WO2008066226A2 - Decoding method and device for detecting transmission signal in multiple-input multiple-output system - Google Patents

Decoding method and device for detecting transmission signal in multiple-input multiple-output system Download PDF

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WO2008066226A2
WO2008066226A2 PCT/KR2007/002396 KR2007002396W WO2008066226A2 WO 2008066226 A2 WO2008066226 A2 WO 2008066226A2 KR 2007002396 W KR2007002396 W KR 2007002396W WO 2008066226 A2 WO2008066226 A2 WO 2008066226A2
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value
vector
calculating
signal
matrix
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WO2008066226A3 (en
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In-Sook Park
Jae-Young Ahn
Seong-Rag Kim
Hyun-Kyu Chung
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Electronics And Telecommunications Research Institute
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/06Dc level restoring means; Bias distortion correction ; Decision circuits providing symbol by symbol detection
    • H04L25/067Dc level restoring means; Bias distortion correction ; Decision circuits providing symbol by symbol detection providing soft decisions, i.e. decisions together with an estimate of reliability
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
    • H04L25/03171Arrangements involving maximum a posteriori probability [MAP] detection
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842Weighted combining
    • H04B7/0848Joint weighting

Definitions

  • the present invention relates to a decoding method and device for detecting a transmission signal in a multiple-input multiple-output (MIMO) system. More particularly, the present invention relates to a decoding method and device for providing detecting performance that is close to the performance of maximum likelihood detection and having low complexity when a transmission signal vector is detected from a received signal vector including a plurality of signals in a MIMO system.
  • MIMO multiple-input multiple-output
  • a conventional wireless mobile communication system is used for a voice service, and a channel coding process is performed to overcome a bad channel environment.
  • the wireless mobile communication system since the need for a high quality multimedia service has increased, the wireless mobile communication system has moved its focus to a data service, and a next generation wireless transmission technique for transmitting more data at a faster speed with lower error probability is required.
  • a forward link including a large amount of data requirement the importance of high-rate data transmission is increased.
  • signal reliability is deteriorated in a mobile communication environment by fading, shadowing, propagation attenuation, noise, and interference.
  • the fading effect is caused by multipaths, in which signals respectively received through different paths are considerably distorted by signals respectively having different phases and size.
  • the fading effect is one of the problems that are required to be solved to perform high-rate data communication, and therefore, various studies for overcoming radio channel characteristics have been conducted.
  • a multiple-input multiple-output (MIMO) technique using a plurality of transmitting/receiving antennas has been suggested.
  • a receiving terminal is required to detect a received signal vector X including M complex numbers from a signal vector Y including N measured complex numbers to improve transmitted data reliability.
  • the received signal vector X is required to be detected to be closest to an original signal.
  • Y is the same as a value obtained by multiplying X by an N X M matrix and adding a noise vector.
  • N X M matrix multiplied with X has been previously estimated at the receiving terminal and that the noise vector is a Gaussian noise vector.
  • each element forming X is one element among the 2Q-QAM. Therefore, it is required to perform at least N x (M+ 1 ) x 2M x Q multiplications when X is calculated by the maximum likelihood detection that has high performance as one single detecting method.
  • One of the methods is a sphere decoding method.
  • Another one of the methods is a QR decomposition and M-algorithm (QRM-MLD) method, in which performance that is close to the performance of the maximum likelihood detection is achieved.
  • QRM-MLD QR decomposition and M-algorithm
  • the present invention has been made in an effort to provide a transmission signal detecting method and device using a maximum likelihood detection method to obtain a high data rate and a high diversity gain when detecting a transmission signal vector from a plurality of received signal vectors in a multiple-input multiple-output (MIMO) system, and reducing a selection range of lattice points performing a calculation operation in a maximum likelihood point detecting process to obtain low complexity.
  • MIMO multiple-input multiple-output
  • a) a sorted QR decomposition for a matrix B that indicates a channel state is performed to calculate a unitary matrix Q and an upper triangular matrix R
  • the received signal Y is multiplied by a transpose matrix Q* of the unitary matrix Q to calculate a vector y
  • an initial detection lattice point and a minimum eigenvalue ⁇ is calculated from the vector y and the upper triangular matrix R
  • a maximum likelihood point is detected by using the initial detection lattice point and the minimum eigenvalue ⁇ .
  • An exemplary device for detecting a transmission signal from a plurality of received signals in a MIMO system includes a QR decomposition unit, a vector calculating unit, an initial detection lattice point detecting unit, an eigenvalue extractor, and a maximum likelihood point detecting unit.
  • the QR decomposition unit performs a sorted QR decomposition for a matrix B indicating a channel so as to increase a signal to noise ratio (SNR) or a signal to interference plus noise ratio (SINR) of the transmission signal as the number of columns of an upper triangular matrix R.
  • the vector calculating unit calculates a vector y by multiplying the received signal by a transpose matrix Q 1 of a unitary matrix Q.
  • the initial detection lattice point detecting unit calculates an initial detection lattice point from the vector y and the upper triangular matrix R.
  • the eigenvalue extractor performs a sorted QR decomposition for a matrix B indicating a channel so as to increase a
  • the maximum likelihood point detecting unit detects a maximum likelihood point by using
  • An exemplary receiving device of a MIMO system includes a first transmission signal detecting device, a second transmission signal detecting device, and a Max-Log maximum a posteriori (MAP) calculator.
  • the first transmission signal detecting device detects a maximum likelihood point from a matrix B indicating the channel and a received signal.
  • the second transmission signal detecting device calculates an (i,k)-maximum likelihood point for a k th bit of an i th signal of a transmission signal vector by using an upper triangular matrix R, a vector y, and the maximum likelihood point calculated by the first transmission signal detecting device (here, i is one of the natural numbers from 1 to a size of the transmission signal vector, and k is one of the natural numbers from 1 to Q(i), where Q(i) denotes a size of a bit sequence forming the i th signal).
  • the Max-Log MAP calculator calculates a log-likelihood ratio (LLR) vector by using the maximum likelihood point detected by the first transmission signal detecting device and (i,k)-maximum likelihood points corresponding to the size (MQ) of the bit sequence forming the transmission signal vector calculated by the second transmission signal detecting device.
  • LLR log-likelihood ratio
  • FIG. 1 is a diagram representing an arrangement of two-dimensional lattice points according to an exemplary embodiment of the present invention.
  • FIG. 2 is a diagram representing a transmission signal detecting method performed by a star-like decoder (SLD) according to the exemplary embodiment of the present invention.
  • FIG. 3 is a flowchart representing a maximum likelihood detecting method according to the exemplary embodiment of the present invention.
  • FIG. 4A and FIG. 4B are flowcharts representing a log-likelihood ratio (LLR) vector calculating method according to a first exemplary embodiment of the present invention.
  • FIG. 5A and FIG. 5B are flowcharts representing an LLR vector calculating method according to a second exemplary embodiment of the present invention.
  • LLR log-likelihood ratio
  • FIG. 6 is a flowchart representing the maximum likelihood detecting method and the LLR vector calculating method according to the exemplary embodiment of the present invention.
  • FIG. 7 is a block diagram of an internal configuration of the star-like decoder according to the exemplary embodiment of the present invention.
  • FIG. 8 is a block diagram representing a receiver of a multiple antenna system including the SLD according to the exemplary embodiment of the present invention.
  • the element When it is described that an element is coupled to another element, the element may be directly coupled to the other element or coupled to the other element through a third element.
  • module will be understood to indicate a unit for processing a predetermined function or operation, which may be realized by hardware, software, or a combination thereof.
  • a transmitted signal vector is estimated or each bit reliability forming the transmitted signal vectors is estimated in a multiple-input multiple-output (MIMO) system having a transceiver using a plurality of antennas and a transmission signal detecting device having performance that is equal or similar to a maximum likelihood detection, whereby complexity is improved.
  • MIMO multiple-input multiple-output
  • the transmission signal detecting device will be referred to as a star-like decoder.
  • FIG. 1 is a diagram representing an arrangement of two-dimensional lattice points according to an exemplary embodiment of the present invention.
  • the arrangement of the two-dimensional lattice points of the MIMO system having the transceiver using the plurality of antennas may be the arrangement shown in FIG. 1.
  • the lattice point actually has a three-dimensional arrangement, but the two-dimensional lattice point will be exemplified in the exemplary embodiment of the present invention.
  • FIG. 1 denotes an initial detection lattice point that is firstly detected in the above arrangement.
  • the initial detection lattice point may be detected by various methods.
  • ai to a 8 respectively denote lattice points neighboring the initial detection lattice point
  • a-i to a 4 respectively denote lattice points positioned to upper, lower, left, and right sides of and
  • ri denotes the distance between ai to a 4
  • a 5 to a & denote lattice points diagonally positioned from .
  • X 2 denotes the distance between as to as and
  • ⁇ Z is V 2.
  • a 9 denotes a lattice point positioned to an upper side of a 1f and a distance r 3 denotes a distance between a 9 and .
  • r 3 is 2.
  • Equation 1 In the MIMO system using M t transmitting antennas, M r receiving antennas, and 2 Q -QAM signal constellation, Equation 1 is used to estimate a transmission signal. [Equation 1]
  • Y denotes a column vector including N signal values known by a receiving terminal
  • X denotes a signal to be calculated
  • the signal is a column vector including
  • B denotes an NXM matrix estimated and calculated by the receiving terminal and each element has a complex number value.
  • M and N may be respectively equal to or different from M t and M r .
  • Z denotes a vector including N probability variables, where generally an average thereof is a zero vector and Zi, Z 2 , ⁇ • ⁇ , and Z N are independent from each other.
  • Zj (1 ⁇ i ⁇ N) is a Gaussian distribution
  • X maximizing a likelihood value with respect to a given Y and B is the same as X minimizing a distance between Y and BX.
  • each element forming X is an element of 2 Q -QAM, it is required to perform a calculation of Nx (M+1)x2 MXQ+2 in a method for calculating the distance between Y and BX by substituting every possible lattice point of X to obtain X having the minimum distance.
  • the LLR is calculated to calculate an input value of a channel decoder, it is required to perform a calculation of
  • a lattice point X minimizing the distance between Y and BX is calculated, and the lattice point X minimizing the distance between Y and BX is calculated based on the distance values r-i to r 8 .
  • a method for calculating the lattice point from distance values of ai to a& positioned in upper, lower, left, right, upper left diagonal, upper right diagonal, lower left diagonal, and lower right diagonal sides of is referred to as a "star-like decoding method”.
  • a decoder for performing a decoding operation by using the star-like decoding method is referred to as a star-like decoder (SLD).
  • FIG. 2 is a diagram representing a transmission signal detecting method performed by the SLD according to the exemplary embodiment of the present invention.
  • the transmission signal detecting method includes a real matrix conversion process S210, a QR decomposition process S220, a vector calculation process S230, an initial detection lattice point detection process S240, a minimum eigenvalue extraction process S250, and a maximum likelihood point detection process S260.
  • the SLD converts a matrix B estimated and calculated by the receiving terminal into a real matrix A.
  • the matrix B shows a channel state.
  • the matrix B is a complex number matrix
  • the number of columns of the matrix A is M
  • each signal of the transmission signal vector is divided into a real part and an imaginary part
  • the number of bits forming a bit sequence corresponding to the real part (or the imaginary part) in the signal constellation is Q.
  • a sorted QR decomposition (hereinafter referred to as an "SQRD") is performed for the matrix A o
  • denotes a square root of a noise variance
  • IM denotes an Mx M identify matrix.
  • Q denotes a unitary matrix
  • R denotes an upper triangular matrix
  • a transmission signal corresponding to a column number of a matrix before the SQRD is performed is different from the transmission signal corresponding to the column number of the matrix R, and it is required to remember a sorted sequence.
  • the SQRD may include a past-sorting algorithm (PSA), and the SQRD is performed in order to increase a signal-to-noise ratio (SNR) or a signal to interference plus noise ratio (SINR) corresponding to the column number as the column number of R increases.
  • PSA past-sorting algorithm
  • SQRD is performed in order to increase a signal-to-noise ratio (SNR) or a signal to interference plus noise ratio (SINR) corresponding to the column number as the column number of R increases.
  • SNR signal-to-noise ratio
  • SINR signal to interference plus noise ratio
  • a vector y is obtained by multiplying a received signal Y by a transpose matrix Q* of the unitary matrix Q. That is, y satisfying
  • an initial detection lattice point X is obtained from Equation 2 through a quantization process and a successive interference cancellation (SIC) process.
  • the initial detection of may be variously performed.
  • i iiss oobbttaaiinneedd, aanndd is obtained for i that is smaller than M.
  • M is greater than or equal to 0, and is an integer that is close
  • obtaining * may be used.
  • ⁇ ⁇ nin of R'R- is calculated.
  • a maximum likelihood point is detected by using calculated in the initial detection lattice point detection
  • FIG. 3 is a flowchart representing the maximum likelihood detecting method according to the exemplary embodiment of the present invention.
  • the lattice point minimizing the distance between y and Rx among possible integer lattice points used as x in Equation 2 is a value of the maximum likelihood detection for Equation 1.
  • Equation 3 satisfies a predetermined vector [Equation 3]
  • the lattice point calculated in the initial detection lattice point detection process S240 is substituted for
  • C ⁇ x) j s a CO st function for x
  • a convex function for Values of the cost functions of the lattice points that are closest to are calculated and compared by using convex characteristics of C( x ), a distance from is increased by one until the desired is obtained, and the values of the cost functions of the lattice points corresponding to each distance are calculated and compared. Since is an element of an M dimensional finite integer lattice set D induced from the signal constellation, it is easy to detect the closest lattice points and distances therebetween, and the next closest lattice points and distances therebetween.
  • Equation 4 when is the center of x and x represents each point on a circumference having a radius of
  • X (X 1 ,' ", ⁇ )
  • r sequentially receives values of 1 , V2, • • • , ⁇ /M J ⁇ • -, and so on, and a
  • step S320 are established in step S320.
  • the real matrix conversion process S210 or the vector calculation process S230 is performed to detect the other signal vector.
  • the real matrix conversion process S210 is performed when a channel variation is great, and the vector calculation process S230 is performed when the channel variation is low.
  • step S330 when it is determined in step S330 that is smaller than or equal t is increased by 1 in step S340.
  • the cost function is calculated for points of D positioned about a r ⁇ distance awa from
  • step S370 are established in step S370 when Ct ⁇ ) is less than In the step S360, and c ⁇ do not vary when C( r i) is greater than or equal tO ⁇ ML -
  • / is compared to a previously established finite repetition value L , and the steps after S330 are repeatedly performed when l is less than L.
  • I becomes the same as the previously established finite repetition value L is calculated as a value to be obtained, and the current signal vector detection process is finished.
  • the real matrix conversion process S210 or the vector calculation process S230 is performed to detect a third signal vector in step S380.
  • Equation 1 if in the QR decomposition process S220, is close to the maximum likelihood detection signal but it is not the same. However,
  • a method for obtaining xpressing as an( j obtaining may be used.
  • the calculated is applied to the maximum likelihood point detection process S260. Accordingly, the maximum likelihood detection is performed from a value of
  • MMSE minimum mean square error
  • x is expressed a and an integer x i corresponds to a one bit sequence including Q binary numbers. In this case, 0 and 1 are used for the binary numbers.
  • a matrix obtained by eliminating an i th column of the matrix B is expressed as B (0 .
  • the SQRD process is performed according to the QR decomposition process S220, and a Max-Log maximum a posteriori (MAP) is applied to Equation 2 to obtain the LLR.
  • MAP Max-Log maximum a posteriori
  • FIG. 4A and FIG. 4B are flowcharts representing the LLR vector calculating method according to a first exemplary embodiment of the present invention. i is established to be 1 in step S402 to calculate an LLR vector. In addition, a
  • step S404 an integer lattice set is established in step S404.
  • k is established to be 1, an integer of which a k th bit of a corresponding bit sequence is different from is selected from among the integers 0 to 2 y -1 in step
  • step S410 When y 1 and y/ are calculated, a re calculated
  • step S412 by using the equation given as When c 1 and b are calculated, C(x) ⁇ s established as _
  • V sequentially uses values of 1, • &, • ⁇ • ,
  • LLR(i,k) is calculated according to Equation 7 in step S420 when is greater than
  • k and Q are compared in step S422.
  • k and Q are compared in step S422.
  • step S424 k + 1
  • steps after S406 are repeatedly performed in step S424.
  • k and Q are the same in step S422, / and M are compared in step
  • n* is less than or the same as in step S418, I is increased by 1 in step S430, and the cost function values of points of D' that are away from by r ⁇ are calculated in step S432.
  • the LLR vector corresponding to one space-time encoded block may be calculated by the processes shown in FIG. 3, FIG.4A and FIG.4B.
  • another LLR vector calculating method reducing the number of calculations may be performed, but in this case, the performance may be slightly deteriorated.
  • FIG. 5A and FIG. 5B are flowcharts representing the LLR vector calculating method according to a second exemplary embodiment of the present invention.
  • step S506 an matrix s having elements of a S th row and an #2 th column that are the same as elements of the s iU row and the r ⁇ th column of R (0 is calculated in step S506 when
  • step S508 an ( h - 1 ) dimensional partial space of D is established as E>' in step S510.
  • step S504 an (M-Ux(M-W) matrix S having the
  • k is set to be 1 , and integers of which a k th bit of the corresponding bit sequence is different from are selected from the integers 0 and 2 ⁇ -1 in step S518.
  • step S520 among the integers 0 to 2 S -1 is selected and established as in step S520.
  • y' and y/ are calculated in step S522.
  • y' and y/ are calculated by using the equation given as
  • step S504 determined in step S504 that i ⁇ z' o , and y' and y/ are calculated by using when it is
  • LLR(i.k) is calculated when ⁇ 1 is greater than C ML(W . in this case, LLR(i.k) may be
  • step S534 k and ⁇ are compared in step S534.
  • * is the same as M 1 the LLR vector calculating process is finished, and steps corresponding to the steps after S422 shown in FIG. 4A and FIG. 4B are repeatedly performed.
  • step S530 when r ⁇ « is less than or equal to in step S530, I is increased by 1 , the cost function value is calculated, and steps corresponding to S430 to S438 shown in FIG. 4A and FIG. 4B are performed in steps S542 to S550.
  • the approximate value of and the number of calculations may be reduced by using a method that is different from FIG. 3 to FIG. 5B with respect to the predetermined i and k.
  • FIG. 6 is a flowchart representing the maximum likelihood detecting method and the LLR vector calculating method according to the exemplary embodiment of the present invention.
  • Equation 11 Equation 11
  • step S606 it is respectively established in step S606 that
  • step S610 It is determined that has a value having a minimum cost function in D, and n c
  • step S612 distances between and are sequentially increased, and the cost function values for the lattice points corresponding to the respective distances are calculated in step S614.
  • n c is increased by 1 in step
  • step S616 When the calculated cost function is greater than R c in step S616, the distance is increased, and the step S614 calculating the cost function value for the lattice point corresponding to each distance is repeatedly performed.
  • step S610 when it is determined in step S610 that * « is less than or equal to / is increased by 1 in step S622.
  • n c and N 0 are compared.
  • the above maximum likelihood detecting method and the LLR vector calculating method may be applied to an iterative receiver.
  • the iterative receiver uses a value obtained by applying a logarithm to a
  • FIG. 7 is a block diagram of an internal configuration of the star-like decoder according to the exemplary embodiment of the present invention.
  • the SLD includes a real number matrix converting unit 710, a QR decomposition unit 720, a vector calculating unit 730, an initial detection lattice point detecting unit 740, an eigenvalue extractor 750, and a maximum likelihood point detecting unit 760.
  • the real number matrix converting unit 710 performing the real matrix conversion process S210 shown in FIG. 2 converts a matrix estimated from a received signal into a real number matrix.
  • the QR decomposition unit 720 performing the QR decomposition process S220 performs the SQRD process so that an SNR or an SINR of a transmission signal may increase as a column number of the upper triangular matrix R obtained after the QR decomposition increases.
  • the vector calculating unit 730 performs the vector calculation process S230 for multiplying the received signal by a transpose matrix of a unitary matrix.
  • the initial detection lattice point detecting unit 740 performs the initial detection lattice point detection process S240 for calculating the initial detection lattice point by using the successive interference cancellation method.
  • the eigenvalue extractor 750 performs the minimum eigenvalue extraction
  • the maximum likelihood point detecting unit 760 detecting the maximum likelihood point by using received from the initial detection lattice point detecting
  • FIG. 8 is a block diagram representing a receiver of a multiple antenna system including the SLD according to the exemplary embodiment of the present invention.
  • the receiver of the multiple antenna system may include a plurality of SLDs.
  • decoder 810 detects the lattice point by using the column vector Y known by a receiving terminal and the matrix B estimated or calculated by the receiving terminal.
  • second to fourth star-like decoders calculate a plurality of LLRs from the upper triangular matrix R 1 the vector Y, and the lattice point X calculated by the first star-like decoder 810.
  • the second star-like decoder 820 shown in FIG. 8 calculates the maximum likelihood point by converting a first bit value of a detected signal (i.e., 0 to 1 , or 1 to 0) and fixing it
  • the third star-like decoder 830 calculates the maximum likelihood point by converting a k th bit value and fixing it.
  • M x Q star-like decoders may be included, and a star-like decoder for calculating the maximum likelihood point by converting an (MXQ)th bit and fixing it is referred to as the "fourth star-like decoder".
  • the Max-Log MAP calculator 850 calculates the LLR by using the lattice point calculated by the first star-like decoder 810 and the maximum likelihood points calculated by the second star-like decoder 820 to the fourth star-like decoder 840.
  • the star-like decoding method and the star-like decoder are used to detect the received signal vector including a plurality of signals in the MIMO system, performance that is similar to the maximum likelihood detecting method may be achieved.

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Abstract

The present invention relates to a decoding method and a decoding device for detecting a transmission signal in a multiple-input multiple-output (MIMO) system. In the method, a sorted QR decomposition for calculating a unitary matrix and an upper triangular matrix, the received signal is multiplied by a transpose matrix of the unitary matrix to calculate a vector, an initial detection lattice point and a minimum eigenvalue is calculated from the vector and the upper triangular matrix, and a maximum likelihood point is detected by using the initial detection lattice point and the minimum eigenvalue. In addition, a transmission signal detecting device includes a QR decomposition unit for performing a sorted QR decomposition for the received signal, a vector calculating unit for calculating a vector by multiplying the received signal by a transpose matrix of a unitary matrix, an initial detection lattice point detecting unit for calculating an initial detection lattice point, an eigenvalue extractor for calculating a minimum eigenvalue, and a maximum likelihood point detecting unit for detecting a maximum likelihood point by using the initial detection lattice point and the minimum eigenvalue.

Description

TITLE OF THE INVENTION
DECODING METHOD AND DEVICE FOR DETECTING TRANSMISSION SIGNAL IN MULTIPLE-INPUT MULTIPLE-OUTPUT SYSTEM
BACKGROUND OF THE INVENTION
(a) Field of the Invention
The present invention relates to a decoding method and device for detecting a transmission signal in a multiple-input multiple-output (MIMO) system. More particularly, the present invention relates to a decoding method and device for providing detecting performance that is close to the performance of maximum likelihood detection and having low complexity when a transmission signal vector is detected from a received signal vector including a plurality of signals in a MIMO system.
(b) Description of the Related Art
A conventional wireless mobile communication system is used for a voice service, and a channel coding process is performed to overcome a bad channel environment. However, since the need for a high quality multimedia service has increased, the wireless mobile communication system has moved its focus to a data service, and a next generation wireless transmission technique for transmitting more data at a faster speed with lower error probability is required. Particularly, in a forward link including a large amount of data requirement, the importance of high-rate data transmission is increased. However, signal reliability is deteriorated in a mobile communication environment by fading, shadowing, propagation attenuation, noise, and interference.
The fading effect is caused by multipaths, in which signals respectively received through different paths are considerably distorted by signals respectively having different phases and size. The fading effect is one of the problems that are required to be solved to perform high-rate data communication, and therefore, various studies for overcoming radio channel characteristics have been conducted. As a result, a multiple-input multiple-output (MIMO) technique using a plurality of transmitting/receiving antennas has been suggested.
In a mobile communication system using the MIMO technique, a receiving terminal is required to detect a received signal vector X including M complex numbers from a signal vector Y including N measured complex numbers to improve transmitted data reliability. In this case, the received signal vector X is required to be detected to be closest to an original signal.
Generally, Y is the same as a value obtained by multiplying X by an N X M matrix and adding a noise vector. In this case, it is assumed that the N X M matrix multiplied with X has been previously estimated at the receiving terminal and that the noise vector is a Gaussian noise vector. When a signal constellation used for transmission is 2Q-quadrature amplitude modulation (QAM), each element forming X is one element among the 2Q-QAM. Therefore, it is required to perform at least N x (M+ 1 ) x 2M x Q multiplications when X is calculated by the maximum likelihood detection that has high performance as one single detecting method. Further, it is required to perform multiplications when a
Figure imgf000004_0001
log-likelihood ratio (LLR) is calculat to calculate an input value of a channel decoder. Accordingly, it is difficult to apply the MIMO technique to an actual system since the number of calculations is exponentially increased as M and Q increase. Accordingly, methods for performing a calculation with a limited range in which a maximum likelihood point is expected have been currently suggested.
One of the methods is a sphere decoding method. Another one of the methods is a QR decomposition and M-algorithm (QRM-MLD) method, in which performance that is close to the performance of the maximum likelihood detection is achieved.
However, there is a limit in improving complexity since the number of calculations is exponentially increased when the number of signals forming the received signal vector and the transmission signal vector is large. The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
SUMMARY OF THE INVENTION
The present invention has been made in an effort to provide a transmission signal detecting method and device using a maximum likelihood detection method to obtain a high data rate and a high diversity gain when detecting a transmission signal vector from a plurality of received signal vectors in a multiple-input multiple-output (MIMO) system, and reducing a selection range of lattice points performing a calculation operation in a maximum likelihood point detecting process to obtain low complexity.
In an exemplary method for detecting a transmission signal from a plurality of received signals in a MIMO system according to an embodiment of the present invention, a) a sorted QR decomposition for a matrix B that indicates a channel state is performed to calculate a unitary matrix Q and an upper triangular matrix R, b) the received signal Y is multiplied by a transpose matrix Q* of the unitary matrix Q to calculate a vector y, c) an initial detection lattice point
Figure imgf000006_0001
and a minimum eigenvalue λ is calculated from the vector y and the upper triangular matrix R, and d) a maximum likelihood point is detected by using the initial detection lattice point
Figure imgf000006_0002
and the minimum eigenvalue λ .
An exemplary device for detecting a transmission signal from a plurality of received signals in a MIMO system according to an embodiment of the present invention includes a QR decomposition unit, a vector calculating unit, an initial detection lattice point detecting unit, an eigenvalue extractor, and a maximum likelihood point detecting unit. The QR decomposition unit performs a sorted QR decomposition for a matrix B indicating a channel so as to increase a signal to noise ratio (SNR) or a signal to interference plus noise ratio (SINR) of the transmission signal as the number of columns of an upper triangular matrix R. The vector calculating unit calculates a vector y by multiplying the received signal by a transpose matrix Q1 of a unitary matrix Q. The initial detection lattice point detecting unit calculates an initial detection lattice point from the vector y and the upper triangular matrix R. The eigenvalue extractor
calculates a minimum eigenvalue 7W from the upper triangular matrix R. The maximum likelihood point detecting unit detects a maximum likelihood point by using
the initial detection lattice point
Figure imgf000006_0003
and the minimum eigenvalue min.
An exemplary receiving device of a MIMO system according to an embodiment of the present invention includes a first transmission signal detecting device, a second transmission signal detecting device, and a Max-Log maximum a posteriori (MAP) calculator. The first transmission signal detecting device detects a maximum likelihood point from a matrix B indicating the channel and a received signal. The second transmission signal detecting device calculates an (i,k)-maximum likelihood point for a kth bit of an ith signal of a transmission signal vector by using an upper triangular matrix R, a vector y, and the maximum likelihood point calculated by the first transmission signal detecting device (here, i is one of the natural numbers from 1 to a size of the transmission signal vector, and k is one of the natural numbers from 1 to Q(i), where Q(i) denotes a size of a bit sequence forming the ith signal). The Max-Log MAP calculator calculates a log-likelihood ratio (LLR) vector by using the maximum likelihood point detected by the first transmission signal detecting device and (i,k)-maximum likelihood points corresponding to the size (MQ) of the bit sequence forming the transmission signal vector calculated by the second transmission signal detecting device.
BRIEF DESCRIPTION QF THE DRAWINGS FIG. 1 is a diagram representing an arrangement of two-dimensional lattice points according to an exemplary embodiment of the present invention.
FIG. 2 is a diagram representing a transmission signal detecting method performed by a star-like decoder (SLD) according to the exemplary embodiment of the present invention. FIG. 3 is a flowchart representing a maximum likelihood detecting method according to the exemplary embodiment of the present invention.
FIG. 4A and FIG. 4B are flowcharts representing a log-likelihood ratio (LLR) vector calculating method according to a first exemplary embodiment of the present invention. FIG. 5A and FIG. 5B are flowcharts representing an LLR vector calculating method according to a second exemplary embodiment of the present invention.
FIG. 6 is a flowchart representing the maximum likelihood detecting method and the LLR vector calculating method according to the exemplary embodiment of the present invention. FIG. 7 is a block diagram of an internal configuration of the star-like decoder according to the exemplary embodiment of the present invention,
FIG. 8 is a block diagram representing a receiver of a multiple antenna system including the SLD according to the exemplary embodiment of the present invention.
DETAILED DESCRIPTION OF THE EMBODIMENTS
In the following detailed description, only certain exemplary embodiments of the present invention have been shown and described, simply by way of illustration. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive. Like reference numerals designate like elements throughout the specification.
When it is described that an element is coupled to another element, the element may be directly coupled to the other element or coupled to the other element through a third element.
In addition, the word "module" will be understood to indicate a unit for processing a predetermined function or operation, which may be realized by hardware, software, or a combination thereof.
In an exemplary embodiment of the present invention, a transmitted signal vector is estimated or each bit reliability forming the transmitted signal vectors is estimated in a multiple-input multiple-output (MIMO) system having a transceiver using a plurality of antennas and a transmission signal detecting device having performance that is equal or similar to a maximum likelihood detection, whereby complexity is improved. Hereinafter, the transmission signal detecting device will be referred to as a star-like decoder.
FIG. 1 is a diagram representing an arrangement of two-dimensional lattice points according to an exemplary embodiment of the present invention.
In the exemplary embodiment of the present invention, the arrangement of the two-dimensional lattice points of the MIMO system having the transceiver using the plurality of antennas may be the arrangement shown in FIG. 1. The lattice point actually has a three-dimensional arrangement, but the two-dimensional lattice point will be exemplified in the exemplary embodiment of the present invention.
In FIG. 1,
Figure imgf000009_0001
denotes an initial detection lattice point that is firstly detected in the above arrangement. In this case, the initial detection lattice point may be detected by various methods. ai to a8 respectively denote lattice points neighboring the initial detection lattice point Here, a-i to a4 respectively denote lattice points positioned to upper, lower, left, and right sides of and ri denotes the distance between ai to a4 and In
Figure imgf000009_0002
Figure imgf000009_0003
addition, a5 to a& denote lattice points diagonally positioned from
Figure imgf000009_0004
. X2 denotes the distance between as to as and
Figure imgf000009_0005
Here, when r-i is 1 , ΪZ is V 2. a9 denotes a lattice point positioned to an upper side of a1f and a distance r3 denotes a distance between a9 and
Figure imgf000009_0006
. In this case, r3 is 2. A method for calculating ri to r3 will now be described with reference to FIG. 2.
In the MIMO system using Mt transmitting antennas, Mr receiving antennas, and 2Q-QAM signal constellation, Equation 1 is used to estimate a transmission signal. [Equation 1]
Figure imgf000010_0001
Here, Y denotes a column vector including N signal values known by a receiving terminal, X denotes a signal to be calculated and the signal is a column vector including
M rows, and B denotes an NXM matrix estimated and calculated by the receiving terminal and each element has a complex number value.
M and N may be respectively equal to or different from Mt and Mr. Z denotes a vector including N probability variables, where generally an average thereof is a zero vector and Zi, Z2, ■ • ■, and ZN are independent from each other.
Here, when Zj (1 ≤i≤N) is a Gaussian distribution, X maximizing a likelihood value with respect to a given Y and B is the same as X minimizing a distance between Y and BX.
When each element forming X is an element of 2Q-QAM, it is required to perform a calculation of Nx (M+1)x2MXQ+2 in a method for calculating the distance between Y and BX by substituting every possible lattice point of X to obtain X having the minimum distance. In addition, when the LLR is calculated to calculate an input value of a channel decoder, it is required to perform a calculation of
Accordingly, the number of calculations is exponentially
Figure imgf000010_0002
increased when M and Q are large.
Since it is difficult to apply an actual system when M and Q are large, it is required to calculate a lattice point X minimizing the distance between Y and BX to reduce the number of calculations. That is, the distance values Pi to re between a^ to as and X shown in FiG. 1 are calculated, and the lattice point X minimizing the distance between Y and BX is calculated based on the distance values r-i to r8. In this case, a method for calculating the lattice point from distance values of ai to a& positioned in upper, lower, left, right, upper left diagonal, upper right diagonal, lower left diagonal, and lower right diagonal sides of is referred to as a "star-like decoding method". In addition, a decoder for performing a decoding operation by using the star-like decoding method is referred to as a star-like decoder (SLD).
FIG. 2 is a diagram representing a transmission signal detecting method performed by the SLD according to the exemplary embodiment of the present invention.
As shown in FIG. 2, the transmission signal detecting method includes a real matrix conversion process S210, a QR decomposition process S220, a vector calculation process S230, an initial detection lattice point detection process S240, a minimum eigenvalue extraction process S250, and a maximum likelihood point detection process S260.
Firstly, in the real matrix conversion process S210, the SLD converts a matrix B estimated and calculated by the receiving terminal into a real matrix A. Here, the matrix B shows a channel state. When the matrix B includes only real numbers, A=B,
and when the matrix B is a complex number matrix,
Figure imgf000011_0001
In this case, when the number of columns of the matrix A is M, and each signal of the transmission signal vector is divided into a real part and an imaginary part, the number of bits forming a bit sequence corresponding to the real part (or the imaginary part) in the signal constellation is Q.
In addition, in the QR decomposition process S220, a sorted QR decomposition (hereinafter referred to as an "SQRD") is performed for the matrix A o
Figure imgf000012_0003
Here, σ denotes a square root of a noise variance, and IM denotes an Mx M identify matrix.
When the SQRD is performed for the matrix A, A=QR, and when the SQRD is
performed fo
Figure imgf000012_0004
Here, Q denotes a unitary matrix, and R denotes an upper triangular matrix.
In this case, a transmission signal corresponding to a column number of a matrix before the SQRD is performed is different from the transmission signal corresponding to the column number of the matrix R, and it is required to remember a sorted sequence. Here, the SQRD may include a past-sorting algorithm (PSA), and the SQRD is performed in order to increase a signal-to-noise ratio (SNR) or a signal to interference plus noise ratio (SINR) corresponding to the column number as the column number of R increases.
In the vector calculation process S230, a vector y is obtained by multiplying a received signal Y by a transpose matrix Q* of the unitary matrix Q. That is, y satisfying
Figure imgf000012_0001
js gjven as Equation 2. [Equation 2]
Figure imgf000012_0002
Re(Z) Im(Z)
In this case, 7I and have the same probabilities.
In the initial detection lattice point detection process S240, an initial detection lattice point X is obtained from Equation 2 through a quantization process and a successive interference cancellation (SIC) process. The initial detection of may
Figure imgf000013_0009
be variously performed.
A method for initially detecting the lattice point by using a successive
Figure imgf000013_0008
interference cancellation method will now be described.
iiss oobbttaaiinneedd,, aanndd
Figure imgf000013_0001
is obtained for i that is
Figure imgf000013_0004
smaller than M. Here,
Figure imgf000013_0007
is greater than or equal to 0, and is an integer that is close
to X among integers that are smaller than 2 . Accordingly, the initial detection
lattice point is given by
Figure imgf000013_0005
In this case, rat er than using a successive interference cancellation method, a
method for obtaining
Figure imgf000013_0002
, and
obtaining *
Figure imgf000013_0003
may be used.
In the minimum eigenvalue extraction process S250, a minimum eigenvalue
Λ λnin of R'R- is calculated. In the maximum likelihood point detection process S260, a maximum likelihood point is detected by using
Figure imgf000013_0006
calculated in the initial detection lattice point detection
process S240 and λ min calculated in the minimum eigenvalue extraction process S250.
Hereinafter, a maximum likelihood detecting method and an LLR vector calculating method will be described with reference to FIG. 3 to FIG. 6. FIG. 3 is a flowchart representing the maximum likelihood detecting method according to the exemplary embodiment of the present invention. When the lattice point
Figure imgf000014_0003
minimizing the distance between y
Figure imgf000014_0002
and Rx among possible integer lattice points used as x in Equation 2 is a value of the maximum likelihood detection for Equation 1. In this case, Equation 3 satisfies a predetermined vector
Figure imgf000014_0004
[Equation 3]
Figure imgf000014_0001
In addition, the lattice point calculated in the initial detection lattice point detection process S240 is substituted for
Figure imgf000014_0005
Here, since
Figure imgf000014_0006
is a known vector,
Figure imgf000014_0007
is a constant that is not a
negative number and
Figure imgf000014_0008
is a constant vector. Accordingly, a method
for obtaining the lattice point
Figure imgf000014_0009
minimizing is the same as a method for
Figure imgf000014_0010
obtaining the lattice point minimizing That jSj
Figure imgf000014_0011
Figure imgf000014_0012
Figure imgf000014_0013
In this case, C{x) js a COst function for x , and a convex function for
Figure imgf000014_0014
Values of the cost functions of the lattice points that are closest to are
Figure imgf000014_0016
calculated and compared by using convex characteristics of C(x), a distance from
Figure imgf000014_0017
is increased by one until the desired
Figure imgf000014_0015
is obtained, and the values of the cost functions of the lattice points corresponding to each distance are calculated and compared. Since
Figure imgf000014_0018
is an element of an M dimensional finite integer lattice set D induced from the signal constellation, it is easy to detect the closest lattice points and distances therebetween, and the next closest lattice points and distances therebetween.
A distance between
Figure imgf000015_0003
and the lattice points calculating the cost function before
obtaining x is gradually increased. The above process will be described in further detail.
Firstly, the constant vector
Figure imgf000015_0005
and the cost function
are estab|isnedi and a minimum value Cr of C(x) \s
Figure imgf000015_0004
a calculated by using the minimum eigenvalue mm calculated in the minimum eigenvalue extraction process S250.
When assuming that x represents an M dimensional real number lattice point,
the minimum value of is given as Equation 4 when
Figure imgf000015_0008
is
Figure imgf000015_0006
the center of x and x represents each point on a circumference having a radius of
Figure imgf000015_0001
[Equation 4]
Figure imgf000015_0007
In addition, an element of the M order integer lattice set D obtained from the signal constellation given by increase/reduction and parallel movement is expressed as
X = (X1,' ", ^) |n thjs casβi X. js one of the jntegers from o to 2δ -l .
Accordingly, r sequentially receives values of 1 , V2, • • •, ^/M J ■ •-, and so on, and a
value thereof is less than
Figure imgf000015_0002
, and
O = ro < t\ < -" < rL is estab|isned in step S310. In addition, are established in step S320.
Figure imgf000016_0003
Further,
Figure imgf000016_0004
is calculated from Equation 4 when
Figure imgf000016_0005
Then, the calculated ^n+1 arid C2^ are compared in step S330.
In this case, when it is determined that
Figure imgf000016_0006
is greater than is
Figure imgf000016_0001
determined as a value to be obtained. Accordingly, a process for detecting the signal vector is finished, and a process for detecting another signal vector is prepared. In this case, the real matrix conversion process S210 or the vector calculation process S230 is performed to detect the other signal vector. Here, the real matrix conversion process S210 is performed when a channel variation is great, and the vector calculation process S230 is performed when the channel variation is low.
However, when it is determined in step S330 that
Figure imgf000016_0007
is smaller than or equal t is increased by 1 in step S340. In addition, the cost function is
Figure imgf000016_0008
calculated for points of D positioned about a rι distance awa from
Figure imgf000016_0009
That is,
Figure imgf000016_0002
js established in step S350.
In addition, C(rι) is compared to
Figure imgf000016_0011
in step S360, and
are established in step S370 when Ctø)
Figure imgf000016_0010
is less than
Figure imgf000016_0012
In the step S360,
Figure imgf000016_0013
and c^ do not vary when C(ri) is greater than or equal tO ^ML -
In addition, / is compared to a previously established finite repetition value L , and the steps after S330 are repeatedly performed when l is less than L. However, when I becomes the same as the previously established finite repetition value L
Figure imgf000017_0002
is calculated as a value to be obtained, and the current signal vector detection process is finished. In this case, the real matrix conversion process S210 or the vector calculation process S230 is performed to detect a third signal vector in step S380.
When the steps S210 to S380 are performed, if A=QR in the QR decomposition process S220, x is the same as a maximum likelihood detection signal with respect to
Equation 1. In addition, if
Figure imgf000017_0001
in the QR decomposition process S220,
Figure imgf000017_0004
is close to the maximum likelihood detection signal but it is not the same. However,
when
Figure imgf000017_0003
, there is a merit in that x more quickly becomes a desired value. Accordingly, in the initial detection lattice point detection process S240 for obtaining the initial detection signal
Figure imgf000017_0012
, rather than using the successive interference
cancellation method, a method for obtaining
Figure imgf000017_0005
xpressing
Figure imgf000017_0006
as
Figure imgf000017_0007
an(j obtaining
Figure imgf000017_0008
may be used. In addition, the calculated
Figure imgf000017_0009
is applied to the maximum likelihood point detection process S260. Accordingly, the maximum likelihood detection is performed from a value of
zero-forcing as a starting point when ^ = QR anc( a value that is close to the performance of the maximum likelihood detection is obtained from a value of a
minimum mean square error (MMSE) as a starting point when
Figure imgf000017_0010
. When
Figure imgf000017_0011
is obtained by the value of zero-forcing or the MMSE, the QR decomposition process for A an omitted, A or is applied instead of R, and IS
Figure imgf000018_0002
Figure imgf000018_0003
Figure imgf000018_0004
applied instead of ^ to perform the maximum likelihood point detection process S260.
While a hard-decision process for detecting the transmission signal from the received signal without considering a channel decoder input type has been described, a method for calculating a vector including the LLRs used as an input of the channel decoder by using the detection method shown in Equation 1 will be described.
Here, x is expressed a
Figure imgf000018_0005
and an integer xi corresponds to a one bit sequence including Q binary numbers. In this case, 0 and 1 are used for the binary numbers. In addition, a vector variable obtained by eliminating the ith variable xt (i=1 ,...,M) of a vector variable x and maintaining a sequence thereof is expressed
as ^v/, and a kth bit of x» is expressed as >>*. A matrix obtained by eliminating an ith column of the matrix B is expressed as B(0 .
The SQRD process is performed according to the QR decomposition process S220, and a Max-Log maximum a posteriori (MAP) is applied to Equation 2 to obtain the LLR.
Firstly, when the LLR of a kth (1 < k < Q) bit of an ifh signal x * (1 <i<M) of a
signal vector x to be detected is LLRj k ^ LLR1 k js gjven as Equation 5. [Equation 5]
Figure imgf000018_0001
js ca|CU|atec| by using C and C1^ calculated in the
Figure imgf000018_0006
maximum likelihood point detection process S260 to calculate a right side of Equation 5, and is calculated. In this case, a method that is similar to the
Figure imgf000019_0003
maximum likelihood point detection process S260 is used to calculated an approximate
value of
Figure imgf000019_0001
FIG. 4A and FIG. 4B are flowcharts representing the LLR vector calculating method according to a first exemplary embodiment of the present invention. i is established to be 1 in step S402 to calculate an LLR vector. In addition, a
value of an upper triangular matrix "W is calculated. It is established that
Figure imgf000019_0004
That is, becomes a vector in which an ith element of
Figure imgf000019_0005
is calculated by the
star-like decoding method. Then, the minimum eigenvalue 4 of R(O R(O is calculated. In addition, an integer lattice set is established in
Figure imgf000019_0006
step S404. k is established to be 1, an integer of which a kth bit of a corresponding bit sequence is different from
Figure imgf000019_0007
is selected from among the integers 0 to 2y-1 in step
S406, and an integer that is closest to
Figure imgf000019_0008
among the integers 0 to 2δ-i is selected
and established as
Figure imgf000019_0009
in step S408.
In addition,
Figure imgf000019_0002
are calculated
in step S410. When y1 and y/ are calculated,
Figure imgf000019_0010
are calculated
in step S412 by using the equation given as
Figure imgf000019_0011
When c1 and b are calculated, C(x) \s established as _ |n ^ case_ when
Figure imgf000019_0012
Figure imgf000019_0013
Figure imgf000020_0005
jhat jSi is approximated to
Figure imgf000020_0006
Accordingly, may be calculated.
Figure imgf000020_0001
Figure imgf000020_0002
In this case, since and
Figure imgf000020_0003
Figure imgf000020_0007
( and jt is estab|jsned tnat / = Q. When assuming that x represents an (M-1) dimensional real number lattice point, the minimum value of js given as Equation 6
Figure imgf000020_0008
when X is the center of x and x represents each point on a circumference having
a radius of in step S414.
Figure imgf000020_0009
[Equation 6]
Figure imgf000020_0010
When x represents points of D', V sequentially uses values of 1, &, •■•,
and s0 on> and a value of T is less than When r js
Figure imgf000020_0011
Figure imgf000020_0012
expressed as and is calculated in step S416
Figure imgf000020_0013
Figure imgf000020_0014
from Equation 6 when
Figure imgf000020_0015
Whe
Figure imgf000020_0016
is calculated, jn step S418, and
Figure imgf000020_0004
LLR(i,k) is calculated according to Equation 7 in step S420 when
Figure imgf000020_0018
is greater than
Figure imgf000020_0017
[Equation 7]
Figure imgf000021_0001
In addition, k and Q are compared in step S422. When k js less than Q,
k is increased to be k = k + 1, and the steps after S406 are repeatedly performed in step S424. When k and Q are the same in step S422, / and M are compared in step
S426. In this case, when / is less than Mt i is increased to be i - i + l, and the steps after S404 are repeatedly performed in step S428. However, when i and M are the same, the LLR vector calculating process is finished since the desired LLR vector is calculated.
Here, when n* is less than or the same as
Figure imgf000021_0002
in step S418, I is increased by 1 in step S430, and the cost function values of points of D' that are away from by rι are calculated in step S432. „, Λ
In addition,
Figure imgf000021_0005
is calculated, and ^W is compared to
QdL (*£) in step S434. It is established that
Figure imgf000021_0003
C(?}) jn step S436 when
is greater than
Figure imgf000021_0004
or equal to HnΛw . in addition, I is compared to L, the steps after S416 are performed when 1 < L , and the steps after S420 are performed when / = ■£ in step S438.
As described above, the LLR vector corresponding to one space-time encoded block may be calculated by the processes shown in FIG. 3, FIG.4A and FIG.4B. Here, another LLR vector calculating method reducing the number of calculations may be performed, but in this case, the performance may be slightly deteriorated.
FIG. 5A and FIG. 5B are flowcharts representing the LLR vector calculating method according to a second exemplary embodiment of the present invention.
Firstly, one integer among row integer numbers 1 to M of the matrix R is
established to be
Figure imgf000022_0008
and i is established to be 1 in step S502.
and i are compared in step S504, an matrix s having
Figure imgf000022_0001
elements of a Sth row and an #2 th column that are the same as elements of the siU row and the røth column of R(0 is calculated in step S506 when
Figure imgf000022_0002
When the matrix S js obtained, a vector including first to lements
Figure imgf000022_0003
o among elements of
Figure imgf000022_0004
is established as
Figure imgf000022_0005
, and the minimum eigenvalue min
of S S is calculated in step S508. In addition, an ( h - 1) dimensional partial space of D is established as E>' in step S510.
Here, when
Figure imgf000022_0009
in step S504, an (M-Ux(M-W) matrix S having the
elements of the §lh row and the mth column that are the same as the elements of a
( S + zo)th row and an ( ™ +*0)th co|umn of R(O js obtained in step S512.
When the matrix S js obtained, a vector including the (zo +* )th and {M-i )th
elements among the elements of is established to be and the minimum
Figure imgf000022_0006
Figure imgf000022_0007
eigenvalue min of S'S js calculated in step S514. In addition, an M~k ~*- dimensional partial space of D is established as D' in step S516.
When Λmin and D' are obtained by the steps S510 and S516, k is set to be 1 , and integers of which a kth bit of the corresponding bit sequence is different from
Figure imgf000023_0005
are selected from the integers 0 and 2δ-1 in step S518. An integer that is closest to
among the integers 0 to 2S-1 is selected and established as
Figure imgf000023_0006
in step S520. y' and y/ are calculated in step S522. In this case, y' and y/ are calculated by using the equation given as
Figure imgf000023_0001
determined in step S504 that i ≤ z'o , and y' and y/ are calculated by using
Figure imgf000023_0007
when it is
determined in step S504 that l > 1O.
When y' and y/ are calculated,
Figure imgf000023_0002
are calculated by using the equation given as
Figure imgf000023_0008
jn step S524.
When c1 and b are calculated, it is established that
Figure imgf000023_0003
value of C(x) may be differently calculated according to i and *° . That is,
Figure imgf000023_0004
In this case, since it is established that
Figure imgf000023_0009
Figure imgf000023_0010
and / = 0. When assuming that x represents a real number lattice point of a predetermined dimension that is the same as D', the minimum value of
Figure imgf000024_0008
Figure imgf000024_0009
is given as Equation 8 when is a center of x and x represents
Figure imgf000024_0003
each point on a circumference having a radius of
Figure imgf000024_0004
[Equation 8]
Figure imgf000024_0005
When x represents points of D', f sequentially uses
Figure imgf000024_0010
and so on, and a value of r is less than
Figure imgf000024_0011
When ^ is expressed
as js calculated in step S528 from
Figure imgf000024_0006
Equation 8 when
Figure imgf000024_0007
When
Figure imgf000024_0001
jn step S530, and LLR(i.k)
is calculated when ^1 is greater than CML(W . in this case, LLR(i.k) may be
differently calculated according to i and ° in step S532. That is, LLR(i,k) is calculated according to Equation 9 when and LLR(i.k) is calculated according
Figure imgf000024_0012
to Equation 10 when l > zo in step S532. [Equation 9]
Figure imgf000024_0002
[Equation 10]
Figure imgf000025_0001
Then, k and δ are compared in step S534. In this case, k is increased to be k=k+1 when k is less than Q and the steps after S518 are repeatedly performed in step S536. i and M are compared in step S538 when k is the same as Q, and i is increased to be i=i+1 when i is less than M and the steps after S504 are repeatedly performed in step S528. When * is the same as M1 the LLR vector calculating process is finished, and steps corresponding to the steps after S422 shown in FIG. 4A and FIG. 4B are repeatedly performed.
In addition, when r<« is less than or equal to
Figure imgf000025_0002
in step S530, I is increased by 1 , the cost function value is calculated, and steps corresponding to S430 to S438 shown in FIG. 4A and FIG. 4B are performed in steps S542 to S550.
Here, when the maximum likelihood point detecting process and the LLR vector
calculating process are performed, the approximate value of
Figure imgf000025_0003
and the number of calculations may be reduced by using a method that is different from FIG. 3 to FIG. 5B with respect to the predetermined i and k.
FIG. 6 is a flowchart representing the maximum likelihood detecting method and the LLR vector calculating method according to the exemplary embodiment of the present invention.
In FIG. 6,
Figure imgf000025_0004
is approximated t
Figure imgf000025_0005
when -Nc points having low cost function values are stored and A denotes a set of the stored points, and in this case, the maximum likelihood point and the LLR vector are calculated.
Firstly, in a like manner of S310, the constant vector
Figure imgf000026_0004
and
the cost function
Figure imgf000026_0005
are established, the minimum
1 eigenvalue Λmin calculated in the minimum eigenvalue extraction process S250 is used, and a f(r) value (i.e., the minimum value of C(x)) jS calculated in step S602.
When the constant vector b, the cost function C(x)t and the minimum value of
C(χ) are calculated, ^c that has a low cost function value is established. In
addition, a constant W js determined according to the established -^ c , and then Rc is calculated. In this case, Rc may be given as Equation 11 in step S604. [Equation 11]
Figure imgf000026_0001
When N0 anc| R0 are calculated, the minimum eigenvalue ^min of R*R is
calculated. For this purpose, it is respectively established in step S606 that
Figure imgf000026_0006
Figure imgf000026_0007
In this case,
Figure imgf000026_0008
sequentially uses 1, S, • ■ •, -JM , and so on, and a
value of
Figure imgf000026_0002
. Here, r is expressed as
Figure imgf000026_0009
, and it is established that O = ro < r\ <"' < rL. |n addition, C^ is calculated from Equation 4 in step S608 when r = rM .
Further, the calculated
Figure imgf000026_0003
are compared in step S610. It is determined that
Figure imgf000027_0003
has a value having a minimum cost function in D, and nc
and N0 are compared in step S612.
When nc = NC jn step S612, LLKk of the signal vector to be detected is
calculated. In this case, LLRi* of the kth bit of the ith signal xi
Figure imgf000027_0004
of the signal vector x to be detected is approximated to a value of
Figure imgf000027_0005
Equation 12.
[Equation 12]
Figure imgf000027_0001
Here, Λ denotes a set of ^^W given as Equation 12 is calculated
Figure imgf000027_0006
by Equation 13.
[Equation 13]
Figure imgf000027_0002
In this case, calculations for all possible i and k are performed according to Equation 13 in step S630.
When nc < NC in step S612, distances between
Figure imgf000027_0007
and
Figure imgf000027_0008
are sequentially increased, and the cost function values for the lattice points corresponding to the respective distances are calculated in step S614. When the calculated cost
function value is less than or equal to Q in step S616, nc is increased by 1 in step
S618, and the corresponding lattice point is stored as
Figure imgf000027_0009
jn step S620. When the lattice point is stored as
Figure imgf000028_0005
the steps after S612 comparing nc
increased by 1 and -^ are repeatedly performed.
When the calculated cost function is greater than Rc in step S616, the distance is increased, and the step S614 calculating the cost function value for the lattice point corresponding to each distance is repeatedly performed.
C In addition, when it is determined in step S610 that *« is less than or equal to
Figure imgf000028_0006
/ is increased by 1 in step S622.
When ™rz) denotes a set of points of D that are away from , the cost
Figure imgf000028_0007
function value C(χ) for each point x of D0i) is calculated in step S624.
When the cost function value is calculated, nc and N0 are compared. In
this case, when , a value g firstly satisfying
When the value g is
Figure imgf000028_0002
calculated, it is established that
Figure imgf000028_0008
When and
Figure imgf000028_0009
nc is increased by 1.
In addition, when
Figure imgf000028_0010
nd
Figure imgf000028_0003
the value g firstly satisfying
Figure imgf000028_0004
is calculated by gradually reducing When the value g is
Figure imgf000028_0011
calculated, it is established that and
Figure imgf000028_0012
Figure imgf000028_0013
in step S626. When the value g for all the points of D<r*) is calculated in step S626, I is
compared to L, and the steps after S608 are performed when 1 < L y anc| the % calculating process according to the step S630 is performed in step S628 when I =L.
The above maximum likelihood detecting method and the LLR vector calculating method may be applied to an iterative receiver.
Since the iterative receiver uses a value obtained by applying a logarithm to a
priori probability ratio to calculate -^^α, LLRι,k jS calculated by using Equation 14 rather than using Equation 13. [Equation 14]
Figure imgf000029_0001
Here, denotes a probability value.
FIG. 7 is a block diagram of an internal configuration of the star-like decoder according to the exemplary embodiment of the present invention.
The SLD according to the exemplary embodiment of the present invention includes a real number matrix converting unit 710, a QR decomposition unit 720, a vector calculating unit 730, an initial detection lattice point detecting unit 740, an eigenvalue extractor 750, and a maximum likelihood point detecting unit 760.
The real number matrix converting unit 710 performing the real matrix conversion process S210 shown in FIG. 2 converts a matrix estimated from a received signal into a real number matrix. The QR decomposition unit 720 performing the QR decomposition process S220 performs the SQRD process so that an SNR or an SINR of a transmission signal may increase as a column number of the upper triangular matrix R obtained after the QR decomposition increases. The vector calculating unit 730 performs the vector calculation process S230 for multiplying the received signal by a transpose matrix of a unitary matrix.
The initial detection lattice point detecting unit 740 performs the initial detection lattice point detection process S240 for calculating the initial detection lattice point
Figure imgf000030_0001
by using the successive interference cancellation method. The eigenvalue extractor 750 performs the minimum eigenvalue extraction
process S250 for calculating a minimum eigenvalue min of R'R .
The maximum likelihood point detecting unit 760 detecting the maximum likelihood point by using
Figure imgf000030_0002
received from the initial detection lattice point detecting
unit 740 and λ min received from the eigenvalue extractor 750 performs the processes shown in FIG. 3 to FIG. 6.
FIG. 8 is a block diagram representing a receiver of a multiple antenna system including the SLD according to the exemplary embodiment of the present invention.
The receiver of the multiple antenna system according to the exemplary embodiment of the present invention may include a plurality of SLDs. A first star-like
decoder 810 detects the lattice point
Figure imgf000030_0003
by using the column vector Y known by a receiving terminal and the matrix B estimated or calculated by the receiving terminal.
When the first star-like decoder 810 detects the lattice point
Figure imgf000030_0004
, second to fourth star-like decoders calculate a plurality of LLRs from the upper triangular matrix R1 the vector Y, and the lattice point X calculated by the first star-like decoder 810.
Here, the second star-like decoder 820 shown in FIG. 8 calculates the maximum likelihood point by converting a first bit value of a detected signal (i.e., 0 to 1 , or 1 to 0) and fixing it, and the third star-like decoder 830 calculates the maximum likelihood point by converting a kth bit value and fixing it. M x Q star-like decoders may be included, and a star-like decoder for calculating the maximum likelihood point by converting an (MXQ)th bit and fixing it is referred to as the "fourth star-like decoder".
The Max-Log MAP calculator 850 calculates the LLR by using the lattice point calculated by the first star-like decoder 810 and the maximum likelihood points calculated by the second star-like decoder 820 to the fourth star-like decoder 840.
The above-described methods and apparatuses are not only realized by the exemplary embodiment of the present invention, but, on the contrary, are intended to be realized by a program for realizing functions corresponding to the configuration of the exemplary embodiment of the present invention or a recording medium for recording the program.
While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
As described above, according to the exemplary embodiment of the present invention, since the star-like decoding method and the star-like decoder are used to detect the received signal vector including a plurality of signals in the MIMO system, performance that is similar to the maximum likelihood detecting method may be achieved.
In addition, since a selection range of the lattice points for calculating the maximum likelihood point is reduced, a decoder having low complexity may be realized, and the number of calculations for detecting the maximum likelihood point may be reduced since the complexity is reduced.

Claims

WHAT IS CLAIMED IS:
1. A method for detecting a signal from a plurality of received signals in a multiple-input multiple-output (MIMO) system, the method comprising: a) performing a sorted QR decomposition for a matrix B that indicates a channel state to calculate a unitary matrix Q and an upper triangular matrix R; b) multiplying the received signal Y by a transpose matrix Q4 of the unitary matrix Q to calculate a vector y; c) calculating an initial detection lattice point and a minimum eigenvalue λ
Figure imgf000033_0003
from the vector y and the upper triangular matrix R; and d) detecting a maximum likelihood point by using the initial detection lattice point and the minimum eigenvalue λ .
2. The method of claim 1 , wherein c) comprises: c1) using a quantization process and a successive interference cancellation (SIC) process to calculate the initial detection lattice point from the vector y; and
Figure imgf000033_0004
c2) calculating the minimum eigenvalue λ of a product R1R of the upper triangular matrix R and a transpose matrix R1 of the upper triangular matrix.
3. The method of claim 1, wherein d) comprises:
d1) calculating a constant vector b
Figure imgf000033_0001
by using the vector y, the upper triangular matrix R1 and the initial detection lattice point , and when respective
Figure imgf000033_0002
elements of lattice points x move within a signal constellation or limited integers induced from the signal constellation, storing values
Figure imgf000034_0001
d2) establishing an initial value of the maximum likelihood point
Figure imgf000034_0004
to be
Figure imgf000034_0003
and a minimum value CML. of a cost function to be CML = 0, and establishing the number I of calculations to be I = 0; d3) calculating a comparison value J VM) corresponding to the number I of
calculations to be
Figure imgf000034_0002
Il Ii from the minimum eigenvalue λ and a distance value rM; d4) comparing the comparison value J VM ) and the minimum value CML of the cost function, transmitting a driving command control signal for performing d7) when the comparison value J VM ) is greater, and transmitting a driving command control signal for performing d5) when the comparison value J VM ) is smaller; d5) increasing the number I of calculations by 1 , calculating a value of the
cost function
Figure imgf000034_0005
of the lattice point x
that is apart from the initial detection lattice point
Figure imgf000034_0006
referring to a minimum value among the calculated values as a local minimum cost function value ^v:), and updating the maximum likelihood point
Figure imgf000034_0007
to be CML = W while updating the lattice point having the local minimum cost function ^v/) as the cost function value to be the maximum likelihood point
Figure imgf000034_0008
when the local minimum cost function value ^v/) is less than the minimum value CML of the cost function; d6) performing the steps after d3) again when the number I of calculations is less than a previously established maximum calculation number L1 and performing the step d7) when the number I of calculations is the same as the previously established maximum calculation number L; and d7) outputting the maximum likelihood point x .
4. The method of claim 3, wherein d) further comprises e) calculating a log-likelihood ratio (LLR) vector corresponding to a transmission signal vector to be detected by applying a Max-Log MAP.
5. The method of claim 4, wherein, in e), an LLR value of a kth bit of an ith signal xι of the detected transmission signal vector is calculated (here, 1 < i< M, where M denotes a size of the transmission signal vector to be detected, and 1 ≤k≤Q, where Q denotes the number of bits forming a bit sequence of respective signal of the transmission signal vector).
6. The method of claim 5, wherein e) comprises: e1) calculating the minimum eigenvalue λ from the upper triangular matrix R; e2) establishing a vector remaining after eliminating the ith element of the maximum likelihood points x to be an i initial detection lattice point
Figure imgf000035_0001
, storing the
values for the lattice points x
Figure imgf000035_0002
including the elements moving within the signal constellation or the limited integers induced from the signal constellation, and calculating the constant vector b; e3) calculating the comparison value fvi+i) corresponding to the number I of calculations by using the minimum eigenvalue λ , the constant vector b, and the distance value ruι; e4) calculating the LLR value LLR(i,k) of the kth bit of a bit sequence corresponding to the ith signal of the transmission signal vector when the comparison value f{rm) is greater than the minimum value CML(i,k) of the cost function (i,k), and increasing the number I of calculations by 1 and establishing the maximum likelihood point (*(*»*)) when the comparison value Ar/+0 is less than or equal to the minimum value CML(i,k) of the cost function (i,k); and e5) performing the steps after e3) again when the number I of calculations is less than the maximum calculation number L, and calculating the LLR value LLR(i,k) of the kth bit of the bit sequence corresponding to the ith signal of the transmission signal vector when the number I of calculations is greater than or equal to the maximum calculation number L.
7. The method of claim 6, wherein e1) comprises: e11) calculating an upper triangular matrix P in which an ith column of the upper triangular matrix R is eliminated; and e12) calculating the minimum eigenvalue λ of a product P'P of the upper triangular matrix P in which the ith column is eliminated and a transpose matrix P1 of the upper triangular matrix P.
8. The method of claim 6 or claim 7, wherein, in e2), the constant vector b
is calculated by using the equation
Figure imgf000036_0001
9. The method of claim 6, wherein, in e3), the comparison value /OM) is calculated by using the equation
Figure imgf000037_0003
10. The method of claim 6, further comprising, after e2): e21) calculating a signal value
Figure imgf000037_0009
that is closest to the ith element of the maximum likelihood points
Figure imgf000037_0008
among elements of the signal constellation having a
value inverted from a value of the k!h bit
Figure imgf000037_0004
of the bit sequence corresponding to the ifh element of the maximum likelihood points x as the value of the kth bit or the integers induced from the signal constellation; e22) subtracting a product of an ith column of the upper triangular matrix R and the signal value
Figure imgf000037_0005
from the vector y, and calculating a deformation vector y*; and e23) establishing an initial point of the (i,k)-maximum likelihood point
Figure imgf000037_0006
to be the ith initial detection lattice point x(0, establishing the minimum value CML(i,k) of the (i,k)-cost function to be CML.(i,k)=0, and establishing the number of calculations to be 1 =0.
11. The method of claim 10, further comprising, between e23) and e3), calculating the vector y, the initial detection lattice point X . and the upper triangular
matrix R, and using the first constant value
Figure imgf000037_0001
vector y , the upper triangular matrix P in which the ifh column is eliminated, and the ith initial
detection lattice point
Figure imgf000037_0007
to calculate a second constant
Figure imgf000037_0002
12. The method of claim 6, wherein, in e4), when the comparison value ■f (rw) is less than of equal to the minimum value CML(i,k) of the (i,k) cost function, the number of calculations is increased by 1 , the cost function values c\x) of the |attjce pojnts χ that are apart from the jth
Figure imgf000038_0003
initial detection lattice point
Figure imgf000038_0004
are calculated, a minimum value among the calculated values is referred to as a (i,k)-local minimum cost function value
Figure imgf000038_0001
), and the (i,k)-maximum likelihood point
Figure imgf000038_0005
is updated to be C^(J, Jc) = C1 ^r1) while updating the lattice point having the (i.k)-local minimum cost function
Figure imgf000038_0002
) as the cost function value to be the (i,k)-maximum likelihood point (*(*» *)) when the (i,k)-local minimum cost function value Cιj^rι) is less than the minimum value CML(i,k) of the (i,k)-cost function.
13. The method of claim 6 or claim 11 , wherein, in e4) or e5), the first constant value c, the second constant value c', the minimum value CML of the cost
function, the minimum value CMi_(i,k) of the (i,k)-cost function, the bit value
Figure imgf000038_0006
and a square root σ of a noise variance are used to calculate the LLR value LLR(i,k) of the kth bit of the bit sequence corresponding to the ith signal of the transmission signal vector.
14. The method of claim 13, wherein, in e4) or e5), the LLR value LLR(i,k) of the kth bit of the bit sequence corresponding to the ith signal of the transmission signal vector is calculated by using the equation
Figure imgf000039_0001
15. The method of claim 6, wherein e1) comprises:
e11) a partial matrix S of a first column to an °th column of a first row to an
° th row of the upper triangular matrix P in which the ith column of the upper triangular
matrix R is eliminated is calculated when the value i is less than an integer ° selected
from the integers 1 to M, and the partial matrix S of an ( o +i)th column to an (M-1)th
column of an ( 1Q +1 )th row to an Mth row of the upper triangular matrix P when the value i
is greater than ° ; and c e12) calculating the minimum eigenvalue λ of S '
16. The method of claim 6 or claim 15, wherein, in e2), the constant vector b
is calculated by using the equation
Figure imgf000039_0002
17. The method of claim 6, wherein, in e2), a vector including a first element
to an ( o+1)th element among elements of the lattice points
Figure imgf000039_0003
in which an ith element
of the maximum likelihood point x is eliminated is established as the ith initial
detection lattice point
Figure imgf000039_0004
when the value i is less than or equal to ° , and a vector
includi n ( o+1)th element to an (M-1)th element among the elements of the lattice
points
Figure imgf000039_0005
is established as the ith initial detection lattice point when the value i is
Figure imgf000039_0006
greater than o .
18. The method of claim 6, further comprising, after e2): e21) calculating a signal value (*.<#>) that is closest to the ith element of the maximum likelihood point
Figure imgf000040_0001
among elements of the signal constellation having a
value inverted from a value of the kth bit
Figure imgf000040_0002
of the bit sequence corresponding to the ith element of the maximum likelihood points
Figure imgf000040_0003
as the value of the kth bit or the integers induced from the signal constellation;
e22) when the value i is less than or equal to ° , calculating a deformation
vector y1 by subtracting a product of the signal value
Figure imgf000040_0004
and a vector including an ith
column of first to °th rows of the upper triangular matrix R from a vector CK1 O) including first to ith elements of the vector y, and subtracting a product of a partial matrix
of ( °+1 )th to Mth columns of first to °th rows of the upper triangular matrix R;
e23) when the value i is greater than zo , calculating the deformation vector /
by subtracting a product of the signal value and a vector including an ith column
Figure imgf000040_0005
of ( zo +i)th to Mth rows of the upper triangular matrix R from a vector (>('. + 1 :^))
including ( o+i)th to Mth columns of the vector y; and e24) establishing an initial point of the (i,k)-maximum likelihood point to
Figure imgf000040_0008
be by usjng the ith initial detection lattice point established in e2),
Figure imgf000040_0006
Figure imgf000040_0007
establishing the minimum value Cy^i.k) of the (i,k)-cost function to be C|viL(i,k)=0, and establishing the number I of calculations to be I =0.
19. The method of claim 18, further comprising, between e2) and e3), using the vector y, the initial detection lattice point and the upper triangular
Figure imgf000041_0003
matrix R, using the constant value
Figure imgf000041_0004
the deformation vector y', the partial matrix S 1 and the ith initial detection lattice point and calculating the constant
Figure imgf000041_0006
va,ue
Figure imgf000041_0005
20. The method of claim 13 or claim 19, wherein, in e4) or e5), the LLR value LLR(i,k) of the kth bit of the bit sequence corresponding to the ith signal of the transmission vector is calculated by using the equation
Figure imgf000041_0001
Rjm denotes an element of an mth column of a jth row of the matrix R, and Vj denotes a j ;t1h
element of the vector y) when the value i is less than or equal to o _ and is calculated by using the equation
when
Figure imgf000041_0002
the value i is greater than ° .
21. The method of claim 1 , wherein d) comprises: d1) operating a constant vector b by using the initial detection lattice point X,
the upper triangular matrix R, and the vector y through the equation
Figure imgf000041_0007
d2) storing values when respective
Figure imgf000041_0008
elements of the lattice point x move within a signal constellation or limited integers induced from the signal constellation;
d3) establishing a maximum value ™c of the number of valid lattice points to be detected to calculate the LLR value, selecting another constant value W according to
the established Nc > ancj calculating a reference value Rc of a cost function value by
u. v using the equation
Figure imgf000042_0005
d4) establishing a first valid lattice point
Figure imgf000042_0006
establishing a first
minimum cost function value
Figure imgf000042_0001
establishing the number of
calculations to be
Figure imgf000042_0002
d5) calculating a minimum eigenvalue
Figure imgf000042_0007
d6) using the minimum eigenvalue
Figure imgf000042_0009
, the constant vector b calculated in d1),
and the distance value
Figure imgf000042_0008
, and calculating a comparison value / fa+i) corresponding to
Figure imgf000042_0010
the number I of calculations by using the equation
Figure imgf000042_0003
d7) comparing the comparison value
Figure imgf000042_0011
, the first minimum cost function value
the size nc of the valid lattice point, the maximum value Nc of the number of
valid lattice points, the number ^ of calculations, and the maximum calculation
number L, and establishing an Mcth valid lattice point
Figure imgf000042_0012
, an nc th minimum cost
function value
Figure imgf000042_0004
cost function values c(x) for the lattice points, a value g firstly
satisfying and a value h firstly satisfying , and
Figure imgf000042_0013
Figure imgf000042_0014
d8) calculating the LLR value corresponding to a kth bit of an ith signal of the
transmission signal vector (here, 1 <i< M, where M denotes the number of
transmission signals to be detected, and 1 ≤k≤ s, where e denotes the number of bits forming a bit sequence of the transmission signal xt ).
22. The method of claim 21 , wherein d7) comprises: d71) when the comparison valu s greater than the first minimum cost
Figure imgf000043_0005
function value omparing the size nc of the valid lattice point and the maximum
Figure imgf000043_0001
value Nc of the number of valid lattice points, performing d73) when
Figure imgf000043_0006
sequentially increasing a distance from by sequentially until
Figure imgf000043_0007
Figure imgf000043_0008
Figure imgf000043_0002
when n e< Nc , calculating each cost function value of
Figure imgf000043_0009
the lattice points x corresponding to the respective distances, increasing nc by 1 when the cost function value c(x) is less than or equal to the reference value Rc of the cost function value, storing the corresponding lattice point as the nath valid lattice point establishing the nciU minimum cost value and
Figure imgf000043_0010
Figure imgf000043_0003
performing d8; d72) when the comparison value
Figure imgf000043_0011
is less than or equal to the first minimum cost value
Figure imgf000043_0012
increasing the number I of calculations by 1 , calculating the cost function values c(x) for the respective lattice points x that are apart from the initial detection lattice poin y reducing the value g from ^-1 by 1 to obtain the value g
Figure imgf000043_0013
Figure imgf000043_0014
firstly satisfying when
Figure imgf000043_0015
Figure imgf000043_0004
and
Figure imgf000043_0016
respectively to be
Figure imgf000043_0017
and oring ancj increasing no by 1 when we< cing
Figure imgf000043_0019
the value g from nc-1 by 1 to obtain the value g hen
Figure imgf000043_0018
and establishing and n° respectively
Figure imgf000043_0020
Figure imgf000043_0021
b
Figure imgf000044_0004
d73) comparing the number I of calculations and the maximum calculation number L, and performing d8) when I =L and performing the steps after d6) when
Figure imgf000044_0005
23. The method of claim 21 , wherein, in d8), a set Λ of the valid lattice points of the transmission signal
Figure imgf000044_0006
vector x , and the square root σ of the noise variance are used, and the LLR value
LLRi,k corresponding to the kth bit of the ith signal of the transmission signal vector to be detected is calculated by using the equation
Figure imgf000044_0001
24. The method of claim 21 , wherein, in d8), a logarithmic value
Figure imgf000044_0002
of a previous probability ratio of the kth bit of the ith signal of the transmission signal vector is calculated, and the LLR value LLR ^A corresponding to the kth bit of the ith signal of the transmission signal vector is calculated by using the calculated &(}>&) according to the equation
Figure imgf000044_0003
25. A device for detecting a transmission signal from a plurality of received signals in a multiple-input multiple-output (MIMO) system, the device comprising: a QR decomposition unit for performing a sorted QR decomposition for a matrix B indicating a channel so as to increase a signal to noise ratio (SNR) or a signal to interference plus noise ratio (SINR) of the transmission signal as the number of columns of an upper triangular matrix R; a vector calculating unit for calculating a vector y by multiplying the received signal by a transpose matrix Q* of a unitary matrix Q; an initial detection lattice point detecting unit for calculating an initial detection
lattice point X from the vector y and the upper triangular matrix R;
2 an eigenvalue extractor for calculating a minimum eigenvalue « from the upper triangular matrix R; and a maximum likelihood point detecting unit for detecting a maximum likelihood
point by using the initial detection lattice point
Figure imgf000045_0001
and the minimum eigenvalue mm.
26. The device of claim 25, further comprising a real number matrix converting unit for converting the matrix B indicating the channel into a real number matrix, wherein the QR decomposition unit performs the sorted QR decomposition for the real number matrix transmitted from the real number matrix converter.
27. A receiving device in a multiple-input multiple-output (MIMO) system, the receiving device comprising: a first transmission signal detecting device for detecting a maximum likelihood point from a matrix B indicating the channel and a received signal; a second transmission signal detecting device for calculating an (i,k)-maximum likelihood point for a kth bit of an ith signal of a transmission signal vector by using an upper triangular matrix Rr a vector y, and the maximum likelihood point calculated by the first transmission signal detecting device (here, i is one of the natural numbers from 1 to a size of the transmission signal vector, and k is one of the natural numbers from 1 to Q(i), where Q(i) denotes a size of a bit sequence forming the ith signal); and a Max-Log MAP calculator for calculating a log-likelihood ratio (LLR) vector by using the maximum likelihood point detected by the first transmission signal detecting device and (i,k)-maximum likelihood points corresponding to the size (MQ) of the bit sequence forming the transmission signal vector calculated by the second transmission signal detecting device.
28. The receiving device of claim 27, wherein the second transmission signal detecting device comprises (i,k) transmission signal detecting devices, and the number of (i,k) transmission signal detecting devices is a size MQ of the bit sequence forming the transmission signal vector.
29. The receiving device of claim 28, wherein the (i,k) transmission signal detecting device converts a kth bit of an ith signal of the maximum likelihood point detected by the first transmission signal detecting device to a value 1 when it has a value 0, and converts it to the value 1 when it has the value 0, so as to calculate the (i,k)-maximum likelihood point.
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