KR100973194B1 - Method and apparatus for decoding using complex rattice reduction in multil antenna system - Google Patents

Abstract

The present invention relates to a decoding method and apparatus using complex lattice reduction in a multi-antenna system. In the method for signal decoding in a multi-antenna system, a method for receiving at least one symbol and a constellation used for transmitting the symbol By determining the closest point in the grid space corresponding to at least one subset of the constellation map, at least partially decoding the received symbols, and the decoding process reduces the basis in the complex space. An orthogonal basis is determined approximately in the lattice space by using an algorithm. Therefore, the complexity of calculation during decoding can be reduced, and the performance can be maintained by outputting the soft decision value.

Multiple antennas, grid reduction, QR decomposition, soft decisions.

Description

Decoding method and apparatus using complex lattice reduction in multi-antenna system {METHOD AND APPARATUS FOR DECODING USING COMPLEX RATTICE REDUCTION IN MULTIL ANTENNA SYSTEM}

The present invention relates to decoding in a multi-antenna system, and more particularly to a decoding method and apparatus for outputting soft decisions using complex-valued integer lattices in a 2x2 multiantenna system. It is about.

A multi-antenna (hereinafter referred to as "MIMO") system represents a multi-antenna transmission and reception system that addresses several disadvantages of conventional single antenna systems. In particular, referring to "Ezio Biglieri, Robert Calderbank, Anthony Constantinides, Andrea Goldsmith, Arogyas-wami Paulraj, H. Vincent Poor, MIMO wireless communications, Cambridge University press, 2007" (hereinafter referred to as [1]), Communication channel capacity, and each receiving antenna at the receiver receives superposition of signals transmitted by a plurality of transmitting antennas, thereby decoding the received signal at the transmitter. It is necessary to consider all the components of the channel matrix that specify the signal propagation channel to the receiver.

In a MIMO system, zero forcing (hereinafter referred to as "ZF"), minimum mean square error (hereinafter referred to as "MMSE"), OSIC (Ordered Serial Interference Cancellation) techniques, etc. Many methods for this have been known. Details of these are described in “Ezio Biglieri, Robert Calderbank, Anthony Constantinides, Andrea Goldsmith, Arogyas-wami Paulraj, H. Vincent Poor, MIMO wireless communications, Cam-bridge University press, 2007” (hereinafter referred to as [1]), In D. Wubben, R. Bohnke, V. Kuhn, and K.-D. Kammeyer, “Near-Maximum-Likelihood Detection of MIMO Systems using MMSE-Based Lattice-Reduction”, in Proc. IEEE Interna-tional Conference on Communications (ICC '04), Volume 2, pp. 798-802, 20-24 June 2004. (hereinafter referred to as [3]), D. Wubben, J. Rinas, R. Bohnke, V. Kuhn, K.D. Kammeyer, “Efficient algorithm for detecting layered space-time codes”, 4th Int. ITG Conference on Source and Channel Coding, Berlin, January 2002. (hereinafter referred to as [6]). However, most ZF, MMSE, and OSIC techniques are less accurate than optimal Maximum Likelihood (ML) techniques [3]. Moreover, many MIMO decoding techniques require significant computational cost.

See the literature [3] above. The technique of lattice reduction (hereinafter referred to as "LR") in a decoding algorithm for a MIMO system is disclosed. The above-mentioned [3] documents that the decision values obtained using the LR technique are close to the ML decision, in which case the complexity of the calculation is compared with the complexity of ZF and MMSE OSIC.

As a recent method with respect to the MIMO decoding technology, the US patent “K.L. Clarkson et al., U.S. Patent 6,724,843 B1, Apr. 20, 2004. ”(hereinafter referred to as [2]). [2] consists of estimating a communication channel, acquiring a channel matrix H with it, and decoding a received signal using the LR technique. The above LR technique initially targets real matrices and vectors, and the channel matrix of the communication system is composed of complex vectors. In this case, in order to convert from a complex value to a real value, it is proposed to use a well-known unfolding transformation such as Equation 1 below.

,

,

Where H is a complex channel matrix, Re (H) is the real part of the complex channel matrix, Im (H) is the imaginary part of the complex channel matrix, x is the transmission vector, and Re (x) is the real number of the transmission vector. Is an imaginary part of the transmission vector. Maintain the result of the matrix-vector product of Hx.

Looking at claims 1 to 9 in the document [2], an essential element of the proposed method is the so-called LLL transform for basis reduction of the vector space of the row of the channel matrix H (see claim 9 of [2]). To use. The original basis is formed by the rows of the matrix Q from the QR decomposition of the channel matrix H. The LLL transform itself consists of two important procedures (first procedure, second procedure).

(reducedness ratio)의 확인을 수행한다. 여기서 r_{i ,j}는 QR 분해 시 행렬 R의 성분이다. 만일 축소비가 완료되지 않을 시, 제 2 절차가 수행된다. 만약 축소비가 완료될 시, 프로세스는 다음 행에 대해 진행한다.First in the first procedure, the non-diagonal components of the matrix R are sequentially reduced. Perform elementary transformations between rows ([3], [5] AK Lenstra, HW Lenstra, and L. Lovasz, “Factoring polynomials with rational coeffi-cients,” Math. Ann., Vol. 261 , pp. 515-534, 1982), the so-called reduction ratio, which is interpreted as the relative increase of the diagonal component of the matrix R and its neighboring components, depending on their row indices.

(reducedness ratio) is performed. Where r _{i , j} are components of matrix R during QR decomposition. If the reduction ratio is not completed, the second procedure is carried out. If the reduction ratio is complete, the process proceeds to the next row.

The second procedure transposes two adjacent k-1th and kth rows of matrix R (along with this, the transpose of the rows of matrix R transforms the triangle shape, i.e., the upper triangle R matrix). Is no longer a matrix of upper triangles) and performs a selective transformation to restore the triangular formation of R. By doing so. There is a possibility that the reduction ratio for the k-2, k-1th rows will deteriorate. In this case, the second procedure is performed for them. Thus, the second procedure can be extended to any rows already processed in the first procedure. As a result, the first to kth diagonal components of the matrix R are obtained in ascending order by the reduction ratio.

The problem with the prior art [2] is that the computational complexity is large. First, the real channel matrix formed as a result of "unfolding" (Equation 1) is very large and requires a calculation amount proportional to the cube of the size when QR decomposition is performed. The row transposition procedure, which continuously restores the characteristics of the R triangle associated with the lattice reduction procedure, performs multiplication and is very expensive to compute.

Another problem is related to the type of decision value obtained. The conventional method is a method such as V-BLAST [4]. In D. Wubben, R. Bohnke, V. Kuhn, and K.-D. Kammeyer, “MMSE Extension of V-BLAST based on Sorted QR Decomposition”, in IEEE Proc. VTC-Fall, Or-lando, Florida, USA, Octo-ber 2003. (hereinafter referred to as [4]) Symbol decoding is performed by rounding to the nearest component to the constellation point, layer by layer, sequentially. Occurs. The symbols thus obtained are generally called hard decisions. The disadvantage of V-BLAST is that it conveys the error due to incorrect symbol decoding for one of the layers in all subsequent layers to the next layer. Incorrect decoding occurs when the calculated symbol value close to the component of the constellation point does not match the actual transmission symbol. The rounding process obviously affects the decoding of the following layers. It is difficult to make an accurate probability estimate of the bit output decision (an estimate called soft decision). Thus, in many implementations, V-BLAST yields only hard decisions when bit probabilities are not considered at all. Other methods, for example, the improved ML detection disclosed in S. Barbarossa, “Multiantenna Wireless Communication Systems”, Artech House, March 2005. (hereinafter referred to as [7]) constitute a probabilistic error estimate and yield soft decision. do. However, the complexity of this technique is very high compared to traditional MMSE detectors.

Many methods for error correction (convolutional code, turbo code, low-density parity-check codes (LDPC) codes) are currently used in communication systems and are used to efficiently correct errors at the output of the MIMO decoder. When exactly computed probability soft decisions of the output bits come into the input data, they all operate more efficiently. The complexity of calculating the MIMO decoder at the ZF OSIC or MMSE OSIC filters level is less important.

Accordingly, there is a need for a decoding method and apparatus for reducing the amount of computation while maintaining performance in a MIMO system.

An object of the present invention is to provide a decoding method and apparatus using complex lattice reduction in a multi-antenna system.

Another object of the present invention is to provide a decoding method and apparatus for outputting soft decision values in a multi-antenna system to maintain performance and reduce computational complexity.

It is another object of the present invention to increase the operation speed by directly performing a grid reduction on a complex channel matrix having a smaller size than a real channel matrix in a multi-antenna system, and to restrain the reduction of non-diagonal components of the upper triangular matrix R. In other words, the present invention provides a signal decoding method and apparatus for reducing the computational complexity of the LR conversion by using a procedure of transposing a row of a channel matrix twice before and after lattice reduction.

According to a first aspect of the present invention for achieving the above objects, in a method for signal decoding in a multi-antenna system, receiving at least one or more symbols, and a constellation map used for the symbol transmission Decoding at least partially the received symbols by determining the closest point in the grid space corresponding to at least one subset of s, and the decoding process uses an algorithm for reducing the basis in complex space. By roughly determining the orthogonal basis in the lattice space.

According to a second aspect of the present invention for achieving the above objects, an apparatus for signal decoding in a multi-antenna system, comprising: an antenna for receiving at least one or more symbols, and a constellation map used for the symbol transmission; A decoder that decodes the received symbols at least partially by determining the closest point in the grid space corresponding to at least one subset of s, wherein the decoder uses an algorithm to reduce the basis in complex space. An orthogonal basis is determined approximately in the lattice space.

As described above, by performing the decoding using complex lattice reduction in the multi-antenna system, the complexity of calculation at the time of decoding can be reduced, and the performance can be maintained by outputting the soft decision value.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description of the present invention, detailed descriptions of related well-known functions or configurations will be omitted if it is determined that the detailed description of the present invention may unnecessarily obscure the subject matter of the present invention. The following terms are defined in consideration of the functions of the present invention, and may be changed according to the intentions or customs of the user, the operator, and the like. Therefore, the definition should be made based on the contents throughout the specification.

Hereinafter, the present invention will be described a decoding method and apparatus for performing complex lattice reduction in a multi-antenna system.

1 shows a performance comparison graph of the present invention and the prior art.

Referring to Figure 1, the prior art is K.L. Clarkson et al., U.S. Patent 6,724,843 B1, Apr. 20, 2004. [2], H. Lee, I. Lee. "New Approach for Coded Layered Space-Time OFDM Systems over Frequency-Selective Channels", http://dx.doi.org/10.1109/ICC.2005.1494423 [8], and the present invention is a real channel in a multi-antenna system. Perform a direct grid reduction on a complex channel matrix of a smaller size than the matrix, and transpose the rows of the channel matrix twice before and after the grid reduction without constraining the reduction of non-diagonal components of the upper triangular matrix R resulting from QR decomposition. A signal decoding technique is used to reduce the computational complexity using a procedure.

The simulation environment is a 2x2 MIMO-OFDM system using an LDPC decoder, and the channel model is referred to as "Channel Models for Fixed Wireless Applications, IEEE 802.16.3c-01 / 29r4, 2001-07-17" (hereinafter referred to as [9]). We used the SUI-3 model described in. Here, LR Soft4 and LR soft have different numbers of vector candidates for the second layer. That is, LR soft4 is a case where there are four vector candidates, and LR soft is a case where a vector candidate is one.

Line 100 corresponds to prior art [2], line 200 corresponds to Lee algorithm [8], and lines 300 and 400 correspond to the present invention. When the present invention is applied, it can be seen that the performance is improved by reducing the BER (reducing the probability of a bit error at the system output).

2 shows a decoder for performing complex lattice reduction according to an embodiment of the present invention. The decoder shows a MMSE OSIC-based lattice reduction decoder. It is assumed that the modulation scheme uses 16QAM scheme.

Referring to FIG. 2, first, in the decoder, the channel converter 205 receives a signal transmitted through two transmission antennas through two reception antennas (not shown). The signal propagation channel is then estimated. For example, the signal propagation channel is a relay two-dimensional MIMO fading channel of two transmitters and two receivers, and is characterized by a channel matrix H having a size of 2 × 2. The received signal may be expressed by Equation 1 below.

y = Hx + v.

Here, y is a reception signal, x is a transmission signal, v is noise, H is a channel matrix, and each element of the channel matrix characterizes a propagation channel between each transmission antenna and the reception antenna.

와 같고,잡음 벡터 v는 제로 평균과 분산이

인 가우시안 분포를 갖는다. 신호대잡음비(Signal-to-Noise Ratio:이하 "SNR" 이라 칭함)의 역의 값(inverse value)은

으로 정의한다. 입력 데이터는 H, α 그리고 y 이다.The average energy of a symbol sent through one transmitter is

Noise vector v is zero mean and variance

Has a Gaussian distribution. The inverse value of the Signal-to-Noise Ratio (hereinafter referred to as "SNR") is

It is defined as Input data are H, α and y.

That is, the channel converter 205 receives the received signal y, the channel matrix H, and the inverse α of the SNR, converts the channel matrix H into an extended channel matrix, and then converts the channel matrix H into an extended channel matrix. Output to QR resolver 206. The extended channel matrix is represented by Equation 3 below.

Where H is the estimated channel matrix, I is the unit matrix, and α is the inverse of the SNR.

)을 하기 <수학식 4>와 같이 분해한다.The first QR decomposer 206 uses Sorted QR Decomposition (SQRD) to expand the extended channel matrix (SQRD).

) Is decomposed as shown in Equation 4 below.

Here, index 1 means first alignment QR decomposition. The matrices P, Q, D, and R are permutation matrices, orthonormal matrices, diagonal matrices, and upper triangular matrices, respectively. The matrixes P, D, and R are matrixes of size 2x2, and the matrix Q is 4x2.

은 변하기 않도록 행렬 T를 변형시킨다. 행 j에서 행 k의 뺄셈은 하기 <수학식 5>에 의해 행렬 R₁과 T₁의 변형을 가져온다.The grid reducer 207 reduces the large non-diagonal component of R ₁ in the second column of R ₁ , at which time the previous row of R ₁ multiplied by the corresponding integer is subtracted from the current row. For example, when the absolute value of component r _jk is larger than 1, the real part and the imaginary part of r _jk are rounded. Thus we obtain a complex integer quantity (μ) and subtract row j multiplied by μ in row k. (Ie each component in row j is multiplied by a complex integer (μ) and subtracted from the corresponding component in row k). By doing so, each non-diagonal component of R ₁ is processed sequentially from above the diagonal. At the same time changing the matrix R ₁ (reducing non-diagonal components),

Transforms the matrix T so that it does not change. Subtraction of row k in row j results in the transformation of matrices R ₁ and T ₁ by Equation 5 below.

Where m is a symbol index and k, j represents an index of a row.

이 표준행렬에 더 가까워지는 것이다. 그러므로 행렬

이용하여 다중안테나 시스템에서 복호함에 있어서, 행렬 R₁를 이용하여 다중안테나 시스템에서 복호하는 것보다 레이어들의 상호 영향이 덜하다.Initially (starting the LR algorithm), the matrix T is an identity matrix of size 2 × 2. Furthermore, through the lattice reducer 207, the matrix T becomes a top unitriangular matrix of complex integers. The purpose of this step is to make the matrix R ₁

It is closer to this standard matrix. Therefore

In decoding in a multi-antenna system, the mutual influence of layers is less than in decoding in a multi-antenna system using a matrix R ₁ .

행렬을 하기 <수학식 6>과 같이 분해한다.The second QR resolver 208 uses alignment QR decomposition (SQRD),

The matrix is decomposed as shown in Equation 6 below.

Here, the matrixes P, Q, D, and R are permutation matrices, orthogonal matrices, diagonal matrices, and upper triangular matrices, respectively. Index 1 means the first alignment QR decomposition, and index 2 means the second alignment QR decomposition.

The linear filter 209 performs linear filtering on the received vector y and outputs the following equation (7).

는 행렬

의 첫 번째의 두 개 열이다. 벡터

이고, 벡터 e는 두 요소는 같고, 행렬

이다. 여기서, 행렬

와 역행렬

은 복소 정수(complex-valued integer-valued) 행렬임이 중요하다.Here, f denotes a signal vector obtained by linearly filtering the received vector y,

Is a matrix

Are the first two columns. vector

Vector e is equal to two elements

to be. Where matrix

And inverse

It is important to note that is a complex-valued integer-valued matrix.

를 갖는다. 예를 들면, 16QAM은

, 이다. 여기서

는 {-2, -1, 0, 1}이다. 유클리디언 거리(Euclidean metric) 내에서 z₂ 에 가까운

의 4개의 성분들(이하 벡터후보로 칭함)이 제 2 후보선택기(110)에 의해 선택되고, 조건 확률은 하기 <수학식 8>에 따라 벡터후보에 할당된다.The nulling unit 210 solves the linear system R2z = f by candidate symbol generation and their probability estimation in each layer. The permutation matrix P ₂ takes only two possible values while generating candidate symbols or performing probability estimation. Permutations corresponding to P ₂ have either "trivial permutation" or "reverse permutation". For trivial permutation, the element z ₂ minus the noise is then a number of complex integer values

Has For example, 16QAM

, to be. here

Is {-2, -1, 0, 1}. Close to z ₂ in Euclidean metric

Four components (hereinafter referred to as vector candidates) are selected by the second candidate selector 110, and the conditional probability is assigned to the vector candidates according to Equation 8 below.

는 잡음 일부가 제거된 성분 z₂ 이다. s는

의 원소이다.here,

Is the component z ₂ from which some of the noise is removed. s

Is an element of.

의 4개의 원소(혹은 다른 방법에 따라 하나의 원소가 선택될 수 있음)들에 의해 근사화된다. 예를 들면,

을 계산하고 여기서 r₁₂는 행렬 R₂의 비대각 원소이다.

는 현재 벡터후보이다.

계산한다. 유클리디언 놈 에서

으로부터 4개(혹은 하나)의 최적의 근사치 x₁ 을 결정한다. 그런 근사치들 중 하나를

으로 지정한다.In solving the above multiple antenna system with matrix R ₂ , each vector candidate is used for reverse substitution, and the obtained x ₁ value is approximated to approximately x1 at Euclidean distance.

Is approximated by four elements (or one element can be selected in different ways). For example,

Where r ₁₂ is the non-diagonal element of the matrix R ₂ .

Is the current vector candidate.

Calculate At the Euclidean

Determine four (or one) best approximations x ₁ from. One of those approximations

To be specified.

에 해당하는 벡터 후보는

이고, 매 벡터 후보의 성분을 위해 계산되는 확률(상기 <수학식 8>)이 벡터 후보에 할당된다. 그밖에 잡음이 제거된 성분 z₂는 더 많은 복소 집합(complex set)을 즉

을 소유한다. 여기서 상기 t₁₂는T 행렬의 1행 2열의 성분이다.

Vector candidates for

And a probability (Equation 8) calculated for the components of every vector candidate is assigned to the vector candidate. In addition, the noise-free component z ₂ represents more complex sets, i.e.

Own it. Where t ₁₂ is a component of one row and two columns of the T matrix.

의 16 복사본의 집합이다.근차화된 집합이 더 복잡하다 것을 고려하여, 유클리디언 거리에서 z₂에 근접한 4개 원소로부터 시작되는 "trivial permutation" P2의 경우에 모든 동작들이 언급되도 록 하는 것이 필요하다.Geometrically, this is shifted by a constant

Considering that the approximated set is more complex, it is necessary to ensure that all operations are mentioned in the case of "trivial permutation" P2 starting from four elements close to z ₂ at Euclidean distance. need.

의 4개의 복사본이 선택되고, 각 복사본에서 4개 근접한 원소들은 선택되고, 획득된 16 원소들은 4개 근접한 원소들을 유지하며 정렬된다. 만일 |t₁₂| < 3이면 그때

의 복사본들은 복소 정수 값을 갖는 격자에서 갭이 없도록 형성되도록 모아진다. 4개의 벡터후보들의 선택 위에 간단한 판정(decision)이 존재한다. 8개의 근접한 이웃한 성분들 각각 확인이 필요하다. Since the full computation of 256 elements is difficult, the first approach to z ₂ at the Euclidean distance

Four copies of are selected, four adjacent elements in each copy are selected, and the 16 elements obtained are aligned keeping the four adjacent elements. If | t ₁₂ | <3 then

Copies of are collected so that there is no gap in the lattice with complex integer values. There is a simple decision above the choice of four vector candidates. Each of the eight adjacent neighboring components needs to be identified.

에서

이 생성되고, 4개(혹은 한 개) 벡터후보들(

)은 z₁에 이 계산된다. 성분 이 계산된다. 만일

이면 그때,

가 나쁘게 구성된다. 반면

이면 벡터 후보

이 생성된다. 상기 <수학식 8>에서 계산된 확률이 각 벡터후보로 할당된 후보벡터의 성분을 위해 계산된다.Simulations are performed on many instances of the inequality in many cases. Furthermore, each vector candidate

in

Is generated and four (or one) vector candidates (

) Is calculated as z ₁ . The component is calculated. if

If then,

Is composed badly. On the other hand

Backside vector candidate

Is generated. The probability calculated in Equation 8 is calculated for the component of the candidate vector assigned to each vector candidate.

The second candidate selector 211 and the first candidate selector 212 calculate bit probabilities through gray codes.

는 예를 들면, 16QAM 기결정된 성상점으로부터 성분들을 갖는지에 대한 사전정보가 있다는 사실과 관련이 있다. 이웃 성상점 사이가 최소거리를 갖는 복소 정수 집합

으로부터 성분들을 갖는

가 실제 전송된 벡터와 일치하도록 하기 위해서, 벡터

을 도입한다. 경판정은 다음과 같이 결과를 얻는다.The premise for this method is that the actual transmitted vector

For example, it is related to the fact that there is preliminary information as to whether there are components from the 16QAM predetermined constellation point. Complex integer set with minimum distance between neighboring constellation points

Having components from

In order to match the actual transmitted vector,

Introduce. Hard decision results as follows.

를 해결하고, 획득한 판정 벡터로

를 지정한다.First, the linear system is rounded up by rounding the decision in each layer to approximate a complex integer value.

Is solved, and with the obtained decision vector

Specifies.

를 출력한다.After that, hard decision

.

와

는 복소 정수 행렬을 가지는 하기 <수학식 9>과 같이 선형 동작에 의해 하나에서 다른 하나로 넘어간다.Important characteristics of the LR technique are as follows. vector

Wow

Is transferred from one to the other by linear operation as shown in Equation 9 having a complex integer matrix.

Equation (9) represents the transition from the original lattice to the modified lattice space (step 13). This property significantly reduces the number of candidate vectors compared to the maximum possible number.

In the two-dimensional instant, Equation 8 may be expressed as Equation 10 below.

Here, p1 (1) is the index of a unity element in the first row of P1, and p1 (2) is the index of a unity element in the second row of P1. ip2 (1) is a single component in the first column of P2, and ip2 (2) is a single component in the second column of P2.

The number of vector candidates in each layer is an algorithm parameter, and the simulation sets its value to 4 for the first layer and its value to 1 for the second layer.

In the present invention, accuracy can be improved while an error is estimated by wrong hard decision, and as a result, multiple antenna characteristics can be improved. It can be confirmed through the BER performance comparison graph shown in FIG.

In the present invention, aligned QR decomposition (SQRD) of a matrix of complex values is performed using the modified Gram-Schmidt (orthonormalization) technique.

Where Q is a unitary matrix, D is a diagonal matrix, and R is a top unitriangular matrix. In general, the description of this technique will take the case of m × n matrix as an example.

The rows of H are h ₁ , h ₂ ,... , h _n , and the rows of Q are q ₁ , q ₂ ,. , q _n . The matrix Q is improved step by step in the iterative process. The repetition step k is k = 1,... , consider n. The Gram-Schmidt technique then involves the following operations.

First, considering only the components of a row that is larger than the k index, a row with the smallest Euclidean length has h _k ,... , h _n , and between. This line is exchanged with h _k . Thus, the row is processed and obtained in a new order.

The Euclidean length of h _k is then calculated and the inverse of this length is recorded in the k-th diagonal component of D. Normalized h _k Is recorded in q _k .

에 따라 다시 계산된다. 여기서, j=k+1,…,n, 스칼라 곱

은 행렬 R의 kj 위치에 기록된다.Finally, the rows h _{k -1} ,. , h _n is an equation

Is recalculated accordingly. Where j = k + 1,... , n, scalar product

Is recorded at the position kj of the matrix R.

Moreover, in the 2 × 2 MIMO system, a comparison of the complexity of the calculation of the present invention (hereinafter referred to as CLR: complex lattice reduction) and the prior art (RLR: real lattice reduction), and well-known MIMO decoding methods (ZF and MMSE) Take as an example.

INIT STAGE DECODE STAGE ZF: 1r ', 2d, 14m, 6a 4m, 2a MMSE: 1r ', 4d, 24m, 14a 4m, 2a RLR: 4r ', 346m', 278a ' 38m ', 34a' CLR: 4r ', 55m, 34a 9 m, 11 a,

Where a is “addition”, d is “division”, r is square root (or inverse square root), “prime” character means arithmetic operations using real numbers, and general character means arithmetic operations using complex numbers. it means.

From Table 1, it can be seen that when comparing the ZF and MMSE methods, the difference is sufficiently large in the complexity of the calculation of the prior art (RLR). There is a serious obstacle to the method of carrying out the prior art.

From Table 1 and Fig. 2, the present invention can significantly reduce the number of calculation operations while maintaining the same decision accuracy as compared with the prior art.

Although the same 4m '(inefficient technique for realizing complex multiplication) operations are required in the early stages, smaller computational operations are required in the decoding stage than RLRs.

The difference between LR and CLR is also what constitutes the number of memory cells that are moved.

INIT DECODE LR: 208p, 628 16p, 72 CLR: 52p, 93 5p, 20

Here, the letter “p” denotes a “clean” operation for transferring memory cells, and operates to copy the components of the channel matrix before performing an ordered R decomposition (SQRD); In the case of RLR, a procedure of representing a "unfolding" complex channel matrix with a four-block real matrix is added. The number without letters is the sum of the columns in Table 1, and every operation assumes data transfer.

In the present invention, an apparatus of a radio technology can be used, and together with this method, it can be used in a MIMO OFDM system because it is simple enough from the viewpoint of implementation complexity.

3 shows a decoding flowchart for performing complex lattice reduction according to an embodiment of the present invention.

Referring to FIG. 3, the decoder receives a signal transmitted through two transmission antennas through two reception antennas in step 300. In step 302, the signal propagation channel is estimated (H).

)로 변환을 수행한다.The decoder then expands the channel matrix H estimated by Equation 3 in step 304 into an extended channel matrix (

To perform the conversion.

)을 상기 <수학식 4>와 같이 행렬 P1, Q1, D1, R1로 각각 순열행렬(permutation matrix), 직교행렬(orthonormal matrix), 대각행렬(diagonal matrix), 상삼각 행렬(upper triangular matrix)로 분해한다.Then, the decoder uses an aligned QR decomposition (SQRD) in step 306, the extended channel matrix (

) Into matrices P1, Q1, D1, and R1, as shown in Equation 4, as a permutation matrix, an orthonormal matrix, a diagonal matrix, and an upper triangular matrix, respectively. Disassemble.

Then, the decoder performs a lattice reduction algorithm in step 308 to reduce the large diagonal non-diagonal component of R ₁ in the second row of R ₁ , and then replace the previous row of R ₁ multiplied by the corresponding integer in the current row. Subtract from For example, when the absolute value of component r _jk is larger than 1/2, the real part and the imaginary part of r _jk are rounded. Thus we obtain a complex integer quantity (μ) and subtract row j multiplied by μ in row k. (Ie each component in row j is multiplied by a complex integer (μ) and subtracted from the corresponding component in row k). <Equation 5 above>

행렬을 상기 <수학식 6>과 같이 QR 분해한다. 상기 제 2 QR 분해를 통해, P2, Q2, D2, R2로 각각 순열행렬, 직교행렬, 대각행렬, 상삼각 행렬로 분해한다.Then, the decoder performs a second QR decomposition in step 310,

QR decomposes the matrix as shown in Equation 6 above. Through the second QR decomposition, P2, Q2, D2, and R2 are decomposed into a permutation matrix, an orthogonal matrix, a diagonal matrix, and an upper triangular matrix, respectively.

Thereafter, the decoder linearly filters and receives the received signal from the result of the second QR decomposition in step 312 (see Equation 7 above).

Then, the decoder selects the vector candidate in step 314 and performs inverse LR in step 316 to move the signal of the grid space to the original space.

In step 318, the decoder outputs an information bit mapped to a constellation point in the original space.

The decoder then terminates the decoding procedure of the present invention.

Meanwhile, in the detailed description of the present invention, specific embodiments have been described, but various modifications are possible without departing from the scope of the present invention. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined not only by the scope of the following claims, but also by the equivalents of the claims.

1 is a performance comparison graph of the present invention and the prior art

2 is a decoder for performing complex lattice reduction according to an embodiment of the present invention;

3 is a flowchart illustrating a decoding method of performing complex lattice reduction according to an embodiment of the present invention.

Claims (14)

In the method for signal decoding in a multi-antenna system, Receiving at least one symbol; Decoding at least partially received symbols by determining a point closest to the at least one subset of the constellation map used for the symbol transmission in grid space corresponding to the at least one subset of constellation maps, The decoding process approximately determines an orthogonal basis in the lattice space by using an algorithm for reducing the basis in a complex space, and the close point is at least one called candidate symbols. The point corresponding to the above close integer value is determined based on component-wise rounding, In the decoding process, a soft bit decision value is calculated by linearly filtering predetermined candidate symbols for each bit stream. The linear filtering method is defined by the following equation.

Here, f is a signal vector obtained by linearly filtering the reception vector y, D ₂ is a diagonal matrix in the second QR decomposition, Q ₂ is an orthogonal matrix in the second QR decomposition, and R ₂ is an image in the second QR decomposition. Triangular matrix,

Is a matrix

Are the first two columns. vector

, Matrix

to be. procession

And inverse

Is a complex-valued integer-valued matrix. delete delete The method of claim 1, The predetermined candidate symbol is Characterized in that it is determined by a preorder tree search performed as a search in all possible permutation matrices in the 2x2 case. The method of claim 1, And assigning a probability to a candidate vector using a conditional probability function in the soft decision calculation. The method of claim 1, The decoding process, The estimated channel matrix (H) is expanded to the extended channel matrix (

) And then the extended channel matrix (

Calculating a permutation matrix (P ₁ ) and an upper triangle matrix (R ₁ ) by performing a first complex alignment QR decomposition (SQRD) Reducing the off-diagonal elements of the matrix R1; A modified channel matrix having the complex value

Calculating a permutation matrix (P ₂ ) and an upper triangular matrix (R ₂ ) by performing a second complex alignment QR decomposition on; Matrix having the complex value (

Multiplying the inverse of the matrix; and converting the received matrix into a reception vector. The method of claim 6, The extended channel matrix is characterized by the following equation (12).

Where H is the estimated channel matrix, I is the unit matrix, and α is the inverse of the SNR. In the apparatus for signal decoding in a multi-antenna system, An antenna for receiving at least one or more symbols, A decoder that at least partially decodes the received symbols by determining at least one subset of the constellation map used for the symbol transmission to the closest point in the grid space corresponding to the at least one subset of constellation maps, The decoder approximately determines an orthogonal basis in the lattice space using an algorithm that reduces the basis in the complex space. The close point is a point corresponding to at least one or more close integer values called candidate symbols, and is determined based on component-wise rounding. The decoder calculates a soft bit decision value by numbering candidate symbols through linear filtering for each bit stream, Wherein the linear filtering is defined by the following equation.

Here, f is a signal vector obtained by linearly filtering the reception vector y, D ₂ is a diagonal matrix in the second QR decomposition, Q ₂ is an orthogonal matrix in the second QR decomposition, and R ₂ is an image in the second QR decomposition. Triangular matrix,

Is a matrix

Are the first two columns. vector

, Matrix

to be. procession

And inverse

Is a complex-valued integer-valued matrix. delete delete The method of claim 8, The predetermined candidate symbol is Device determined by a preorder tree search performed as a search in all possible permutation matrices in the 2x2 case. The method of claim 8, And assigning a probability to a candidate vector using a conditional probability function in the soft decision calculation. The method of claim 8, The decoder, The estimated channel matrix (H) is expanded to the extended channel matrix (

) And then the extended channel matrix (

A first aligned QR decomposer performing a first complex aligned QR decomposition (SQRD) to calculate a permutation matrix (P ₁ ) and an upper triangle matrix (R1), A lattice reducer for reducing off-diagonal elements of the matrix R ₁ ; A modified channel matrix having the complex value

A second QR decomposer for performing a second complex aligned QR decomposition on the Δ, to calculate a permutation matrix P ₂ and an upper triangle matrix R ₂ ; Matrix having the complex value (

And an inverse transformer for multiplying an inverse matrix and converting the received matrix into a reception vector. The method of claim 13, And the extended channel matrix is represented by Equation (13).

Where H is the estimated channel matrix, I is the unit matrix, and α is the inverse of the SNR.

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