CN100369390C

CN100369390C - Method of receiving radio transmission by multiple antenna array

Info

Publication number: CN100369390C
Application number: CNB2004100546017A
Authority: CN
Inventors: 朱胡飞
Original assignee: ZTE Corp
Current assignee: ZTE Corp
Priority date: 2004-07-22
Filing date: 2004-07-22
Publication date: 2008-02-13
Anticipated expiration: 2024-07-22
Also published as: CN1725666A

Abstract

The present invention discloses a method for receiving and wirelessly transmitting multiple antenna arrays. The linear least mean square error estimation of transmitted signal vectors s is obtained through a least mean square error signal estimation matrix G. In the method of the present invention, only P<1/2> needs to be found, and in the iterative procedure in which a zero forcing vector is obtained, only P<1/2> needs to be updated each time. Compared with the prior art, the amount of calculation is reduced, and numerical stability and robustness and convenience for hardware implementation can be ensured.

Description

Method for receiving wireless transmission by multi-antenna array

Technical Field

The present invention relates to wireless and radio frequency communication systems, and more particularly, to a signal receiving method for a digital wireless communication system using multiple antenna arrays at both the transmitting end and the receiving end.

Background

Factors that determine the ultimate achievable bit rate for transmitting data in a digital wireless communication system based on predictions from information theory include: total transmit power at the transmitting end, number of antenna elements at the transmitting end and the receiving end, bandwidth, noise power at the receiving end, and characteristics of the propagation environment. Most conventional systems use a single transmit antenna element and a single receive antenna element. However, it has been recognized that the use of multiple antenna arrays at the transmitting end, the receiving end, or both, can provide significant bit rate improvements. U.S. patent No.6,097,771 proposes a wireless communication system with space-time architecture using multiple antenna arrays simultaneously at the transmitting and receiving ends. In addition, the patent 6,600,796 also proposes a known scheme of using multiple antenna arrays at both the transmitting end and the receiving end, as shown in fig. 1. This scheme operates in a "rayleigh scattering environment", that is, in such a signal propagation environment, the individual elements of the channel matrix can be approximately regarded as statistically independent. As shown, in the illustrated system, a data sequence is divided into M uncorrelated symbol subsequences. Each sub-sequence is transmitted by one of M transmit antennas. After being affected by a channel with a channel matrix of H, the M subsequences are received by N receiving antennas at a receiving end. Transmitting signal s ₁ ，…，s _M Respectively transmitted through M different antenna elements 10-1, …, 10-M. Corresponding received signal x ₁ ，…，x _N Received from N different antenna elements 15-1, …,15-N, respectively. In this scheme, the number of transmit antenna elements M is at least 2, and the number of receive antenna elements N is at least M. The channel matrix H is an N × M matrix in which the elements in the ith row and j column represent the coupling of the ith receive antenna and the jth transmit antenna through the transmission channel. Received signal x ₁ ，…，x _N Is processed in a digital signal processor to produce a recovered transmit signal  ₁ ，…， _M 。

Also shown in this figure are summation components 12-1, 12-2, 12-N, which represent the contained unavoidable noise signal w ₁ ，w ₂ ，…，w _N These noise signals are added to the signals received by the receive antenna units 15-1, 15-2, …,15-N, respectively.

In particular, the channel matrix H comprises a channel vector H _:1 To h _:M The effect of the channel on each of the M transmission signals is indicated separately. More specifically, the channel vector h _:1 Comprising a channel matrix entry h ₁₁ To h _N1 Denotes a channel pair transmission signal s at each of the receiving antenna units 15-1 to 15-N, respectively ₁ The influence of (a); letterTrack vector h _:2 Comprising a channel matrix entry h ₁₂ To h _N2 Denotes a channel pair transmission signal s at each of the receiving antenna units 15-1 to 15-N, respectively ₂ The influence of (a); channel vector h _:M Comprising a channel matrix entry h _1M To h _NM Denotes a channel pair transmission signal s at each of the receiving antenna units 15-1 to 15-N, respectively _M The influence of (c).

A more formal description of such a multiple input multiple output (multiple antenna array used simultaneously at both the transmitting and receiving ends) architecture is as follows. First, at the receiving end, one can get:

here, the

Is a vector of the received signal in N dimensions,

is an N x M complex matrix that is assumed to be constant over a period of K symbols. Vector h _n: And h _:m Are M and N, respectively,

is an M-dimensional transmit signal vector,

is an Additive White Gaussian Noise (AWGN) vector of zero-mean complex number, its variance

While ^T And ^* respectively representing transpositions and conjugate transpositions of matrices or vectors, whereas I is here _N×N Representing an N × N identity matrix. (additive noise is assumed here)Are statistically independent in both the time and spatial domains. )

In this system, the signals transmitted by the multiple antennas at the transmitting end are detected one by one at the receiving end in an optimal order, and the influence of the newly detected signal is eliminated (cancelled) one by one from the remaining signal detection problems to reduce the dimension of the signal detection problem at the next step; in the process of detecting the transmitted signals one by one, for each signal to be detected, a zero forcing (nulling) vector is found and used to eliminate the influence of all remaining interfering signals, so as to obtain an estimate of the signal to be detected.

For the above wireless communication system, a new and efficient method for determining zero forcing vectors and optimal sequence is disclosed in U.S. Pat. No.6,600,796. The steps of the method are shown in fig. 2, 3, 4 and 5, and a key part of the method is that the zero tracking vector and the optimal sequence can be called as P ^1/2 And Q _α The matrix of (2) is derived without the need for matrix squaring and matrix inversion. Matrix P ^1/2 And Q _α Obtained by propagating a matrix squaring algorithm. The only input to this algorithm is the row of the channel matrix H and the inverse of the average signal-to-noise ratio a. To implement the open-square algorithm, a suitable unitary matrix must also be introduced, which is selected according to the input values.

Matrix product P ^1/2 Q _α ^* (the symbol ". Times.denotes a conjugate transpose) is equal to the generalized inverse H of an extended matrix comprising the channel matrix H as a sub-matrix _α ⁺ . The vector of the transmitted signal can be obtained by the matrix

Linear minimum mean square error estimate of (d):

is obviously H _α ⁺ Correspond to

The first N columns of (a).

P ^1/2 And Q _α Is selected from anotherThe appropriate unitary matrix is completed and the transform provides values for insertion into a simple formula for calculating the zero-forcing vector for the next signal, the detection of which is optimal. After each zero-forcing vector is obtained, the effects of the newly obtained signal are removed from the remaining signal detection problems, P ^1/2 And Q _α Is reduced and another transformation is applied. This procedure iterates until all zero-forcing vectors are obtained.

It is noted that P is only required once ^1/2 And Q _α Therefore, only one time of matrix-solving generalized inverse operation is carried out. This approach may reduce matrix inversion operations and thus improve stability in the numbers. Because the generalized inverse operation of matrix solving is carried out only once, compared with the prior method, the computational complexity can be reduced by one order of magnitude. This method is efficient andis numerically stable because it uses unitary transforms to avoid matrix squaring and matrix inversion. However, as can be seen from its implementation steps, there is still room to increase its efficiency.

Disclosure of Invention

The invention provides a method for receiving wireless transmission by a multi-antenna array, which can further improve the processing efficiency. Compared with the United states patent No.6,600,796, the key of the invention is that the zero forcing vector and the optimal sequence can be called as P ^1/2 And in the method of us patent No.6,600,796, the zero-forcing vectors and the optimal order are a pair called P ^1/2 And Q _α Is derived. In other words, the calculation of Q can be avoided _α . Wherein P in the process of the invention ^1/2 And P in the method of U.S. Pat. No.6,600,796 ^1/2 The same is true.

The invention relates to a method for receiving wireless transmission by a multi-antenna array, which is used for detecting at least two transmitting signals in a multi-input multi-output communication system, wherein the transmitting signals are transmitted by different transmitting antennas and pass through a channel, and the method specifically comprises the following steps:

a) Collecting at least two receiving signals from different receiving antennas, wherein the receiving signals are signals collected by the receiving antennas after the signals transmitted by the transmitting antennas pass through channels;

b) Multiplying a vector of said at least two received signals by a zero-forcing vector to provide a linear minimum mean square error estimate, said estimate corresponding to a particular one of said at least two transmitted signals, to enable detection of said particular transmitted signal;

c) At least partially canceling the effect of the detected signal in said at least two transmitted signals from said received signal vector, said canceling the effect of the detected signal being based on a calculated estimate of said detected signal;

d) Repeating steps b), c) in a preferred sequence until corresponding to each of said at least two transmitted signals; wherein a corresponding linear minimum mean square error estimate has been provided;

it is characterized in that the preparation method is characterized in that,

e) The preferred order and each zero-forcing vector are derived from a channel matrix H, which is composed of estimated channel coefficients;

f) Computing the matrix P ^1/2 Said matrix being related to an error covariance matrix P, the error covariance matrix P = (α I + H) ^* H) ^-1 Where α is the average signal-to-noise ratio and I is the identity matrix, the relationship between them being according to the formula P representing the relationship between them ^1/2 (P ^1/2 ) ^* = P, where denotes conjugate transpose;

g) Each of all zero-forcing vectors is a slave matrix P ^1/2 Derived, obtaining each of several zero-forcing vectors, including efficient triangularization P ^1/2 (ii) a Zero forcing vector G _J Obtained from the following equation:

wherein J = M, M-1, 1 is the index of the J-th transmitting antenna or J-th transmitting signal, M is the number of transmitting antennas,

each of the above scalar coefficients p _J ^1/2 Is a matrix P that has been triangulated ^(J)/2 The diagonal elements of (1);

each of the above vectors [ P _J ^(J-1)/2 ) ^* (p _J ^1/2 ) ^* ]Is a matrix P that has been triangulated ^(J)/2 The conjugate transpose of the last column of (a); h ^(J) The channel matrix H is a channel matrix after column exchange or a reduced channel matrix after column exchange and column deletion are alternately carried out.

h) Defining a minimum mean square error signal estimation matrix G, wherein G is defined by: g = P ^1/2 (P ^1/2 ) ^* H ^* The above zero forcing vector G _J Is equivalent to calculating one row of the corresponding matrix G in each iteration of the first execution of the above-mentioned step b) or of the subsequent step b), while the number of rows of the above-mentioned corresponding matrix G is gradually reduced.

Each channel matrix H in said step g) ^(J) The obtaining comprises the following processes: in each first execution of the above-mentioned step b) or in each subsequent repetition of step b), the original size or reduced channel matrix H must be aligned before being used for calculating the above-mentioned zero-forcing vector ^(J) Exchanging columns; at the same time, each of the above original size or reduced channel matrices H ^(J) Deleting the channel matrix H after being used to calculate the zero-forcing vector in each first execution of the above step b) or in each subsequent repetition of step b) ^(J) Can obtain the channel matrix H for the next iteration of step b) ^(J-1) 。

The column switching of the matrix specifically includes: the exchange of a column of the matrix corresponding to the above-mentioned transmission signal detected by the previous execution of step b) with a column of the matrix corresponding to the last of the above-mentioned transmission signals not yet detected.

The preferred order is from the above-mentioned matrix P ^(J)/2 Is determined.

Matrix P ^1/2 The open-square operation of the error covariance matrix P is achieved by introducing a unitary matrix, obtained from the channel matrix H.

Error covariance matrix P = (α I + H) ^* H) ^-1 Where α is the average signal-to-noise ratio and I is the identity matrix.

The method of us patent No.6,600,796 uses a generalized inverse matrix associated with the channel matrix H to obtain each of several zero-forcing vectors, while the method of the present invention uses a minimum mean square error signal estimation matrix associated with the channel matrix H to obtain each of several zero-forcing vectors. Correspondingly, the method of U.S. Pat. No.6,600,796 requires the determination of P ^1/2 And Q _α And in the iterative process of obtaining the zero-forcing vector, P is updated simultaneously every time ^1/2 And Q _α (ii) a The method of the invention only needs to obtain P ^1/2 And in the iterative process of obtaining the zero-forcing vector, only P needs to be updated every time ^1/2 . It is clear that the method of the present invention requires less calculation than the method of us patent No.6,600,796. Further analysis can demonstrate that the method of the present invention is 36% faster than the method of U.S. Pat. No.6,600,796, using a standard in the number of multiplications and additions required. At the same time, since the matrix Q need not be used at all _α The method of the invention also requires less memory. Because the method of the invention uses unitary transformation to avoid matrix square operation and matrix solvingConversely, it retains the advantages of the method of us patent No.6,600,796, such as stability in number, robustness and ease of hardware implementation.

Drawings

Fig. 1 is a schematic diagram of a multiple-input multiple-output (MIMO) wireless communication system using multiple transmit antenna elements and multiple receive antenna elements;

fig. 2 is a flow chart of a process for detecting a received signal in the communication system of us patent 6,600,796;

FIG. 3 is a flow chart of an extension of the matrix squaring algorithm in U.S. Pat. No.6,600,796;

FIG. 4 is a flow chart of the process of obtaining zero forcing vector of the United states patent 6,600,796;

FIG. 5 is a flow chart of the application of zero forcing vector detection signal in US patent 6,600,796;

FIG. 6 is a process flow diagram of the core algorithm of the present invention;

FIG. 7 is a flow chart of an extension of a matrix squaring algorithm in the present invention;

FIG. 8 is a flow chart of the process of obtaining a zero-forcing vector of the present invention;

FIG. 9 is a flow chart of the present invention for applying a zero-forcing vector detection signal;

FIG. 10 is a flow chart of an overall implementation of the method according to the invention;

FIG. 11 is a graphical representation comparing the calculated amount of the method of the present invention with that of the method of U.S. Pat. No. 5, 6,600,796.

Detailed Description

In the method of U.S. Pat. No.6,600,796 is by a generalized inverse matrix

A linear minimum mean square error estimate of the transmit signal vector s is obtained. In the method of the invention, a linear minimum mean square error estimate of the transmit signal vector s is obtained by means of another matrix G:

the matrix G, referred to herein as the minimum mean square error signal estimation matrix, is defined by:

G＝P ^1/2 (P ^1/2 ) ^* H ^*

from P ^1/2 The formula for deriving the Mth zero-forcing vector is

Wherein p is _M ^1/2 And P _M ^(M-1)/2 Are as defined in U.S. Pat. No.6,600,796, and are all relative to the unitary matrix pair P ^1/2 Intermediate results from the transformation are made. H is the channel matrix. Using this formula, the remaining M-1 zero-forcing vectors G can be obtained by iterating the procedures of blocks 215-235 _J ，J＝M-1，...，1。

Note that G is used here _J J = M, M-1.., 1 as the optimal zero-forcing vector for the J-th signal, itThe most-zero-forcing vector H used in U.S. Pat. No.6,600,796 _α，J ⁺ Different.

The matrix P is the same as the corresponding algorithm in U.S. Pat. No.6,600,796 ^1/2 By propagating a matrix squaring algorithm, the only input to this algorithm is the row of the channel matrix H and the inverse of the average signal-to-noise ratio α.

To implement the square-opening algorithm, it is also necessary to introduce a suitable unitary matrix, chosen according to the input values, as will be explained below. P ^1/2 The transform is performed by selecting another suitable unitary matrix, which provides values for insertion into a simple formula for calculating the zero-forcing vector for the next signal, the detection of which is optimal. After each zero-forcing vector is obtained, the effects of the newly obtained signal are removed from the remaining signal detection problems, P ^1/2 Is reduced and another transformation is applied. This procedure iterates until all zero-forcing vectors are obtained.

It is noted that P is only required once ^1/2 So that the least mean square error signal estimation matrix G = P is only implemented once ^1/2 (P ^1/2 ) ^* H ^* Efficient calculation of (1). Like the method of us patent No.6,600,796, the method is efficient and numerically stable because it also uses unitary transforms to avoid matrix squaring and matrix inversion.

The following set of equations compares the principles underlying the method of the present invention with those underlying the method of U.S. Pat. No.6,600,796. It must be noted that the invention herein uses G _J As the most zero-forcing vector for the J-th signal, it is the most zero-forcing vector H used in U.S. Pat. No.6,600,796 _α，J ⁺ Different. The left part of this set of equations illustrates G _J The derivation process of (1); and H is illustrated on the right _α，J ⁺ And the channel matrix H and matrix P ^1/2 、Q _α The relation between them is based on the well-known QR decomposition theorem.

The method of us patent No.6,600,796 is summarized at the basic conceptual level in fig. 2. As shown in block diagram 110Showing, matrix P ^1/2 And Q _α Is obtained. At block 115, the next signal to be detected is passed through the matrix P ^1/2 And (6) determining. At 120 block diagram, matrix P ^1/2 And Q _α Is used to derive the current zero-forcing vector, which is used for signal detection as described below. At block 125, by using P ^1/2 One sub-matrix of itself replaces P ^1/2 And with Q _α One sub-matrix of the self replaces Q _α C, the order of the problem is reduced by one. The steps of the block diagrams 115 to 125 are iterated until the most probable one is detectedThe latter signal.

Find P ^1/2 And Q _α The iterative process of (a) is shown in fig. 3. This process is called an "open square algorithm". In a square-on-square algorithm, in each iteration with index i, the form is X _i Θ _i ＝Y _i Is performed. Each theta _i Is a unitary transform which introduces zeros into the transformed matrix Y _i Several locations are specified. After each iteration, from the transformed matrix Y _i The retrieved specific values are fed back as a pre-transform matrix X _i+1 For the next iteration. These iterations of matrix multiplication are referred to as "expanding" this algorithm.

The process shown in fig. 3, in each iteration i, i =1 _|i ^1/2 And Q _i Is updated.

After the Nth iteration, P ^1/2 Is set to P _|N ^1/2 Are equal to, and Q _α Is set to Q _N And equal, as shown in block 145. As shown in block 130, P is initialized by the following equation _|i ^1/2

Where I is an M × M identity matrix, and Q =0 is set _(N×M) Initialization Q _i Here 0 _(N×M) Is an N x M matrix with all entries being zero.

At block 140, shaped as X _i Θ _i ＝Y _i The matrix multiplication of (2) is performed. Matrix X before transformation _i Is an (N + M + 1) × (M + 1) matrix defined by the following formula:

where 0 _M Is a column vector with all M terms being zero, and e _i Is the ith unit column vector of dimension N. Each time sequence number is shown in block 140In an iteration of i, H _i Is the corresponding ith row of the channel matrix.

In each iteration with index i, the corresponding matrix Θ _i Is any one of the pre-transform matrices X _i Block-down triangulated unitary transform. By "triangularization under blocks" is meant a transformed matrix Y of (N + M + 1) × (M + 1) _i The last M entries of the first row are all zeros. It is well known to find suitable methods for such a unitary transform, such as using a Householder transform or a series of Givens rotations. The decision of an appropriate unitary transform is shown in block 135.

Transformed matrix Y _i Each sub-matrix of (a) is represented by the following formula:

submatrix P _|i ^1/2 And Q _i As already defined above. As shown in

block

140, 0 _M ^T Is an M-dimensional all-zero row vector. Those "x" represent items not relevant to the discussion herein.

Therefore, each time an iteration of the block diagram 140 is completed, the sub-matrix P _|i ^1/2 And Q _i Is fed back to X and the next row of the channel matrix H _i For the next iteration.

As previously mentioned, P after the last, nth, iteration _|i ^1/2 And Q _i Is the value of P sought ^1/2 And Q _α As shown in block 145.

P ^1/2 And Q _α Is calculated to form a generalized inverse H _α ⁺ One efficient calculation of (2). It is worth noting that in this method, such efficient calculation occurs only once.

FIG. 4 illustrates how the matrix P can be used ^1/2 And Q _α Obtain zero forcing vector H _α，J ⁺ J = M, M-1,.., 1. In block diagram 150, matrix P ^1/2 The minimum length row is determined. This determines the best detected signal in the current iteration. In block 155, the signal indices are permuted and renumbered so that the selected optimum signal will be the mth signal. Accordingly, the columns of the channel matrix H are also permuted so that the column corresponding to the selected optimum signal is the mth column.

In block 160, a unitary transform sigma is found which triangulates a matrix P over the block ^1/2 . That is, Σ is an arbitrary unitary transform as long as it makes a matrix product P ^1/2 Σ the first M-1 terms of the last row (i.e., row M) are all zeros. A suitable transform sigma can be easily found by standard techniques from the previous description of the lower triangular transform.

M matrix P ^1/2 The various sub-matrices of Σ are as follows:

in the above formula, P ^(M-1)/2 Is a (M-1) × (M-1) -dimensional sub-matrix, P _M ^(M-1)/2 Is an M-1 dimensional column vector, 0 _M-1 ^T Is a row vector with M-1 dimensions of elements all zero, and p _M ^1/2 Is a scalar. As explained below, in the next iteration of block 160, P ^(M-1)/2 Will substitute P ^1/2 . Scalar p _M ^1/2 Will be used to derive the mth zero-forcing vector. After the unitary transform sigma is obtained in block 160, it is used to transform the matrix Q _α As shown in block 165. That is, Q _α Is updated to Q _α And (sigma). As also indicated by block 165, updated Q _α Conjugate transpose of (Q) _α ^* Is obtained, and Q _α ^* Is obtained and used

And (4) showing.

As shown in block 170, the Mth zero forcingVector H _α，M ⁺ Is obtained as the product

The process of blocks 150 through 170 is iterated to obtain the remaining M-1 zero-forcing vectors H, as shown in block 175 _α，J ⁺ J = M-1,M-2. In each iteration of

blocks

150 and 155, the signal indices are permuted and renumbered so that P is currently updated ^1/2 (now by P ^(J)/2 Representation) is row J. In each iteration of the block diagram 160, a unitary transformation sigma is found such that the matrix product P ^(J)/2 Σ last row satisfies the division of the last term (i.e. item J, scalar p) _J ^1/2 ) All but zero. In each iteration of block 165, the vector

As (Q) _α ^J ) ^* Line J of (a) is obtained. In each iteration of the block diagram 170, the jth zero-forcing vector H _α，J ⁺ As a product of

Is obtained.

At the beginning of each iteration of blocks 150 through 170, P ^(J)/2 Is updated to P of the last iteration ^(J)/2 Σ upper left sub-matrix. That is, P ^(J)/2 Is given by the previous P ^(J)/2 The first J-1 row of the first J-1 column of Σ. Therefore, as mentioned previously, the updated P used to derive the M-1 st zero-forcing vector ^(J)/2 Is P ^(M-1)/2 。

At the beginning of each iteration of blocks 150 through 170, Q _α The value of (c) is also updated. Updated Q _α Value is Q _α ^J J = M-1,. …,1. Each Q _α ^J By deleting the previous Q that has undergone the transformation in block 165 on the last iteration _α ^J The last column of (2) is obtained. So, for example, the updated Q for the M-1 st zero-forcing vector _α By Q _α ^M-1 And it includes the original Q transformed in block 165 _α Head column M-1.

Importantly, a repeat of P ^(J)/2 Is equivalent to one P ^1/2 Triangularization on the block. As a result, each scalar coefficient p _J ^1/2 Can be regarded as an upper triangulated P ^1/2 The diagonal elements of (a). Furthermore, since the trigonometry is achieved on each block by applying a unitary transform, each vector is transformed by applying a unitary transform

Or is (Q) _α ^J ) ^* One row of, or is (Q) _α ^J ) ^* One row of the map under a unitary transform.

As previously described, each iteration of the block diagram 170 produces a zero-forcing vector H _α，J ⁺ . FIG. 5 shows how these zero-forcing vectors can be used to obtain each detected signal (the detected signal)  _j . As shown in block 177, each detected signal is derived from a corresponding zero-forcing vector and a received signal vectorThe vector product of (a) is obtained, i.e.,

after the detected signal, or recovered signal, is obtained from the above equation, a slicing step is performed to identify the detected signal, or recovered signal, as a member of a symbol constellation (symbol) that modulates the transmitted signal. Notably, the vector is used for the next detection before it is used

Is repairedTo eliminate the effect of the last detected signal. This step is illustrated in block 179, where after the jth signal is detected, J = M

Is updated to

In the foregoing formula, the vector h _:J Watch (A)The column of the channel matrix H corresponding to the jth signal is shown.

As can be seen from the detailed implementation steps of the method of U.S. Pat. No.6,600,796, the entire zero-forcing matrix Q is computed for each reduced sub-channel matrix _α And only one column is used (calculate the optimal zero-forcing vector); intermediate result P _M ^(M-1)/2 Is not used. The invention uses P _M ^(M-1)/2 Calculating the optimal zero-forcing vector and avoiding calculating Q _α . At the same time, the robustness of the method of U.S. patent No.6,600,796 is maintained because there is no matrix squaring and matrix inversion.

From a relation of transmitted and received signals

A Minimum Mean Square Error (MMSE) estimate of the transmitted signal is readily obtained:

here, the symbol "", denotes a conjugate transpose. The above equation for Minimum Mean Square Error (MMSE) estimation of a transmitted signal is well known to those skilled in the art.

Let

G＝(αI+H ^* H) ^-1 H ^*

Where G may be referred to as a minimum mean square error signal estimation matrix, then

Here, the

R＝(H ^H ·H+αI _M×M )

The contrast matrix for the error signal e (k) = s (k) -y (k) is:

R _ee ＝E{e(k)e ^H (k)}

＝σ _w ² R ^-1 ＝σ _w ² Q

it is clear that the element with the highest signal-to-noise ratio (SNR) of y (k) is the element with the smallest mean square error, so there is:

where q is _mm Matrix Q = R ^-1 The diagonal elements of (a).

Estimate error e = covariance matrix of s- :

E{(s-)(s-) ^* }＝(αI+H ^* H) ^-1 ≡P

therefore, it is

G＝(αI+H ^* H) ^-1 H ^* ＝PH ^*

The square root of the above matrix P is defined as follows:

P＝P ^1/2 (P ^1/2 ) ^*

then it can be deduced

G＝P ^1/2 (P ^1/2 ) ^* H ^*

In the block diagram 160 of fig. 4, which represents the process flow of us patent 6,600,796 to obtain zero-forcing vectors, a unitary transformation Σ is found which triangulates the matrix P in blocks ^1/2 ：

Because of the inherent nature of unitary transforms (which is well known to those skilled in the art) ∑ Σ ^* = I, it can be concluded

G＝P ^1/2 ∑·(P ^1/2 ∑) ^* ·H ^*

Then

The optimal zero-forcing vector for the mth signal, corresponding to row mth of G, can be obtained by the following equation:

now not using Q _α The optimal zero-forcing vector for the Mth signal can be obtained, so that the method of the invention can avoid Q _α And (4) calculating.

The implementation of the method of the present invention is shown in fig. 6, 7, 8 and 9, which are modifications of fig. 2, 3, 4 and 5, respectively, representing the implementation of the method of us patent No.6,600,796. Fig. 6, fig. 7, fig. 8 and fig. 9, which together illustrate an implementation of the inventive method, an overall flow diagram of an embodiment of the inventive method is shown in fig. 10.

As shown in block 235 of fig. 8, by product p _M ^1/2 [(P _M ^(M-1)/2 ) ^* (p _M ^1/2 ) ^* ]H ^* The Mth zero-forcing vector G can be obtained _M . As shown in block 240 of FIG. 8, the process of blocks 215-235 is iterated to obtain the remaining M-1 zero-forcing vectors G _J ，J＝M-1，…，1。

Here the invention uses G _J As the optimal zero-forcing vector for the J-th signal, it is the optimal zero-forcing vector H used in U.S. Pat. No.6,600,796 _α，J ⁺ Different.

The implementation of the solution is described in further detail below with reference to fig. 6, 7, 8 and 9, and the invention can be easily implemented by those skilled in the same field according to these block diagrams.

The invention is summarized in figure 6 at the basic conceptual level. As shown in the block diagram 180, the matrix P ^1/2 Is obtained. At block 185, the next signal to be detected passes through the matrix P ^1/2 And (6) determining. At 190, the block diagram, matrix P ^1/2 Is used to derive the current zero-forcing vector, which is used for signal detection as described below. At block 195, by using P ^1/2 One sub-matrix of itself instead of P ^1/2 The order of the problem is reduced by one. The steps of the block diagrams 185 to 195 are iterated until the last signal is detected.

Finding P ^1/2 The iterative process of (a) is shown in fig. 7, and this process is referred to as an "open square algorithm". FIG. 3 shows obtaining P ^1/2 And Q _α As can be readily seen, in contrast to fig. 3, the iterative process represented in fig. 7 does not require Q _α And thus the iterative process represented by fig. 7 requires a smaller amount of computation.

Attention is now directed to the process shown in fig. 7, with i =1 _|i ^1/2 Is updated. After the Nth iteration, P ^1/2 Is set to P _|N ^1/2 And equal, as shown in block 215. As shown in block diagram 200, P is initialized by the following equation _|i ^1/2

Where I is an M identity matrix.

At block 210, shaped as X _i Θ _i ＝Y _i The matrix multiplication of (2) is performed. Matrix X before transformation _i Is a (M + 1) × (M + 1) matrix defined by the following equation:

where 0 _M Is a column vector where all M terms are zero. In each iteration with index i, H, as shown in block 210 _i Is the corresponding ith row of the channel matrix.

In each iteration with index i, the corresponding matrix Θ _i Is any one of the pre-transform matrices X _i Block-down triangulated unitary transform. By "triangularization under blocks" is meant a transformed matrix Y of (M + 1) × (M + 1) _i The last M entries of the first row are all zeros. Finding suitable methods for such a unitary transform, such as using a Householder transform or a series of Givens rotations, as described above, is well known.

submatrix P _|i ^1/2 As already defined above. As shown in

block

210, 0 _M ^T Is an M-dimensional all-zero row vector. Those"X" indicates an item not relevant to the discussion herein.

Therefore, each time the iteration of block 210 is completed, the submatrix P _|i ^1/2 Is fed back to X and the next row of the channel matrix H _i For the next iteration. As previously mentioned, P after the last, nth, iteration _|i ^1/2 Is the value of P sought ^1/2 As shown in block 215.

P ^1/2 Form an estimation matrix G = P for the minimum mean square error signal ^1/2 (P ^1/2 ) ^* H ^* One efficient calculation of (2). It is worth noting that in the present method, such efficient calculation occurs only once.

FIG. 8 illustrates how the matrix P can be used ^1/2 Obtain zero forcing vector G _J J = M, M-1, …,1. In block 220, the matrix P ^1/2 Minimum lengthA row is determined. This determines the best detected transmit signal in the current iteration. In block 225, the signal indices are permuted and renumbered so that the selected optimal transmit signal will be the mth signal. Accordingly, the columns of the channel matrix H are also permuted by swapping the column corresponding to the detected signal with the last column so that the column corresponding to the selected optimum transmit signal is the mth column.

In block 230, a unitary transform sigma is found which triangulates a matrix P over the block ^1/2 . That is, Σ is an arbitrary unitary transform as long as it makes a matrix product P ^1/2 Σ the first M-1 terms of the last row (i.e., row M) are all zeros. A suitable transform sigma can be easily found by standard techniques from the previous description of the lower triangular transform.

M matrix P ^1/2 The various sub-matrices of Σ are as follows:

in the above formula, P ^(M-1)/2 Is a (M-1) × (M-1) -dimensional sub-matrix, P _M ^(M-1)/2 Is an M-1 dimensional column vector, 0 _M-1 ^T Is a row vector with M-1 dimensions of elements all zero, and p _M ^1/2 Is a scalar. As explained below, in the next iteration of block 230, P ^(M-1)/2 Will substitute P ^1/2 . Scalar p _M ^1/2 Will be used to derive the mth zero-forcing vector. As shown in block 235, the Mth zero-forcing vector G _M Is obtained as the product p _M ^1/2 [P _M ^(M-1)/2 ) ^* (p _M ^1/2 ) ^* ]H ^* . The process of blocks 220 through 235 is iterated to obtain the remaining M-1 zero-forcing vectors G, as shown in block 240 _J J = M-1,M-2. In each iteration of

blocks

220 and 225, the signal indices are permuted and renumbered so that P is currently updated ^1/2 (now by P ^(J)/2 Representation) of the sameThe length row is the jth row. In each iteration of the block 230, a unitary transformation sigma is found such that the matrix product P ^(J)2 Σ last row satisfies the division of the last term (i.e. J-th term, scalar p) _J ^1/2 ) All but zero. In each iteration of block 235, the jth zero-forcing vector G _J As product p _M ^1/2 [(P _M ^(M-1)/2 ) ^* (p _M ^1/2 ) ^* ]H ^* Is obtained.

At the beginning of each iteration of blocks 220 through 235, P ^(J)/2 Is updated to P of the last iteration ^(J)/2 ∑ The sub-matrix in the upper left corner. That is, P ^(J)/2 Is given by the previous P ^(J)/2 The first J-1 row of the first J-1 column of Σ. So, as mentioned previously, the updated P used to derive the M-1 st zero-forcing vector ^(J)/2 Is P ^(M-1)/2 。

At the beginning of each iteration of blocks 220 through 235, the values of the channel matrix H are also updated. Updated H value is H ^(J) J = M-1,. …,1. Each H ^(J) By deleting the previous H that has undergone a sequence change in block diagram 225 at the last iteration ^(J) Is obtained in the last column, where H ^(J) The last column of (a) corresponds to the best detected transmit signal selected in the previous implementation. So, for example, the updated H-th zero forcing vector is obtained ^(M-1) And it includes the first M-1 column of the original H that has undergone the permuting in block 225.

Importantly, a repeat of P ^(J)/2 Is equivalent to one P ^1/2 Triangularization on the block. As a result, each scalar coefficient p _J ^1/2 Can be regarded as an upper triangulated P ^1/2 The diagonal elements of (a).

As previously described, each iteration of block 235 produces a zero-forcing vector G, respectively _J . FIG. 9 shows how these zero-forcing vectors can be used to obtain each detected signal  _j . As shown in block 245, each detected signal is derived from a corresponding zero-forcing vector and received signal vector

The vector product of (a) is obtained, i.e.,

after the detected signal, or recovered signal (thermally recovered signal), is obtained from the above equation, a slicing step is performed to identify the detected signal, or recovered signal, as a member of a symbol constellation (symbol constellation) that modulates the transmitted signal. Notably, the vector is used for the next detection before it is used

Modified to cancel the effect of the last detected signal. This step is illustrated in block 250, where after the jth signal is detected, J = M

Is updated toIn the foregoing formula, the vector h _:J Which represents the column of the channel matrix H corresponding to the jth signal.

With reference to fig. 6, 7, 8 and 9, which together illustrate an implementation of the method of the present invention, a more formal overall flow diagram according to an embodiment of the method of the present invention is shown in fig. 10, which includes the following steps:

an initialization step:

(i) (shown as block 255:) determining a received signal x (k); the training sequence is used to determine the initial matrix H.

(ii) (shown as block 260) the initial P is obtained using the method shown in FIG. 7 ^1/2 。

(iii) (as shown in block 265: ) Initialization J = M, initialized P ^(M)/2 ＝P ^1/2 And initialized channel matrix H ^(M) ＝H。

(iv)f＝[1，2，…，M] ^T The transmitted signal index is recorded with vector f.

Recursion (later iteration), when J = M, M-1,.., 2:

(a) (shown as block 270:) find P ^(J)/2 Corresponding to the detected signal in this iteration.

(b) (shown as block 275:) at P ^(J)/2 The line where the minimum length line vector is located is exchanged and recorded as the L-th line and the last line, and the signal indexes are numbered again by exchanging the L-th item and the J-th item in the vector f; corresponding pair channel matrix H ^(J) The sequence of the column is changed, and the L-th column and the last column corresponding to the detected signal are exchanged.

(c) (as shown in block 280:.) finding a unitary transformation e such that P ^(J)/2 Sigma the last row is (0,0.. 0,p _J ^1/2 )

(d) (see block 285 in the figure:) find the zero-forcing vector:

(e) (as indicated by block 290) the currently detected signal, or recovered signal, is

A slicing step is then performed to identify the detected signal, or recovered signal, as a member of a symbol constellation (symbol constellation) that modulates the transmitted signal. .

(f) (as shown in block diagram 300.)

(g) (as shown in block 305:) J ← J-1J, minus 1.

(h) (see block 310. In the figure.) P is determined for the value of J minus 1 ^(J)/2 And H ^(J) ：P ^(J)/2 Is the previous value of P ^(J+1)/2 The sub-matrix in the upper left corner of Σ, i.e. P ^(J)/2 Is given by the previous value of P ^(J+1)/2 The first J row of the first J column of Σ; at the same time, by deleting H ^(J+1) Last column, by H ^(J+1) Determination of H ^(J) 。

Note that the block diagram 295 in the figure is used to end the recursive process described above, while it is easy to see that when J =1, only the above steps (a) - (f) are performed to get

And performing a slicing step to cut  ₁ Identified as a member of the symbol constellation (symbol) of a modulated transmitted signal.

Solving the following steps:

the estimation of the transmitted signal, according to the detected sequence, is: [  _M ， _M-1 ，… ₁ ] ^T Note that the subscript of the transmit signal estimate in the above vector only indicates the order in which this transmit signal was detected. The information of the signal index exchange during the signal detection process recorded by the vector f can restore the original signal index. In particular, let f _m M = M, M-1, ·,1 denotes the mth term of the vector f, and then the vector [  _M ， _M-1 ，…， ₁ ] ^T Estimation of mid-transmitted signal  _m The subscript M of M = M, M-1, ·,1 is changed to f _m The resulting vector [  _fM ， _fM-1 ，…， _f1 ] ^T The subscript of the medium transmit signal estimate represents the original signal index.

The method of U.S. Pat. No.6,600,796 requires P to be determined ^1/2 And Q _α And in the iterative process of obtaining the zero-forcing vector, P is updated simultaneously every time ^1/2 And Q _α . The method of the invention only needs to obtain P ^1/2 And in the iterative process of obtaining the zero forcing vector, only P needs to be updated each time ^1/2 . It is clear that the method of the present invention requires less calculation than the method of U.S. Pat. No.6,600,796. Further analysis can demonstrate that the method of the present invention is 36% faster than the method of U.S. patent No.6,600,796, using the criteria of the number of multiplications and additions required. At the same time, since the matrix Q need not be used at all _α The method of the invention also requires less memory. Fig. 11 shows the results of numerical experiments to find the amount of calculation required for each data sample when the method of us patent No.6,600,796 and the method of the present invention are used, respectively, for different numbers of transmit/receive antennas. These results can be seen to be consistent with a theoretical analysis.

Claims

1. A method for receiving a wireless transmission by a multi-antenna array for detecting at least two transmit signals transmitted by different transmit antennas and traversing a channel in a multiple-input multiple-output communication system, said method comprising the steps of:

a) Collecting at least two receiving signals from different receiving antennas, wherein the receiving signals are signals transmitted by a transmitting antenna and collected by the receiving antennas after passing through a channel;

characterized in that the method further comprises the steps of:

f) Calculating a matrix P ^1/2 Said matrix being related to an error covariance matrix P, the error covariance matrix P = (aI + H) ^* H) ^-1 Where α is the average signal-to-noise ratio and I is the identity matrix, the relationship between them being according to the formula P representing the relationship between them ^1/2 (P ^1/2 ) ^* = P, where denotes conjugate transpose;

g) Each of all zero-forcing vectors is a slave matrix P ^1/2 Derived, obtaining each of several zero-forcing vectors, including efficient triangularization P ^1/2 (ii) a Zero forcing vector G _J Obtained from the following equation:wherein J = M, M-1, 1 is the index of the J-th transmitting antenna or J-th transmitting signal, M is the number of transmitting antennas,

each of the above vectors [ (P) _J ^(J-1)/2 ) ^* (p _J ^1/2 ) ^* ]Is a matrix P that has been triangulated ^(J)/2 The conjugate transpose of the last column of (1); h ^(J) The channel matrix H is a channel matrix after column exchange, or a reduced channel matrix after column exchange and column deletion are alternately carried out;

2. The method of claim 1, wherein each channel matrix H in step g) is ^(J) The obtaining comprises the following processes: at each first execution of the above-mentioned step b) or each subsequent repetition of step b)In complex, the original size or reduced channel matrix H must be aligned before it can be used to calculate the zero-forcing vector described above ^(J) Exchange of columns is carried out; at the same time, each of the above original size or reduced channel matrices H ^(J) Deleting the channel matrix H after being used for calculating the zero-forcing vector in each first execution of the above step b) or in each subsequent repetition of the above step b) ^(J) Can get the channel matrix H for the next iteration of step b) ^(J-1) 。

3. The method of claim 2, wherein the column swapping of the matrix specifically comprises: the exchange of a column of the matrix corresponding to the above-mentioned transmission signal detected by the previous execution of step b) with a column of the matrix corresponding to the last of the above-mentioned transmission signals not yet detected.

4. The method of claim 1 wherein the preferred order is from the matrix P ^(J)/2 Is determined.

5. The method of claim 1, wherein the matrix P is ^1/2 Derived from the channel matrix H by introducing a unitary matrixNow the open square operation of the error covariance matrix P.