CN109981154A - Low complex degree array antenna multi-input multi-output system mixing precoding algorithms - Google Patents

Abstract

The invention discloses a hybrid precoding algorithm for a low-complexity array antenna multiple-input multiple-output system. Given an initial solution and a maximum number of calculations for calculating the optimal coding of an antenna sub-array, an effective channel matrix of a partial connection structure is obtained; The solution and the effective channel matrix are used to calculate the auxiliary vector, and the auxiliary vector with the largest modulus value is selected as the eigenvalue vector; the value of the current calculation times is judged, and the intermediate result is obtained; the current calculation result is obtained according to the intermediate result and the auxiliary vector; repeat Calculate until the maximum number of calculations is reached, obtain intermediate results and calculation results, and then calculate the optimal coding of each antenna sub-array in the partial connection architecture system, and combine the optimal coding of each antenna sub-array to obtain the partial connection structure The hybrid precoding matrix of the system; the method of the present invention can reduce the computational complexity and time consumption of the large-scale antenna coding matrix on the basis of the existing hardware connection, and shorten the network transmission delay.

Description

Hybrid Precoding Algorithm for Low Complexity Array Antenna Multiple Input Multiple Output System

【Technical field】

The invention belongs to the technical field of mobile communication, and in particular relates to a hybrid precoding algorithm of a low-complexity array antenna multiple-input multiple-output system.

【Background technique】

In order to meet the explosive growth of mobile data traffic in the fifth generation (5G) mobile communication, 5G adopts the 30-300GHz millimeter wave frequency band, which greatly improves the spectrum resources.

Due to the relatively short wavelength of millimeter wave, the physical size of the antenna array is greatly reduced, so massive antennas can be installed at the base station, so that the millimeter wave system can be perfectly combined with massive Massive MIMO technology. Therefore, Massive MIMO technology has become the focus of research by scholars at home and abroad in mobile communications.

With the development and research of hybrid beamforming technology in Massive MIMO systems, the existing hybrid precoding schemes can be divided into two categories. It is transformed into a sparse approximation problem, and an orthogonal matching solution pursuit (OMP) algorithm is used to make the antenna array achieve near-optimal performance; the second category proposes a codebook-based hybrid precoding method, which is between pre-defined codebooks An iterative search is performed to find the optimal hybrid precoding matrix. However, these algorithms are based on the fully connected architecture, which is not only difficult to implement in hardware, but also has a high algorithm complexity.

Because the MMSE hybrid precoding algorithm using OMP iteration based on sparse scattering needs to perform large-scale matrix inversion and singular value decomposition calculation, the calculation complexity is very high, so the requirements for hardware structure design are relatively high, and the hardware needs to be redesigned. connection, which increases the data storage requirements within the base station and increases the network transmission delay.

[Content of the invention]

The purpose of the present invention is to provide a low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm, which reduces the computational complexity and time consumption of large-scale antenna coding matrices and shortens network transmission delay on the basis of existing hardware connections.

The present invention adopts the following technical solutions: a low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm, comprising the following steps:

According to the state information of the partially connected architecture system, the initial solution and the maximum number of iterations S for calculating the optimal coding of the antenna subarray are given, and the effective channel matrix of the partially connected architecture is obtained; the auxiliary vector is calculated by combining the initial solution and the effective channel matrix z ^(s) , screen out the auxiliary vector with the largest modulus value, and take the eigenvalue m ^(s) with the largest modulus value;

Judging the value of the current iteration number s, when 1≤s≤2, n ^(s) = m ^(s) , n ^(s) is the intermediate result, when s > 2, Obtain the current calculation result u ^(s) according to the intermediate result and the auxiliary vector;

Continue to iterate until the maximum number of calculations S is reached, obtain the intermediate results and calculation results of the S-th time, and then calculate the optimal coding of each antenna sub-array in the partially connected architecture system, combined with the optimal coding of each antenna sub-array The encoding results in a hybrid precoding matrix for a partially connected architecture system.

Further, the effective channel matrix is passed through It is obtained, in which, is the effective channel matrix, A is the antenna vector matrix, and H is the channel matrix.

Further, the auxiliary vector is passed through It is obtained, where z ^(s) is the auxiliary vector of the s-th calculation, and u ^(s-1) is the calculation result of the s-1th time.

Further, before screening the eigenvalue vector, the calculation results are compared, and the same calculation results are combined into one calculation result, and the auxiliary vector set to be screened is obtained. Among them, i is the number of different auxiliary vectors in the s auxiliary vectors.

pass Auxiliary vector set to be filtered out Screening is performed, and the largest modulus value corresponding to the auxiliary vector is selected as the largest eigenvalue.

Further, by Calculate the calculation result, where u ^(s) is the calculation result of the s-th calculation.

Further, the optimal coding calculation method for each antenna sub-array is as follows:

Assign the intermediate result n ^(s) to the largest singular value Σ ₁ of the effective channel matrix, by Calculate the first right singular value v ₁ of the effective channel matrix;

pass and Calculate the optimal digital precoding of the nth row of the digital precoding matrix W and the optimal analog precoding of the nth antenna subarray of the analog precoding matrix F in the partially connected architecture system;

pass The optimal coding of the nth antenna subarray in the partially connected architecture system is calculated.

The beneficial effects of the present invention are as follows: the present invention proposes a SIC hybrid precoding scheme based on a partial connection structure, which converts the non-convex problem of optimizing system capacity into solving a series of simple sub-rate optimization sums (that is, the sum of antenna sub-array rates). ) problem; reasonably and skillfully avoid large-scale matrix-matrix inversion and singular value decomposition problems, greatly reduce the complexity of the algorithm, save the signal transmission delay of the low-complexity array antenna multiple-input multiple-output system, and pass the complex algorithm. Through degree analysis and system capacity performance simulation, it is concluded that the performance of the algorithm can be close to the optimal unconstrained algorithm, and the performance is stable and the algorithm complexity is 10% of that based on sparse scattering precoding.

【Description of drawings】

Fig. 1 is the system model diagram of partial connection in the prior art;

FIG. 2 is a system capacity diagram when NM×K=64×16 (N=8) in an embodiment of the present invention;

FIG. 3 is a system capacity diagram when NM×K=128×32 (N=16) in an embodiment of the present invention.

【Detailed ways】

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

In the existing time division duplex downlink multi-user Massive MIMO system, as shown in Figure 1, it is assumed that the base station has complete channel state information, that is, the channel matrix H, N radio frequency chains, each radio frequency chain is connected to M antennas, the base station Assemble N _t antennas, the user is a multi-antenna N _r receiving antenna, and the number of users is K.

N _s data streams, W=diag[w ₁ ,w ₂ ,...,w _N ] is the digital precoding matrix, F is the NM×N analog precoding matrix, which consists of N analog weight vectors composition,

The millimeter-wave narrowband signal vector y=[y ₁ , y ₂ ,...,y _k ] ^T received by the user terminal can be expressed as follows:

Among them, ρ is the average received power; H∈C ^K×NM , is the baseband transmit signal vector with normalized signal power (that is, the signal satisfies the power constraint), I _N is an N*N-dimensional identity matrix, and P=FW is an NM×N hybrid precoding matrix, which satisfies the total transmission power constraint ||P|| _F ≤N, a=[ a ₁ ,a ₂ ,…a _N ] ^T is an additive white Gaussian noise vector, and its elements obey the independent and identical distribution (iid)CN(0,σ ² ), then the total achievable rate of the system can be expressed as:

Among them, I _k is the identity matrix.

Theoretically and practically, the performance of traditional all-digital precoding is optimal, therefore, adopting hybrid precoding performance close to all-digital precoding performance is the optimization goal.

In a fully loaded system with the same number of users as the transmit antenna, the performance of ZF (ie zero-breaking) or precoding does not increase linearly. According to the reciprocity of the channel, the non-normalized hybrid precoding matrix P ^MMSE is obtained by the MMSE method (ie, the minimum mean square error method). In the traditional digital precoding algorithm, the MMSE method is compared with the ZF method (zero-breaking method) and BD. The method (that is, the block method) takes a compromise between complexity and performance. Therefore, the present invention first adopts the MMSE code matrix P ^MMSE to replace FW, then solving formula (2) is equivalent to solving the following problems:

is the MMSE encoding matrix, is the effective channel matrix, and A is the antenna vector matrix. Solving the above problem can be transformed into the problem of solving the optimal solution of the rate of the antenna subarray, namely

The sub-antenna coding vectors are removed from the superscript, where ψ contains all MMSE coding vectors that satisfy the constant modulus constraints and power constraints. Because the p _n ^opt here does not meet the constant modulus constraint, it cannot be directly used as the optimal solution. Therefore, problem (4) can be transformed into the following problem:

Here _v1 is the effective channel matrix The first column of the right singular matrix of , Equation (5) shows that a feasible precoding vector can be found The precoding vector v ₁ that is close enough to be optimal (Euclidean distance) but cannot be used directly to maximize the achievable rate of the nth antenna subarray, the digital precoding and analog precoding are:

in, is the digital precoding of the nth row of the digital precoding matrix W, is the conjugate transpose _of v1. is the analog precoding of the nth antenna subarray of the analog precoding matrix,

represents the optimal solution of analog precoding for the nth antenna subarray, is the normalization factor, M represents the number of antennas in each antenna sub-array, jangle(v ₁ ) represents the angle information in v ₁ , then the optimal encoding of the n-th antenna sub-array (that is, the n-th column) It can be expressed as:

because It satisfies the properties of the Hermitian matrix, that is, it is the Hermitian matrix, which follows the following two properties: 1) is also a diagonalizable matrix; 2) The right singular value matrix of is similar to the eigenvalue matrix of the eigenvalue decomposition. Therefore, the power iteration algorithm can be used to calculate v ₁ , and can also be used to calculate The largest eigenvalue Σ ₁ of .

In the algorithm of this embodiment, the iteration starts from the initial solution u ⁽⁰⁾ ∈ C ^M×1 , which is set to [1,1,...,1] ^T in this embodiment, but without loss of generality. In each iteration, the auxiliary vector is first calculated Then the modulus value m ^(s) of the auxiliary vector z ^(s) with the largest modulus value is extracted.

After that, u ^(s) is updated to u ^(s) = z ^(s) /m ^(s) for the next iteration. The algorithm of the present invention stops until the number of iterations reaches a predefined value S. Finally, m ^(s) and u ^(s) /||u ^(s) || ₂ will be the largest singular values Σ ₁ and The first right singular vector.

In order to reduce the computational complexity when solving formula (8), the algorithm of the present invention is used to solve v ₁ to avoid SVD decomposition and matrix inversion problems. -Vector multiplication, that is, it is not just the calculation of a matrix symbol, but is actually a multiplication between a large-scale matrix and a matrix. The method of the present invention directly extracts the most useful column in the matrix, and replaces the multiplication of the matrix with the matrix. Multiplication between a matrix and a single vector, the amount of calculation is greatly reduced.

The algorithm steps of the present invention are as follows:

Step 1. According to the state information of the partially connected architecture system, given the initial solution u ⁽⁰⁾ ∈ C ^M×1 and the maximum number of computations S for calculating the optimal encoding of the antenna subarray, the initial solution is given as [1,1 ,…,1] ^T .

Obtain the effective channel matrix for a partially connected architecture By combining the initial solution and the effective channel matrix The auxiliary vector z ^(s) is calculated, 1≤s≤S, which is the current iteration number.

Compare the calculation results before screening the eigenvalue vectors, combine the same calculation results into one calculation result, and obtain the auxiliary vector set to be screened Among the i auxiliary vectors, by The one with the largest modulus value is selected as the eigenvalue vector m ^(s) , and i represents the number of different auxiliary vectors in the s auxiliary vectors.

After obtaining the eigenvalue vector, continue the iterative calculation to determine the number of iterations s:

When 1≤s≤2, n ^(s) = m ^(s) , and n ^(s) is an intermediate result.

When s>2,

Substitute the value of n ^(s) into , obtain u ^(s) of the iteration result after the sth iteration.

Through the above steps, it can be obtained that the effective channel matrix The largest singular value of Σ ₁ =n ^(s) and the first right singular value

pass The largest singular value Σ ₁ and the first right singular value v ₁ of , combined with equations (6) and (7) to get and Finally, according to formula (8), the optimal coding of the nth antenna subarray is obtained The optimal coding of each antenna sub-array is combined to obtain the hybrid precoding matrix of the partially connected architecture system.

Part of the program code design in the algorithm is also listed in this embodiment, as follows:

Input: (1)

(2) Initial solution u ⁽⁰⁾ ;

(3) The maximum number of iterations S;

For 1≤s≤2

1)

2)

3)If 1≤s≤2

n ^(s) = m ^(s)

Else

End if

4)

End for

Output: (1) Maximum singular value Σ ₁ =n ^(s)

(2) The first right singular value

Step 2: Solve for Hybrid Precoding

Input:

For 1≤n≤N

1) Calculated by Algorithm 2 of v ₁ and Σ ₁

2)

End for

Output: (1)

(2)

(3) P=FW

Example: Complexity Analysis

Table 1 Algorithm complexity comparison

It can be seen from Table 1 that the complexity of hybrid precoding based on MMSE iterative algorithm and the complexity of hybrid precoding based on spatial sparsity proposed in the prior art are compared. Under a typical millimeter-wave MIMO system, when N=8 , M=8, K=16, L=3, L is the number of effective paths. It is observed that the SIC based hybrid precoding algorithm complexity requires 4×10 ³ multiplications and 10 ² divisions. Set S=5. In comparison, the spatial sparsity-based precoding algorithm complexity requires about 5×10 ⁴ multiplications and 10 ³ divisions. It can be seen that the complexity of the hybrid precoding algorithm based on SIC proposed by the present invention is 10% of the complexity of the hybrid precoding algorithm based on spatial sparsity.

Example: Analysis of Simulation Results

Simulation conditions:

The simulation conditions are described below, the number of valid channel paths is L=3, and the carrier frequency is set to 28GHz. Both transmit and receive antenna arrays are ULAs (Uniform Linear Arrays) with antenna spacing d=λ/2. The AoD (angle of arrival) is assumed to be uniformly distributed over [-π/6, π/6]. At the same time, due to the random distribution of user locations, AOA is assumed to be uniformly distributed on [-π/2, π/2]. Also, the maximum number of iterations when running Algorithm 2 is set to S=5. Finally, the SNR (Signal to Noise Ratio) is defined as

System performance simulation:

From Fig. 2, it can be seen that the proposed SIC coding system capacity under perfect channel information is better than the traditional analog precoding with sub-connected architecture in the whole SNR range, and is close to the optimal unconstrained fully-connected structure coding and spatial sparse scattering based Sexual coding. Figure 3 increases the size of the antenna, and it can be observed from Figure 3 that the same trend as Figure 2 shows that the proposed SIC algorithm not only has low algorithm complexity, but also meets the system performance requirements and increases the number of antennas. Still has stable performance.

Claims (6)

1. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm is characterized in that, comprising the following steps: According to the state information of the partially connected architecture system, the initial solution for calculating the optimal coding of the antenna subarray and the maximum number of iterations S are given, and the effective channel matrix of the partially connected architecture is obtained; Auxiliary vector z ^(s) , screen out the auxiliary vector with the largest modulus value, and take the eigenvalue m ^(s) with the largest modulus value; Judging the value of the current iteration number s, when 1≤s≤2, n ^(s) = m ^(s) , n ^(s) is the intermediate result, when s > 2, Obtain the current calculation result u ^(s) according to the intermediate result and the auxiliary vector; Continue to iterate until the maximum number of calculations S is reached, obtain the intermediate results and calculation results of the S-th time, and then calculate the optimal coding of each antenna sub-array in the partially connected architecture system, and combine each of the antenna sub-arrays. The optimal coding of the matrix results in the hybrid precoding matrix of the partially connected architecture system. 2. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm of claim 1, wherein the effective channel matrix passes It is obtained, in which, is the effective channel matrix, A is the antenna vector matrix, and H is the channel matrix. 3. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm according to claim 2, wherein the auxiliary vector is obtained by It is obtained, where z ^(s) is the auxiliary vector of the s-th calculation, and u ^(s-1) is the calculation result of the s-1th time. 4. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm according to claim 1, 2 or 3, wherein the calculation results are compared before the eigenvalue vectors are screened, and the same calculation results are compared with each other. Combined into one calculation result, get the auxiliary vector set to be screened Among them, i is the number of different auxiliary vectors in the s auxiliary vectors; pass Auxiliary vector set to be filtered out Perform screening, and select the largest modulus value corresponding to the auxiliary vector as the largest eigenvalue. 5. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm according to claim 4, wherein the current calculation result passes Calculated, where u ^(s) is the calculation result of the s-th calculation. 6. The low-complexity array antenna multiple-input multiple-output system hybrid precoding algorithm according to claim 1, 2 or 3, wherein the optimal coding calculation method of each antenna subarray is specifically: Assign the intermediate result n ^(s) to the largest singular value Σ ₁ of the effective channel matrix, by Calculate the first right singular value v ₁ of the effective channel matrix; pass and respectively calculating the optimal digital precoding of the nth row of the digital precoding matrix W and the optimal analog precoding of the nth antenna subarray of the analog precoding matrix F in the partially connected architecture system; pass The optimal coding of the nth antenna subarray in the partially connected architecture system is obtained by calculation.