WO2015131382A1

WO2015131382A1 - Method and apparatus for determining pre-coding matrix

Info

Publication number: WO2015131382A1
Application number: PCT/CN2014/073014
Authority: WO
Inventors: 吴强; 刘建琴
Original assignee: 华为技术有限公司
Priority date: 2014-03-06
Filing date: 2014-03-06
Publication date: 2015-09-11
Also published as: CN105103468B; CN105103468A

Abstract

Disclosed are a method and apparatus for determining a pre-coding matrix. The method comprises: receiving a reference signal sent by a base station; determining a pre-coding matrix from a code book according to the reference signal; reporting a pre-coding matrix indicator corresponding to the pre-coding matrix to the base station, wherein the pre-coding matrix W is a kronecker product of a matrix W_a and a matrix W_v , W = W_a ⊗ W_v , W_a or W_v is a first matrix, and the first matrix is obtained by operating a matrix unit V_n which is a matrix of M x 1 and has a form as shown in (I), where P = M or P = π/sin(π/Μ), M is an integer and M equals the row number of the first matrix or half of the row number of the first matrix, N₁ is an integer greater than 1, n is an integer and 0 ≤ n ≤ (N₁-1), j=√-1, and s is a preset real number. The method and apparatus for determining a pre-coding matrix in the present invention are mainly applied to the scenario where a base station has a circular cylinder antenna array, and can improve the transmission performance of downlink information and user experience.

Description

Method and device for determining precoding matrix

Embodiments of the present invention relate to the field of communications and, more particularly, to methods and apparatus for determining a precoding matrix. Background technique

In wireless communication systems, multiple antennas are used in a spatially multiplexed manner to achieve higher transmission rates. In addition, in order to further improve the transmission performance of the system, the wireless communication system employs a feedback enhancement technique. Specifically, the base station sends a pre-defined pilot signal, and the user equipment (User Equipment, UE) performs channel state information (CSI) measurement according to the pilot signal sent by the base station, and reports the CSI measurement to the base station. The measurement result, where the CSI reported by the UE may include at least one of the following information: a Rank Indicator (RI), a Pre-coding Matrix Indicator (PMI), and a Wideband Channel Quality Indicator (Channel Quality). In this way, the base station can schedule the UE according to the CSI reported by the UE, and can send a signal to the UE according to the PMI reported by the UE by using a corresponding precoding technology.

As the size of the antenna increases, in order to effectively reduce the size of the antenna, the commonly used antennas are in a cylindrical array or a planar array, in which all antenna elements in a cylindrical array are arranged on the side surface of the cylinder.

A codebook structure for a cylindrical antenna array. Summary of the invention

The present invention provides a method and apparatus for determining a precoding matrix, which can be applied to communication between a base station and a UE in a scenario in which a base station has a cylindrical antenna array.

In a first aspect, the present invention provides a method for determining a precoding matrix, including: receiving a reference signal sent by a base station; determining a precoding matrix from the codebook according to the reference signal; and reporting, to the base station, the precoding matrix corresponding to the precoding matrix A precoding matrix indication; wherein the precoding matrix W is a matrix W. And the Kronecker product of the matrix W _v W = W. ®W _V , ^ or ^ is the first matrix, which is obtained by computing the matrix unit V„, which is an MX 1 matrix and has the following form: e

^J , N, M '

= ec _o ― ^)

e

π

Where P = M P = -, M is an integer, M is an integer and M is equal to the number

Sm ^/ )

The number of rows of a matrix or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ 11 ≤ (^-1), j = i-i, s is a real number.

In a first possible implementation, if the rank of the precoding matrix is 1, the matrix W. And the number of columns of 1 is 1, and the first matrix \\^ has the following form:

, where ψ _χ =^ ^πχ ' , is the normalization factor,

¹ Λ

Is an integer greater than 1.

In combination with the foregoing possible implementation manners, in a second possible implementation manner, another matrix other than the first matrix in ^ and ^ is a second matrix, and the second matrix W ₂ has the following form:

Where V is an integer and

V is equal to the number of rows of the second matrix, K and N ₃ are integers greater than 1, and t and q are integers.

In combination with the foregoing possible implementation manners, in a third possible implementation manner, if the rank of the precoding matrix is greater than or equal to 2, the first matrix has the following form:

W _x = I-2W _0>n W ₀ ^H _n /W ₀ ^H _n W _0>n , where I is an identity matrix and the dimension of the I is Μ, _οη is a matrix of Μ χ 1 and the W. , the first row element of „ is the same as the first row element of the matrix unit V„,

W. The second row to the Mth row element of „ are the opposite numbers of the second row to the Mth row element of the matrix unit V„, respectively, representing the pair matrix ^W. ," Perform a conjugate transpose operation.

In combination with the foregoing possible implementation manners, in a fourth possible implementation manner, if the rank of the precoding matrix is equal to 2, the first matrix \\^ has the following form:

≤11' ≤ (^-1).

With reference to the foregoing possible implementation manners, in a fifth possible implementation manner, if the rank of the precoding matrix is equal to 2, the second matrix W _{2 of the} W _a and W _v except the first matrix has the following form:

1

Jlnt'lK

Where t and t' are integers and 1 ≤ t, t' ≤ (K - l), and V is the number of rows of the second matrix.

In a second aspect, the present invention provides another method for determining a precoding matrix, including: transmitting a reference signal to a user equipment UE; receiving a precoding matrix indication sent by the UE according to the reference signal; and indicating according to the precoding matrix Determining a precoding matrix; wherein the precoding matrix W is a matrix W. And the Kroneck product of the matrix W _v W = W. ®W _V , ^ or ^ is the first matrix, which is obtained by computing the matrix unit V„, which is an MX 1 matrix and has the following form: e = e

Where P = M , M is an integer and M is equal to the row of the first matrix

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l), j = yR, s is a preset real number. In a first possible implementation, if the rank of the precoding matrix is 1, the matrix W. The number of columns of ^ and ^ is 1, and the first matrix \\^ has the following form:

W, =― , where ψ _χ =^ ^πχ ' , is the normalization factor,

1 Λ An integer of 1.

In combination with the foregoing possible implementation manners, in a second possible implementation manner, another matrix other than a matrix in ^ and ^ is a second matrix, and the second matrix w ₂ has the following form:

Where V is an integer and

W _x = I -2W _0>n W ₀ ^H _n /W ₀ ^H _n W _0>n , where I is an identity matrix and the dimension of the I is Μ, _{ο η} is a Μ χ 1 matrix and the first row The elements are identical to the first row element of the matrix unit V„, and the second row to the Mth row element are respectively opposite numbers of the second row to the Mth row element of the matrix unit V„, representing the pair matrix ^W. ," Perform a conjugate transpose operation.

≤11' ≤ (^-1).

1

In a third aspect, the present invention provides an apparatus for determining a precoding matrix, including: a receiving module, configured to receive a reference signal sent by a base station; and a determining module, configured to receive the a pre-coding matrix is determined from the codebook, and a sending module is configured to report, to the base station, a precoding matrix indication corresponding to the precoding matrix determined by the determining module, where the precoding matrix W is a matrix w _a and a matrix ^ Kroneck product w = w. ®w _v , ^ or ^ is the first matrix, the first matrix pass operation is obtained, V „ is the MX 1 matrix and has the following form:

Where P = M P = - π

_t , -, M is an integer and M is equal to the number of rows of the first matrix or half of the number of rows of the first matrix, is an integer greater than 1, n is an integer and 0 ≤ n < (Nj-l) , j = ^ , s is the default real number.

In a first possible implementation, if the rank of the precoding matrix is 1, the matrix W. The number of columns of ^ and ^ is 1, and the first matrix ^ ^ has the following form:

Where _ψχ : _ε ]; , is the normalization factor, X is an integer, Ν _:

Is an integer greater than 1.

Where V is an integer and

W, = I -2W _on W ₀ ^H _n IW ₀ ^H _n W ₀ ^ _n , where I is an identity matrix and the dimension of the I is Μ, Ψ _{ο η} is a matrix of Μ χ 1 and the W. , the first row element of „ is the same as the first row element of the matrix unit,

Possible combination of the above implementation manner, in a fourth possible implementation, if the precoding matrix is equal to the rank 2, W ₁ of the first matrix has the following form: Where n' is an integer and 0≤

11' ≤ (^-1).

1

Jlnt'lK

In a fourth aspect, the present invention provides another apparatus for determining a precoding matrix, including: a sending module, configured to send a reference signal to a user equipment UE; and a receiving module, configured to receive, by the UE, the reference signal sent by the sending module And a determining module, configured to determine a precoding matrix according to the precoding matrix indication received by the receiving module, where the precoding matrix W is a matrix W. And the Kroneck product of the matrix W _v W = W. ®W _V , ^ or ^ is the first matrix, which is obtained by computing the matrix unit V„, which is an MX 1 matrix and has the following form: e = e

Where P = M , M is an integer and M is equal to the row of the first matrix

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l) , j = y , s is a preset real number. In a first possible implementation, if the rank of the precoding matrix is 1, the matrix W. The number of columns of ^ and ^ is 1, and the first matrix \\^ has the following form: Wherein W _{_t,} ψχ two "2, ₁ is a normalization factor, J is an integer, v ₂

Is an integer greater than 1.

In combination with the above possible implementation manners, in a second possible implementation manner, W. And another matrix other than the first matrix in W _v is a second matrix, the second matrix W ₂ having the following form:

Where V is an integer and

V is equal to the number of rows of the second matrix, and Κ and Ν ₃ are integers greater than 1, and t and q are integers.

W _{ = I -2W _on W ₀ ^H _n /W ₀ ^H _n W ₀ ^ _n , where I is an identity matrix and the dimension of the I is M, Ψ _{ο η} is a Μ X 1 matrix and the W. The first row element of „ is the same as the first row element of the matrix unit, and the second row to the Mth row element of the W, „ are the opposite of the second row to the Mth row element of the matrix unit V„ , W. ^ denotes the matrix, "to perform a conjugate transpose operation.

Possible combination of the above implementation manner, in a fourth possible implementation, if the precoding matrix is equal to the rank 2, W ₁ having the first matrix

Where n' is the whole

Number and O n' S CNrl

With reference to the foregoing possible implementation manners, in a fifth possible implementation manner, if the rank of the precoding matrix is equal to 2, and 1⁄2; the second matrix W ₂ except the first matrix has the following form:

Based on the foregoing technical solution, the method for determining a precoding matrix provided by the present invention, a base station and a UE Communicating based on the new codebook, the UE performs measurement on the reference signal sent by the base station to determine a precoding matrix in the codebook, and sends a PMI corresponding to the precoding matrix to the base station according to the UE. The reported PMI processes the downlink information sent to the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array, which can improve the transmission performance of the downlink information and improve the user body.

DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings to be used in the embodiments of the present invention or the description of the prior art will be briefly described below. Obviously, the drawings described below are merely the present invention. Some of the embodiments can be obtained by those skilled in the art from the drawings without any creative work.

FIG. 1 is a schematic flowchart of a method for determining a precoding matrix according to an embodiment of the present invention.

2 is a perspective view of a cylindrical antenna array according to an embodiment of the present invention.

Figure 3 is a plan view of the cylindrical antenna array shown in Figure 2.

FIG. 4 is a schematic flowchart of a method for determining a precoding matrix according to another embodiment of the present invention. FIG. 5 is a schematic block diagram of an apparatus for determining a precoding matrix according to an embodiment of the present invention.

6 is a schematic block diagram of an apparatus for determining a precoding matrix according to another embodiment of the present invention.

FIG. 7 is a schematic block diagram of an apparatus for determining a precoding matrix according to still another embodiment of the present invention.

FIG. 8 is a schematic block diagram of an apparatus for determining a precoding matrix according to still another embodiment of the present invention. detailed description

The technical solutions in the embodiments of the present invention are clearly and completely described in the following with reference to the accompanying drawings in the embodiments of the present invention. It is obvious that the described embodiments are a part of the embodiments of the present invention, and not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without making creative labor are within the scope of the present invention.

It should be understood that the technical solutions of the embodiments of the present invention can be applied to various communication systems, such as: Global System of Mobile communication ("GSM") system, Code Division Multiple Access (Code Division Multiple Access) Called "CDMA") system, Wideband Code Division Multiple Access ("WCDMA") system, General Packet Radio Service ("General Packet Radio Service"), Long Term Evolution ( Long Term Evolution, called "LTE" system, LTE frequency division duplex ( Division Duplex, the tube called "FDD" system, LTE time division duplex (Time Division Duplex, called "TDD"), Universal Mobile Telecommunication System (UMTS), global interconnected microwave Access (Worldwide Interoperability for Microwave Access, called "WiMAX") communication system.

It should also be understood that in the embodiment of the present invention, a user equipment (User Equipment, referred to as "UE") may be referred to as a terminal, a mobile station ("Mobile" ("MS"), and a mobile terminal ( Mobile Terminal), etc., the user equipment can communicate with one or more core networks via a Radio Access Network ("RAN"), for example, the user equipment can be a mobile phone (or "cellular" "Telephone", a computer with a mobile terminal, etc., for example, the user device can also be a portable, pocket, handheld, computer built-in or in-vehicle mobile device that exchanges voice and/or data with the wireless access network.

It should also be understood that, in the embodiment of the present invention, the base station may be a base station (Base Transceiver Station, called "BTS") in GSM or CDMA, or a base station (NodeB) in WCDMA, or may be in LTE. The evolved base station (evolved Node B, referred to as "eNB" or "e-NodeB") is not limited in the present invention.

It should also be understood that the method and apparatus for determining a precoding matrix provided by the embodiments of the present invention are mainly applied to a scenario of a cylindrical antenna array, but may be applied to other scenarios, which is not limited by the embodiment of the present invention. The method can be performed by the UE. As shown in FIG. 1, the method 100 includes:

S110. Receive a reference signal sent by the base station.

S120. Determine, according to the reference signal, a precoding matrix from the codebook.

S130. Report, to the base station, a precoding matrix indication corresponding to the precoding matrix.

The precoding matrix W is a matrix w. And the Kroneck product w = w of the matrix w _v . ®w _v , ^ or ^ is the first matrix, which is obtained by computing the matrix unit V„, which is an M 1 matrix and has

Where P = M ^ P = . ^π , , , Μ is an integer and Μ is equal to the number of rows of the first matrix sm(^-/ )

The half of the number of rows of the first matrix or the first matrix is an integer greater than 1, n is an integer and 0 ≤ n ≤ (N l), j = Tl , and s is a preset real number.

Therefore, according to the method for determining a precoding matrix, the base station and the UE perform communication based on a new codebook, and the UE performs measurement on the reference signal sent by the base station to determine a precoding matrix in the codebook, and The PMI corresponding to the precoding matrix is reported to the base station, and the base station processes the downlink information sent by the UE according to the PMI reported by the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array, which can improve downlink information transmission performance. Improve the user experience.

In this embodiment of the present invention, the base station and the UE communicate according to a new codebook, and the at least one precoding matrix included in the codebook is the precoding matrix w. Specifically, the precoding matrix W determined by the UE in step S120 is a matrix W. And the Kroneck product of the matrix W _v , where W. The dimension is XM ₂ , the dimension of the matrix W _v is M ₃ XM ₄ , and the matrix W _a and the matrix W _v may respectively correspond to components of the precoding matrix W in two dimensions, for example, the matrix W. The matrix is the component of the precoding matrix W on the bottom surface of the cylinder, and the matrix is the component of the precoding matrix W in the direction of the axis of the cylinder; or vice versa, the embodiment of the invention does not limit this.

In the embodiment of the invention, the matrix w is used. One of the matrices in the sum matrix w _v is referred to as a first matrix w and the other matrix is referred to as a second matrix w ₂ , wherein the first matrix is obtained by performing an operation on the matrix unit v„, optionally, the first A matrix itself may be equal to the matrix unit v„, or the matrix unit V„ is part of the first matrix, or the first matrix is obtained by matrix transformation of the matrix unit V„, etc., This is not limited.

The dimension M of the matrix unit V „ may be equal to the number of rows of the first matrix or equal to half of the number of rows of the first matrix. Optionally, if the antenna shape in the dimension corresponding to the first matrix is a unipolar form, Then, the M may be equal to the number of rows of the first matrix, specifically, if the matrix ^ is the first matrix, then M = M ₁ and if the matrix W _v is the first matrix, then M = M ₃ ; if the first matrix corresponds The antenna shape on the dimension is a dual-polarized form, then the M can be equal to half the number of rows of the first matrix. Specifically, if the matrix ^ is the first matrix, then M = Mi/2, and if the matrix W _v is the first matrix, then M = M ₃ /2. It can be seen that the M can represent the number of ports in each of the polarization directions in the at least one polarization direction in the dimension corresponding to the first matrix Wj, but Embodiments of the invention are not limited thereto. The element e M ^M (=1, 2, ..., M) of the matrix unit V „ can represent the weighting factor of the first antenna. As shown in Fig. 2, the antenna elements of the cylindrical antenna array are distributed in the cylinder On the side, FIG. 3 shows a top view of the cylindrical antenna array shown in FIG. 2, assuming that the number of antenna ports distributed on the circumference of the bottom surface is Μ and the antenna shape is a single polarization form, the radius of the bottom surface is r, any adjacent The angle between the two antenna elements is α, in which the direction between the two antenna elements is the y-axis, and the antenna array in the positive direction of the y-axis is recorded as the first antenna, then the root antenna angle _[alpha]; determined by the following formula:

^ = ^(! ~^ , i =1, 2, ... , M (2) Assuming that the angle between an incident beam and the y-axis is Θ, the wave path difference of the first antenna relative to the origin is Determine:

d _i = rcos(or _; -6>) = rcos(^ — 0) (3) Correspondingly,

Where f is the frequency of the wave, λ is the wavelength of the wave, and fx = c, c is the speed of light. Assuming that the arc length between any two antennas is _δ λ, you can get:

2π^2 Ms (5) Bringing the formula (4) into the equation (3) gives:

φ _ι = sM cos( a ¹ ) ^{2 Γ} -θ) (6)

Μ

In order to compensate for the phase difference caused by the wave path difference of each antenna, a weighting factor ( ) can be introduced for the first antenna and Θ2≡■, then the weighting factor of the first antenna can be expressed as

^1

j _s M _C0£ (2r" — 2τ(- 1))

e M M corresponds to the case where P = M in the formula d), but the embodiment of the invention is not limited thereto.

Optionally, as another embodiment, if the chord length between any two antennas is _δ λ, then: (7) λ 2ύη{πΙΜ) Correspondingly, bringing equation (7) into equation (4) yields:

( 8) ύη πΙ Μ) Ν, Μ

₍ 3⁄4 π_2^ ₌ 1) ₎

J-r,

At this time, the weighting factor of the first antenna can be expressed as e

In the case of ρ = · in the formula (1), the embodiment of the invention is not limited thereto ₍

Optionally, if the rank of the precoding matrix W is 1, then:

Can have

Optionally, the value of the J is 0 ≤ X < (N ₂ -1), and the N ₂ may be a preset integer. Alternatively, as another embodiment, the second matrix W ₂ may have the following form:

Wherein, _qq = _e ^ll V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ are integers greater than 1, and t and q are integers.

Optionally, the value range of ί is 0 ≤ ί ≤ (^Γ-1), and the value ranges from 0 ≤ ≤ (Ν ₃ -1), and the Κ and Ν ₃ may be preset integers, but the present invention The embodiment is not limited to this.

Optionally, as another embodiment, the precoding matrix W with a rank greater than or equal to 2 may have a Discrete Fourier Transform (DFT) form or a Householder transform matrix form, optionally Ground, when the precoding matrix W has the DFT form,

Where n' is an integer and O n 'CNi-l);

Accordingly, the second matrix W ₂ may have the following form:

Specifically, if matrix W. For the first matrix, then M = M ₁ and if the matrix ^ is the first matrix, then M = M ₃ , which is not limited by the embodiment of the present invention. Optionally, when the rank of the precoding matrix W is greater than 2, the \\ and W ₂ may also be represented by a similar form, which is not limited by the embodiment of the present invention.

Optionally, as another embodiment, when the precoding matrix W has the Householder transform matrix form, if the rank of the precoding matrix is greater than or equal to 2, the first matrix \\^ may have the following form:

Where I is an identity matrix and the dimension of the I is M, W. , „ is the M 1 matrix and the first row element of the W., „ is the same as the first row element, the W. The second row to the Mth row element of „ are the opposite numbers of the second row to the Mth row element of the V „, respectively, representing the pair of matrices ^W . ," Perform a conjugate transpose operation.

As mentioned above, matrix W. , „ can have the following form:

-e ( 14 )

-e

In the embodiment of the present invention, when the first matrix has the above Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Alternatively, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown by the formula (12), but the embodiment of the present invention is not limited thereto.

Therefore, according to the method for determining a precoding matrix according to an embodiment of the present invention, a communication between a base station and a UE is performed based on a new codebook, and the UE measures the reference signal transmitted by the base station to determine the code. The precoding matrix of the present invention reports the PMI corresponding to the precoding matrix to the base station, and the base station processes the downlink information sent to the UE according to the PMI reported by the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array. It can improve the transmission performance of downlink information and improve the user experience.

With reference to FIG. 1 to FIG. 3 above, a method for determining a precoding matrix according to an embodiment of the present invention is described in detail from the perspective of a UE, and a determination according to another embodiment of the present invention will be described in detail from the perspective of a base station in conjunction with FIG. The method of precoding the matrix.

FIG. 4 is a schematic flowchart of a method 200 for determining a precoding matrix according to another embodiment of the present invention. The method may be performed by a base station. As shown in FIG. 4, the method 200 includes:

S210. Send a reference signal to the user equipment UE.

S220. Receive a precoding matrix indication sent by the UE according to the reference signal.

S230, determining a precoding matrix according to the precoding matrix indication;

The precoding matrix W is a matrix w. And the Kroneck product w = w of the matrix w _v . ®w _v ,

W. Or W _v is a first matrix, and the first matrix is obtained by performing an operation on the matrix unit V „, which is an M 1 matrix and has

Where P = M ^ P = . ^π , , , M is an integer and M is equal to the row sm(^-/ ) of the first matrix

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l) , j = y , s is a preset real number.

In the embodiment of the invention, the matrix w. The sum matrix W _v may correspond to a component of the precoding matrix W in two dimensions, for example, the matrix W. Precoding matrix W in the part of the bottom surface of the cylinder, an integral part of the matrix W _V precoding matrix W in the direction of the axis of the cylinder is located; or vice versa, embodiments of the present invention is not limited to this embodiment. In the embodiment of the present invention, W. The dimension is XM ₂ , the dimension of the matrix W _v is M ₃ XM ₄ , and the matrix W. One of the matrices in the matrix W _v is referred to as a first matrix, and the other matrix is referred to as a second matrix W ₂ , wherein the first matrix is obtained by performing an operation on the matrix unit V„, optionally, the first A matrix itself may be equal to the matrix unit V„, or the matrix unit V„ is part of the first matrix, or the first matrix is obtained by matrix transformation of the matrix unit V„, etc., This is not limited.

Optionally, if the rank of the precoding matrix is 1, then M ₂ =M ₄ = 1, and the first matrix has the following form:

Wherein, _x = e ^{z; rx} " ^V2 , the input is a normalization factor, J is an integer, and N ₂ is greater than 1. Optionally, as another embodiment, the second matrix W ₂ has the following form:

Wherein, _{0.00q = e} ] " , V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ are integers greater than 1, and t and q are integers.

Optionally, as another embodiment, if the rank of the precoding matrix is equal to 2, the first matrix Wj has

Where n' is an integer and O n' CNi-l

The corresponding second matrix W ₂ may have the following form:

Where t and t' are integers and 1≤t, t'≤(Kl), and V is the number of rows of the second matrix.

Optionally, as another embodiment, if the rank of the precoding matrix is greater than or equal to 2, the first matrix has the following form:

Where I is the identity matrix and the dimension of the I is M, W ^ is the M 1 matrix and the first row element of the W ^ is the same as the first row element of the matrix unit V„, the second row of the W., „ The elements to the Mth row are the opposite of the elements of the second row to the Mth row of the matrix unit, respectively, representing the pair of matrices ^W. ," Perform a conjugate transpose operation.

As mentioned above, matrix W. , „ can have the following form:

^n,

( twenty one )

—, _co ― In the embodiment of the present invention, when the first matrix has the above Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Alternatively, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown by the formula (19), but the embodiment of the present invention is not limited thereto.

The method of determining a precoding matrix according to an embodiment of the present invention is described in detail above with reference to Figs. 1 through 4, and an apparatus for determining a precoding matrix according to an embodiment of the present invention will be described in detail below with reference to Figs.

FIG. 5 shows a schematic block diagram of an apparatus 300 for determining a precoding matrix according to an embodiment of the present invention. As shown in FIG. 5, the apparatus 300 includes:

The receiving module 310 is configured to receive a reference signal sent by the base station;

a determining module 320, configured to determine a precoding matrix from the codebook according to the reference signal received by the receiving module 310; The sending module 330 is configured to report, to the base station, a precoding matrix indication corresponding to the precoding matrix determined by the determining module 320.

The precoding matrix W is a matrix W. And the Kronecker product of the matrix W _v W = W. ® W _V , W. Or W _v is a first matrix obtained by computing the matrix unit V „ , V „ is an M 1 matrix and has the following form:

(twenty two)

Where P = MM is equal to the row of the first matrix

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l), j = yR, s is a preset real number.

Therefore, according to the apparatus for determining a precoding matrix, the base station and the UE communicate according to a new codebook, and the UE performs measurement on the reference signal sent by the base station to determine a precoding matrix in the codebook, and The PMI corresponding to the precoding matrix is reported to the base station, and the base station processes the downlink information sent by the UE according to the PMI reported by the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array, which can improve downlink information transmission performance. Improve the user experience.

In the embodiment of the present invention, W. The dimension is XM ₂ and the dimension of the matrix W _v is M ₃ M ₄ . Optionally, if the rank of the precoding matrix is 1, then M ₂ =M ₄ = 1, and the first matrix has the following form:

(twenty three)

Where _x = ^{2; ΓΧ / Λ} " ² , the ^input is the normalization factor, which is an integer, and N ₂ is greater than 1

Optionally, as another embodiment, the second matrix W ₂ has the following form:

Where _ψe _e ], V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ is an integer greater than 1, and both t and q are integers.

Optionally, as another embodiment, if the rank of the precoding matrix is equal to 2,

Wj has

Where n' is an integer and O n' CNi-l

Accordingly, the second matrix W ₂ may have the following form:

Wherein I is an identity matrix and the dimension of the I is M, „ is an M 1 matrix and the first row element is the same as the first row element of the matrix unit, and the second row to the Mth row element are respectively The inverse of the second row to the third row element of the matrix unit indicates that the conjugate transpose operation is performed on the matrix ^.

As mentioned above, the matrix is Ψ. ,,, can have the following form: e

One e ( 28 )

-e

In the embodiment of the present invention, when the first matrix has the above Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Optionally, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown in the formula (27), but the embodiment of the present invention Not limited to this.

The apparatus 300 for determining a precoding matrix according to an embodiment of the present invention may correspond to a base station in a method of determining a precoding matrix according to an embodiment of the present invention, and determining the above and other operations of respective modules in the apparatus 300 of the precoding matrix In order to implement the corresponding processes of the respective methods in FIG. 1 , the functions are not described here.

FIG. 6 shows a schematic block diagram of an apparatus 400 for determining a precoding matrix according to another embodiment of the present invention. As shown in FIG. 6, the apparatus 400 includes:

The sending module 410 is configured to send a reference signal to the user equipment UE.

The receiving module 420 is configured to receive a precoding matrix indication sent by the UE according to the reference signal sent by the sending module 410.

a determining module 430, configured to determine a precoding matrix according to the precoding matrix indication received by the receiving module 420;

The precoding matrix W is a matrix W. And the Kronecker product of the matrix W _v W = W. ® W _V , W. Or W _v is a first matrix obtained by performing an operation on the matrix unit V„, which is an M 1 matrix and has the following form: e

jsPco&(——---)

= e ( 29 ) j _sPcos( 2^_(M^2, _}

e

Where π

P = M ^i P = . , , - , M is an integer and M is equal to the line sm(^-/ ) of the first matrix

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l), j = R , s is a preset real number.

Therefore, according to the apparatus for determining a precoding matrix according to an embodiment of the present invention, the base station and the UE communicate based on a new codebook, and the UE measures the reference signal sent by the base station to determine the code. The precoding matrix of the present invention reports the PMI corresponding to the precoding matrix to the base station, and the base station processes the downlink information sent to the UE according to the PMI reported by the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array. It can improve the transmission performance of downlink information and improve the user experience.

(30)

Wherein, _{0.00q = e} ] " , V is an integer and V is equal to the number of rows of the second matrix, K and ^ are integers greater than 1, and t and q are integers.

Where n' is an integer and O n' CNi-l

Corresponding second matrix W ₂ can

Optionally, as another embodiment, if the rank of the precoding matrix is greater than or equal to 2, the first The matrix has the following form:

Matrix W as described above. , „ can have the following form:

In the embodiment of the present invention, when the first matrix has the above Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Alternatively, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown by the formula (33), but the embodiment of the present invention is not limited thereto.

The apparatus 400 for determining a precoding matrix according to an embodiment of the present invention may correspond to a base station in a method of determining a precoding matrix according to an embodiment of the present invention, and determining the above and other operations of respective modules in the apparatus 400 of the precoding matrix In order to implement the corresponding processes of the respective methods in FIG. 4, the functions are not described here.

FIG. 7 shows a schematic block diagram of an apparatus 500 for determining a precoding matrix according to an embodiment of the present invention. As shown in FIG. 7, the apparatus 500 includes:

The receiver 510 is configured to receive a reference signal sent by the base station.

The processor 520 is configured to determine, according to the reference signal received by the receiver 510, a precoding matrix from the codebook;

The transmitter 530 is configured to report, to the base station, the precoding matrix corresponding to the processor 520. Precoding matrix indication;

W. Or W _v is a first matrix obtained by performing an operation on the matrix unit V „, which is an M 1 matrix and has the following form:

Where ρ = Μ or Ρ

The number or half of the number of rows of the first matrix is an integer greater than 1, n is an integer and 0 ≤ n < (N l), and j = C s is a preset real number.

Therefore, according to the apparatus for determining a precoding matrix, the base station and the UE communicate according to a new codebook, and the UE performs measurement on the reference signal sent by the base station to determine a precoding matrix in the codebook, and Reporting, to the base station, a PMI corresponding to the precoding matrix, according to the base station

The PMI reported by the UE processes the downlink information sent to the UE, and is mainly applied to a scenario in which the base station has a cylindrical antenna array, which can improve downlink information transmission performance and improve user experience.

It should be understood that, in the embodiment of the present invention, the processor 520 may be a central processing unit (a central processing unit), and the processor 520 may also be another general-purpose processor, a digital signal processor (DSP). ), application specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, and the like. The general purpose processor may be a microprocessor or the processor or any conventional processor or the like.

The apparatus 500 can also include a memory for storing a codebook, the memory can include read only memory and random access memory, and provide instructions and data to the processor 520. Portions of the memory may also include non-volatile random access memory. For example, the memory can also store information about the type of device.

In the implementation process, each step of the foregoing method may be completed by an integrated logic circuit of hardware in the processor 520 or an instruction in a form of software. The steps of the method disclosed in the embodiments of the present invention may be directly implemented as a hardware processor, or may be performed by a combination of hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read only memory, programmable only Read memory or electrically erasable programmable memory, registers, etc., which are well-established in the field of storage media. The storage medium is located in the memory, and the processor 520 reads the information in the memory and completes the steps of the above method in combination with the hardware. To avoid repetition, it will not be described in detail here.

(37)

Wherein, _0.00q = _e ] , V is an integer and V is equal to the number of rows of the second matrix, K and ^ are integers greater than 1, and t and q are integers.

Where n' is an integer and O n' CNi-l

Corresponding second matrix W ₂ can

2W. , U / d ( 41 ) where I is the identity matrix and the dimension of the I is M, W ^ is the M 1 matrix and the first row element of the W ^ is the same as the first row element of the matrix unit V„, The second row to the Mth row element of „ are the opposite numbers of the second row to the Mth row element of the matrix unit, respectively, representing the pair of matrices ^W. ," Perform a conjugate transpose operation.

As mentioned above, matrix W. , „ can have the following form: e ¹

j _S p _C0S ( - )

W, „ = \ -e . ^N , ^M I ( 42 )

_^ N _x M ' In the embodiment of the present invention, when the first matrix has the above-described Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Alternatively, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown by the formula (40), but the embodiment of the present invention is not limited thereto.

The apparatus 500 for determining a precoding matrix according to an embodiment of the present invention may correspond to a base station in a method of determining a precoding matrix according to an embodiment of the present invention, and determining the above and other operations of respective modules in the apparatus 500 of the precoding matrix In order to implement the corresponding processes of the respective methods in FIG. 1 , the functions are not described here.

FIG. 8 shows a schematic block diagram of an apparatus 600 for determining a precoding matrix according to another embodiment of the present invention. As shown in FIG. 8, the apparatus 600 includes:

The transmitter 610 is configured to send a reference signal to the user equipment UE.

The receiver 620 receives an indication of a precoding matrix sent by the UE according to the reference signal sent by the transmitter 610.

The processor 630 is configured to determine, according to the precoding matrix indication received by the receiver 620, Coding matrix

Where P = M

It should be understood that, in the embodiment of the present invention, the processor 630 may be a central processing unit (CPU), and the processor 630 may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), Ready-to-use programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, and more. The general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The apparatus 600 can also include a memory that can include read only memory and random access memory and provides instructions and data to the processor 630. A portion of the memory may also include non-volatile random access memory. For example, the memory can also store information of the device type.

In the implementation process, each step of the foregoing method may be completed by an integrated logic circuit of hardware in the processor 630 or an instruction in a form of software. The steps of the method disclosed in the embodiments of the present invention may be directly implemented as a hardware processor, or may be performed by a combination of hardware and software modules in the processor. The software modules can be located in a conventional storage medium such as random access memory, flash memory, read only memory, programmable read only memory or electrically erasable programmable memory, registers, and the like. The storage medium is located in the memory, and the processor 630 reads the information in the memory and completes the steps of the above method in combination with the hardware. To avoid repetition, it will not be described in detail here.

(44)

Wherein 2, eight ₁ is a normalization factor, is an integer, N ₂ is an integer greater than 1. Alternatively, in another embodiment, the second matrix \ ¥ ₂ has the following form:

Wherein, _0.00q = _e ]„, V is an integer and V is equal to the number of rows of the second matrix, Κ is an integer greater than 1, and t and q are integers.

Where n' is an integer and O n' CNi-l

Accordingly, the second matrix W ₂ may have the following form:

As mentioned above, matrix W. , „ can have the following form: e ¹

j _S p _C0S ( - )

W, „ = \ -e . ^N , ^M I ( 49 )

_^ N _x M ' In the embodiment of the present invention, when the first matrix has the above-described Householder matrix transformation form, the second matrix W ₂ may have any suitable form. Alternatively, when the rank of the precoding matrix W is equal to 2, the second matrix W ₂ may have the form shown by the formula (47), but the embodiment of the present invention is not limited thereto.

The apparatus 600 for determining a precoding matrix according to an embodiment of the present invention may correspond to a base station in a method of determining a precoding matrix according to an embodiment of the present invention, and determining the above and other operations of respective modules in the apparatus 600 of the precoding matrix In order to implement the corresponding processes of the respective methods in FIG. 4, the functions are not described here.

It should be understood that in the embodiments of the present invention, the term "and/or" is merely an association relationship describing an associated object, indicating that there may be three relationships. For example, A and / or B can mean: There are three cases of A, B and A and B alone. In addition, the character " /" in this article generally indicates that the contextual object is an "or" relationship.

Those skilled in the art will appreciate that the various method steps and elements described in connection with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both, in order to clearly illustrate hardware and software. Interchangeability, in accordance with the functional generality in the above description The steps and composition of the various embodiments are described. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the solution. Different methods may be used to implement the described functionality for each particular application, but such implementation should not be considered to be beyond the scope of the present invention.

A person skilled in the art can clearly understand that, for the convenience and the cleaning of the description, the specific working processes of the system, the device and the unit described above can refer to the corresponding processes in the foregoing method embodiments, and details are not described herein again.

In the several embodiments provided herein, it should be understood that the disclosed systems, devices, and methods may be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the unit is only a logical function division. In actual implementation, there may be another division manner, for example, multiple units or components may be combined or Can be integrated into another system, or some features can be ignored, or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, or an electrical, mechanical or other form of connection.

The units described as separate components may or may not be physically separate, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the objectives of the embodiments of the present invention.

In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

The integrated unit, if implemented in the form of a software functional unit and sold or used as a standalone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention contributes in essence or to the prior art, or all or part of the technical solution may be embodied in the form of a software product stored in a storage medium. A number of instructions are included to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: a USB flash drive, a mobile hard disk, a read-only memory (called "ROM"), a random access memory ("RAM" called "RAM"), a disk or A variety of media such as optical discs that can store program code. The above is only the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any equivalent person can be easily conceived within the technical scope of the present invention. Modifications or substitutions are intended to be included within the scope of the invention. Therefore, the scope of the invention should be determined by the scope of the claims.

Claims

Rights request

1. A method for determining a precoding matrix, characterized in that it includes:

Receive the reference signal sent by the base station;

According to the reference signal, determine a precoding matrix from the codebook;

Report the precoding matrix indication corresponding to the precoding matrix to the base station;

Wherein, the precoding matrix W is a matrix w. and the Kronecker product w =w _a ®w _v , W of the matrix w _v . Or w _v is the first matrix, the first matrix is obtained by operating on the matrix unit v„, is the MX 1 matrix and has the following form: e

jsPcos{————)

= e ^J Ν, Μ ' j _sP∞s( 2^_(M^ _}

e

Among them, π

P = M ^i P = . _r , - , M is an integer and M is equal to the row sm(^-/) of the first matrix

number or half the number of rows of the first matrix, is an integer greater than 1, n is an integer and 0≤n < (N l), j = y, s is a preset real number.

2. The method according to claim 1, characterized in that if the rank of the precoding matrix is 1, then the matrix W. The number of columns of and W _v is both 1, and the first matrix \\^ has the following form:

Among them, 2 is the normalization factor, J is an integer, and N ₂ is an integer greater than 1.

3. The method according to claim 2, characterized in that: W. and another matrix other than the first matrix is a second matrix, and the second matrix W ₂ has the following form:

Wherein, V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ are both greater than 1

Both t and q are integers.

4. The method according to any one of claims 1 to 3, characterized in that if the predetermined The rank of the coding matrix is greater than or equal to 2, and the first matrix has the following form:

W ^yr \ =I ¹ -2W o,n W ^yr ο ^H ,η ' IW ^yv o ^H ,nW ^yv o,n ·i

Wherein, I is the identity matrix and the dimensions of I are M, W. ,„ is an M 1 matrix and the first row elements of W.,„ are the same as the first row elements of the matrix unit V„, and the elements of the second row to the Mth row are respectively the second rows of the matrix unit V„ The inverse of the element in row M represents the pair matrix ^W. ," Perform conjugate transpose operation.

5. The method according to any one of claims 1 to 3, characterized in that, if the rank of the precoding matrix is equal to 2, the first matrix has the following form:

Where, n' is an integer and O n' CNi-l

6. The method according to claim 4 or 5, characterized in that, if the rank of the precoding matrix is equal to 2, the second matrix W except the first matrix W in W _a and _W has the following form : jlnt'lK

Wherein, t and t' are integers and 1≤t,t'≤(K-l), and V is the number of rows of the second matrix.

7. A method for determining a precoding matrix, characterized by including:

Send the reference signal to the user equipment UE;

Receive a precoding matrix indication sent by the UE according to the reference signal;

Determine a precoding matrix according to the precoding matrix indication;

Wherein, the precoding matrix W is matrix W. and the Kronecker product of matrix W _v W = W _a ®W _v , W . Or W _v is the first matrix, the first matrix is obtained by operating on the matrix unit V„, V„ is the MX 1 matrix and has the following form: e

jsPcos{————)

= e

e

π

Where, P = M P = . , , -, M is an integer and M is equal to the row of the first matrix sm(^-/ )

number or half the number of rows of the first matrix, is an integer greater than 1, n is an integer and 0≤n <(N l), j = C s is a preset real number.

8. The method according to claim 7, characterized in that if the rank of the precoding matrix is 1, then the matrix W. The number of columns of and W _v is both 1, and the first matrix \\^ has the following form:

Among them, _ψχ = ^πχι is the normalization factor, J is an integer, and N ₂ is an integer greater than 1.

9. The method according to claim 8, characterized in that: W. and another matrix other than the first matrix is a second matrix, and the second matrix W ₂ has the following form:

1

jlntlK I2-\)2ntlK

Wherein, V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ are both numbers greater than 1, and t and q are both integers.

10. The method according to any one of claims 7 to 9, characterized in that, if the rank of the precoding matrix is greater than or equal to 2, the first matrix has the following form:

W ^yr \ =I ¹ -2W o,n W ^yr ο ^H ,η ' IW ^yv o ^H ,nW ^yv o,n ·i

11. The method according to any one of claims 7 to 9, characterized in that, if the rank of the precoding matrix is equal to 2, the first matrix has the following form:

Where, n' is an integer and O n' O^-l^

12. The method according to claim 10 or 11, characterized in that if the rank of the precoding matrix is equal to 2, W. and the second matrix W ₂ in W _v in addition to the first matrix has the following form:

Wherein, t and t' are integers and 1≤ t, t'≤ (K-l), and V is the number of rows of the second matrix.

13. A device for determining a precoding matrix, characterized in that it includes:

The receiving module is used to receive the reference signal sent by the base station;

Determining module, configured to determine a precoding matrix from the codebook according to the reference signal received by the receiving module;

A sending module, configured to report to the base station the precoding matrix indication corresponding to the precoding matrix determined by the determining module;

Wherein, the precoding matrix W is matrix W. And the Kronecker product of matrix W _v W=W _a <S>W _v , ^or! ^ is the first matrix, which is obtained by operating on the matrix unit V„, and is the MX 1 matrix and has the following form:

= j _sPcos( ^≡-(Mr}2^

N M

π

Where, P = MP = - . _{/ ;} -, M is an integer and M is equal to the number of rows of the first matrix or half of the number of rows of the first matrix, is an integer greater than 1, n is an integer and 0≤ n <(N l), 7 = = , s is a preset real number.

14. The device according to claim 13, characterized in that, if the precoding matrix The rank is 1, then the matrix W. The number of columns of and W _v is both 1, and the first matrix \\^ has the following form

Among them, _ψχ = ^πχι1 , is the normalization factor, is an integer, and N ₂ is an integer greater than 1.

15. The device according to claim 14, characterized in that: W. The other matrix in W _v except the first matrix is the second matrix, and the second matrix w ₂ has the following form:

16. The device according to any one of claims 13 to 15, characterized in that, if the rank of the precoding matrix is greater than or equal to 2, the first matrix has the following form:

W ^yv ^l = ¹ 1 ^- 2- ^W ^yv ^ο ^, ⁿ

Wherein, I is the identity matrix and the dimensions of I are M, W. ,„ is an M 1 matrix and the first row elements of W.,„ are the same as the first row elements of matrix unit V„, and the second row to Mth row elements of W.,„ are respectively the matrix unit V„. The inverse number of the elements in the second row to the Mth row represents the conjugate transpose operation on the matrix ^W. ,".

17. The device according to any one of claims 13 to 16, characterized in that if the pre-programmed form:

where n' is an integer and 1 n' CNi-l

18. The device according to claim 16 or 17, characterized in that if the rank of the precoding matrix is equal to 2, W. and the second matrix W ₂ in W _v in addition to the first matrix has the following form: 1

jlnt'lK

Among them, t and t' are integers and 1≤t,t'≤(K-l), and V is the number of rows of the second matrix.

19. A device for determining a precoding matrix, characterized in that it includes:

A sending module, used to send the reference signal to the user equipment UE;

A receiving module, receiving a precoding matrix indication sent by the UE according to the reference signal sent by the sending module;

Determining module, configured to determine a precoding matrix according to the precoding matrix indication received by the receiving module;

Wherein, the precoding matrix W is matrix W. and the Kronecker product of matrix W _v W = W _a ®W _v , W . Or W _v is the first matrix, which is obtained by operating on the matrix unit V„, V„ is the MX 1 matrix and has the following form: e

jsPcos (——---)

J , ' N , M ' c _o ― i ^)

e

Among them, π

p = M or P . , , -, M is an integer and M is equal to the row of the first matrix sm(^-/ )

number or half the number of rows of the first matrix, is an integer greater than 1, n is an integer and 0≤n <(N l), j = R, s is a preset real number.

20. The device according to claim 19, characterized in that if the rank of the precoding matrix is 1, then the matrix W. The number of columns of and W _v is both 1, and the first matrix \\^ has the following form

Among them, _ψχ = ^πχι1 , ij is the normalization factor, J is an integer, and Ν ₂ is an integer greater than 1.

21. The device according to claim 20, characterized in that: W. The other matrix in W _v except the first matrix is the second matrix, and the second matrix w ₂ has the following form:

Wherein, V is an integer and V is equal to the number of rows of the second matrix, K and N ₃ are both integers greater than 1, and t and q are both integers.

22. The device according to any one of claims 19 to 21, characterized in that, if the rank of the precoding matrix is greater than or equal to 2, the first matrix has the following form:

W ^yv ^l = ¹ 1 ^- 2- ^W ^yv ^ο ^, ⁿ

23. The device according to any one of claims 19 to 21, characterized in that if the preprogrammed formula:

Where, n' is an integer and O n' CNi-l

24. The device according to claim 22 or 23, characterized in that if the rank of the precoding matrix is equal to 2, W. and the second matrix W ₂ in W _v in addition to the first matrix has the following form:

Among them, t and t' are integers and 1≤t,t'≤(K-l), V is the number of rows of the second matrix