JP2007013455A - Channel matrix arithmetic unit, channel matrix arithmetic method, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a new and improved channel matrix arithmetic unit for efficiently performing the inverse matrix arithmetic operation of a channel matrix by systematizing it, and for enabling a transmission/reception antenna to be compatible with an M×N system in a multi-carrier system MIMO system. <P>SOLUTION: This channel matrix arithmetic unit where a transmission/reception antenna is incorporated into a MIMO-OFDM transmission/reception device equipped with M×N(M and N are natural numbers which are 2 or more) transmission channels of variable sizes is provided with a small matrix dividing part for dividing a matrix H into 2×2 type matrix by using the element h<SB>ij</SB>(i is a natural number which is M or less, j is a natural number which is N or less) and a cofactor calculating part for calculating the cofactor of the divided 2×2 type matrix, a determinant calculating part for calculating the determinant of matrix ¾H¾ of the matrix H by using the calculated cofactor and a rank-down decision part (803) for deciding whether or not the matrix H is ranked down by using the determinant ¾H¾. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  TECHNICAL FIELD The present invention relates to a channel matrix operation in a MIMO-OFDM transmission / reception apparatus in which the number of transmission / reception antennas is M × N (for example, M, N = 2, 3, 4) and the number of antennas is variable in a wireless radio communication system using MIMO. The present invention relates to a channel matrix computing device, a channel matrix computing method, and related techniques.

  A MIMO transmission system is known as a technique that can significantly improve communication capacity or transmission speed by using a plurality of antenna elements for transmission, reception, or both. A MIMO transmission model with the number of transmitting antennas M and the number of receiving antennas N can be generally expressed as:

  Here, X is an M × 1 type transmission signal vector, Y is an N × 1 type reception signal vector, H is an M × N type channel matrix, and n is an N × 1 type noise + interference vector. The channel matrix H is generally represented by the following model.

Here, h _nm is an element of the channel matrix H and can be expressed as follows.

D is the number of incoming waves, R _i is the propagation distance of each i-th incoming wave from the transmitting antenna m to the receiving antenna n for each incoming wave, and λ is the wavelength.

In order to obtain the channel matrix H on the receiving side, a method of transmitting a known training sequence and the like and estimating from the training sequence on the receiving side is often used. When the channel matrix is obtained, in the case of an open loop type MIMO receiver, the transmission signal can be estimated by using the inverse matrix H ⁻¹ of the channel matrix. Typical techniques include the following ZF (Zero Forcing) method and MMSE (Minimum Mean Square Error) method.

  ZF method:

  MMSE method:

Here, the subscript “ ^H ” represents a conjugate transpose, and σ _n ² is assumed to be equal to each channel in noise variance. Comparing the ZF method and the MMSE method, it is known that substantially the same characteristics can be obtained at high SNR, and that MMSE can obtain better characteristics at low SNR.

R _{ZF in the} equation (4) has the same form as the Moore-penrose general inverse matrix of the following equation, and when the matrix H has no rank drop, H ⁻¹ = (H ^H H) ⁻¹ H ^H The same result as the inverse matrix operation is obtained. In addition, when there is a rank drop, an accurate inverse matrix cannot be obtained. Therefore, when calculating H ⁻¹ , if an appropriate value is added to the reciprocal of the determinant, overflow can be avoided, and there is a failure on the device. Does not occur.

JP-A-6-231163

  As described above, when an inverse matrix operation is implemented as a device, a method of performing rank determination and performing an inverse matrix operation efficiently according to the determination result is desired, but an inverse matrix operation method that satisfies the above system requirements is provided. However, there is a problem that the scale of the device becomes large.

  The present invention has been made in view of the above-mentioned problems of the prior art, and an object of the present invention is to systematically calculate the channel matrix of all subcarriers necessary for OFDM transmission, for example, It is possible to correspond to a system in which the calculation within the OFDM symbol period or the number of transmitting and receiving antennas is variable as M × N (for example, M, N = 2, 3, 4), and further, rank determination is performed. It is an object of the present invention to provide a new and improved channel matrix calculation apparatus and channel matrix calculation method capable of efficiently performing an inverse matrix calculation according to a determination result, and a related technique (computer program or the like).

In order to solve the above problems, according to a first aspect of the present invention, a transmission / reception antenna is incorporated into a MIMO-OFDM transmission / reception apparatus having M × N (M and N are natural numbers of 2 or more) and having a variable-size transmission channel. A channel matrix computing device is provided. The channel matrix arithmetic unit of the present invention uses a small matrix dividing unit that divides the matrix H into a 2 × 2 matrix using elements h _{ij of the} matrix H (i is a natural number of M or less, j is a natural number of N or less). A cofactor calculation unit for calculating a cofactor of the divided 2 × 2 matrix, and a determinant calculation for calculating a determinant | H | of the matrix H using the calculated cofactor And a rank drop determination unit that determines whether the matrix H is rank-down using the determinant | H |.

  According to such a configuration, the determinant calculation can be processed only with a small matrix divided into 2 × 2 type or less, and a channel matrix computing device using rank drop determination information can be provided.

  The rank drop determination unit compares all elements of the matrix H with a predetermined element determination threshold, and all elements of a specific column or row of the matrix H are equal to or lower than a predetermined element determination threshold. If the determinant | H | is less than or equal to the determinant determination threshold, the matrix H may be determined to be rank-down. According to such a configuration, in the rank drop determination, by performing an element determination as to whether or not a specific column or row is close to 0 before the determinant calculation, a rank drop is clearly made such that the specific column or row is 0. In this case, since the determination can be made without calculating the determinant, it is possible to provide a channel matrix arithmetic apparatus that can omit useless calculations.

  A cofactor setting unit that sets and outputs a cofactor based on the determination result of the rank drop determination unit is provided, and the cofactor setting unit is determined by the rank drop determination unit that the matrix H is not rank drop. The cofactor calculated by the cofactor calculation unit is output, and when the rank deficient determination unit determines that the matrix H is rank deficient, the cofactor is replaced with the determinant determination threshold. You may make it do. According to such a configuration, when there is no rank drop, the cofactor is output by replacing it with a preset value (determinant decision threshold) when rank drop is avoided, thereby avoiding numerical failure during inverse matrix calculation. A determinant column arithmetic device can be provided.

  The inverse matrix of the matrix H may be calculated using the cofactor output from the cofactor setting unit or the determinant determination threshold. According to such a configuration, when using the sub-matrix division method for the inverse matrix calculation, the values required for the inverse matrix calculation use the values set in the rank drop determination unit, so that the calculation is not required in the inverse matrix calculation. Thus, it is possible to provide a channel matrix arithmetic apparatus capable of reducing the amount of calculation of the inverse matrix. As for the inverse matrix operation using the matrix partitioning method, there is a technique of Japanese Patent Application No. 2005-39164 already filed by the present applicant.

According to another aspect of the present invention, there is provided a channel matrix calculation method in a MIMO-OFDM transmission / reception apparatus having a transmission / reception antenna of M × N (M and N are natural numbers of 2 or more) and a variable-size transmission channel. The channel matrix calculation method according to the present invention is a sub-matrix dividing step of dividing the matrix H into a 2 × 2 matrix using elements h _{ij of the} matrix H (i is a natural number of M or less, j is a natural number of N or less). A cofactor calculation step for calculating the cofactor of the divided 2 × 2 matrix, and a determinant calculation for calculating the determinant | H | of the matrix H using the calculated cofactor And a rank drop determination step of determining whether or not the matrix H is rank dropped using the determinant | H |.

  According to such a configuration, the determinant calculation can be processed only with a small matrix divided into 2 × 2 type or less, and a channel matrix calculation method using rank drop determination information can be provided.

  According to another aspect of the present invention, there is provided a computer program that causes a computer to function as the channel matrix arithmetic device according to the first aspect of the present invention, and a computer-readable recording medium that records the computer program Is done. Here, the computer program may be described in any programming language. In addition, as a recording medium, for example, a recording medium that is currently used as a recording medium capable of recording a program, such as a CD-ROM, a DVD-ROM, or a flexible disk, or any recording medium that is used in the future should be adopted. Can do.

前記分割された２×２型行列の余因子|A₁₁|，|A₂₂|，|A₁₂|，|A₂₁|，|B₁|，|B₂|，|B₃|，|B₄|，|B₅|，|B₆|，|B₇|，|B₈|の計算を行う余因子計算部と，
前記計算された余因子を用いて，前記行列Ｈの行列式

の計算を行う行列式計算部と，
前記行列式|Ｈ|を用いて，前記行列Ｈがランク落ちであるかを判定するランク落ち判定部と，を備えたことを特徴とする。 In order to solve the above-described problem, according to a second aspect of the present invention, there is provided a MIMO-OFDM transmission / reception apparatus having a transmission channel of M × N (M, N = 2, 3, 4) and a variable-size transmission channel. An integrated channel matrix computing device is provided. The channel matrix computing device of the present invention is a small matrix that divides the matrix H into the following 2 × 2 type matrix for the elements h _ij (i, j = 1, 2, 3, 4) of the 4 × 4 type matrix H. A matrix partitioning unit;

Cofactors of the divided 2 × 2 matrix | A ₁₁ |, | A ₂₂ |, | A ₁₂ |, | A ₂₁ |, | B ₁ |, | B ₂ |, | B ₃ |, | B ₄ |, | B ₅ |, | B ₆ |, | B ₇ |, | B ₈ |
The determinant of the matrix H using the calculated cofactor

A determinant calculation unit for calculating
A rank drop determination unit that determines whether the matrix H is rank-down using the determinant | H |.

  According to such a configuration, the determinant calculation of 4 × 4 type, 3 × 3 type, and 2 × 2 type matrix can be processed with only a small matrix divided into 2 × 2 type or less, and rank-decision judgment information is used. Thus, a channel matrix computing device can be provided.

  The rank drop determination unit compares all elements of the matrix H with a predetermined element determination threshold, and all elements of a specific column or row of the matrix H are equal to or lower than a predetermined element determination threshold. If the determinant | H | is less than or equal to the determinant determination threshold, the matrix H may be determined to be rank-down. According to such a configuration, in the rank drop determination, by performing an element determination as to whether or not a specific column or row is close to 0 before the determinant calculation, a rank drop is clearly made such that the specific column or row is 0. In this case, since the determination can be made without calculating the determinant, it is possible to provide a channel matrix arithmetic apparatus that can omit useless calculations.

A cofactor setting unit that sets and outputs a cofactor based on the determination result of the rank drop determination unit is provided, and the cofactor setting unit is determined by the rank drop determination unit that the matrix H is not rank drop. If the surplus cofactor calculated by factor computation unit | a ₁₁ |, | a ₂₂ | outputs, by the rank deficient determination unit, if the matrix H is determined to be rank deficient, cofactor | A ₁₁ | and | A ₂₂ | may be replaced with the determinant determination threshold value and output. According to such a configuration, the cofactors | A ₁₁ | and | A ₂₂ | are set when there is no rank drop, and | A ₁₁ | and | A ₂₂ | By replacing and outputting, it is possible to provide a determinant column operation device that avoids the numerical failure of 1 / | A ₁₁ | or 1 / | A ₂₂ | required for inverse matrix calculation.

The inverse matrix of the matrix H may be calculated using the cofactors | A ₁₁ |, | A ₂₂ | output from the cofactor setting unit or the determinant determination threshold. According to such a configuration, when the submatrix division method is used for the inverse matrix calculation, A ₁₁ and A ₂₂ required for the inverse matrix calculation use those values set by the rank drop determination unit, so that the inverse matrix calculation uses those values. It is possible to provide a channel matrix calculation device that eliminates the need for calculation and can reduce the amount of calculation of the inverse matrix. As for the inverse matrix operation using the matrix partitioning method, there is a technique of Japanese Patent Application No. 2005-39164 already filed by the present applicant.

前記分割された２×２型行列の余因子|A₁₁|，|A₂₂|，|A₁₂|，|A₂₁|，|B₁|，|B₂|，|B₃|，|B₄|，|B₅|，|B₆|，|B₇|，|B₈|の計算を行う余因子計算工程と，前記計算された余因子を用いて，前記行列Ｈの行列式

の計算を行う行列式計算工程と，前記行列式|Ｈ|を用いて，前記行列Ｈがランク落ちであるかを判定するランク落ち判定工程と，を含むことを特徴とする。 According to another aspect of the present invention, there is provided a channel matrix calculation method in a MIMO-OFDM transmission / reception apparatus having a transmission / reception antenna of M × N (M, N = 2, 3, 4) and a variable-size transmission channel. . The channel matrix computation method of the present invention is a small matrix that divides the matrix H into the following 2 × 2 type matrix for the elements h _ij (i, j = 1, 2, 3, 4) of the 4 × 4 type matrix H. Matrix partitioning process;

Cofactors of the divided 2 × 2 matrix | A ₁₁ |, | A ₂₂ |, | A ₁₂ |, | A ₂₁ |, | B ₁ |, | B ₂ |, | B ₃ |, | B ₄ |, | B ₅ |, | B ₆ |, | B ₇ |, | B ₈ |, and a determinant of the matrix H using the calculated cofactor

A determinant calculating step for calculating the above, and a rank drop determining step for determining whether or not the matrix H is rank dropped using the determinant | H |.

  According to this method, the determinant calculation of 4 × 4 type, 3 × 3 type, and 2 × 2 type matrix can be processed only with a small matrix divided into 2 × 2 type or less, and rank-decision judgment information is used. A channel matrix calculation method can be provided.

  According to another aspect of the present invention, there is provided a computer program that causes a computer to function as the channel matrix arithmetic device according to the second aspect of the present invention, and a computer-readable recording medium that records the computer program Is done. Here, the computer program may be described in any programming language. In addition, as a recording medium, for example, a recording medium that is currently used as a recording medium capable of recording a program, such as a CD-ROM, a DVD-ROM, or a flexible disk, or any recording medium that is used in the future should be adopted. Can do.

  As described above, according to the present invention, a determinant calculation can be processed only with a small matrix divided into 2 × 2 types or less, and a channel matrix computing device using rank drop judgment information can be provided. . Also, in the rank drop determination, by performing element determination whether or not a specific column or row is close to 0 before the determinant calculation, in the case of a clear rank drop such as 0 for a specific column or row Since the determination can be made without calculating the determinant, useless calculation can be omitted. In addition, if there is no rank drop, the cofactor is output by replacing it with a preset value (determinant decision threshold) if rank drop, thereby avoiding numerical failure of the value required for inverse matrix calculation. Can do. In addition, when the small matrix partitioning method is used for the inverse matrix calculation, the values required for the inverse matrix calculation use the values set by the rank drop judgment unit, so that those calculations become unnecessary in the inverse matrix calculation. The amount of calculation can be reduced.

  Hereinafter, preferred embodiments of a channel matrix computing device, a channel matrix computing method, and a computer program according to the present invention will be described in detail with reference to the accompanying drawings. In the present specification and drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant description is omitted.

(1) Schematic Configuration of Channel Inverse Matrix Operation Device An outline configuration of an example of an OFDM transmission / reception device using a MIMO system will be described with reference to FIGS. In the present embodiment, an example of a 4 × 4 type MIMO system including four transmission antennas and four reception antennas will be described. Assume that the number of subcarriers employed in OFDM is 52, and training symbols having a known sequence are periodically inserted into the OFDM symbols.

<FIG. 1: 4 × 4 MIMO-OFDM Transmitter Example>
As shown in FIG. 1, the 4 × 4 MIMO-OFDM transmission apparatus 100 includes a modulation unit 101, an OFDM symbol generation unit 102, a MIMO signal generation unit 103, an IFFT 104, and MIMO-RF transmission units 105a to 105d. It is configured to include.

  The 4 × 4 MIMO-OFDM transmission apparatus 100 inputs data as transmission data to the modulation unit 101 after processing such as data framing and channel coding, performs modulation determined for each OFDM subcarrier, and generates an OFDM symbol generation unit After being converted to an OFDM symbol such as pilot carrier insertion at 102, a data stream to be transmitted by each of the four transmission antennas is generated according to the MIMO format defined by the MIMO signal transmission unit 103. These four data streams are subjected to inverse Fourier transform in IFFT 104 to form 52 subcarriers, guard symbols, etc. are added, and then four data are transmitted by each D / A converter of MIMO-RF transmitters 105a to 105d. Are converted to analog signals, up-converted by the RF unit, and four stream signals are transmitted from each transmission antenna at an appropriate timing.

<FIG. 2: Example of 4 × 4 MIMO-OFDM Receiver>
As shown in FIG. 2, the 4 × 4 MIMO-OFDM receiver 200 includes MIMO-RF receivers 201a to 201d, an FFT 202, a MIMO signal receiver 203, a demodulator 204, a channel matrix estimator 205, And a channel matrix processing unit 206.

The 4 × 4 MIMO-OFDM receiver 200 receives four streams of signals transmitted from the receiving antennas of the MIMO-RF receivers 201a to 201d, and the signals of the streams are down-converted by the RF unit. It is converted into a baseband signal by a D converter. The FFT 202 performs FFT on each stream at an appropriate timing to reproduce a signal corresponding to 52 subcarriers, separates the data and training symbols in the MIMO signal receiving unit, the data to the demodulation unit 204, and the training symbols to the channel. The result is output to the matrix estimator 205. The channel matrix estimator 205 estimates the elements of the channel matrix H by a process such as correlation between a known sequence and a training symbol. The channel matrix processing unit 206 calculates R _ZF when using the ZF method, and R _MMSE when using the MMSE method for 52 subcarriers for each OFDM symbol, and the demodulating unit 204 calculates for each subcarrier. (4) In the case of the MMSE method, the received signal vector is demodulated by calculating equation (5), and output as demodulated data for each transmitted stream.

(2) Outline of general inverse matrix calculation process using small matrix division method (2.1) Inverse matrix calculation by small matrix division An outline of general inverse matrix calculation process by the small matrix division method according to the present embodiment will be described.
In the system of the present embodiment, the maximum number of elements in the inverse matrix calculation is a 4 × 4 complex number with 4 transmission antennas and 4 reception antennas. When an inverse matrix is obtained using the Gaussian elimination method or LU decomposition, an operation is performed on 4 × 4 elements. Therefore, when implementing a device, it is difficult to construct an efficient module. Therefore, in this embodiment, the matrix is divided by the small matrix partitioning method, the calculation is based on the calculation of the 2 × 2 matrix, the 1 × 2, 2 × 1 vector and the scalar, and the feature of the Hermitian matrix. Process.

First, the principle of the submatrix partitioning method is explained (“Statistical and Adaptive Signal Processing”, DG Manolakis, VK Ingle,
S. M. See Kogon). A matrix smaller than the 4 × 4 type that is the object of the present embodiment is divided into four matrixes of 2 × 2 type or less as follows.

(1) 4 × 4 type:

  Each submatrix can be expressed as follows:

(2) For 3 × 3 type:

  Each submatrix can be expressed as follows:

  Each submatrix can be expressed as follows:

(3) For 4 × 3 type:

  Each submatrix can be expressed as follows:

(4) For 3 × 4 type:

  Each submatrix can be expressed as follows:

(5) For 3 × 2 type:

  Each submatrix can be expressed as follows:

(6) For 2 × 3 type:

  Each submatrix can be expressed as follows:

When each sub-matrix divided in this way is used, the inverse matrix A ^-1 of the matrix A can be expressed as follows.

Here, the matrices E ₁ , F ₁ , E ₂ , and F ₂ are set as follows.

In addition, it is assumed that A ₁₂ = A ₂₁ and the inverse matrices A ₁₁ ⁻¹ and A ₂₂ ⁻¹ exist.

In the case of the general inverse matrix, the matrix A in the equation (22) is targeted for (H ^H H) in the equation (4) and (H ^H H + σ ² I) in the equation (5). Both are square matrices and Hermitian matrices. Therefore, only the 4 × 4 type and 3 × 3 type sub-matrices described above need be considered.

  The inverse matrix of the 2 × 2 matrix can be obtained directly from the following equation.

  From equation (22), it is necessary to calculate inverse matrices for the following four.

In the case of a 4 × 4 matrix, the sub-matrices in Equation (25) are all 2 × 2 matrices, and can be calculated using Equation (24). In the case of a 3 × 3 matrix, since A ₂₂ ⁻¹ and E ₁ ⁻¹ are scalar real numbers, their reciprocals may be obtained.

(2.2) Inverse matrix operation by sub-matrix division Since the determinant is used for rank determination, it is calculated before the inverse matrix operation. Here, | H | represents a determinant.

(A) In the case of a 4 × 4 type matrix For H in Expression (10) of the above “(2.1) Inverse matrix operation by submatrix division”, cofactor decomposition is performed up to a 2 × 2 type matrix as follows. .

By decomposing in this way, a 4 × 4 determinant can be calculated using only a 2 × 2 determinant. Here, the submatrices A ₂₂ and A ₂₁ used in the equation (10) of “(2.1) Inverse matrix operation by submatrix division” are rewritten.

  here,

Furthermore, by modifying as follows, the sub-matrices A ₁₁ and A ₁₂ used in the equation (10) of “(2.1) Inverse matrix operation by sub-matrix division” can also be written.

  Further deformation yields

As a result, | A ₁₁ | and | A ₂₂ | are calculated by determinant arithmetic. These need to be calculated in the inverse matrix operation when performing the inverse matrix operation using the matrix partitioning method. Therefore, if these are stored in a register and read when calculating the inverse matrix, there is no need to calculate again.

(B) In the case of a 3 × 3 matrix,
Cofactor decomposition is performed on the third row based on the equation (11) of “(2.1) Inverse matrix operation by submatrix division”.

As a result, | A ₁₁ | is obtained by determinant calculation. A ₂₂ is a scalar. Similar to the 4 × 4 matrix, when performing inverse matrix operation using the matrix partitioning method, if these are stored in a register and read when calculating the inverse matrix, there is no need to calculate again.

(C) In the case of a 2 × 2 matrix,

In this case, the determinant operation is | A ₁₁ | itself. Similarly to the 4 × 4 matrix, when performing the inverse matrix operation using the matrix partitioning method, this is stored in the register and the inverse matrix calculation is performed. If it is read at times, there is no need to calculate again.

(3) Schematic Configuration of Inverse Matrix Operation Device Based on Submatrix Division Method With regard to the schematic configuration of an example of the general inverse matrix operation device based on the submatrix division method according to the present embodiment, a case where the channel matrix H is 4 × 4 is taken as an example This will be described with reference to FIG.

<Figure 3: Channel matrix computing device>
FIG. 3 shows a schematic configuration of an example of a channel matrix calculation apparatus using small matrix division described in “(2) Outline of general inverse matrix calculation process using small matrix division method”. As shown in FIG. 3, the channel matrix arithmetic unit 300 includes a register 301, an input matrix module 302, a conjugate transposition unit 303, an inverse matrix multiplication module 304, a matrix multiplication module (A) 305, and a matrix subtraction unit. 306, an inverse matrix multiplication module 307, a matrix multiplication module (B) 308, an output matrix module 309, a rank determination unit 310, and a control unit 311.

In the present embodiment, when the channel matrix H is a square matrix such as 4 × 4 type, 3 × 3 type, and 2 × 2 type and there is no rank drop using the channel inverse matrix arithmetic unit, it is normally assumed that C _x = H An inverse matrix operation is performed to obtain H- ¹ . If there is a rank drop, a matrix calculation is performed by replacing the determinant of the cofactor with a preset threshold value to obtain H- ¹ .

A vertically long non-square matrix such that H is 4 × k type and k = 2, 3, 3 × 2 type is C _x = H′H, whereas horizontal type such as k × 4 type, k = 2, 3, 2 × 3 type non-square matrices to calculate the C _{x =} HH ', after obtaining the square matrix C _x determined by the lesser of the number of rows and columns, and calculates the inverse matrix C _x ^-1 of C _x, the elongated The pseudo square matrix is obtained by H ⁻¹ = C _x ⁻¹ H ′ for the non-square matrix and H ⁻¹ = H′C _x ^{−1 for} the horizontally long non-square matrix. If there is a rank drop in C _x , as in the square matrix, C _x ⁻¹ is obtained by performing a matrix operation by replacing the determinant of the cofactor with a preset threshold value.

The rank drop determination is performed before the inverse matrix calculation by the rank determination unit 310. If there is no rank drop, the inverse matrix is used by using the cofactors | A ₁₁ | and | A ₂₂ | shown in Expressions (31) and (32). An inverse matrix operation is performed by the operation module 304 to the matrix multiplication module 308. On the other hand, if there is a rank drop, the cofactors | A ₁₁ | and | A ₂₂ | are replaced with a preset threshold, for example, 10 ⁻⁴ , and then the inverse matrix calculation module 304 to the matrix multiplication module 308 perform the inverse matrix calculation. . Here, the predetermined threshold value for replacing the cofactor | A ₁₁ | or | A ₂₂ | can be set to any value as long as the inverse matrix calculation does not fail. The threshold value th_b may be set to the same value.

In the case of a square matrix, the matrix C _x is a matrix having arbitrary elements. On the other hand, in the case of a non-square matrix, the matrix C _x is a Hermitian matrix. An efficient inverse matrix computing device for Hermitian matrix is the technology of Japanese Patent Application No. 2005-39164 already filed by the present applicant. Here, processing when an arbitrary element is included will be described. In the rank drop determination, the element determination threshold is th_a, and the determinant determination threshold is th_b.

The main parts (inverse matrix operation, rank determination) of each block in FIG. 3 are shown in FIGS.
The inverse matrix calculation is performed by the inverse matrix calculation module 304 to the matrix multiplication module (B) 308.

<Figure 4: Inverse matrix calculation module>
The inverse matrix calculation modules 304 and 307 are composed of an inverse matrix calculation unit 401 and a register 402 as shown in FIG. The inverse matrix calculation unit 401 will be described with reference to FIG.

<FIG. 5: Inverse matrix calculation unit>
As shown in FIG. 5, the inverse matrix calculation unit 401 includes a selector (I) 501, complex multipliers 502 a and 502 b, registers 503 a and 503 b, a subtraction unit 504, a selector (II) 505, an inverse operation unit 506, and a register 507. , Complex multipliers 508a, 508b, 508c, 508d, and sign inversion units 509a, 509b.

<FIG. 6: Matrix Multiplication Module (A)>
As shown in FIG. 6, the matrix multiplication module (A) 305 includes a selector 601, a matrix multiplication unit 602, a register 603, and a selector (II) 604.

<FIG. 7: Matrix Multiplication Module (B)>
The matrix multiplication module (B) 308 includes a matrix multiplication unit 701 and a register 702 as shown in FIG.

<FIG. 8: Rank determination unit>
Rank determination is performed by the rank determination unit 310. As shown in FIG. 8, the rank determining unit 310 includes an element determining unit 801, a determinant calculating unit 802, a determinant determining unit 803, and a cofactor setting unit 804.

<FIG. 9: Determinant Calculation Unit>
As shown in FIG. 9, the determinant calculation unit 802 includes a selector 901, complex multiplication units 902a, 902b, 904, a subtraction unit 903, a register (I) 905, a register (II) 906, an addition unit 907, a register (III 908.

  Hereinafter, an outline of inverse matrix calculation will be described by taking a 4 × 4 square matrix, 4 × 3 or 3 × 4 matrix as an example.

(A) Rank Determination The channel matrix H obtained by the channel matrix estimation unit 205 is stored in the register 301.

  When H is a square matrix, H is output from the register 301 to the rank determination unit 310. The rank determination unit 301 compares the element in the column or row with the threshold th_a in the element determination unit 801 and outputs the result to the rank drop determination unit 803. The rank drop determination unit 803 determines rank drop and outputs the result to the cofactor setting unit 804 if all elements in a specific column or row are equal to or less than the threshold value.

If the element determination result is not a rank drop, the determinant calculation unit 802 calculates the determinant | H | by dividing it into sub-matrices by the selector 901 according to the equations (27) to (30), and is obtained during the calculation. The cofactors | A ₁₁ | and | A ₂₂ | are stored in the register (II). The calculation result of the determinant | H | is output from the register (III) 908 to the rank drop determination unit 803, and the cofactors | A ₁₁ | and | A ₂₂ | are output from the register (II) 906 to the cofactor setting unit 804, respectively. . The rank drop determination unit 803 compares the determinant | H | and the threshold th_b. If | H |> th_b, it is determined that there is no rank drop and if | H | ≦ th_b, the rank drop is determined, and the result is set as a cofactor. Output to the unit 804.

The rank drop determination unit 803 outputs a rank drop presence / absence flag based on the above two types of rank drop determination results. When there is no rank drop, the cofactor setting unit 804 outputs the cofactors | A ₁₁ | and | A ₂₂ | as they are. On the other hand, if there is a rank drop, the cofactors are replaced with | A ₁₁ | = th_b, | A ₂₂ | = th_b, and output.

When H is a non-square matrix, H is output from the register 301 to the matrix input module 302, C _x = H′H is calculated for the vertical matrix, and C _x = HH ′ is calculated for the horizontal matrix, and the number of rows and columns is small. The square matrix C _x determined by the direction is output to the rank determination unit 310. Rank determination unit 310, the C _x performs the same rank determined in the case of the square matrix H described above.

(B) Inverse Matrix Calculation From the result of the determinant calculation, when the inverse matrix calculation is performed, processing is performed in the following procedure. That is, when H is a square matrix, the inverse matrix A ₁₁ ⁻¹ of A ₁₁ and A ₂₂ of Equation (10) is obtained for H that is submatrix-divided into 2 × 2 type that is passed through the matrix input module 302 without doing anything. , A ₂₂ ⁻¹ is calculated by the inverse matrix calculation unit 304. Since the determinants | A ₁₁ | and | A ₂₂ | required for the calculation use the set values of the cofactor setting unit 804, the values are selected by the selector (I) 501 and the selector (II) 502 so that these values can be output. 1 / | A ₁₁ |, 1 / | A ₂₂ | is calculated and stored in the register 507, and inverse matrices A ₁₁ ⁻¹ and A ₂₂ ⁻¹ are calculated according to the equation (24).

When H is a non-square matrix, small matrix decomposition is performed on C _x calculated by the matrix input module 302. In this case, since the matrix H is 3 × 4 type or 4 × 3 type, C _x is 3 × 3 type. When divided as shown in Equation (13), the sub-matrix of 2 × 2 type is only A ₁₁ , and the inverse matrix calculation unit 304 calculates an inverse matrix for A ₁₁ as described above. On the other hand, since A ₂₂ is a scalar, 1 / A ₂₂ is calculated by the reciprocal calculation unit 506.

Subsequently, E ₁ ⁻¹ , −E ₁ ⁻¹ F ₁ , −E ₂ ⁻¹ F ₂ , and E ₂ ⁻¹ are calculated according to the equation (22). These matrix multiplication module performing multiplication of A × B × C (A) a matrix performing 305,2 one subtraction matrix subtraction unit _306, E 1, _{E 2} of the inverse matrix _E ¹ _-1, the ^{E 2 -1} The inverse matrix module 307 that performs the calculation, -E ₁ ⁻¹ and F ₁ , and the matrix multiplication module 308 that performs the multiplication of E ₂ ⁻¹ and F perform each processing. As a result, when H is a square matrix, H ⁻¹ is obtained, and the matrix output module 309 outputs it without doing anything. H is for non-square matrices obtained _C ^{x -1,} the case of the matrix output module 309 in the elongated non-square matrix ^{_{H -1 = C x -1 H '}} , if the oblong non-square matrix ^{H -1} Calculate the pseudo inverse matrix by = H′C _x ⁻¹ and output the result.

(4) Rank determination and channel matrix reliability When rank drop determination unit 803 determines rank drop, | A ₁₁ | and | A ₂₂ | are replaced by threshold th_b in cofactor setting unit. This occurs when | A ₁₁ | or | A ₂₂ | is close to zero. Therefore, if | A ₁₁ | and | A ₂₂ | are used in inverse matrix calculation as they are, the value becomes very large when 1 / | A ₁₁ | or 1 / | A ₂₂ | is calculated. It overflows. Even if the value does not overflow, the inverse matrix element becomes large and the channel matrix H itself can be regarded as a singular matrix, so that the reliability of the estimated channel matrix itself can be regarded as low. For this reason, there is no point in finding exactly the inverse matrix for a matrix close to singularity. Therefore, when it is determined that the rank is dropped, | A ₁₁ | or | A ₂₂ | is set to a value that does not cause the inverse matrix calculation to fail. The threshold th_b may be selected. In addition, if there is a margin in processing speed and device scale, if it is determined that the rank is lowered, one method is to obtain a pseudo inverse matrix using singular value decomposition.

  When the technique described in this embodiment is applied to a wireless LAN, it is necessary to calculate an inverse matrix for 52 subcarriers using OFDM. When the channel frequency characteristics are almost the same for all subcarriers, the propagation path configuration between transmission and reception is almost the same for all subcarriers, and there is almost no time variation, the channel matrix for each subcarrier has almost the same characteristics. In such an environment, when a rank drop is determined for a certain subcarrier, there is a high possibility that adjacent subcarriers will also drop in rank, and rank drop may occur in a plurality of adjacent subcarriers. For example, in a propagation environment where a single diffracted wave is dominant, the channel matrix contracts and rank drops occur. If rank drop is observed in a plurality of adjacent subcarriers, it can be determined that the channel matrix reliability is low. The rank drop determination can also be used as the reliability information of such a propagation path.

  The channel matrix calculation device 300 and the channel matrix calculation method using the same according to the present embodiment have been described above. Such a channel matrix computing device 300 can cause a computer to function as the channel matrix computing device 300 by incorporating a computer program for realizing the above functions into the computer. Such a computer program can be distributed in the market in a form recorded on a predetermined recording medium (for example, a CD-ROM) or downloaded via an electronic network.

  The preferred embodiments of the channel matrix computing device, the channel matrix computing method, and the computer program according to the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to such examples. It will be obvious to those skilled in the art that various changes or modifications can be conceived within the scope of the technical idea described in the claims, and these are naturally within the technical scope of the present invention. It is understood that it belongs.

  For example, in the above embodiment, as a specific example of the inverse matrix operation, a 4 × 4 square matrix, a 4 × 3 or 3 × 4 matrix, and the like have been described as examples. However, the present invention is not limited to this, The present invention can be applied to an arbitrary M × N matrix (M and N are natural numbers of 2 or more).

  In addition, as the inverse matrix calculation technique to which the above embodiment can be applied, the technique (inverse matrix calculation using the matrix division method) of Japanese Patent Application No. 2005-39164 already filed by the present applicant has been described. The invention is not limited to this, and can be applied to any inverse matrix operation.

  The present invention relates to a channel of a MIMO-OFDM transmission / reception apparatus having a transmission / reception antenna of M × N (for example, M, N = 2, 3, 4) and a variable-size transmission channel in a wireless radio communication system using multiple antennas. It is a technique related to matrix calculation, and can be used for a channel matrix calculation device, a channel matrix calculation method, and related techniques.

It is explanatory drawing of a 4x4 MIMO-OFDM transmission apparatus. It is explanatory drawing of a 4x4 MIMO-OFDM receiver. It is explanatory drawing of a channel matrix calculating apparatus. It is explanatory drawing of an inverse matrix calculating module. It is explanatory drawing of an inverse matrix calculation part. It is explanatory drawing of a matrix multiplication module (A). It is explanatory drawing of a matrix multiplication module (B). It is explanatory drawing of a rank determination part. It is explanatory drawing of a determinant calculation part.

Explanation of symbols

100 4 × 4 MIMO-OFDM transmitter 200 4 × 4 MIMO-OFDM receiver 300 Channel matrix computing device 301 Register 302 Matrix input / output module 303 Conjugate transposition unit 304 Inverse matrix computing module 305 Matrix multiplication module (A)
306 Matrix Subtraction Unit 307 Inverse Matrix Operation Module 308 Matrix Multiplication Module (B)
309 Matrix output module 310 Rank determination unit 311 Control unit 401 Inverse matrix calculation unit 800 Rank determination unit 900 Determinant calculation unit

Claims (12)

A channel matrix computing device incorporated in a MIMO-OFDM transceiver device having a transmission / reception antenna of M × N (M and N are natural numbers of 2 or more) and a variable-size transmission channel,
A sub-matrix dividing unit that divides the matrix H into 2 × 2 type matrices using elements h _{ij of the} matrix H (i is a natural number of M or less and j is a natural number of N or less);
A cofactor calculation unit for calculating cofactors of the divided 2 × 2 matrix;
A determinant calculating unit that calculates a determinant | H | of the matrix H using the calculated cofactor;
Using the determinant | H |, a rank drop determination unit that determines whether the matrix H is rank drop;
A channel matrix computing device comprising: The rank drop determination unit
All elements of the matrix H are compared with a predetermined element determination threshold, and all elements in a specific column or row of the matrix H are equal to or less than a predetermined element determination threshold, or the determinant | H | 2. The channel matrix computing device according to claim 1, wherein the matrix H is determined to be rank deficient if is equal to or less than a determinant determination threshold. A cofactor setting unit that sets and outputs a cofactor based on the determination result of the rank drop determination unit;
The cofactor setting part is:
When the rank drop determination unit determines that the matrix H is not rank drop, outputs the cofactor calculated by the cofactor calculation unit;
3. The channel matrix computing device according to claim 2, wherein, when the rank drop determination unit determines that the matrix H is rank drop, a cofactor is output after being replaced with the determinant determination threshold value. .   4. The channel matrix computing apparatus according to claim 3, wherein an inverse matrix of the matrix H is calculated using the cofactor output by the cofactor setting unit or the determinant determination threshold. A channel matrix calculation method in a MIMO-OFDM transmitter / receiver having a transmission / reception antenna of M × N (M and N are natural numbers of 2 or more) and a variable-size transmission channel,
A sub-matrix dividing step of dividing the matrix H into a 2 × 2 matrix using elements h _{ij of the} matrix H (i is a natural number of M or less, j is a natural number of N or less);
A cofactor calculation step of calculating a cofactor of the divided 2 × 2 matrix;
A determinant calculating step of calculating a determinant | H | of the matrix H using the calculated cofactor;
A rank drop determination step of determining whether the matrix H is rank-down using the determinant | H |;
A channel matrix calculation method comprising:   A computer program for causing a computer to function as the channel matrix arithmetic device according to any one of claims 1 to 4. A channel matrix arithmetic device incorporated in a MIMO-OFDM transceiver device having a transmission / reception antenna of M × N (M, N = 2, 3, 4) and a variable-size transmission channel,
A sub-matrix dividing unit that divides the matrix H into the following 2 × 2-type matrix for the elements h _ij (i, j = 1, 2, 3, 4) of the 4 × 4-type matrix H;

Cofactors of the divided 2 × 2 matrix | A ₁₁ |, | A ₂₂ |, | A ₁₂ |, | A ₂₁ |, | B ₁ |, | B ₂ |, | B ₃ |, | B ₄ |, | B ₅ |, | B ₆ |, | B ₇ |, | B ₈ |
The determinant of the matrix H using the calculated cofactor

A determinant calculation unit for calculating
Using the determinant | H |, a rank drop determination unit that determines whether the matrix H is rank drop;
A channel matrix computing device comprising: The rank drop determination unit
All elements of the matrix H are compared with a predetermined element determination threshold, and all elements in a specific column or row of the matrix H are equal to or less than a predetermined element determination threshold, or the determinant | H | 8. The channel matrix computing device according to claim 7, wherein if the value is equal to or less than a determinant determination threshold, the matrix H is determined to be rank-down. A cofactor setting unit that sets and outputs a cofactor based on the determination result of the rank drop determination unit;
The cofactor setting part is:
When the rank drop determination unit determines that the matrix H is not rank drop, outputs the cofactors | A ₁₁ |, | A ₂₂ | calculated by the cofactor calculation unit;
When the rank drop determination unit determines that the matrix H is rank drop, cofactors | A ₁₁ | and | A ₂₂ | are replaced with the determinant determination threshold and output. Item 9. The channel matrix computing device according to Item 8. 10. The inverse matrix of the matrix H is calculated using the cofactors | A ₁₁ |, | A ₂₂ | output from the cofactor setting unit or the determinant determination threshold value. Channel matrix arithmetic unit. A channel matrix calculation method in a MIMO-OFDM transceiver apparatus having a transmission / reception antenna of M × N (M, N = 2, 3, 4) and a variable-size transmission channel,
A sub-matrix dividing step of dividing the matrix H into the following 2 × 2-type matrix for the elements h _ij (i, j = 1, 2, 3, 4) of the 4 × 4 type matrix H;

Cofactors of the divided 2 × 2 matrix | A ₁₁ |, | A ₂₂ |, | A ₁₂ |, | A ₂₁ |, | B ₁ |, | B ₂ |, | B ₃ |, | B ₄ |, | B ₅ |, | B ₆ |, | B ₇ |, | B ₈ |
The determinant of the matrix H using the calculated cofactor

A determinant calculation process for calculating
A rank drop determination step of determining whether the matrix H is rank-down using the determinant | H |;
A channel matrix calculation method comprising:   A computer program for causing a computer to function as the channel matrix arithmetic device according to any one of claims 7 to 10.

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