CN109743090A - A kind of fast algorithm of non-code book linear predictive coding - Google Patents

Abstract

The present invention provides a kind of fast algorithms of non-code book linear predictive coding, comprising the following steps: S1, the QR with displacement are decomposed；The method for precoding that S2, SVD singular value decomposition are combined with power water injection technology.The beneficial effects of the present invention are: solving the problems, such as that matrix convergence is slow, operand is huge.

Description

A kind of fast algorithm of non-code book linear predictive coding

Technical field

The present invention relates to communication more particularly to a kind of fast algorithms of non-code book linear predictive coding.

Background technique

With constantly advancing for society, demand of the people to mobile Internet is also continuously increased, mobile Internet weight Life newly is moulded, " being in cannot be without network, and mobile phone cannot be left behind by going out " has become the common impression of many people.It is higher Rate, bigger capacity requirement push always the development of development of Mobile Internet technology.

Mobile more only technologies are from FDMA, TDMA to CDMA, then arrive OFDMA, and the utilization rate of frequency spectrum resource is higher and higher, frequency spectrum The utilization rate of resource has performed to ultimate attainment, and frequency spectrum resource is limited, and in certain frequency range, SISO is point-to-point Running time-frequency resource has been difficult to bigger revolutionary breakthrough, and the MIMO technology of multiple-input and multiple-output can be realized and expand to space Power system capacity is opened up, therefore, MIMO technology is an important topic of Future Mobile Communication development.

MIMO precoding technique is a kind of pre- to data to be sent progress in the transmitting terminal of system according to channel state information The technology of processing, the technology can effectively inhibit the interference between parallel signal, provide system stability and reliability Meanwhile, it is capable to largely simplify the processing complexity of receiving end.The operation carried out according to receiver is different, and MIMO prelists Code technology is divided into linear predictive coding and nonlinear precoding technology.Linear Precoding obtains position according to pre-coding matrix again Difference and be divided into codebook-based precoding technique and the precoding technique based on non-code book.

Precoding technique based on non-code book, can be more fully as long as channel estimation is accurate because its code book is unrestricted Using instant channel state information, precoding processing is carried out to information to be sent, therefore obtain bigger development space, at For current research emphasis.

However, the premise that the precoding technique based on non-code book can play its advantage is that channel estimation is accurate, in channel Many matrix operations involved in estimation, such as: ask characteristic value, ask feature vector, battle array of inverting, matrix orthogonalization, matrix rotation, How matrix decomposition etc. quickly and accurately estimates instant channel status, becomes the pass of the precoding technique based on non-code book Key, operand is excessive, may cause the generation of two problems: first is that channel estimation is not in time；Second is that channel estimation is inaccurate.

Based on the precoding technique of non-code book, when channel estimation, channel decomposing, generally requires and asks characteristic value, feature vector, To obtain the orthogonal matrix of channel relevancy, the decomposition to channel is realized.

Currently characteristic value, the method for feature vector is asked to have very much, such as power method, inverse power method, Jacobi method etc., but all There is a problem of one it is common, operand is huge, and under the premise of limited computation amount, there are certain error, precision for required characteristic value Not enough, cause channel decomposing inaccurate.

Therefore, if solve operand it is huge, matrix restrain slow problem be those skilled in the art it is urgently to be resolved Technical problem.

Summary of the invention

In order to solve the problems in the prior art, the present invention provides a kind of fast algorithms of non-code book linear predictive coding.

The present invention provides a kind of fast algorithms of non-code book linear predictive coding, comprising the following steps:

S1, the QR with displacement are decomposed；

The method for precoding that S2, SVD singular value decomposition are combined with power water injection technology.

As a further improvement of the present invention, step S1 includes following sub-step:

S11, basic QR decomposition method；

The simplification of S12, general matrix；

The QR algorithm of S13, quasi- upper triangular matrix；

S14, the QR decomposition method with displacement.

As a further improvement of the present invention, step S11 includes:

Enable A₀=A decomposes A to k=1,2 ..._k-1=Q_k-1R_k-1；

Enable A_k=R_k-1Q_k-1, wherein Q_k-1For orthogonal matrix, R_k-1For upper triangular matrix；

Obtained matrix sequence A_kIt is similar to A, to have identical characteristic value in A, this is because A_k-1=Q_k-1R_k-1, Q_k-1It is reversible, thereforeTo

Matrix sequence A under certain condition_kSubstantially piecemeal upper triangular matrix R is converged on,

Wherein diagonal sub-block R₁₁Work as R for 1x1 or 2x2 matrix_iiWhen for single order square matrix, R_iiIt is exactly the characteristic value of A；Work as R_iiFor When square Matrix, characteristic value is a pair of of conjugate complex number and the characteristic value of A.

As a further improvement of the present invention, step S12 includes:

General matrix A is first reduced to quasi- upper triangular matrix, also known as Hessenberg matrix, i.e., element is complete below minor diagonal For 0 Special matrix；

The process for simplifying Householder matrix is as follows:

H=I-2uu^T

Wherein, u isUnit vector, easily demonstrate,prove its symmetrical, positive definite:

H^T=(I-2uu^T)^T=I-2uu^T=H

H^TH=(I-2uu^T)(I-2uu^T)

=I-2uu^T-2uu^T+4u(u^Tu)u^T

=I-4uu^T+4uu^T=l

Therefore, the linear transformation y=Hx of vector x must keep modular invariance: | | y | |₂=| | x | |₂,

Therefore, it is converted with Householder known vector a=(a₁ a₂ … a_n)^TBecome b=(a₁ a₂ … a_r c 0 … 0)^T, only need to enable

C should meet herein:

Therefore

A-b=(0 ... 0 a_r+1 -c a_r+2 … a_n)^T

It takes

Then

So

For any vector,

The Householder determined by above-mentioned formula, which is converted, becomes x

Wherein,

The rear n-r-1 component of direction vector a is become the Householder transformation that 0, preceding n component remains unchanged, is applied When any vector x, preceding r component is also remained unchanged, and rear n-r component then calculates according to the above method；

It is converted using this Householder, Arbitrary Matrix A can be turned to similar quasi- upper triangular matrix, steps are as follows:

Make Householder matrix H₁, make H₁A first element of each column is constant, but makes each below second element of first row Element becomes 0, at this point, H₁A becomes following shape:

Make matrix

Then because of H₁For orthogonal matrix, necessarily have

Show A₁~A andIt is H₁The same Householder matrix H of A₁Matrix obtained by premultiplication, thereforeThe first row is constant, A₁First row is constant, thus the similar matrix A of A₁Still have shaped like above-mentioned H₁The matrix form of A remakes Householder matrix H₂, so that H₂A₁First and second element of each column is constant, i.e. A₁First and second row is constant, but makes each below secondary series third element Element becomes 0, and each element still becomes 0 below first row third element at this time, therefore H₂A₁Become lower shape:

Show A₂~A₁AndIt is H₂A₁With same Householder matrix H₂Matrix obtained by premultiplication, thereforeThe first, Two rows are constant, A₂First and second column it is constant, thus the similar matrix A of A₂Still have shaped like above-mentioned H₂A₁Matrix form, so It continues, it is at most left and right to multiply n-2 times, A is just melted into similar quasi- upper triangular matrix A_n-2。

As a further improvement of the present invention, step S13 includes:

Choose spin matrix P₁=R (2,1, θ₁), make A⁽¹⁾=P₁A_k-1First row time diagonal element

Spin matrix P is chosen again₂=R (3,2, θ₂), make A⁽²⁾=P₂A⁽¹⁾Diagonal element... so continue Go down, is at most walked through n-1, A^(n-1)Necessarily become upper triangular matrix R_k-1, i.e.,

P_n-1…P₂P₁A_k-1=R_k-1

In above-mentioned decomposable process, with spin matrix R (i+1, i, θ_i) premultiplication A^(i-1)Become A⁽ⁱ⁾, only i-th, i+1 row becomes It turns to

To makeθ should be chosen_iMake

Therefore

Therefore, by A_k-1, A⁽ⁱ⁾, R_k-1It is stored in A, decomposable process is written as:

To i=1~n-1, do

1) it enables

2) it to j=i~n, enables

QR algorithm calculates A_k=R_k-1Q_k-1When, it is noted that

Know A_kIt can be by R_k-1The right side multipliesIt completes, therefore calculating process are as follows:

To i=1~n-1, do

To j=i, i+1, enable

Above-mentioned two process is repeated, until A_kBecome approximate Shu Er matrix, can obtain the approximate eigenvalue of A.

As a further improvement of the present invention, step S14 includes:

Enable A₀=A, A are quasi- triangular matrixes, decompose A to k=1,2 ..._k-1-μ_k-1I=Q_k-1R_k-1, enable A_k=R_k-1Q_k-1+μ_{k- 1}L, herein μ_k-1Referred to as shift amount is taken as a certain characteristic value of A；

A is taken as when engineering calculation_k-1Lower right corner elementOr it is taken as approaching in the 2x2 matrix exgenvalue of the lower right cornerPerson；

According to assumed above

Because of A_k-1-μ_k-1I=Q_k-1R_k-1

Have

Then have

Obvious A_kIt is still the similar matrix of A.

As a further improvement of the present invention, step S2 includes the method for precoding based on non-code book of down direction, should The process of the method for precoding based on non-code book of down direction is as follows:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains Channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and precoding square is determined to channel matrix decomposition Battle array；

4, eNodeB implements pre-encode operation；

5, eNodeB sends the data and dedicated pilot of precoding；

6, UE receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute channel, solves Adjusting data symbol.

Step S2 includes the method for precoding based on non-code book of up direction, the up direction based on the pre- of non-code book The process of coding method is as follows:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains Channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and precoding square is determined to channel matrix decomposition Battle array；

4, precoding matrix information obtained is sent opposite end UE by eNodeB；

5, UE implements pre-encode operation according to precoding matrix information obtained；

6, UE sends the data and dedicated pilot of precoding；

7, eNodeB receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute to channel Meter, demodulating data symbols.

As a further improvement of the present invention, step S2 uses the method based on singular value decomposition and realizes to precoding square The acquisition of battle array is resolved into mimo channel multiple mutually independent by carrying out singular value decomposition to channel matrix obtained Equivalent MIMO subchannel.

As a further improvement of the present invention, in step S2, the process of singular value decomposition is as follows:

The first step, it is assumed that system is the aerial array of MxN sending and receiving, and M root antenna receives, the transmitting of N root antenna, channel matrix Order for H, channel matrix H is k=Rank (H), and k≤min (m, n) then has channel relevancy matrix H^TH；

Second step is decomposed according to based on the QR with displacement, to channel relevancy matrix H^TH solve characteristic value and feature to Amount remembers that the characteristic value of non-zero is λ₁、λ₂、…、λ_k；Remember that corresponding feature vector is v₁、v₂、…、v_k, to v₁、v₂、…、v_kExpanded Open up v_k+1、…、v_n, this n-k vector be present in the kernel of H, i.e. the base of the solution space of Hx=0, so that v₁、v₂、…、v_nFor One group of orthogonal basis in n-dimensional space constitutes orthogonal matrix V；

Third step takes unit vector:

As k < i≤m, to u₁、u₂、…、u_kIt is extended u_(k+1)、…、u_mFor one group of orthogonal basis in m-dimensional space；

Gained u₁、u₂、…、u_nMatrix U is constituted,

NoteWith σ₁、σ₂、…、σ_kFor the diagonal element of top left region, the diagonal matrix of diagonal matrix mxn is constructed ∑:

4th step, the then singular value decomposition of channel matrix H are as follows:

And then the singular value decomposition of available H-matrix:

H=U ∑ V^T

V is the orthogonal matrix of nxn, and U is the orthogonal matrix of mxm, and ∑ is the diagonal matrix of mxn；

5th step, according to the singular value decomposition for entering matrix H, available pre-coding matrix:

W=V；

Power water injection technology comprises the following processes:

The first step combines SVD precoding with power water injection technology, and power water filling passes through the subchannel to mimo system Specific power is distributed to increase the signal-to-noise ratio of poor subchannel, to obtain power system capacity more higher than average power allocation With preferable bit error rate performance, constraint condition are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel；

Mimo system capacity after sending power normalization is expressed as:

Wherein λ_iIndicate channel relevancy matrix H^TI-th of element on the diagonal line of H,

σ²For system noise, capacity obtains the constraint condition of maximum value are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel, meet P_i>=0,η is a constant, with derivation Mode can determine during seeking C maximum capacity；

Second step, the pre-coding matrix after power water filling is added are as follows:

W=VP^1/2。

The beneficial effects of the present invention are: solving the problems, such as that matrix convergence is slow, operand is huge.

Detailed description of the invention

Fig. 1 is a kind of pre-coding scheme system based on non-code book of the fast algorithm of non-code book linear predictive coding of the present invention Model, the schematic diagram of downlink precoding.

Fig. 2 is a kind of pre-coding scheme system based on non-code book of the fast algorithm of non-code book linear predictive coding of the present invention Model, the schematic diagram of uplink precoding.

Fig. 3 is that a kind of downlink of the precoding based on non-code book of the fast algorithm of non-code book linear predictive coding of the present invention is more The schematic diagram of antenna transmission.

Fig. 4 is that a kind of uplink of the precoding based on non-code book of the fast algorithm of non-code book linear predictive coding of the present invention is more The schematic diagram of antenna transmission.

Fig. 5 is a kind of schematic diagram of the power water-filling algorithm of the fast algorithm of non-code book linear predictive coding of the present invention.

Specific embodiment

The invention will be further described for explanation and specific embodiment with reference to the accompanying drawing.

As shown in Figures 1 to 5, a kind of fast algorithm of non-code book linear predictive coding, comprising the following steps:

S1, the QR with displacement are decomposed, and the QR decomposition of band displacement realizes characteristic value to correlation matrix, feature vector Rapid solving；

The method for precoding that S2, SVD singular value decomposition are combined with power water injection technology, SVD singular value decomposition realize Decomposition to channel matrix generates corresponding precoding information, effectively relieves multi-antenna array according to the characteristic of channel matrix The correlation of middle interchannel, so that MIMO spatial reuse is effectively realized, lifting system capacity.

Step S1 includes following sub-step:

S11, basic QR decomposition method, the feature value-acquiring method of matrix A have very much, and QR decomposition is that one of which relatively has The method of effect；

The simplification of S12, general matrix；

The QR algorithm of S13, quasi- upper triangular matrix；

S14, the QR decomposition method with displacement.

As a further improvement of the present invention, step S11 includes:

Enable A₀=A decomposes A to k=1,2 ..._k-1=Q_k-1R_k-1；

Enable A_k=R_k-1Q_k-1, wherein Q_k-1For orthogonal matrix, R_k-1For upper triangular matrix；

Obtained matrix sequence A_kIt is similar to A, to have identical characteristic value in A, this is because A_k-1=Q_k-1R_k-1, Q_k-1It is reversible, thereforeTo

Matrix sequence A under certain condition_kSubstantially piecemeal upper triangular matrix R is converged on,

Wherein diagonal sub-block R₁₁Work as R for 1x1 or 2x2 matrix_iiWhen for single order square matrix, R_iiIt is exactly the characteristic value of A；Work as R_iiFor When square Matrix, characteristic value is a pair of of conjugate complex number and the characteristic value of A.

Step S12 includes:

The each step of QR method requires to decompose A_k-1=Q_k-1R_k-1And calculate A_k-1=Q_k-1R_k-1, operand is very big.To save General matrix A is first reduced to quasi- upper triangular matrix, also known as Heisenberg (Hessenberg) matrix by operand, i.e., secondary diagonal Element is all 0 Special matrix below line；

The process for simplifying Householder matrix is as follows:

H=I-2uu^T

Wherein, u isUnit vector, easily demonstrate,prove its symmetrical, positive definite:

H^T=(I-2uu^T)^T=I-2uu^T=H

H^TH=(I-2uu^T)(I-2uu^T)

=I-2uu^T-2uu^T+4u(u^Tu)u^T

=I-4uu^T+4uu^T=I

Therefore, the linear transformation y=Hx of vector x must keep modular invariance: | | y | |₂=| | x | |₂,

Therefore, it is converted with Householder known vector a=(a₁ a₂ … a_n)^TBecome b=(a₁ a₂ … a_r c 0 … 0)^T, only need to enable

C should meet herein:

Therefore

A-b=(0 ... 0 a_r+1-c a_r+2 … a_n)^T

It takes

Then

So

For any vector,

The Householder determined by above-mentioned formula, which is converted, becomes x

Wherein,

The rear n-r-1 component of direction vector a is become the Householder transformation that 0, preceding n component remains unchanged, is applied When any vector x, preceding r component is also remained unchanged, and rear n-r component then calculates according to the above method；

It is converted using this Householder, Arbitrary Matrix A can be turned to similar quasi- upper triangular matrix, steps are as follows:

Make Householder matrix H₁, make H₁A first element of each column is constant, but makes each below second element of first row Element becomes 0, at this point, H₁A becomes following shape:

Make matrix

Then because of H₁For orthogonal matrix, necessarily have

Show A₁~A andIt is H₁The same Householder matrix H of A₁Matrix obtained by premultiplication, thereforeThe first row is not Become, A₁First row is constant, thus the similar matrix A of A₁Still have shaped like above-mentioned H₁The matrix form of A remakes Householder square Battle array H₂, so that H₂A₁First and second element of each column is constant, i.e. A₁First and second row is constant, but makes below secondary series third element Each element becomes 0, and each element still becomes 0 below first row third element at this time, therefore H₂A₁Become lower shape:

Show A₂~A₁AndIt is H₂A₁With same Householder matrix H₂Matrix obtained by premultiplication, thereforeFirst and second Constant, the A of row₂First and second column it is constant, thus the similar matrix A of A₂Still have shaped like above-mentioned H₂A₁Matrix form, so after Continue down, it is at most left and right to multiply n-2 times, A is just melted into similar quasi- upper triangular matrix A_n-2。

Step S13 includes:

To quasi- upper triangular matrix QR algorithm, the matrix sequence A of generation_kAll it is quasi- upper triangular matrix, calculation amount can be saved in this way.

Choose spin matrix P₁=R (2,1, θ₁), make A⁽¹⁾=P₁A_k-1First row time diagonal element

Spin matrix P is chosen again₂=R (3,2, θ₂), make A⁽²⁾=P₂A⁽¹⁾Diagonal element... so continue Go down, is at most walked through n-1, A^(n-1)Necessarily become upper triangular matrix R_K-1, i.e.,

p_n-1…P₂P₁A_k-1=R_k-1

In above-mentioned decomposable process, with spin matrix R (i+1, i, θ_i) premultiplication A^(i-1)Become A⁽ⁱ⁾, only i-th, i+1 row becomes It turns to

To makeθ should be chosen_iMake

Therefore

Therefore, by A_k-1, A⁽ⁱ⁾, R_k-1It is stored in A, decomposable process is written as:

To i=1~n-1, do

1) it enables

2) it to j=i~n, enables

QR algorithm calculates A_k=R_k-1Q_k-1When, it is noted that

Know A_kIt can be by R_k-1The right side multipliesIt completes, therefore calculating process are as follows:

To i=1~n-1, do

To j=i, i+1, enable

Above-mentioned two process is repeated, until A_kBecome approximate Shu Er matrix, can obtain the approximate eigenvalue of A.

Step S14 includes:

Enable A₀=A, A are quasi- triangular matrixes, decompose A to k=1,2 ..._k-1-μ_k-1I=Q_k-1R_k-1, enable A_k=R_k-1Q_k-1+μ_{k- 1}I, herein μ_k-1Referred to as shift amount is taken as a certain characteristic value of A；

A is taken as when engineering calculation_k-1Lower right corner elementOr it is taken as approaching in the 2x2 matrix exgenvalue of the lower right cornerPerson；

According to assumed above

Because of A_k-1-μ_k-1I=Q_k-1R_k-1

Have

Then have

Obvious A_kIt is still the similar matrix of A.

Understand from mathematics, engineering viewpoint, A_k-1=μ_k-1I is relative to A_k-1, A_k-1-μ_k-1Pair that I has been equivalent to matrix smaller Component on linea angulata, to increase " dynamics " rotated in the QR algorithm of quasi- upper triangular matrix, that is, the θ rotated_iAngle, this Point is from algorithm to θ_iCalculating it can be seen that

It is smaller, θ_iBigger, under limiting case, 90 degree of rotation adjustment is equivalent to the energy on quasi- diagonal line is complete It is added on diagonal line.

Based on the QR method with displacement, matrix sequence A_kIt is restrained rapidly, significantly reduces operand, in limited computation Under conditions of amount, the precision of obtained characteristic value is obviously improved, and then calculating feature vector is more accurate, to channel correlation matrix H^HThe calculating of the orthogonal basis V of H is also more accurate.

Based on the QR method of above band displacement, the characteristic value of matrix is obtained, and then passes through the solution available square of linear equation The feature vector of battle array, the method for solving linear equation is simple, has highly developed algorithm at present and realizes which is not described herein again.

It should be noted that for real symmetric matrix, different eigenvalue λs_i, corresponding feature vector is mutually orthogonal , and for identical eigenvalue λ_i, corresponding feature vector is linear independence, needs to be orthogonalized processing, specifically Schimdt orthogonalization method can be used, which is not described herein again.

In step s 2, in the Linear Precoding based on code book and based on non-code book, the acquisition side of pre-coding matrix Formula is completely different: in codebook-based pre-coding scheme, receiving end is according to channel state information, in the existing codebook set of system It is middle to choose the code book for being best suitable for system requirements, and the PMI value of the code book is fed back into transmitting terminal；And the precoding based on non-code book In scheme, transmitting terminal is pre- to obtain by carrying out the decomposition on data sense to channel matrix according to channel status channel information Encoder matrix.What the present invention discussed is the specific implementation of the pre-coding scheme based on non-code book.

It is the pre-coding scheme system model based on non-code book of down direction as shown in Figure 1, which includes two serious offenses Journey: pre-coding matrix operating process and pre-encode operation process, specific implementation process include the following steps:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains Channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and precoding square is determined to channel matrix decomposition Battle array；

4, eNodeB implements pre-encode operation；

5, eNodeB sends the data and dedicated pilot of precoding, is embodied if Fig. 3 is " the precoding based on non-code book Shown in downlink multi-antenna transmission "；

6, UE receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute channel, solves Adjusting data symbol.

It is the pre-coding scheme system model based on non-code book of up direction as shown in Figure 2, which includes two serious offenses Journey: pre-coding matrix operating process and pre-encode operation process, specific implementation process include the following steps:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains Channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and precoding square is determined to channel matrix decomposition Battle array；

4, precoding matrix information obtained is sent opposite end UE by eNodeB；

5, UE implements pre-encode operation according to precoding matrix information obtained；

6, UE sends the data and dedicated pilot of precoding, specific implementation such as Fig. 4 " uplink of the precoding based on non-code book Shown in multi-antenna transmission "；

7, eNodeB receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute to channel Meter, demodulating data symbols.

The key point of embodiments above is the acquisition and precoding of the pre-coding matrix based on current channel condition Power distribution reasonability problem.

Present invention employs the methods based on singular value decomposition (SVD) to realize the acquisition to pre-coding matrix, by institute The channel matrix of acquisition carries out SVD decomposition, and mimo channel is resolved into multiple mutually independent equivalent MIMO subchannels, by To non-interfering subchannel achieve the purpose that eliminate inter-antenna interference, the channel capacity of simultaneity factor also gets a promotion.

In step s 2, the process that singular value (SVD) is decomposed is as follows:

The first step, it is assumed that system is the aerial array of MxN sending and receiving, and M root antenna receives, the transmitting of N root antenna, channel matrix Order for H, channel matrix H is k=Rank (H), and k≤min (m, n) then has channel relevancy matrix H^TH；

Second step is decomposed according to based on the QR with displacement, to channel relevancy matrix H^TH solve characteristic value and feature to Amount remembers that the characteristic value of non-zero is λ₁、λ₂、…、λ_k；Remember that corresponding feature vector is v₁、v₂、…、v_k, to v₁、v₂、…、v_kExpanded Open up v_k+1、…、v_n, this n-k vector be present in the kernel of H, i.e. the base of the solution space of Hx=0, so that v₁、v₂、…、v_nFor One group of orthogonal basis in n-dimensional space constitutes orthogonal matrix V；

Third step takes unit vector:

As k < i≤m, to u₁、u₂、…、u_kIt is extended u_(k+1)、…、u_mFor one group of orthogonal basis in m-dimensional space；

Gained u₁、u₂、…、u_nMatrix U is constituted,

NoteWith σ₁、σ₂、…、σ_kFor the diagonal element of top left region, the diagonal matrix of diagonal matrix mxn is constructed ∑:

4th step, the then singular value decomposition of channel matrix H are as follows:

And then the singular value decomposition of available H-matrix:

H=U ∑ V^T

V is the orthogonal matrix of nxn, and U is the orthogonal matrix of mxm, and ∑ is the diagonal matrix of mxn；

It is convenient to discuss, once realize consider be NxN antenna full rank the case where, processing method class the case where non-full rank Seemingly, it is only necessary to be suitably modified.

5th step, according to the singular value decomposition for entering matrix H, available pre-coding matrix:

W=V；

Power water injection technology comprises the following processes:

The first step, 1, since there are biggish difference, each sub- letters for the signal-to-noise ratio between each subchannel for being decomposed based on SVD The gain coefficient in road influences the bit error rate performance and volumetric properties of system, therefore the error rate of system performance ratio of poor subchannel again Poor, capacity also will receive biggish loss.In view of this, the present invention combines SVD precoding with power water injection technology, function Rate water filling increases the signal-to-noise ratio of poor subchannel by the specific power of subchannel distribution to mimo system, to obtain Power system capacity more higher than average power allocation and preferable bit error rate performance, constraint condition are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel；

Mimo system capacity after sending power normalization is expressed as:

Wherein λ_iIndicate channel relevancy matrix H^TI-th of element on the diagonal line of H,

σ²For system noise, capacity obtains the constraint condition of maximum value are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel, meet P_i>=0,η is a constant, in the hope of The mode of leading can determine during seeking C maximum capacity；

Second step, the pre-coding matrix after power water filling is added are as follows:

W=VP^1/2

Here it is the finally obtained precoding squares for reaching mimo system maximum capacity of the technical solution through the invention Battle array.

It is illustrated below with the performance that a calculated examples optimize QR decomposition algorithm.

Assuming that there is matrix A

1, it is converted using Householder and matrix A is turned into similar quasi- upper triangular matrix, to be become with Householder Change the first row (- 12 1) A^TBecome (- 1 c 0)^T, according to equations

Then

2, the characteristic value of quasi- upper triangular matrix is sought using traditional QR algorithm

c₁=cos θ₁

s₁=sin θ₁

Then

It enables

c₂=cos θ₂, s₂=sin θ₂

Then

Therefore

It can similarly obtain

By 88 interative computations, to obtain the characteristic value of matrix:

λ₁=-6.421066621

λ₂=-4.866925530

λ₃=0.287992139

From present case as it can be seen that A_kAfter 88 interative computations, diagonal matrix is finally converged to, very slow (but the phase of convergence rate For power method, inverse power method, Jacobi method at last more effectively a kind of method.

3, the QR method rapid solving with displacement is utilized

One displacement of solution measures lower right corner element, enables μ₀=-6.4 are decomposed

Wherein

θ₁=-0.392590761

θ₂=-0.114997409

?

Similarly

By 15 interative computations, to obtain the characteristic value of matrix:

λ₁=0.287992138

λ₂=-4.866925525

λ₃=-6.421066615

A_kAfter 15 interative computations, diagonal matrix is finally converged to, convergence rate is obviously improved.Solve two displacement μ_k-1 It is taken as lower right corner 2x2 matrix exgenvalue.

It enables

μ₀=-6.469693846

It is obtained similar to Xie Yike

It can similarly obtain

By 13 interative computations, to obtain the characteristic value of matrix:

λ₁=0.287992139

λ₂=-4.866925526

λ₃=-6.421066615

A_kAfter 13 interative computations, diagonal matrix is finally converged to, convergence rate is obviously improved.

Compare the operand of both algorithms.

1, general QR decomposition method convergence is slow, it can be seen that a simple 3x3 matrix, by 88 interative computations Afterwards, the feature vector λ of matrix is finally obtained₁、λ₂、λ₃。

2, using the QR decomposition method with displacement, convergence rate is obviously accelerated, the 3x3 matrix in example, by 13~15 After secondary interative computation, the feature vector λ of matrix is finally obtained₁、λ₂、λ₃。

The MIMO technology of LTE could support up 8x8 aerial array at present, and usually each subframe (i.e. 1ms) needs to carry out primary Channel estimation, according to algorithm, NxN antenna operand is, a simple 3x3 matrix, by 88 time increased according to square number After interative computation, the feature vector of matrix is finally obtained, it is generally the case that a 8x8 matrix is needed by 500 magnitudes Interative computation can be completed, final convergence obtains the feature vector of matrix.

Further, a large amount of Householder is related to for interative computation each time according to above-mentioned derivation process Transformation, spin matrix operation, and all these operations, eNodeB, especially UE needs are completed in 1ms, it can be seen that, operation Amount is huge.

Referring again to seeing, using the QR decomposition method with displacement, as soon as 8x8 matrix, needing can be complete by about 100 magnitudes At interative computation, operand successively decreases 80% and reaches same computational accuracy, undoubtedly dramatically reduces.

(2) SVD singular value decomposition and power water filling combine the performance evaluation of precoding

According to the mimo system capacity expression after transmission power normalization:

Since channel is objective reality, can not artificially change namely λ_iIt is determining.

Power system capacity C will reach maximum value, then P_iIt wants and λ_iMatch.

λ_iIt is bigger, illustrate that channel gain is bigger, the power for needing to distribute is bigger, so that the potential of channel is given full play to, it is real The maximum transmitted of existing information.

Fig. 5 is power water filling schematic diagram, and the power distribution of power water-filling algorithm is exactly to be carried out according to the gain of subchannel, The more power specific gravity of the preferable subchannel distribution of channel condition, on the contrary, the subchannel distribution specific gravity to bad channel conditions is lower Or not distribution power.

It in scheme of the present invention, is obtained in a manner of derivation, capacity obtains the constraint condition of maximum value are as follows:

To theoretically demonstrate, the power scheme can get maximum system capacity C.

The present invention provides a kind of fast algorithm of non-code book linear predictive coding, " the side QR with displacement decomposed based on QR Method " introduces a μ displacement to the matrix decomposed, chooses the lower right corner element a of matrix_nnOr take lower right corner 2x2 matrix character Close to a in value_nnPerson realizes that the acceleration to matrix A restrains as μ displacement, with lesser operand, to realize to channel The accurate decomposition of SVD singular value, using most suitable precoding technique, finally realizes pair according to estimated channel status The promotion of channel capacity.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention Protection scope.

Claims (10)

1. a kind of fast algorithm of non-code book linear predictive coding, which comprises the following steps:

S1, the QR with displacement are decomposed；

The method for precoding that S2, SVD singular value decomposition are combined with power water injection technology.

2. the fast algorithm of non-code book linear predictive coding according to claim 1, which is characterized in that step S1 includes following Sub-step:

S11, basic QR decomposition method；

The simplification of S12, general matrix；

The QR algorithm of S13, quasi- upper triangular matrix；

S14, the QR decomposition method with displacement.

3. the fast algorithm of non-code book linear predictive coding according to claim 2, which is characterized in that step S11 includes:

Enable A₀=A decomposes A to k=1,2 ..._k-1=Q_k-1R_k-1；

Enable A_k=R_k-1Q_k-1, wherein Q_k-1For orthogonal matrix, R_k-1For upper triangular matrix；

Obtained matrix sequence A_kIt is similar to A, to have identical characteristic value in A, this is because A_k-1=Q_k-1R_k-1, Q_k-1It can It is inverse, thereforeTo

Matrix sequence A under certain condition_kSubstantially piecemeal upper triangular matrix R is converged on,

Wherein diagonal sub-block R₁₁Work as R for 1x1 or 2x2 matrix_iiWhen for single order square matrix, R_iiIt is exactly the characteristic value of A；Work as R_iiFor second order When square matrix, characteristic value is a pair of of conjugate complex number and the characteristic value of A.

4. the fast algorithm of non-code book linear predictive coding according to claim 3, which is characterized in that step S12 includes:

General matrix A is first reduced to quasi- upper triangular matrix, also known as Hessenberg matrix, i.e., element is all 0 below minor diagonal Special matrix；

The process for simplifying Householder matrix is as follows:

H=I-2uu^T

Wherein, u isUnit vector, easily demonstrate,prove its symmetrical, positive definite:

H^T=(I-2uu^T)^T=I-2uu^T=H

H^TH=(I-2uu^T)(I-2uu^T)

=I-2uu^T-2uu^T+4u(u^Tu)u^T

=I-4uu^T+4uu^T=I

Therefore, the linear transformation y=Hx of vector x must keep modular invariance: | | y | |₂=| | x | |₂,

Therefore, it is converted with Householder known vector a=(a₁ a₂ … a_n)^TBecome b=(a₁ a₂ … a_r c 0 … 0)^T, only need to enable

H=I-2uu^T

C should meet herein:

Therefore

A-b=(0 ... 0 a_r+1-c a_r+2…a_n)^T

It takes

Then

So

For any vector,

The Householder determined by above-mentioned formula, which is converted, becomes x

Wherein,

The rear n-r-1 component of direction vector a is become the Householder transformation that 0, preceding n component remains unchanged, imposes on and appoints When vector x of anticipating, preceding r component is also remained unchanged, and rear n-r component then calculates according to the above method；

It is converted using this Householder, Arbitrary Matrix A can be turned to similar quasi- upper triangular matrix, steps are as follows:

Make Householder matrix H₁, make H₁A first element of each column is constant, but makes each element below second element of first row Become 0, at this point, H₁A becomes following shape:

Make matrix

Then because of H₁For orthogonal matrix, necessarily have

Show A₁~A andIt is H₁The same Householder matrix H of A₁Matrix obtained by premultiplication, thereforeThe first row is constant, A₁The One column are constant, thus the similar matrix A of A₁Still have shaped like above-mentioned H₁The matrix form of A remakes Householder matrix H₂, make Obtain H₂A₁First and second element of each column is constant, i.e. A₁First and second row is constant, but becomes each element below secondary series third element It is 0, each element still becomes 0 below first row third element at this time, therefore H₂A₁Become lower shape:

Show A₂~A₁AndIt is H₂A₁With same Householder matrix H₂Matrix obtained by premultiplication, thereforeFirst and second it is capable not Become, A₂First and second column it is constant, thus the similar matrix A of A₂Still have shaped like above-mentioned H₂A₁Matrix form, under so continuing It goes, it is at most left and right to multiply n-2 times, A is just melted into similar quasi- upper triangular matrix A_n-2。

5. the fast algorithm of non-code book linear predictive coding according to claim 4, which is characterized in that step S13 includes:

Choose spin matrix P₁=R (2,1, θ₁), make A⁽¹⁾=P₁A_k-1First row time diagonal element

Spin matrix P is chosen again₂=R (3,2, θ₂), make A⁽²⁾=P₂A⁽¹⁾Diagonal element... so continue, It is at most walked through n-1, A^(n-1)Necessarily become upper triangular matrix R_k-1, i.e.,

P_n-1…P₂P₁A_k-1=R_k-1

In above-mentioned decomposable process, with spin matrix R (i+1, i, θ_i) premultiplication A^(i-1)Become A⁽ⁱ⁾, only i-th, i+1 row, which changes, is

To makeθ should be chosen_iMakeTherefore

Therefore, by A_k-1, A⁽ⁱ⁾, R_k-1It is stored in A, decomposable process is written as:

To i=1~n-1, do

1) it enables

2) it to j=i~n, enables

QR algorithm calculates A_k=R_k-1Q_k-1When, it is noted that

Know A_kIt can be by R_k-1The right side multipliesIt completes, therefore calculating process are as follows:

To i=1~n-1, do

To j=i, i+1, enable

Above-mentioned two process is repeated, until A_kBecome approximate Shu Er matrix, can obtain the approximate eigenvalue of A.

6. the fast algorithm of non-code book linear predictive coding according to claim 1, which is characterized in that step S14 includes:

Enable A₀=A, A are quasi- triangular matrixes, decompose A to k=1,2 ..._k-1-μ_k-1I=Q_k-1R_k-1, enable A_k=R_k-1Q_k-1+μ_k-1I, this Locate μ_k-1Referred to as shift amount is taken as a certain characteristic value of A；

A is taken as when engineering calculation_k-1Lower right corner elementOr it is taken as approaching in the 2x2 matrix exgenvalue of the lower right corner Person；

According to assumed above

Because of A_k-1-μ_k-1I=Q_k-1R_k-1

Have

Then have

Obvious A_kIt is still the similar matrix of A.

7. the fast algorithm of non-code book linear predictive coding according to claim 1, it is characterised in that: step S2 includes downlink The process of the method for precoding based on non-code book in direction, the method for precoding based on non-code book of the down direction is as follows:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and pre-coding matrix is determined to channel matrix decomposition；

4, eNodeB implements pre-encode operation；

5, eNodeB sends the data and dedicated pilot of precoding；

6, UE receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute channel, demodulates number According to symbol.

8. the fast algorithm of non-code book linear predictive coding according to claim 1, it is characterised in that: step S2 includes uplink The process of the method for precoding based on non-code book in direction, the method for precoding based on non-code book of the up direction is as follows:

1, UE sends uplink SRS detecting pilot frequency signal；

2, eNodeB receives uplink SRS detecting pilot frequency signal, carries out channel estimation according to the received pilot signal of institute, obtains channel CSI status information；

3, it is based on CSI channel state information, channel relevancy matrix is solved and pre-coding matrix is determined to channel matrix decomposition；

4, precoding matrix information obtained is sent opposite end UE by eNodeB；

5, UE implements pre-encode operation according to precoding matrix information obtained；

6, UE sends the data and dedicated pilot of precoding；

7, eNodeB receives the data and dedicated pilot of precoding, estimates according to the received dedicated pilot of institute channel, solves Adjusting data symbol.

9. the fast algorithm of non-code book linear predictive coding according to claim 1, it is characterised in that: step S2 uses base The acquisition to pre-coding matrix is realized in the method for singular value decomposition, by carrying out singular value point to channel matrix obtained Solution, resolves into multiple mutually independent equivalent MIMO subchannels for mimo channel.

10. the fast algorithm of non-code book linear predictive coding according to claim 9, it is characterised in that: unusual in step S2 It is as follows to be worth the process decomposed:

The first step, it is assumed that system is the aerial array of MxN sending and receiving, and M root antenna receives, the transmitting of N root antenna, channel matrix H, The order of channel matrix H is k=Rank (H), and k≤min (m, n) then has channel relevancy matrix H^TH；

Second step is decomposed according to based on the QR with displacement, to channel relevancy matrix H^TH solves characteristic value and feature vector, remembers non- Zero characteristic value is λ₁、λ₂、…、λ_k；Remember that corresponding feature vector is v₁、v₂、…、v_k, to v₁、v₂、…、v_kIt is extended v_k+1、…、v_n, this n-k vector be present in the kernel of H, i.e. the base of the solution space of Hx=0, so that v₁、v₂、…、v_nFor n One group of orthogonal basis in dimension space constitutes orthogonal matrix V；

Third step takes unit vector:

As k < i≤m, to u₁、u₂、…、u_kIt is extended u_(k+1)、…、u_mFor one group of orthogonal basis in m-dimensional space；

Gained u₁、u₂、…、u_nMatrix U is constituted,

NoteWith σ₁、σ₂、…、σ_kFor the diagonal element of top left region, the diagonal matrix ∑ of diagonal matrix mxn is constructed:

4th step, the then singular value decomposition of channel matrix H are as follows:

And then the singular value decomposition of available H-matrix:

H=U ∑ V^T

V is the orthogonal matrix of nxn, and U is the orthogonal matrix of mxm, and ∑ is the diagonal matrix of mxn；

5th step, according to the singular value decomposition for entering matrix H, available pre-coding matrix:

W=V；

Power water injection technology comprises the following processes:

The first step combines SVD precoding with power water injection technology, and power water filling passes through the subchannel distribution to mimo system Specific power increases the signal-to-noise ratio of poor subchannel, thus obtained power system capacity more higher than average power allocation and compared with Good bit error rate performance, constraint condition are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel；

Mimo system capacity after sending power normalization is expressed as:

Wherein λ_iIndicate channel relevancy matrix H^TI-th of element on the diagonal line of H,

σ²For system noise, capacity obtains the constraint condition of maximum value are as follows:

Wherein P_iFor the power for distributing to i-th of subchannel, meet P_i>=0,η is a constant, in a manner of derivation It can determine during seeking C maximum capacity；

Second step, the pre-coding matrix after power water filling is added are as follows:

W=VP^1/2。