CN114900216A - Iterative signal-to-interference-and-noise ratio design method of large-scale MIMO robust precoder - Google Patents
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Abstract
The invention discloses an iterative signal-to-interference-and-noise ratio (ISINR) design method of a large-scale MIMO robust precoder. The method decomposes a precoding vector into a precoding direction part and a power distribution part which are respectively expressed as a maximum generalized characteristic vector and a closed form, and further alternately iterates a signal-to-interference-and-noise ratio (SINR) and the precoding vector to approximate to a maximum traversal rate. The invention can make precoder design converge with less iteration times, thereby reducing computation complexity while approaching maximum traversal and rate.
Description
Technical Field
The invention belongs to the field of wireless communication downlink precoding, and particularly relates to an iterative signal-to-interference-and-noise ratio design method of a large-scale MIMO robust precoder.
Background
By deploying a large number of antennas at a Base Station (BS), a large-scale multiple-input-multiple-output (MIMO) technology can provide services for a large number of users at the same time, thereby significantly improving the spectral efficiency of the system. The base station should reasonably design the precoder for all users to mitigate inter-user interference.
Precoder design depends on Channel State Information (CSI) available to the base station. For the case of perfect CSI, regularized zero-forcing (RZF) and signal-to-leakage-and-noise ratio (SLNR) precoders may simply implement the precoder. Weighted minimum mean-square error (WMMSE) precoders iteratively designed by the convex problem are the optimal precoders to maximize sum rate.
However, due to large pilot overhead, channel aging, etc., in massive MIMO, especially in high mobility scenarios, it is challenging to acquire accurate CSI, 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 sub-optimal sum rates. To directly maximize and rate, a random WMMSE precoder requires iteration over a large number of channel realizations, but each iteration involves a computationally expensive matrix inversion.
To solve this problem, deep learning is actively explored. However, labels for supervised learning require offline iterations, while guarantees of generalization performance require a large number of samples. Furthermore, there is inevitable online training for transfer learning across the generalization of scenarios. Therefore, it is necessary to explore fast converging precoder iterative design methods.
Disclosure of Invention
The invention aims to provide an iterative signal-to-interference-and-noise ratio design method of a large-scale MIMO robust precoder, so as to solve the technical problem of high computational complexity.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
an iterative signal-to-interference-and-noise ratio (SINR) design method for a large-scale MIMO robust precoder, the method comprising: the base station designs a robust iterative signal-to-interference-and-noise ratio (ISINR) precoder according to the traversing and velocity of all users or the traversing and velocity approximation value maximization criterion of all users by using the channel estimation value and the statistical parameter of the channel estimation error of each user terminal, and dynamically updates a precoding vector corresponding to each user terminal so as to carry out 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 error are obtained through statistics of the channel estimation value;
the robust ISINR precoder comprises: and deriving a structure of a precoding vector through problem conversion, and alternately iterating the signal-to-interference-and-noise ratio and the precoding vector to approximate the maximum traversal rate.
Furthermore, the structure of the precoding vector is divided into a precoding direction and a power allocation; the precoding direction is a generalized eigenvector corresponding to the maximum generalized eigenvalue of a matrix pair, the eigenvalue is a signal-to-interference-and-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 the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-noise ratio, the precoding direction, and the lagrange multiplier.
Further, the structure of the precoding vector is related to a Lagrange multiplier; by deriving the KKT condition, the Lagrangian multiplier is computed in a closed form that is related to the channel covariance matrix, the precoding vector, and the signal-to-interference-and-noise ratio.
Further, the iteration comprises the following steps:
step 1, initializing a pre-coding vector;
step 2, calculating the signal-to-interference-and-noise ratio;
step 3, calculating Lagrange multipliers in a closed mode;
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-and-noise ratio by using the maximum generalized characteristic value;
step 6, calculating power distribution in a closed mode;
and 7, repeating the steps 2-6 until convergence.
Further, under the condition that the channel state information is perfect, the precoding vector has a simpler structure, which specifically includes: the precoding direction is calculated in a closed form, wherein the closed form is related to a channel covariance matrix, a Lagrange multiplier and a noise variance; the power allocation is calculated by the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-noise ratio, the precoding direction, and the lagrange multiplier.
Further, under the condition that the channel state information is perfect, an iteration step with simpler calculation is provided, which specifically comprises the following steps:
step a, initializing a pre-coding vector;
step b, calculating the signal-to-interference-and-noise ratio;
step c, calculating Lagrange multipliers in a closed mode;
d, updating the precoding direction through closed type calculation;
step e, updating the signal-to-interference-and-noise ratio through closed type calculation;
step f, calculating power distribution in a closed mode;
and g, repeating the steps b-f until convergence.
The iterative signal-to-interference-and-noise ratio design method of the large-scale MIMO robust precoder has the following advantages:
1. for the problem of precoder design for traversal and rate maximization, the invention characterizes the structure of precoding vectors by problem transformation, where complex computations related to expectations are computed closed-form using an a posteriori channel model.
2. An iterative signal-to-interference-plus-noise-ratio (ISINR) design method of a robust precoder is provided by alternately iterating a signal-to-interference-plus-noise-ratio (SINR) and the precoder. The RZF precoder is used as an initial value, the robust ISINR precoder is converged within two times, the maximum traversal and rate performance is approached, and the computation complexity is effectively reduced due to the fast convergence.
Drawings
Fig. 1 is a flowchart of a robust ISINR precoder design method according to the present invention.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, the iterative snr design method of the massive MIMO robust precoder according to the present invention is described in further detail below with reference to the accompanying drawings.
In the iterative signal-to-interference-and-noise ratio design method of the large-scale MIMO robust precoder disclosed by the embodiment of the invention, a base station designs a robust iterative signal-to-interference-and-noise ratio (ISINR) precoder according to the traversing and velocity of all users or the traversing and velocity approximation value maximization criteria of all users by utilizing the channel estimation value and the statistical parameter of channel estimation error of each user terminal, and dynamically updates a precoding vector corresponding to each user terminal so as to carry out 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 error are obtained through statistics of the channel estimation value;
the robust ISINR precoder comprises: and deriving a structure of a precoding vector through problem conversion, and alternately iterating the signal-to-interference-and-noise ratio and the precoding vector to approximate the maximum traversal rate.
The structure of the pre-coding vector comprises that the structure of the pre-coding vector is divided into a pre-coding direction and a power distribution part; the precoding direction is a generalized eigenvector corresponding to the maximum generalized eigenvalue of a matrix pair, the eigenvalue is a signal-to-interference-and-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 the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-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 Lagrangian multiplier is computed in a closed form that is related to the channel covariance matrix, the precoding vector, and the signal-to-interference-and-noise ratio.
The iteration step comprises: step 1, initializing a pre-coding vector; step 2, calculating the signal-to-interference-and-noise ratio through definition; step 3, calculating Lagrange multipliers in a closed mode; 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-and-noise ratio by using the maximum generalized characteristic value; step 6, calculating power distribution in a closed mode; and 7, repeating the steps 2-6 until convergence.
Under the condition that the channel state information is perfect, the precoding vector has a simpler structure, and specifically comprises the following steps: the precoding direction is calculated in a closed form, wherein the closed form is related to a channel covariance matrix, a Lagrange multiplier and a noise variance; the power allocation is calculated by the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-noise ratio, the precoding direction, and the lagrange multiplier.
Under the condition that the channel state information is perfect, iteration steps with simpler calculation are provided, which specifically comprise: step a, initializing a pre-coding vector; b, calculating the signal-to-interference-and-noise ratio through definition; step c, calculating Lagrange multipliers in a closed mode; d, updating the precoding direction through closed type calculation; step e, updating the signal-to-interference-and-noise ratio through closed type calculation; step f, calculating power distribution in a closed mode; and g, repeating the steps b-f until convergence.
The method of the embodiment of the present invention is further described below with reference to specific implementation scenarios, the method of the present invention is not limited to the specific scenarios, and for other implementations other than the exemplary scenarios of the present invention, a person skilled in the art can make an adaptive adjustment according to the specific scenarios by using existing knowledge according to the technical idea of the present invention.
1) System model
Consider a massive MIMO downlink transmission system consisting of one base station and K randomly distributed users. Wherein the base station is equipped with M t A root antenna, each user equipped with a single antenna. The system works in a Time Division Duplex (TDD) mode, time resources are divided into time slots, and each time slot comprises N b A symbol. The first symbol of each slot is used for uplink sounding, and the other symbols are used for downlink transmission.
Note x k,n For the transmitted signal of the k user at the n symbol, satisfy
The received signal of the kth user at the nth symbol is
Wherein the content of the first and second substances,
for the channel vector at the nth symbol for the kth user,
for the precoding vector at the nth symbol for the kth user,
complex gaussian noise at the nth symbol for the kth user; sigma 2 Is the noise variance.
For uniform linear arrays in massive MIMO, the joint correlation channel can accurately simulate the physical channel, i.e.
Wherein the content of the first and second substances,
is a Discrete Fourier Transform (DFT) matrix; m is k Is a deterministic vector with non-zero elements; w is a k,n The vector is a complex Gaussian random vector, elements of the vector are independently and uniformly distributed, the mean value is 0, and the variance is 1. This is an a priori channel model prior to channel estimation.
In order to characterize the time correlation between the symbols, a posteriori channel model is adopted, and the channel vector of the k-th user at the nth symbol is expressed as
Wherein the content of the first and second substances,
representing the channel estimate at the first symbol; beta is a k,n ∈[0,1]The time correlation coefficient is calculated by an autocorrelation model of Jakes. Base station obtains channel estimation value through uplink detection
And channel coupling vector
2) Robust ISINR precoder
The base station performs precoding once per symbol, assuming that the channel remains constant in each symbol and varies from symbol to symbol. For the sake of brevity, subscript n is omitted below. The traversal rate of the k-th user is expressed as
The optimal design of the robust precoder is to design the precoding vector p 1 ,p 2 ,...,p K To maximize traversal and rate
The precoding vector satisfies the total power constraint of the base station, and P is a total power threshold. However, the expectations involved in this optimization problem result in higher computational complexity, since the traversal and rate have no closed form expression.
Defining the signal-to-interference-plus-noise-ratio (SINR) of the kth user as
Wherein, the first and the second end of the pipe are connected with each other,
note the book
The traversal rate of the k-th user is approximated as
The error of this approximation decreases as the number of base station antennas increases, and is therefore more accurate in massive MIMO. The problem P1 can be expressed approximately as
Which is equivalent to the following optimization problem P2
{p k And { gamma } k Contains the optimization variables for all users. The channel covariance matrix in the optimization problem can be calculated by the following formula through a posteriori channel model
Wherein, Λ k Is a diagonal matrix with diagonal elements of [ Lambda k ] mm ＝[ω k ] m . The solution of problem P2 is discussed below.
Will constrain the condition SINR k ≥γ k Equivalently converting into quadratic form
Thus, the Lagrangian is expressed as
Wherein λ is k And ∈ is the Lagrangian multiplier. Record mu k ＝λ k The/. epsilon, KKT condition is expressed as
μ k C k ＝0 (15)
Can be obtained by
Note S k ＝μ k R k ，
Then the precoding vector p k Is a matrix pair (S) k ,N k ) The feature vector of (2) has a corresponding feature value of γ k . Note that μ k 0 means that the kth user is not activated when μ k When not equal to 0, C is obtained from the formula k 0, to which is left-multiplied by mu k Then there is
Paired left-hand ride
Can obtain the product
United and available
This means that precoding vectors constructed from arbitrary eigenvectors satisfy the power constraint, while larger eigenvalues γ k Corresponding to this larger optimization objective. Thus, the precoding vector p k Is a matrix pair (S) k ,N k ) The largest feature vector of (2). Note the book
Where ρ is k For the power allocated to the k-th user, p k Is a normalized precoding vector. Then there is
p k ＝x max (S k ,N k ) (20)
γ k ＝λ max (S k ,N k ) (21)
Wherein λ is max (. and x) max (. cndot.) denotes the maximum generalized eigenvalue and its corresponding generalized eigenvector, respectively.
Can be obtained by
Due to the fact that
The lagrange multiplier e is considered as a normalization factor. Thus, the precoding vector p k Can be derived from the parameter mu k And calculating by the formula. On the other hand, the compounds can be obtained by
Thus, the parameter μ k Can also be formed by a precoding vector p k And calculating by the formula.
Based on the above analysis, the precoding vector can be calculated as the following iterative steps:
step 1: initializing precoders (such as RZF precoders) that satisfy a total power constraint;
step 2: and calculating the signal-to-interference-and-noise ratio:
and step 3: computing a lagrange multiplier:
and 4, step 4: calculating a normalized precoding vector:
p k ←x max (S k ,N k )
and 5: and calculating the signal-to-interference-and-noise ratio:
γ' k ←λ max (S k ,N k )
step 6: calculating a power parameter:
and 7: repeating the steps 2-6 until
Where ξ is a preset threshold.
The iterative design is robust to imperfect CSI due to channel error statistics being considered. In addition, the signal to interference and noise ratio and precoder are updated every iteration. Therefore, this iterative design is referred to as a robust iterative signal-to-interference-and-noise ratio (ISINR) precoder.
3) Special case when CSI is perfect: ISINR precoder
When the CSI is perfect (i.e.
) When formula is changed to
In this case, the normalized precoding vector need not be obtained by solving the maximum generalized eigenvector, but is given by
Wherein the content of the first and second substances,
paired left-hand ride
The maximum generalized eigenvalue required in the iterative design is given by
The iterative design resulting from equations and alternative steps 4 and 5 is called the ISINR precoder, which is simpler than a robust ISINR precoder.
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (6)
1. An iterative signal-to-interference-and-noise ratio (SINR) design method for a large-scale MIMO robust precoder is characterized in that: the base station designs a robust iterative signal-to-interference-and-noise ratio (ISINR) precoder according to the traversing and speed of all users or the traversing and speed approximation value maximization criterion of all users by using the channel estimation value of each user terminal and the statistical parameters of the channel estimation error, and dynamically updates a 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 error are obtained through statistics of the channel estimation value;
the robust ISINR precoder comprises: and deriving a structure of a precoding vector through problem conversion, and alternately iterating the signal-to-interference-and-noise ratio and the precoding vector to approximate the maximum traversal rate.
2. The iterative SINR design method of the massive MIMO robust precoder of claim 1, wherein the structure of the precoding vector is divided into two parts, namely precoding direction and power allocation; the precoding direction is a generalized eigenvector corresponding to the maximum generalized eigenvalue of a matrix pair, the eigenvalue is a signal-to-interference-and-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 the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-noise ratio, the precoding direction, and the lagrange multiplier.
3. The iterative SINR design method for massive MIMO robust precoders according to claim 1, wherein the structure of said precoding vector is related to Lagrangian multipliers; by deriving the KKT condition, the Lagrangian multiplier is computed in a closed form that is related to the channel covariance matrix, the precoding vector, and the signal-to-interference-and-noise ratio.
4. The iterative SINR design method for massive MIMO robust precoders according to claim 1, wherein said iteration comprises the steps of:
step 1, initializing a pre-coding vector;
step 2, calculating the signal-to-interference-and-noise ratio;
step 3, calculating Lagrange multipliers in a closed mode;
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-and-noise ratio by using the maximum generalized characteristic value;
step 6, calculating power distribution in a closed mode;
and 7, repeating the steps 2-6 until convergence.
5. The iterative signal-to-interference-and-noise ratio design method of the massive MIMO robust precoder according to claim 1, wherein the precoding vector has a simpler structure under the condition that the channel state information is perfect, specifically comprising: the precoding direction is calculated in a closed form, wherein the closed form is related to a channel covariance matrix, a Lagrange multiplier and a noise variance; the power allocation is calculated by the closed form, which is related to the channel covariance matrix, the signal-to-interference-and-noise ratio, the precoding direction, and the lagrange multiplier.
6. The iterative signal-to-interference-and-noise ratio design method of the massive MIMO robust precoder according to claim 1, wherein under the condition of perfect channel state information, an iterative step with simpler calculation is provided, specifically comprising:
step a, initializing a pre-coding vector;
step b, calculating the signal-to-interference-and-noise ratio;
step c, calculating Lagrange multipliers in a closed mode;
d, updating the precoding direction through closed type calculation;
step e, updating the signal-to-interference-and-noise ratio through closed type calculation;
step f, calculating power distribution in a closed mode;
and g, repeating the steps b-f until convergence.
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