector f; the analog vector F may be considered as a residual matrix F_resA principal component of column space;

let the analog vector f be f ═ f_(m)+f_(-m)Wherein f is_(m)The m-th element of the vector is the same as the simulation vector f, and other elements are column vectors of zero; f. of_(-m)The m-th element of the simulation vector is zero, and other elements are column vectors which are the same as the simulation vector f;

defining an intermediate matrix F_{res_product}＝F_resF_res ^HInitializing an analog vector F to an analog precoding matrix F_RFDefining and initializing the iteration number i to 1;

step S22: initializing m to 1;

step S23: updating the column vector for the ith iteration using equation (3)

Is obtained moreColumn vector of new ith iteration

In the formula (3), fⁱA simulation vector representing the ith iteration;

step S24: updating the simulation vector f of the ith iteration by using equation (4)ⁱObtaining a simulation vector f 'of the updated ith iteration'ⁱ：

In the formula (4), the reaction mixture is,

denotes f_(-m)Column vectors at the ith iteration;

step S25: assigning m +1 to m; and repeating steps S23 through S25 until m is N_tTo update the simulation vector f of the ith iterationⁱAll elements of (1), wherein, N_tIs the number of transmit antennas;

step S3: the updated simulation vector f 'of the ith iteration is subjected to equation (5)'ⁱNormalization is carried out to obtain a normalized analog vector f of the (i + 1) th iterationⁱ⁺¹：

In the formula (5), the reaction mixture is,

is Hadamard division, i.e. two vectors divided element by element, abs (f'ⁱ) Represents a pair of fⁱElement-by-element modulus taking;

step S4: assigning i +1 to i, and repeating the steps S22 to S4 until i is imax; to obtain the final analog vector f^imaxAnd assigns it to the analog precoding matrix F_RFThe nth column of (1);

step S5: obtaining an updated residual matrix F 'by equation (6)'_res：

F′_res＝F_res-F_weight (6)

In the formula (6), F_weightIs a residual matrix F_resAt the analog vector f^imaxA matrix of components in a direction, and having:

in the formula (6), the reaction mixture is,

representing a residual matrix F_resAt the final analog vector f^imaxThe projection in the direction is that of the direction,

is kronecker product;

step S6: after N +1 is assigned to N, steps S2-S6 are repeated until N ═ N_RF，N_RFFor the number of radio frequency chains, thereby constructing N_RFCombining the analog vectors to form an analog precoding matrix F_RF；

Step S7: calculating a digital precoding matrix F using a least square method shown in equation (8)_BB：

In the formula (8), the reaction mixture is,

for simulating a precoding matrix F_RFThe pseudo-inverse of (1);

step S8: digital precoding matrix F using equation (9)_BBNormalizing to obtain a normalized digital precoding matrix F'_BB：

Step S9: at the receiving end, the first N of the channel matrix H_sA left singular vector constituting W_optAnd as an optimal unconstrained combination matrix, the optimal unconstrained all-digital pre-coding matrix F_optReplacement by the optimal unconstrained combining matrix W_optThus, according to the steps S1-S8, the simulation combination matrix W is obtained_RFAnd a normalized digital combined matrix W'_BB。

Images