CN114900216B - Iterative signal-to-interference-and-noise ratio design method of large-scale MIMO robust precoder - Google Patents

Abstract

The invention discloses an iterative signal-to-interference-and-noise ratio (ISINR) design method of a large-scale MIMO robust precoder, a base station designs a robust ISINR precoder according to traversal and speed of all users or an approximation value maximization criterion thereof by utilizing channel estimation values and statistical parameters of channel estimation errors of all user terminals, calculates a precoding vector corresponding to each user terminal, and performs downlink robust ISINR precoding transmission. The method decomposes the pre-coding vector into a pre-coding direction and a power distribution, which are respectively expressed as a maximum generalized characteristic vector and a closed form, and further alternately iterates the signal-to-interference-plus-noise ratio and the pre-coding vector to approximate the maximum traversal and speed. The invention can enable the design of the precoder to converge with fewer iteration times, thereby reducing the computational complexity while approaching the maximum traversal and rate.

Description

Iterative Signal-to-Interference-Noise Ratio Design Method for Massive MIMO Robust Precoder

Technical Field

The invention belongs to the field of wireless communication downlink precoding, and in particular relates to an iterative signal-to-interference-noise ratio design method for a large-scale MIMO robust precoder.

Background Art

By deploying a large number of antennas at the base station (BS), massive multiple-input-multiple-output (MIMO) technology can provide services to a large number of users simultaneously, thereby significantly improving the spectrum efficiency of the system. The base station should reasonably design the precoder for all users to reduce inter-user interference.

The precoder design depends on the channel state information (CSI) available at the base station. For the case of perfect CSI, regularized zero-forcing (RZF) and signal-to-leakage-and-noise ratio (SLNR) precoders can simply implement the precoder. The weighted minimum mean-square-error (WMMSE) precoder designed iteratively by a convex problem is the optimal precoder to maximize the sum rate.

However, due to large pilot overhead and channel aging, it is challenging to obtain accurate CSI in massive MIMO, especially in high mobility scenarios, and the resulting channel estimation errors may cause performance degradation of these precoders. To combat the potential inaccuracy of CSI, robust RZF precoders and robust SLNR precoders can be applied to achieve suboptimal sum rates. To directly maximize the sum rate, the random WMMSE precoder needs to iterate over a large number of channel realizations, but each iteration involves computationally expensive matrix inversion.

To solve this problem, deep learning has been actively explored. However, labels for supervised learning require offline iteration, and a large number of samples are required to ensure generalization performance. In addition, transfer learning for generalization across scenarios inevitably requires online training. Therefore, it is necessary to explore fast-converging precoder iterative design methods.

Summary of the invention

The present invention aims to provide an iterative signal-to-interference-noise ratio design method for a large-scale MIMO robust precoder to solve the technical problem of high computational complexity.

In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

A method for iterative signal to interference and noise ratio design of a massive MIMO robust precoder, wherein: a base station uses a channel estimation value of each user terminal and a statistical parameter of a channel estimation error, designs a robust iterative signal to interference and noise ratio (ISINR) precoder according to a criterion of maximizing the ergodic sum rate of all users or the ergodic sum rate approximation value of all users, and dynamically updates a precoding vector corresponding to each user terminal to perform downlink robust ISINR precoding transmission;

The channel estimation value is obtained by using a pilot signal periodically sent by each user, and the statistical parameter of the channel estimation error is obtained by performing statistics on the channel estimation value;

The robust ISINR precoder includes: deriving a precoding vector structure through problem conversion, and alternately iterating the signal to interference noise ratio and the precoding vector to approach the maximum traversal rate.

Furthermore, the structure of the precoding vector is divided into two parts: precoding direction and power allocation; wherein the precoding direction is a generalized eigenvector corresponding to the maximum generalized eigenvalue of a matrix pair, the eigenvalue is the signal to interference plus noise ratio, and the matrix pair is related to the channel covariance matrix, the Lagrange multiplier and the noise variance; the power allocation is calculated by a closed form, which is related to the channel covariance matrix, the signal to interference plus noise ratio, the precoding direction and the Lagrange multiplier.

Furthermore, the structure of the precoding vector is related to the Lagrange multiplier; by deriving the KKT condition, the Lagrange multiplier is calculated by a closed form, which is related to the channel covariance matrix, the precoding vector and the signal to interference noise ratio.

Furthermore, the iteration comprises the following steps:

Step 1: Initialize the precoding vector;

Step 2: Calculate the signal to interference and noise ratio;

Step 3, calculate the Lagrange multiplier by closed form;

Step 4: Solve the generalized eigenvalue problem and use the maximum generalized eigenvector to update the precoding direction;

Step 5: Update the signal to interference noise ratio using the maximum generalized eigenvalue;

Step 6: Power distribution by closed-form calculation;

Step 7. Repeat steps 2-6 until convergence.

Furthermore, in the case where the channel state information is perfect, the precoding vector has a simpler structure, specifically including: the precoding direction is calculated by a closed form, which is related to the channel covariance matrix, Lagrange multipliers and noise variance; the power allocation is calculated by a closed form, which is related to the channel covariance matrix, signal to interference noise ratio, precoding direction and Lagrange multipliers.

Furthermore, for the case where the channel state information is perfect, there are simpler iterative steps, including:

Step a, initializing the precoding vector;

Step b, calculating the signal to interference and noise ratio;

Step c, calculating the Lagrange multiplier by closed form;

Step d, updating the precoding direction by closed-form calculation;

Step e, updating the signal to interference and noise ratio by closed-form calculation;

Step f, calculating power distribution by closed form;

Step g: Repeat steps b-f until convergence.

The iterative signal-to-interference-noise ratio design method of the massive MIMO robust precoder of the present invention has the following advantages:

1. Aiming at the problem of traversal and rate maximization of precoder design, the present invention characterizes the structure of the precoding vector by problem transformation, wherein the complex calculations related to the expectation are calculated by closed form using a posterior channel model.

2. By alternately iterating the signal-to-interference-plus-noise-ratio and precoder, an iterative signal-to-interference-plus-noise-ratio (ISINR) design method for robust precoder is proposed. With the RZF precoder as the initial value, the robust ISINR precoder converges within two times, approaching the maximum traversal and rate performance, and its fast convergence effectively reduces the computational complexity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a robust ISINR precoder design method of the present invention.

DETAILED DESCRIPTION

In order to better understand the purpose, structure and function of the present invention, the iterative signal to interference and noise ratio design method of a large-scale MIMO robust precoder of the present invention is further described in detail below with reference to the accompanying drawings.

In the iterative signal to interference and noise ratio design method of a massive MIMO robust precoder disclosed in an embodiment of the present invention, a base station uses the channel estimation value of each user terminal and the statistical parameters of the channel estimation error, designs a robust iterative signal to interference and noise ratio (ISINR) precoder according to the criterion of maximizing the ergodic sum rate of all users or the ergodic sum rate approximation value of all users, and dynamically updates the precoding vector corresponding to each user terminal to perform downlink robust ISINR precoding transmission;

The channel estimation value is obtained by using the pilot signal periodically sent by each user, and the statistical parameter of the channel estimation error is obtained by performing statistics on the channel estimation value;

The robust ISINR precoder includes: deriving a structure of a precoding vector by problem transformation, and alternately iterating a signal to interference noise ratio and a precoding vector to approach a maximum traversal sum rate.

The structure of the precoding vector includes: the structure of the precoding vector is divided into two parts: precoding direction and power allocation; wherein the precoding direction is a generalized eigenvector corresponding to the maximum generalized eigenvalue of a matrix pair, the eigenvalue is a signal to interference plus noise ratio, and the matrix pair is related to a channel covariance matrix, a Lagrange multiplier and a noise variance; the power allocation is calculated by a closed form, and the closed form is related to the channel covariance matrix, the signal to interference plus noise ratio, the precoding direction and the Lagrange multiplier.

The structure of the precoding vector is related to the Lagrange multiplier; by deriving the KKT condition, the Lagrange multiplier is calculated by a closed form, which is related to the channel covariance matrix, the precoding vector and the signal to interference and noise ratio.

The iterative steps include: step 1, initializing the precoding vector; step 2, calculating the signal to interference plus noise ratio by definition; step 3, calculating the Lagrange multiplier by closed form; step 4, solving the generalized eigenvalue problem, and updating the precoding direction by using the maximum generalized eigenvector; step 5, updating the signal to interference plus noise ratio by using the maximum generalized eigenvalue; step 6, calculating the power allocation by closed form; step 7, repeating steps 2-6 until convergence.

When the channel state information is perfect, the precoding vector has a simpler structure, specifically including: the precoding direction is calculated by a closed form, which is related to the channel covariance matrix, Lagrange multipliers and noise variance; the power allocation is calculated by a closed form, which is related to the channel covariance matrix, signal to interference noise ratio, precoding direction and Lagrange multipliers.

In the case of perfect channel state information, there are iterative steps with simpler calculations, specifically including: step a, initializing the precoding vector; step b, calculating the signal to interference plus noise ratio by definition; step c, calculating the Lagrange multiplier by closed-form calculation; step d, updating the precoding direction by closed-form calculation; step e, updating the signal to interference plus noise ratio by closed-form calculation; step f, calculating the power allocation by closed-form calculation; step g, repeating steps b-f until convergence.

The method of the embodiment of the present invention is further introduced below in conjunction with a specific implementation scenario. The method of the present invention is not limited to a specific scenario. For other implementations outside the exemplary scenario of the present invention, those skilled in the art can make adaptive adjustments according to the specific scenario based on the technical ideas of the present invention and existing knowledge.

1) System Model

Consider a massive MIMO downlink transmission system consisting of a base station and K randomly distributed users. The base station is equipped with M _t antennas and each user is equipped with a single antenna. The system works in time division duplexing (TDD) mode, where time resources are divided into time slots, each of which contains N _b symbols. The first symbol of each time slot is used for uplink detection, and the other symbols are used for downlink transmission.

Let _xk,n be the transmitted signal of the kth user at the nth symbol, satisfying Then the received signal of the kth user at the nth symbol is

in, is the channel vector of the kth user at the nth symbol, is the precoding vector of the kth user at the nth symbol, is the complex Gaussian noise of the kth user at the nth symbol; σ ² is the noise variance.

For uniform linear arrays in massive MIMO, the joint correlated channel can accurately simulate the physical channel, i.e.

in, is the discrete Fourier transform (DFT) matrix; m _k is a deterministic vector with non-zero elements; w _k,n is a complex Gaussian random vector whose elements are independent and identically distributed, with a mean of 0 and a variance of 1. This is the a priori channel model before channel estimation.

In order to characterize the time correlation between symbols, the a posteriori channel model is used, and the channel vector of the kth user at the nth symbol is expressed as

in, represents the channel estimation value at the first symbol; β _k,n ∈[0,1] is the time correlation coefficient, which is calculated by Jakes' autocorrelation model. The base station obtains the channel estimation value through uplink detection. and channel coupling vector

2) Robust ISINR precoder

Assume that the channel remains constant within each symbol but changes between symbols, so the base station performs precoding once for each symbol. For simplicity, the subscript n is omitted below. The ergodic rate of the kth user is expressed as

The optimal design of a robust precoder is to design the precoding vectors p ₁ ,p ₂ ,...,p _K to maximize the ergodicity and rate

Among them, the precoding vector satisfies the total power constraint of the base station, and P is the total power threshold. However, since there is no closed-form expression for the traversal and rate, the expectation involved in this optimization problem will lead to high computational complexity.

The signal-to-interference-plus-noise-ratio (SINR) of the kth user is defined as

in, remember The traversal rate of the kth user is approximated as

The error of this approximation decreases as the number of base station antennas increases, so it is more accurate in large-scale MIMO. Problem P1 can be approximately stated as

It is equivalent to the following optimization problem P2

{p _k } and {γ _k } contain the optimization variables for all users. Using the a posteriori channel model, the channel covariance matrix in the optimization problem can be calculated as follows:

Here, Λ _k is a diagonal matrix, and its diagonal elements are [Λ _k ] _mm = [ω _k ] _m . Next, we discuss the solution of problem P2.

The constraint SINR _k ≥γ _k is equivalently transformed into the following quadratic form

Therefore, the Lagrangian operator is expressed as

Where λ _k and ∈ are Lagrange multipliers. Let μ _k = λ _k /∈, and the KKT condition is expressed as

μ _k C _k = 0 (15)

From the formula we can get

Let S _k = μ _k R _k , Then the precoding vector p _k is the eigenvector of the matrix pair (S _k ,N _k ), and its corresponding eigenvalue is γ _k . Note that μ _k = 0 means that the kth user is not activated. When μ _k ≠ 0, it can be obtained from the formula that C _k = 0. Multiplying it by μ _k on the left, we have

Multiply the left Available

Combined and available

This means that the precoding vector constructed by any eigenvector satisfies the power constraint, and a larger eigenvalue γ _k corresponds to a larger optimization target. Therefore, the precoding vector p _k is the largest eigenvector of the matrix pair (S _k ,N _k ). Where ρ _k is the power allocated to the kth user, and p _k is the normalized precoding vector. Then we have

p _k = x _max ( S _k , N _k ) (20)

γ _k =λ _max (S _k ,N _k ) (21)

Wherein, λ _max (·) and x _max (·) represent the maximum generalized eigenvalue and its corresponding generalized eigenvector, respectively.

From the formula we can get

because The Lagrange multiplier ∈ is regarded as a normalization factor. In this way, the precoding vector p _k can be calculated by the parameter μ _k through the formula and. On the other hand, it can be obtained from the formula

In this way, the parameter μ _k can also be calculated by the precoding vector p _k through the formula and.

According to the above analysis, the precoding vector can be calculated by the following iterative steps:

Step 1: Initialize a precoder that meets the total power constraint (such as an RZF precoder);

Step 2: Calculate the signal-to-interference-noise ratio:

Step 3: Calculate the Lagrange multipliers:

Step 4: Calculate the normalized precoding vector:

p _k ← x _max (S _k ,N _k )

Step 5: Calculate the signal-to-interference-noise ratio:

γ' _k ←λ _max (S _k ,N _k )

Step 6: Calculate the power parameters:

Step 7: Repeat steps 2-6 until

Where ξ is the preset threshold.

This iterative design is robust to imperfect CSI because it takes into account the channel error statistics. In addition, the SINR and precoder are updated at each iteration. Therefore, this iterative design is called a robust iterative SINR (ISINR) precoder.

3) Special case with perfect CSI: ISINR precoder

When CSI is perfect (i.e. ), the formula becomes

In this case, the normalized precoding vector does not need to be obtained by solving the maximum generalized eigenvector, but is given by

in, Multiply the left The maximum generalized eigenvalue required in the iterative design is given by

The iterative design obtained by replacing steps 4 and 5 is called ISINR precoder, which has a simpler iterative design than the robust ISINR precoder.

It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims (4)

1. A method for designing iterative signal-to-interference-and-noise ratio of a large-scale MIMO robust precoder is characterized in that: the base station designs a robust iterative signal-to-interference-plus-noise ratio ISINR precoder according to the traversal and the speed of all users or the traversal and the speed approximation value maximization criterion of all users by utilizing the channel estimation value of each user terminal and the statistical parameter of the channel estimation error, and dynamically updates the precoding vector corresponding to each user terminal so as to perform downlink robust ISINR precoding transmission;

the channel estimation value is obtained through pilot signals periodically sent by each user, and the statistical parameters of the channel estimation errors are obtained through statistics of the channel estimation value;

The robust ISINR precoder includes: obtaining a structure of a precoding vector through problem transformation deduction, and alternately iterating a signal-to-interference-and-noise ratio and the precoding vector to approximate the maximum traversal and speed;

The structure of the precoding vector is divided into a precoding direction and a power distribution part; wherein the precoding direction is a generalized eigenvector corresponding to a maximum generalized eigenvalue of a matrix pair, the eigenvalue being a signal-to-interference-and-noise ratio, the matrix pair (S _k,N_k) being related to a channel covariance matrix R _k, a lagrangian multiplier mu _k and a noise variance sigma ², i.e. S _k＝μ_kR_k, Wherein I _M is an M-dimensional unit array, and k and I are user indexes; the power allocation is calculated by matrix inversion-free closed form, which is related to the channel covariance matrix R _k, the signal-to-interference-plus-noise ratio gamma _k, the precoding direction p _k and the lagrangian multipliers e and mu _k, i.e. the power allocated to the kth user is

The structure of the precoding vector is related to Lagrangian multipliers; by deriving the KKT condition, the Lagrangian multiplier μ _k is calculated by a closed-form calculation, the closed-form calculation being related to the channel covariance matrix R _k, the precoding vector p _k and the signal-to-interference-and-noise ratio γ _k, i.e

2. The iterative signal-to-interference-and-noise ratio design method of a massive MIMO robust precoder according to claim 1, wherein the iteration comprises the steps of:

step 1, initializing a precoding vector;

Step2, calculating the signal-to-interference-and-noise ratio;

step 3, calculating Lagrange multipliers through a closed mode;

Step 4, solving a generalized eigenvalue problem, and updating a precoding direction by using a maximum generalized eigenvector;

Step 5, updating the signal-to-interference-and-noise ratio by using the maximum generalized eigenvalue;

Step 6, distributing power through closed calculation;

And 7, repeating the steps 2-6 until convergence.

3. The iterative signal-to-interference-and-noise ratio design method of a massive MIMO robust precoder according to claim 1, wherein the precoding vector has a simpler structure in case of perfect channel state information, comprising: the precoding direction is calculated by a closed form, the closed form and the channel covariance matrixLagrangian multiplier μ _k is related to noise variance σ ², i.eThe power allocation is calculated by a closed form, which is related to the channel covariance matrix R _k, the signal-to-interference-plus-noise ratio y _k, the precoding direction p _k and the lagrangian multipliers e and μ _k, i.e.

4. The iterative signal-to-interference-and-noise ratio design method of a massive MIMO robust precoder according to claim 1, characterized by having an iterative step with simpler computation in case of perfect channel state information, comprising:

Step a, initializing a precoding vector;

step b, calculating the signal-to-interference-and-noise ratio;

step c, calculating Lagrange multipliers through a closed mode;

step d, updating the precoding direction through closed calculation;

step e, updating the signal-to-interference-and-noise ratio through closed calculation;

F, calculating power distribution through a closed type;

and g, repeating the steps b-f until convergence.