CN106027434A - Precoding method based on CSM (Cholesky-Decompositionand Sherman-Morrison lemma) - Google Patents

Abstract

The embodiment of this invention discloses a precoding method based on CSM (Cholesky-Decompositionand Sherman-Morrison lemma). The method is applicable when an inversion matrix satisfies the form of W=H.HH+omega.I or the character of positive definite hermitian in precoding. The method provided in this invention uses regularized zero-forcing precoding algorithm to illustrate, and comprises the following steps: complete procedure declaration and theoretical proof (method process and theoretical proof of Cholesky decomposition and Sherman-Morrison formula), performance analysis of improved regularized zero-forcing precoding algorithm, and applicable situation and performance optimization of the structure given in the form of the embodiment. The method provided in this invention uses regularized zero-forcing precoding algorithm to illustrate, but is not limited to the algorithm; for example, this method is further applicable to MMSE (Minimum Mean Square Error) algorithm, and the like. The method provided by this embodiment of this invention effectively reduces the computation complexity of precoding in Massive MIMO (Multiple Input Multiple Output) communication system, improves the resultant velocity, reduces the bit error rate, and improves and optimizes the performance of this type of technology.

Description

A kind of method for precoding based on CSM

Technical field

The present invention relates to communication technical field, meet W=H H particularly to when the matrix needing in precoding to invert^H+ Method for precoding when ω I form or positive definite Hermetian character.

This patent introduces the principle of the invention as a example by RZF, but is not limited to RZF algorithm, as long as precoding needs invert Matrix meets W=H H^H+ ω I form or positive definite Hermetian character, just can use the technology of the present invention.

It is noted that this patent introduces the method principle in communication as a example by precoding, but the method that this patent proposes Being not limited only to the communications field, as long as needing to carry out matrix inversion operation in any modern industrial technology, and matrix meets one Fixed condition, just may be by the method that this patent proposes.

Background technology

1) technical background

Extensive MIMO technology is as a key technology in 5G communication system, it is possible to effectively utilize Spatial Dimension, Thus significantly improve power system capacity, spectrum efficiency, reduce energy expenditure.Extensive MIMO technology is by unnecessary spatial degrees of freedom The signal processing complexity of terminal can be substantially reduced, and use simple signal processing algorithm just can eliminate in base station end Intra-cell interference, presence of intercell interference, channel estimation errors and effect of noise, thus reach optimal system performance.On big rule In mould MIMO, low complex degree signal detection and precoding technique are often thought of as optimal candidate scheme, such as maximum-ratio combing (maximum ratio combining is called for short MRC), high specific send (maximum ratio transmission, abbreviation MRT), ZF (zero-forcing, be called for short ZF), regularization ZF (regularized zero-forcing is called for short RZF), Least mean-square error etc..In extensive MIMO, although RZF and MMSE precoding is obtained in that the performance of near-optimization, but During the realization of RZF or MMSE, needing to calculate an extensive inverse of a matrix, this is to cause RZF or MMSE algorithm complicated Spending the highest main cause, in order to reduce the complexity of these algorithms, industry has carried out a lot of research.

2) prior art of matrix inversion

Method for precoding based on Neumann sequence approximate data by being converted into a series of matrix-vector by matrix inversion It is multiplied and can significantly reduce the complexity of matrix inversion；SOR (successiveoverrelaxation) is extensive by utilizing The progressive orthogonality of mimo channel matrix, it is also possible to reduce the complexity of matrix inversion；

3) problem that prior art exists

Although method for precoding based on Neumann algorithm can significantly reduce the complexity of matrix inversion, but performance (such as: close speed, bit error rate and robustness) is poor, although calculating based on approaching RZF in SOR algorithm channel capacity Method, but the bit error rate is the highest, is compared to Neumann algorithm simultaneously, and when iterations is more, the complexity of algorithm can become Obtain the highest.

Summary of the invention

Current existing Massive MIMO precoding technique is all based on the algorithm of ZF, RZF and MMSE, and at these Carry out reducing the research of computation complexity on the basis of algorithm.But these technology the most all can cause performance indications The loss of (closing speed, bit error rate and robustness).

In order to solve these problems, this patent proposes based on C (Cholesky-Decomposition) SM (Sherman- Morrison lemma) method for precoding.The sharpest edges of the method are to ensure that computation complexity is with existing algorithm such as On the premise of Neumann or SOR algorithm maintains an equal level, performance is close with RZF ideal performance index to greatest extent even to be overlapped, i.e. originally Patent institute extracting method also decreases unlike Neumann or SOR algorithm performance while reducing complexity.And the method energy Make full use of hardware to process channel condition information (CSI).

By performance simulation, the method for precoding (CSM-RZF) proposed in this patent is closing speed, bit error rate and robust These main performance indications of performance are substantially better than current existing algorithm, it is worth mentioning at this point that, almost ensureing and these On the premise of the computation complexity that algorithm is consistent or lower slightly, performance but has huge lifting, even with the RZF under ideal conditions Effect is close or overlaps.

Accompanying drawing explanation

Fig. 1 is Massive mimo system illustraton of model；

Fig. 2 precoding based on CSM algorithm flow chart；

Fig. 3 is to close rate capability simulation result figure (antenna number: 256 × number of users: 32)；

Fig. 4 is performance of BER simulation result figure (antenna number: 256 × number of users: 16)；

Fig. 5 is performance of BER simulation result figure (antenna number: 256 × number of users: 32)；

Detailed description of the invention

1) system model, implementation process and theoretical proof:

System model such as Fig. 1, there is a center base station each community, and this base station equipment N root launches antenna.MPS process In the range of to have K user, each user be single antenna pattern (K < < M).System uses modulation system (this modulation of TDD The advantage of mode is that up-downgoing channel CSI within a coherence time is essentially identical).Channel uses Reyleigh and declines Fall channel.

Received signal vectorMeet:

Y=H x+n

Wherein,Descending channel information matrix, and by multipath fading (each element independent same distribution and fromMultiple Gauss distribution) and large scale decline (being calculated by path loss and shadow fading) be jointly calculated.It is the transmission information vector after precoding, and meets power limited: It is high This white noise is vectorial and meets

Then have:

X=T s

Wherein,It is in pre-coding matrix,It it is the information vector sent.Equally, base station i is needed Meet Power Limitation:

$tr(H_i\&CenterDot;H_i^H)=P_i$

The invention provides a kind of method for precoding canonical ZF improved based on CSM, it is also possible to MMSE is entered Row improves, as long as or needing the matrix inverted to meet W=H H in precoding^H+ ω I form or positive definite Hermetian character Time, just may be by this patent and carry out precoding.Traditional RZF precoding model is:

T_RZF=ρ_RZF·H^H·(H·H^H+α·I)^-1

The community covered for base station j has:

$T_{RZF,j}={\mathrm{\&rho;}}_j\&CenterDot;H_j^H\&CenterDot;{(H_j\&CenterDot;H_j^H+\mathrm{\&alpha;}\&CenterDot;I)}^{-1}={\mathrm{\&rho;}}_j\&CenterDot;H_j^H\&CenterDot;W_j^{-1}$

Wherein: α is regularization regulation coefficient, in order to embody the generality of algorithm in this patent, this coefficient meetsρ_jBeing the power limited factor, it meets:

${\mathrm{\&rho;}}_j=\sqrt{K/tr(W_j\&CenterDot;W_j^H)}$

So,

X=T_RZFS=ρ_RZF·H^H·W^-1·s

As can be seen here, the transmission vector after precoding to be obtained, it is necessary to matrix W is inverted, but matrix W Dimension is very big, if directly inverted, computation complexity is high, and hardware deterioration is the biggest.

Based on the problems referred to above, this patent proposes based on C (Cholesky-Decomposition) SM (Sherman- Morrison lemma) RZF method for precoding.

First, mathematical knowledge is passed through, it was demonstrated that going out matrix W is a positively definite hermitian matrix:

AssumeIt is the column vector of a non-zero, then has

t·W·t^H=t (H H^H+α·I)·t^H=t H (t H)^H+t·α·I·t^H＞ 0

In addition

P^H=(H H^H+α·I)^H=P

Thus prove out that matrix W is a positively definite hermitian matrix.

On the premise of so, matrix W just can carry out Cholesky decomposition:

W=L*L^H

Wherein matrix L is lower triangular matrix.Then

W^-1=(L^H)^-1*L^-1

Thus the problem inverting matrix W is transformed into the inversion problem to matrix L.

In order to reduce the complexity inverting matrix L, this patent uses Sherman-Morrison formula to carry out iterative, The most first explanation Sherman-Morrison formula:

Assuming that matrix A is a reversible matrix, x and y is column vector respectively.And meet (A+x y^H) reversible, 1+ y^H·A^-1X ≠ 0, then Sherman-Morrison formula:

${(A+x\&CenterDot;y^H)}^{-1}=A^{-1}-\frac{A^{-1}\&CenterDot;x\&CenterDot;y^H\&CenterDot;A^{-1}}{1+y^H\&CenterDot;A^{-1}\&CenterDot;x}$

In order to utilize Sherman-Morrison formula, need exist for matrix L is carried out at suitable deformation and mathematics Reason:

L=D+L '

Wherein: D is a diagonal matrix, meets D=diag (l_1,1,l_2,2,…,l_K,K).L ' is matrix L diagonal entry The lower triangular matrix all set to 0.

Then matrix L can continue twice decomposition:

L=D+L '=D+l₁′·e₁+l₂′·e₂+…+l_K-1′·e_K-1+0·e_k

Wherein e_iRepresentation unit battle array I_KThe i-th row.

So, based on above-mentioned Mathematical treatment, calculating the inverse of matrix L can be completed by following process:

$L^{-1}={(F_{K-2}+l_{K-1}^{\&prime;}\&CenterDot;e_{K-1})}^{-1}={\left(F_{K-2}\right)}^{-1}-\frac{{\left(F_{K-2}\right)}^{-1}\&CenterDot;l_{K-1}^{\&prime;}\&CenterDot;e_{K-1}\&CenterDot;{\left(F_{K-2}\right)}^{-1}}{1+e_{K-1}\&CenterDot;{\left(F_{K-2}\right)}^{-1}\&CenterDot;l_{K-1}^{\&prime;}}$

WhereinContinue to seek F_K-2Inverse:

${F_{K-2}}^{-1}={(F_{K-3}+l_{K-2}^{\&prime;}\&CenterDot;e_{K-2})}^{-1}={\left(F_{K-3}\right)}^{-1}-\frac{{\left(F_{K-3}\right)}^{-1}\&CenterDot;l_{K-2}^{\&prime;}\&CenterDot;e_{K-2}\&CenterDot;{\left(F_{K-3}\right)}^{-1}}{1+e_{K-2}\&CenterDot;{\left(F_{K-3}\right)}^{-1}\&CenterDot;l_{K-2}^{\&prime;}}$

WhereinBy that analogy, finally give:

$F_1^{-1}={(F_0+l_0^{\&prime;}\&CenterDot;e_1)}^{-1}={\left(F_0\right)}^{-1}-\frac{{\left(F_0\right)}^{-1}\&CenterDot;l_1^{\&prime;}\&CenterDot;e_1\&CenterDot;{\left(F_0\right)}^{-1}}{1+e_1\&CenterDot;{\left(F_0\right)}^{-1}\&CenterDot;l_1^{\&prime;}}$

Wherein F₀=D.

Finally, through the iteration of K-1 time, the inverse of matrix L is obtained.

2) performance evaluation

Simulated environment uses MATLAB2015.Assume that system model is: there are a center base station, this base in each community Station is equipped with N root and launches antenna.Having K user, each user in cell coverage area is single antenna pattern (K < < N).System (advantage of this modulation system is that up-downgoing channel CSI within a coherence time is basic to use the modulation system of TDD Identical).Channel uses Reyleigh fading channel.Curve corresponding for RZF in figure is all the time as the effect under ideal conditions Really, it is therefore an objective to be used for contrasting algorithms of different and the gap under ideal conditions.

(1) complexity

First by hardware (such as: FPGA), the matrix W obtained in formula is carried out Cholesky decomposition.Here decomposition step Rapid computation complexity is under the operation of hardware pipeline mode of operation, and complexity is extremely low, for follow-up calculating, this Computation complexity can be ignored.Fraction item in Sherman-Morrison formulaSparse utilizing Computation complexity under the estimated performance of matrix and sparse vector is O (4K+1), so through the iteration of K-1 time, this seeks square The inverse computation complexity of battle array L is: O (4K²-3K-1).This is relative to the complexity O (K directly inverted matrix W³For), i.e. Compared with RZF algorithm, the computation complexity of CSM-RZF is greatly reduced, relative to other innovatory algorithm (Neumann at present Or SOR algorithm) for, computation complexity almost maintains an equal level.

(2) speed is closed

Fig. 3 represents in Base Transmitter antenna number N=256, number of users K=32, in the case of keeping N/K constant, and different calculations The trend that the conjunction speed of method changes with signal to noise ratio (SNR) change.What in figure, RZF curve represented is conjunction speed the most ideally Rate performance.Can be seen that, along with the increase of SNR, the conjunction speed of all algorithms is all rising.And in order to performance is described Effect, is exaggerated local, preferably to show result in figure.Changing during i represents SOR and Neumann algorithm in figure Generation number.Although as the increase of iterations i, the effect of SOR and Neumann is improving, but it closes rate index all the time It is worse than in this patent CSM-RZF and the RZF ideal curve proposed.The CSM-RZF that i.e. this patent proposes is reducing the same of complexity Time, performance compared with RZF algorithm almost without any loss.

(3) bit error rate

Fig. 4 represents in Base Transmitter antenna number N=256, number of users K=16, in the case of keeping N/K constant, and different calculations The trend that the bit error rate (BER) of method changes with signal to noise ratio (SNR) change, it can be seen that along with the increase of SNR, all calculations The BER performance of method is all rising (that is, the numerical value of BER is declining).Although as the increase of iterations i, the effect of Neumann Improving, but the BER performance of SOR algorithm the most significantly changing, this illustrate this class algorithm in BER performance the most Shortcoming.But in this patent propose algorithm (CSM-RZF) in the performance of BER the most all the time with the (perfect condition of RZF in figure Under) this curve close to even overlapping.This explanation compared with RZF, CSM-RZF while being substantially reduced computation complexity also Do not reduce performance of BER.

Fig. 5 still represents the trend that the bit error rate (BER) of algorithms of different changes with signal to noise ratio (SNR) change, simply Number of users K becomes 32, and other conditions are constant.Comparison diagram 4 with Fig. 5 it is found that along with number of users K increases, the mistake of all algorithms Bit-rate performance all can have loss, but compared with other algorithms, CSM-RZF performance loss under similarity condition is minimum, robust Property best, and the convergence of its bit error rate is the fastest.

So, understand, by above-mentioned three figures, the method for precoding (CSM-RZF) proposed in this patent and closing speed, by mistake than Be superior to current Neumann or SOR algorithm in special rate and these main performance indications of robust performance, and with preferable bar Under part, the effect of RZF algorithm is almost consistent, but its computation complexity is substantially reduced.

Embodiment

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing Have technology to be briefly described, it should be apparent that, described below for those of ordinary skill in the art, do not paying creation Property work on the premise of, it is also possible to according to these describe obtain additive method.

Embodiment 1:

The highest in order to solve high-dimensional matrix inversion complexity in the precoding problem of existing Massive MIMO technology Problem, the embodiment of the present invention provides a kind of based on C (Cholesky-Decomposition) on the basis of tradition RZF algorithm The RZF method for precoding of SM (Sherman-Morrison lemma), the method flow chart is as in figure 2 it is shown, the method includes:

The first step, utilizes the character that TDD modulates, and terminal makes base station end profit by sending signaling to base station at up channel Obtain the channel condition information (CSI) of down channel with the channel reciprocity of TDD and obtain channel gain matrix H.

Second step, obtains the matrix W=H H needing to invert according to the precoding formula of RZF^H+ω·I。

3rd step, utilizes the calculating advantages characteristic of hardware pipeline, and matrix W carries out quick Cholesky decomposition, and And obtain lower triangular matrix L.

4th step, carries out mathematical deformation process to lower triangular matrix L and (is processed into L=D+L'=D+l₁'·e₁+ l₂'·e₂+…+l_K-1'·e_K-1+0·e_K) and secondary equivalent transformation, recycle Sherman-Morrison formula, pass through iteration Mode obtain the inverse of lower triangular matrix L.

5th step, then passes through formula W^-1=(L^H)^-1*L^-1Obtain the inverse of matrix W, finally give after precoding Transmission vector, complete base station and the data of terminal transmitted.

Embodiment 2:

The problem of high-dimensional matrix inversion in the precoding problem of existing Massive MIMO technology, the embodiment of the present invention is same Sample can provide a kind of based on C (Cholesky-Decomposition) SM on the basis of tradition MMSE algorithm The MMSE precoding algorithms of (Sherman-Morrison lemma), the method flow chart is as in figure 2 it is shown, the method includes:

The first step, utilizes the character that TDD modulates, and terminal makes base station end profit by sending signaling to base station at up channel Obtain the channel condition information (CSI) of down channel with the channel reciprocity of TDD and obtain channel gain matrix H.

Second step, obtains the matrix W=H H needing to invert according to the precoding formula of MMSE^H+ω·I。

3rd step, utilizes the calculating advantages characteristic of hardware pipeline, and matrix W carries out quick Cholesky decomposition, and And obtain lower triangular matrix L.

4th step, carries out mathematical deformation process to lower triangular matrix L and (is processed into L=D+L'=D+l₁'·e₁+ l₂'·e₂+…+l_K-1'·e_K-1+0·e_K) and secondary equivalent transformation, recycle Sherman-Morrison formula, pass through iteration Mode obtain the inverse of lower triangular matrix L.

5th step, then passes through formula W^-1=(L^H)^-1*L^-1Obtain the inverse of matrix W, finally give after precoding Transmission vector, complete base station and the data of terminal transmitted.

Embodiment 3:

The highest in order to solve high-dimensional matrix inversion complexity in the precoding problem of existing Massive MIMO technology Problem, meets when wherein needing the matrix invertedThe matrix W that such form or needs are inverted meets The such premise of positively definite hermitian matrix, can use in this patent propose based on C (Cholesky- Decomposition) method for precoding of SM (Sherman-Morrison lemma), the method flow chart is as in figure 2 it is shown, be somebody's turn to do Method includes:

The first step, utilizes the character that TDD modulates, and terminal makes base station end profit by sending signaling to base station at up channel Obtain the channel condition information (CSI) of down channel with the channel reciprocity of TDD and obtain channel gain matrix H.

Second step, obtains, according to all precoding formula meeting above-mentioned condition, matrix W=H H that needs are inverted^H+ ω·I。

3rd step, utilizes the calculating advantages characteristic of the streamline of hardware, and matrix W carries out quick Cholesky decomposition, And obtain lower triangular matrix L.

4th step, carries out mathematical deformation process to lower triangular matrix L and (is processed into L=D+L '=D+l₁′·e₁+ l₂′·e₂+…+l_K-1′·e_K-1+0·e_k) and secondary equivalent transformation, recycle Sherman-Morrison formula, pass through iteration Mode obtain the inverse of lower triangular matrix L.

5th step, then passes through formula W^-1=(L^H)^-1*L^-1Obtain the inverse of matrix W, finally give after precoding Transmission vector, complete base station and the data of terminal transmitted.

Embodiment 4:

First three embodiment completes under conditions of modulation system is TDD.The algorithm proposed in the same present invention is fitted, Being equally applicable for FDD modulation system, even full duplex (simultaneously with frequency, use TDD and FDD modulation system simultaneously) is all feasible. Because, as long as base station end can be estimated to obtain channel gain matrix H, the precoding of existing Massive MIMO technology by channel Problem is required for high-dimensional matrix inversion.When the matrix part wherein needing to invert meets W=H H^HThe such shape of+ω I The matrix W that formula or needs are inverted meets the such premise of positively definite hermitian matrix, then can use proposition in this patent Precoding algorithms based on C (Cholesky-Decomposition) SM (Sherman-Morrison lemma), the method stream Journey figure ibid, repeats no more.

Embodiment 5:

Front four embodiments are to be used in the embodiment communicated and in terms of signal processing.The calculation proposed in the same present invention Method, this technology is equally applicable to current modern industry (utilizing automaton to cut, air detection etc.).Because, the most in the industry It is required on the basis of linear algebra higher dimensional matrix is inverted.When the matrix wherein needing to invert meets W=H H^H+ The matrix W that the such form of ω I or needs are inverted meets the such premise of positively definite hermitian matrix, then can use this The algorithm based on C (Cholesky-Decomposition) SM (Sherman-Morrison lemma) proposed in patent, should Method flow diagram ibid, repeats no more.

Embodiment of above is merely to illustrate the present invention, and by non-limitation of the present invention, common about technical field Technical staff, without departing from the spirit and scope of the present invention, it is also possible to make a variety of changes and deform, therefore owning Equivalent technical scheme fall within scope of the invention, the scope of patent protection of the present invention should have the right requirement limit.

Claims (5)

1. a precoding side based on CSM (Cholesky-Decompositionand Sherman-Morrison lemma) Method, it is characterised in that:

By abstract for the scene canonical system model for Massive MIMO, under Different Modulations, obtain its channel status respectively Information (CSI), and utilize Cholesky to decompose with Sherman-Morrison iteration to calculate inverse of a matrix.Carry at this patent Under the operating process gone out and algorithmic model, carry out the calculating of pre-coding matrix with relatively low computation complexity, complete transmission information Precoding.

2. the method for claim 1, it is characterised in that: its multiple debud mode is respectively as follows: TDD, FDD and full duplex (simultaneously with frequency, use TDD and FDD modulation system the most simultaneously), and utilize the feature of different modulating mode to obtain channel status Information (CSI).

3. the method for claim 1, it is characterised in that operating process and algorithmic model: utilize the flow work of hardware Feature, to needing the matrix W inverted to carry out the matrix L that Cholesky decomposition obtains decomposing in precoding process, then utilizes this specially Matrix L is decomposed and uses Sherman-Morrison iteration to try to achieve the inverse of L by the matrix twice decomposition mode proposed in profit, Finally try to achieve the inverse of matrix W again.

4. method as claimed in claim 3, it is characterised in that: meet W=when precoding process needs the matrix W inverted H·H^HDuring+ω I (that is: meeting finding the inverse matrix is positively definite hermitian matrix), when such as method for precoding is RZF or MMSE Matrix just meets this condition, then proposition CSM algorithm in this patent can be used to try to achieve the inverse of W, and grasp eventually through this precoding Process of making carries out precoding processing to sending signal.

5. method as claimed in claim 3, it is characterised in that: utilize the pipeline work of hardware that matrix W is carried out Cholesky decomposes, and is allowed to the form becoming reducing computation complexity, i.e. obtains matrix L.Recycling this patent proposes Matrix L is done twice decomposition deformation by mode, in order to utilize Sherman-Morrison mode to be iterated, thus in terms of relatively low Calculate complexity and obtain the result being better than current algorithm performance.