KR101729064B1 - Method for detecting symbol based on maximum likelihood and receiver performing the same - Google Patents

Abstract

A maximum likelihood detection method may include the following steps of: (a) determining an initial determination variable on the basis of a channel coefficient estimated by using M symbols selected from a signal received by a receiver; (b) dividing the M symbols into four (n)-level subsets; (c) selecting any one subset of the four (n)-level subsets and determining a position of a central point symbol of the selected (n)-level subsets by using a determination variable of (n-1)-level subsets; (d) shifting the symbol of the selected (n)-level subsets as much as the central point symbol of the (n)-level subsets; (e) determining a determination variable of the (n)-level subsets on the basis of the position of the central point symbol of the (n)-level subsets and the determination variable of the (n-1)-level subsets; (h) determining positions of the (n)-level subsets and the central point symbol of the (n)-level subsets while increasing the number (n) of the level by one and repeating the steps from (b) to (e) until the determination variable of the (n)-level subsets is determined; and (i) determining a symbol at a position obtained by addition from the position of the central symbol of 1-level subsets to the position of the central symbol of the (n)-level subsets as a solution of the ML detection.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a symbol detection method using a maximum likelihood method,

The present invention relates to a method for detecting a symbol or a signal using a maximum likelihood (ML) method and a receiver for performing the method.

로 나타낼 수 있다. 여기서,

는 스퀘어 직교 진폭 변조 성상도(square QAM constellation)에서 선택된 송신 심볼을 의미하고,

는 가우시안 분포를 가지는 채널 계수를 의미하고,

는 가우시안 분포를 가지는 잡음 변수를 의미한다.

,

,

등은 행렬의 형태로 표현될 수 있다.The ML method is a symbol detection method widely used in fields such as wireless communication systems, networks, signal processing such as image and audio, and the like. Discrete signals received at a receiver of a data transmission system, including a communication system,

. here,

Denotes a transmission symbol selected from a square quadrature amplitude modulation constellation,

Denotes a channel coefficient having a Gaussian distribution,

Is a noise parameter with a Gaussian distribution.

,

,

Etc. can be expressed in the form of a matrix.

In the conventional ML detection method, metric values indicating errors are obtained for all square QAM constellation symbols, and a square QAM constellation symbol with a minimum metric is selected as the ML detection period. This method can be expressed as Equation (1) below.

는 M-ary square QAM constellation을 의미하며,

는 수신기에서 추정한 채널 계수를 의미하고,

는

와

의 유클리디안(Euclidean) 거리를 나타내는 metric을 의미한다.In Equation (1)

Denotes an M-ary square QAM constellation,

Denotes the channel coefficient estimated by the receiver,

The

Wow

Of the Euclidean distance.

Meanwhile, regarding the M-ary square QAM constellation, M metric calculation is required to implement the conventional ML detection method. In general, to implement a single metric, six Real Multiplications (= RM) and five Real Additions are required. Therefore, in order to implement the conventional ML detection with respect to the M-ary square QAM constellation, a total of 6M RMs and 5M RAs were required. As can be seen from the complexity result according to the above calculation, the complexity of the conventional ML detection increases in direct proportion to the size of the square QAM constellation and the number of symbols. In particular, the complexity of this complexity is particularly noticeable in Orthogonal Frequency Division Multiplexing (OFDM) systems. If the number of subcarriers in the OFDM system is N, the complexity of conventional ML detection is 6MN RMs and 5MN RAs, which increases the complexity considerably.

The background technology of the present application is disclosed in Korean Patent Registration No. 10-0965728.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems of the prior art, and it is an object of the present invention to provide an ML detection method and a receiver using the ML detection method.

It is to be understood, however, that the technical scope of the present invention is not limited to the above-described technical problems, and other technical problems may exist.

이고, 상기 n은

을 만족할 수 있다.According to an aspect of the present invention, there is provided an ML detection method including: (a) determining an initial decision variable based on a channel coefficient estimated using M symbols selected from a signal received at a receiver, Level subset; (b) dividing the M symbols into four (n) -level subsets; (c) selecting a subset of any of the four (n) level subsets of the selected (n) -level subset using the decision variable of the (n-1) -level subset; (d) level subsets of the (n-1) -level subset by a midpoint symbol of the (n-1) -level subset; (e) Determining a decision variable of the (n) -level subset based on level subset, and (h) determining the position of the (N) -level subset and the midpoint symbol of the (N) -level subset by increasing the number of levels (n) by 1 (N) (I) repeating steps (b) through (e) until a (n) -level subset of the center point symbols of the Determining as a solution of the ML detection a symbol of the sum of N and N,

, And n is

Can be satisfied.

As a technical means for accomplishing the above technical object, a receiver for performing ML detection according to an embodiment of the present invention includes a signal receiving unit for receiving a signal, a channel estimating unit for selecting M symbols from the received signal, And a ML detector for performing ML detection on the M symbols, wherein the ML detector is configured to detect an M < th > symbol according to an embodiment of the present invention (B) to (i) of the ML detection method according to the present invention.

The above-described task solution is merely exemplary and should not be construed as limiting the present invention. In addition to the exemplary embodiments described above, there may be additional embodiments described in the drawings and the detailed description of the invention.

According to any one of the above objects of the present invention, the ML detection solution can be quickly detected while exhibiting the same detection performance as that of the conventional method while reducing the computational complexity of the ML detection method.

1 is a block diagram of an ML detection receiver according to an embodiment of the present invention.
2 is a diagram illustrating a complex plane for explaining an example of an ML detection method according to an embodiment of the present invention.
3 is a flowchart of an ML detection method according to an embodiment of the present invention.
FIG. 4 is a simulation graph comparing bit error rates of the ML detection method and the conventional ML detection method according to an embodiment of the present invention.
FIG. 5 is a graph comparing the computation time required for the ML detection method and the conventional ML detection method according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention. It should be understood, however, that the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In the drawings, the same reference numbers are used throughout the specification to refer to the same or like parts.

Throughout this specification, when a part is referred to as being "connected" to another part, it is not limited to a case where it is "directly connected" but also includes the case where it is "electrically connected" do.

Throughout this specification, when a member is " on " another member, it includes not only when the member is in contact with the other member, but also when there is another member between the two members.

Throughout this specification, when an element is referred to as "including " an element, it is understood that the element may include other elements as well, without departing from the other elements unless specifically stated otherwise. The terms "about "," substantially ", etc. used to the extent that they are used throughout the specification are intended to be taken to mean the approximation of the manufacturing and material tolerances inherent in the stated sense, Accurate or absolute numbers are used to help prevent unauthorized exploitation by unauthorized intruders of the referenced disclosure. The word " step (or step) "or" step "used to the extent that it is used throughout the specification does not mean" step for.

The receiver for performing the ML detection method and the ML detection method of the present invention can be applied to an OFDM system based on a wireless mobile communication terminal device, a base station device, a wireless mobile communication device (for example, a router), and an SLM (Selected Mapping) A multiple-input multiple-output wireless communication system that increases the number of symbols by increasing the number of symbols, and a system that uses a method of lowering a peak-to-average-power ratio .

In the ML detection method of the present application, it is assumed that the addition sign as shown in the following Equation 2 is used.

1 is a block diagram of an ML detection receiver according to an embodiment of the present invention. 1, a receiver 100 according to an embodiment of the present invention includes a signal receiving unit 110, a channel estimating unit 120, a decision variable generating unit 130, and an ML detecting unit 140 . The ML detection unit 140 may include a phase detection unit 142, a center point determination unit 144, and an ML determination unit 146. Although not shown in FIG. 1, the receiver 100 may demodulate a received or detected signal using a demodulation scheme corresponding to a modulation scheme applied to the transmitter, or a demodulation scheme based on a decoding scheme corresponding to a coding scheme applied to the transmitter, And a decoding unit for decoding the data bits.

The signal receiving unit 110 may receive the symbols or signals transmitted from the transmitter. For example, the signal receiving unit 110 may include one or more antennas.

는 채널 추정부(120)가 추정한 채널 계수를 의미한다.The channel estimator 120 may estimate a channel coefficient using the symbols received from the signal receiver 110. [ The channel estimator 120 may estimate M channel coefficients from the received signals. The method of estimating the channel coefficient by the channel estimating unit 120 is similar to that of the conventional art, and thus a detailed description thereof will be omitted. M denotes the number of possible representations of the constellation of the signal modulation. Below

Denotes a channel coefficient estimated by the channel estimation unit 120. [

The decision variable generating unit 130 may determine an initial decision variable based on the signal received by the signal receiving unit 110 and the channel coefficient estimated by the channel estimating unit 120. [ The decision variable generator 130 also generates a decision variable for the initial decision variable (or the decision variable of the previous level (n-1) -level subsets) and the midpoint symbol of the (n) -level subset of M symbols on the QAM constellation Level subset based on the location of the (n) -level subset. In this specification, M is equal to or greater than 4, the M symbols are square M-ary Quadrature Amplitude Modulation (QAM) symbols, and the average symbol power of the M symbols is 1 have.

ML detection unit 140 may divide M symbols into four (n) -level subsets. In addition, the ML detector 140 may select any one of the four (n) -level subsets. According to an embodiment of the present invention, the ML detection unit 140 detects a symbol having the smallest distance from the decision variable of the (n-1) -level subset among the M symbols among the four (n) You can select the subset to which it belongs. (For example, when a 1-level subset is selected, a subset to which the symbol with the smallest distance from the initial decision variable (0-level) belongs is selected as a 1-level subset) The set may have a representative symbol (four corner points on the complex plane), and a subset represented by the representative symbol having the smallest distance from the decision variable of the (n-1) -level subset may be selected.

In addition, the ML detector 140 may determine the position of the midpoint symbol of the selected (n) -level subset using the (n-1) -level subset of the decision variable. According to one embodiment of the present invention, the ML detection unit 140 detects the position of a symbol closest to the origin among the symbols of the selected (n) -level subset and the position of the symbol closest to the origin, (N) is obtained by averaging the positions of symbols having the smallest distance from the variable (e.g., a symbol having the smallest distance from the initial decision variable (0-level) when a 1-level subset is selected) - can be determined as the midpoint symbol of the level subset.

The ML detection unit 140 detects the symbols of the selected (n) -level subsets from the center point symbols of the (n) -level subset so that the midpoint symbols of the (n) It is possible to shift by a position value.

When the symbols of the (n) -level subset selected by the ML detector 140 are shifted by the center point symbol of the (n) -level subset, the ML detector 140 determines Level subset based on the determined variable of the (n-1) -level subset and the location of the midpoint symbol of the (n) -level subset.

In the determination of the position of the midpoint symbol of the (n) -level subset and the determination variable of the (n) -level subset, the ML detector 140 determines the phase of the decision variable of the (n-1) It is necessary to find out. ML detection unit 140 may determine the phase of a decision variable of the (n-1) -level subset based on the real and imaginary values of the decision variable of the (n-1) -level subset (142).

이고, 상기 n은

를 만족한다.ML detection unit 140 determines the position of the (N) -level subset and the midpoint symbol of the (N) -level subset by increasing the number of levels n by 1, (The center point decision unit 144) until the determination variable of the subset is determined. Here, N is

, And n is

.

In this manner, the ML detector 140 divides the M symbols of each level into four next level subsets, selects one of the next level subsets, and determines the position of the midpoint symbol of the selected next level subset Shifted by the position of the midpoint symbol, and determines the decision variable of the next level subset.

Finally, the ML detection unit 140 detects a symbol of a position from the position of the midpoint symbol of the 1-level (first level) subset to the position of the midpoint symbol of the (N) -level (last level) (ML detection section 146).

Hereinafter, the ML detection method according to the present invention will be described for 4 QAM and 16 QAM, respectively, and then the ML detection method according to the present invention will be generalized as general square M-ary QAM.

[Basic conditions of the present invention]

는 실제의 가우시안 분포를 가지는 채널 계수

와 거의 같은 것으로 가정한다. 이 경우, 결정 변수 생성부(130)가 생성한 초기 결정 변수

는

와 같이 근사화 할 수 있다. 본 명세서에 있어서,

는 complex conjugate를 의미하고,

는 amplitude를 의미한다.In the present invention, the channel estimator 120 estimates channel coefficients

Is a channel coefficient having an actual Gaussian distribution

. In this case, the initial decision variable generated by the decision variable generating unit 130

The

As shown in FIG. In the present specification,

Is a complex conjugate,

Is the amplitude.

와

가 독립이기 때문에

는 평균이 0인 가우시안 잡음으로 생각할 수 있다. 만약 하나의 집합

을 정의한다면, 평균 심볼 파워가 1인 인 4 QAM constellation 내의 4개의 점들을

와 같이 나타낼 수 있다.

Wow

Is independent

Can be thought of as Gaussian noise with an average of zero. If one set

, Four points in a 4 QAM constellation with an average symbol power of 1

As shown in Fig.

로 나타낼 수 있는데, 이 때,

는

로 주어지는 파워 normalization factor이다.In general, a set of four corner points of a square M-ary QAM constellation with a mean symbol power of 1

. At this time,

The

Is the power normalization factor given by.

으로 표시할 수 있는데, 이 때, N은

로 주어지는 양의 정수이다.Also, the size of the square M-ary QAM constellation

, Where N is the number of

Is a positive integer.

[For 4 QAM constellation]

는

의 위상을 참조하여 하기의 수학식 3과 같이 추정할 수 있다.Since the four corner points of the 4 QAM constellation are symmetrically placed about the real axis and the imaginary axis on the complex plane,

The

Can be estimated as shown in Equation (3) below.

는 z의 페이즈 각(phase angle)을 의미한다.here,

Is the phase angle of z.

The method of Equation (3) can be said to be optimal since the symbol estimation method obtained by the method of Equation (3) calculates the same result as the existing ML estimation method of Equation (1).

에 대한 함수를 하기의 수학식 4와 같이 정의한다.According to one embodiment of the present invention, according to the ML detection method,

Is defined as Equation (4) below. &Quot; (4) "

와

는 각각

의 실수부 값 및 허수부 값을 의미한다.here,

Wow

Respectively

The real part value and the imaginary part value.

를 하기의 수학식 5와 같이 표시할 수 있다.According to Equation (4), Equation

Can be expressed by the following equation (5).

[For 16 QAM constellation]

16 QAM constellation will be described with reference to FIG. 2 is a diagram illustrating a complex plane for explaining an example of an ML detection method according to an embodiment of the present invention. In FIG. 2, (a) represents a 0-level subset, (b) represents a selected and shifted 1-level subset, and (c) represents a selected and shifted 2-level subset. A rectangle represented by a dotted line represents a subset of the next level, a solid diamond represents corner points of a subset of the current level, a solid line circle represents points on the constellation, And the black rectangle represents the determination variable of the subset of the current level.

라고 표시하고, 이것을 0-레벨 부분 집합이라고 한다. 또한 결정변수

를

라고 표시하고, 이것을 0-레벨 결정 변수(초기 결정 변수)라고 한다. 초기 결정 변수

는 복수의 심볼 중 상기 초기 결정 변수와의 거리가 가장 작은 ML 검출의 해를 결정하기 위한 기준이 되는 위치일 수 있다. 16 QAM constellation 의 경우, 앞서 본 발명의 기본 조건에서 설명한

와

에 따르면,

와

은 각각

과 2로 주어진다.In this specification, a 16 QAM constellation with an average symbol power of 1

And this is called a 0-level subset. Also,

To

And this is called a 0-level decision variable (initial decision variable). Initial decision variable

May be a position that is a reference for determining a solution of ML detection having a smallest distance from the initial decision variable among a plurality of symbols. In the case of 16 QAM constellation,

Wow

According to,

Wow

Respectively

And 2, respectively.

의 4개의 코너 점들을 잇는 square의 한 변의 길이는

이다.

의 4개 코너 점들로 이루어진 집합을

와 같이

를 사용해 나타낼 수 있다.

The length of one side of the square connecting the four corner points of

to be.

A set of four corner points of

together with

.

를 아래와 같이 4개의 부분 집합들로 나눌 수 있다. 수신기(100)는

를 4개의 1-레벨(첫 번째 레벨) 부분 집합으로 나눌 수 있다. 여기서, 1-레벨의 부분 집합 이란, 최초의 0-레벨 부분 집합을 처음으로 나눈 4개의 부분 집합을 의미한다. 아래의 16개의 점들은 도 2의 (a)에서 실선의 원으로 표시된 16개의 위치에 대응할 수 있다. 또한,

는 각각 도 2의 (a)에서 1, 2, 3, 4분면에 위치하는 심볼을 나타낸다.As a first step, a receiver 100 that performs an ML detection method according to an embodiment of the present invention includes M (for example, 16) symbols using a real axis and an imaginary axis of a complex plane

Can be divided into four subsets as shown below. Receiver 100

Can be divided into four 1-level (first level) subsets. Here, a 1-level subset means 4 subsets of the first 0-level subset. The following sixteen points may correspond to the sixteen positions indicated by solid circles in FIG. 2 (a). Also,

Represent symbols located on the first, second, third, and fourth surfaces in FIG. 2 (a), respectively.

의 4개 코너 점들, 즉,

의 원소(점, 심볼)들이 각각

를 대표하는 점들이 된다. 수신기(100)는 결정 변수

와의 거리가 제일 작은

의 원소가 대표하는 부분 집합을 선택할 수 있다. (예를 들어, 도 2의 (a)에서 3사분면의 1-레벨 부분 집합)

의 4개 원소들 각각은 그 크기(=absolute value)가

이다. 또한 결정변수

와의 거리가 가장 가까운

의 원소의 위상은

이다. 여기서,

는 상기 수학식 4에 의해 결정될 수 있다. 따라서, 결정변수

와의 거리가 제일 작은

의 원소는

로 나타낼 수 있다.In addition, the receiver 100 may select a subset of any one of the four 1-level subsets. For subset selection

Four corner points, i.e.,

(Points, symbols) of

Are the representative points. The receiver 100 determines

The smallest distance from

Can be selected. (E. G., A one-level subset of the third quadrant in Figure 2 (a)),

Each of the four elements has an absolute value of

to be. Also,

Nearest to

The phase of the element of

to be. here,

Can be determined by Equation (4). Therefore,

The smallest distance from

The element of

.

일 수 있다. 둘째 점은 선택된 1-레벨 부분 집합의 대표 점이며, 이는 위에서 설명된 것처럼

일 수 있다. 따라서, 선택된 1-레벨 부분 집합의 중앙 위치는

일 수 있다. 또한, 선택된 1-레벨 부분 집합의 4개의 코너 점들을 잇는 square의 한 변의 길이는

일 수 있다.According to one embodiment of the present invention, the receiver 100 may determine the position of the midpoint of the selected one-level subset. The center position of the selected one-level subset can be obtained by averaging the following two points. The first point is the point closest to the origin of the selected 1-level subset of points,

Lt; / RTI > The second point is the representative point of the selected one-level subset,

Lt; / RTI > Thus, the center position of the selected one-level subset is

Lt; / RTI > In addition, the length of one side of a square connecting the four corner points of the selected one-level subset is

Lt; / RTI >

와 같이 집합

를 사용해 나타낼 수 있으며,

일 수 있다.A set of four corner points of a selected one-level subset

Such as

, ≪ / RTI >

Lt; / RTI >

의 위치만큼 쉬프트하여, 선택되고 쉬프트된 1-레벨 부분 집합의 중심이 복소 평면의 원점에 놓이도록 한다. (도 2의 (b)) 선택되고 쉬프트 된 1-레벨 부분 집합의 4개 코너 점들은

의 4개 원소들과 같게 된다. 본 명세서에서, 선택되고 쉬프트 된 1-레벨 부분 집합을

이라고 표시한다.As a second step, the receiver 100 converts the selected one-level subset into a central point symbol of the selected one-level subset

So that the center of the selected, shifted 1-level subset is at the origin of the complex plane. (Fig. 2 (b)) The four corner points of the selected and shifted 1-level subset

Of the four elements. In this specification, a selected and shifted 1-level subset

.

역시

만큼 쉬프트 되며, 이를 통해

이라는 새로운 결정변수를 얻는다 (즉,

). 만약

과의 거리(=Euclidean distance)가 가장 작은

의 원소를

이라고 한다면,

와의 거리가 가장 작은

의 원소는

일 수 있다. 이와 같이, 본원의 일 실시예에 따른 수신기(100)는 상기 초기 결정 변수(이전 레벨 결정 변수)와 상기 1-레벨(현재 레벨) 부분 집합의 중앙점 심볼의 위치에 기초하여 상기 1-레벨(현재 레벨) 부분 집합의 결정 변수를 결정한다.Decision variable

Also

To be shifted

(That is,

). if

(= Euclidean distance) is the smallest

Element of

If so,

The smallest distance from

The element of

Lt; / RTI > As described above, the receiver 100 according to an embodiment of the present invention calculates the 1-level (current level) subset based on the initial determination variable (previous level determination variable) and the position of the midpoint symbol of the 1-level Current level) subset.

과

에 다시 적용한다면, 2-레벨 부분 집합

와 2-레벨 부분 집합의 결정 변수

를 얻을 수 있다. 여기서, 2-레벨이란, 1-레벨 부분 집합을 한번 더 복소 평면 상에서 4개로 나누었음을 의미한다. 본 명세서에서, 선택되고 쉬프트 된 2-레벨 부분 집합을

이라고 표시한다.The first and second steps described above

and

Lt; RTI ID = 0.0 > 2-level < / RTI &

And the decision variable of the 2-level subset

Can be obtained. Here, the 2-level means that the 1-level subset is further divided into 4 on the complex plane. In the present specification, a selected and shifted 2-level subset

.

을 앞에서

로 유도한 것과 유사하게,

를 얻기 위해 필요한 쉬프트의 크기

를

로 구할 수 있다.

는 선택된 2-레벨 부분 집합의 중앙점의 위치이다. 2-레벨 부분 집합의 결정 변수

는

일 수 있다. 앞에서

의 4개 코너 점들로 이루어진 집합을

로 나타낸 것과 마찬가지로,

의 4개 코너 점들로 이루어지는 집합을

로 나타낼 수 있다. 16 QAM constellation의 경우 N=2 이며, 이 경우,

이 되며,

라고 할 수 있다.

와의 거리가 가장 작은

의 원소는

이므로,

과의 거리가 가장 작은

의 원소는

이고, 마찬가지로

와의 거리가 가장 작은

의 원소는

일 수 있다. 여기서

는 상기 수학식 1에서와 같은 기존의 ML 추정 방법과 같은 결과를 나타낸다.

In front of

, ≪ / RTI >

The size of the shift needed to obtain

To

.

Is the position of the midpoint of the selected two-level subset. The decision variable of a two-level subset

The

Lt; / RTI > in front

A set of four corner points of

, ≪ / RTI >

A set of four corner points of

. In the case of 16 QAM constellation, N = 2,

Lt; / RTI &

.

The smallest distance from

The element of

Because of,

The smallest distance from

The element of

And similarly

The smallest distance from

The element of

Lt; / RTI > here

Represents the same result as the conventional ML estimation method as in Equation (1).

[For a typical square M-ary QAM constellation]

, N-레벨 부분 집합의 중앙점 심볼의 위치, N-레벨 부분 집합의 결정 변수

이 결정될 때까지 반복 수행할 수 있다.In the case of a general square M-ary QAM, the receiver 100 increases the number of levels of the first and second steps described above by one,

, The position of the midpoint symbol of the N-level subset, the decision variable of the N- level subset

Can be repeated until it is determined.

이 오직 한 요소, 즉 0만을 포함하는 집합이기 때문에,

과의 거리가 가장 작은

의 요소는

이다. 또한, 각 레벨의 결정 변수들이

라는 식을 통해 관계되므로, 각 레벨의 결정 변수는 하기의 수학식 6으로 정의될 수 있다. 즉, 현재 (n)-레벨의 결정 변수는 이전 (n-1)-레벨의 결정 변수의 위치에서 현재 (n)-레벨의 부분 집합의 중앙점 심볼의 위치를 뺀 위치로 결정되고, 이러한 관계에 따르면, 수학식 6과 같이, 현재 (n)-레벨의 결정 변수의 위치는 초기 결정 변수의 위치에서 현재 (n)-레벨까지의 각 레벨의 부분 집합의 중앙점 심볼의 위치의 합을 뺀 위치로 결정될 수 있다.The subset of the last level

Is a set containing only one element, i.e., 0,

The smallest distance from

The element of

to be. Also, the decision variables of each level

, The decision variable of each level can be defined by the following equation (6). &Quot; (6) " That is, the decision variable of the current (n) -level is determined to be a position obtained by subtracting the position of the central point symbol of the subset of the current (n) -level at the position of the decision variable of the previous (n-1) , The position of the decision variable of the current (n) -level is calculated by subtracting the sum of the positions of the central point symbols of the subset of each level from the position of the initial decision variable to the current (n) -level, Position.

이기 때문에,

와의 거리가 가장 작은

의 원소는 하기의 수학식 7과 같이 정의될 수 있다.Also,

Therefore,

The smallest distance from

Can be defined as Equation (7) below. &Quot; (7) "

은 하기의 수학식 8에 의해 결정될 수 있다.here,

Can be determined by the following equation (8).

와

에 따르면, 4 QAM constellation의 경우

와

은 각각

와 1로 주어진다. 이 경우, 상기 수학식 7 및 수학식 8로부터

를 얻을 수 있으며, 이 결과는 앞서 수학식 5를 통해 얻은 결과와 일치한다.According to Equation (8), the position of the center point of the current (n) -level subset may vary according to the phase of the decision variable of the (n-1) -level subset, which is the previous level. As described in the basic conditions of the present invention

Wow

According to the 4 QAM constellation case

Wow

Respectively

And 1, respectively. In this case, Equations (7) and (8)

And the result is consistent with the result obtained by the above equation (5).

임을 적용하면, 종래의 수학식 1을 통해 얻을 수 있는 square M-ary QAM 심볼을 수신신호

와 수신기(100)에서 추정한 채널

를 변수로 포함하는 하기의 수학식 9 및 수학식 10과 같은 closed 함수의 형태로서 나타낼 수 있다.Further, according to the ML detection method of the present invention,

, A square M-ary QAM symbol, which can be obtained by the conventional Equation 1,

And a channel estimated by the receiver 100

As a function of a closed function such as Equations (9) and (10) below.

이다.here,

to be.

3 is a flowchart of an ML detection method according to an embodiment of the present invention. The ML detection method shown in FIG. 3 can be performed by the receiver 100 that performs the ML detection described above with reference to FIG. Therefore, even if omitted below, the description of the receiver 100 through FIG. 1 also applies to FIG.

In step S302, the receiver 100 selects M symbols from the received signal, and estimates channel coefficients using the selected M symbols. In addition, the receiver 100 may determine an initial decision variable based on the estimated channel coefficient.

In step S304, the receiver 100 may divide the set of 0-levels composed of the received M symbols into four (n) -level subsets. Here, n is a natural number starting from 1.

In step S306, the receiver 100 may select a subset of any of the (n) -level subsets. In accordance with an embodiment of the present invention, the receiver 100 may include a subset (n) to which the symbol having the smallest distance from the decision variable of the (n-1) -level subset among the four - can be selected as a representative subset of the level subset.

In step S308, the receiver 100 may determine the position of the midpoint symbol of the selected (n) -level subset. According to an embodiment of the present invention, the receiver 100 calculates the (n-1) -level subset of the symbols of the selected (n-1) As a midpoint symbol of the (n) -level subset of the symbols obtained by averaging the positions of the smallest symbols.

로, 결정 변수의 실수부가 0이하이고 허수부가 0초과인 경우 결정 변수의 위상을

로, 결정 변수의 실수부가 0미만이고 허수부가 0이하인 경우 결정 변수의 위상을

로, 결정 변수의 실수부가 0이상이고 허수부가 0미만인 경우 결정 변수의 위상을

로 결정할 수 있다.Here, the position of the center point symbol of the (n) -level subset may be determined according to the phase value of the decision variable of the previous level ((n-1) -level) The phase value of the decision variable of the previous level subset may be determined by Equation (4) based on the real part value and the imaginary part value of the decision variable of the previous level subset. According to Equation (4), when the real part of the decision variable is over 0 and the imaginary part is over 0, the phase of the decision variable is

, When the real part of the decision variable is 0 or less and the imaginary part is over 0, the phase of the decision variable is

If the real part of the decision variable is less than 0 and the imaginary part is less than or equal to 0,

, When the real part of the decision variable is 0 or more and the imaginary part is less than 0, the phase of the decision variable is

.

In step S310, the receiver 100 may shift the symbols of the selected (n) -level subset by the midpoint symbol of the (n) -level subset.

At step S312, the receiver 100 may determine the decision variable of the selected (n) -level subset. The receiver 100 may determine the (n) -level subset of the (n) -level subset based on the previous level, i.e., the decision variable of the (n-1) -level subset and the location of the midpoint symbol of the selected The decision variable can be determined.

이다.In step S314, the receiver 100 may determine whether n is less than N. [

to be.

If it is determined in step S314 that n is less than N, in step S316, the receiver 100 adds 1 to n and performs steps S306 to S314 recursively. According to the ML detection method according to an embodiment of the present invention, the receiver 100 increases the number (n) of levels by (1) and the middle point symbol of the (N) And repeats steps S306 through S314 until the determination variable of the (N) -level subset is determined.

Steps S306 to S314 are repeated. If it is determined in step S314 that n is not less than N, that is, the position of the central point symbol from the one-level subset to the N- level subset and the position of the determination variable are determined , Then in step S318, the receiver 100 can determine the solution of the ML detection. According to an embodiment of the present invention, the receiver 100 uses a symbol of a position from the position of the midpoint symbol of the 1-level subset to the position of the midpoint symbol of the (N) -level subset as a solution of ML detection You can decide. This is explained in detail by deriving Equation (9) and Equation (10).

와 수신기에서 추정한 채널

를 바탕으로 closed 형태로서 나타낸 결과 식(수학식 9 및 수학식 10) 및 위상값을 도출하는 식(수학식 4)을 통해 결정함으로써, 연산 복잡도를 낮추면서도 신속하게 기존의 방법과 동일한 해를 결정할 수 있다.As described above, according to the ML detection method according to the embodiment of the present invention,

And the channel estimated by the receiver

(Equation 9 and Equation 10) and a formula for deriving the phase value (Equation 4), which are shown as a closed form on the basis of Equation (4), the same solution as that of the existing method is quickly determined while reducing the computational complexity .

[Performance analysis of the present invention]

FIG. 4 is a simulation graph comparing a bit error rate (BER) of a conventional ML detection method with an ML detection method according to an embodiment of the present invention. In FIG. 4, the ML is the conventional method, and the PR is based on the ML detection method according to an embodiment of the present invention. As can be seen from FIG. 4, the ML detection method according to an embodiment of the present invention and the conventional ML detection method (method according to Equation 1) have the same BER performance. This means that the ML detection method of the present invention is an efficient method that can greatly reduce the complexity even though it has the same detection performance as the conventional ML detection method. The ML detection method of the present invention can be applied to all systems that use ML detection for a received signal including a transmission symbol, a Gaussian channel coefficient and a noise parameter, and can greatly reduce the ML detection complexity of such a system. The same performance can be exhibited while lowering the computational complexity of ML detection, so that the construction cost of the system using ML detection can be greatly reduced.

FIG. 5 is a graph comparing the computation time required for the ML detection method and the conventional ML detection method according to an embodiment of the present invention. 5 compares the time required for 100,000 repetitions of the conventional ML detection method (method according to Equation (1)) and the ML detection method of the present invention implemented in MATLAB, respectively.

에 비례하여) 증가함에 비해, 본 발명의 ML 검출 방법에 소요되는 시간은 거의 변화가 없거나 선형적으로 완만하게 증가함을 볼 수 있다. 이와 같이, 본 발명에 따른 ML 검출 방법은 기존의 ML 검출 방법에 비해 더 작은 구현 복잡도를 가지며 연산 속도가 훨씬 빠름을 알 수 있다.In FIG. 5, N = 1 means 4 QAM constellation, N = 2 means 16 QAM constellation, N = 3 means 64 QAM constellation, N = 4 means 256 QAM constellation, Means 1024 QAM constellation, and N = 6 means 4096 QAM constellation. As the size of the M-ary QAM becomes larger, the time required for the conventional ML detection method becomes exponentially (

, It can be seen that the time required for the ML detection method of the present invention is substantially unchanged or linearly increases gradually. As described above, the ML detection method according to the present invention has a smaller implementation complexity and a much higher computation speed than the conventional ML detection method.

The ML detection method in a receiver performing ML detection may also be implemented in the form of a recording medium including instructions executable by a computer such as a program module executed by a computer. Computer readable media can be any available media that can be accessed by a computer and includes both volatile and nonvolatile media, removable and non-removable media. In addition, the computer readable medium may include both computer storage media. Computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data.

The ML detection method described above can also be implemented in the form of a computer program stored in a recording medium.

It will be understood by those of ordinary skill in the art that the foregoing description of the embodiments is for illustrative purposes and that those skilled in the art can easily modify the invention without departing from the spirit or essential characteristics thereof. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive. For example, each component described as a single entity may be distributed and implemented, and components described as being distributed may also be implemented in a combined form.

The scope of the present invention is defined by the appended claims rather than the detailed description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included within the scope of the present invention.

100: receiver
110:
120: channel estimation unit
130:
140: ML detector
142:
144: center point determining unit
146: ML decision unit

Claims (17)

In a maximum likelihood (ML) detection method,
(a) determining an initial decision variable based on an estimated channel coefficient using a selected M symbols from a signal received at a receiver;
(b) dividing the M symbols into four (n) -level subsets;
(c) selecting a subset of any of the four (n) -level subset and using the decision variable of the (n-1) Determining a position of a symbol;
(d) shifting the symbol of the selected (n) -level subset by the midpoint symbol of the (n) -level subset;
(e) determining a decision variable of the (n) -level subset based on the decision variable of the (n-1) -level subset and the position of the midpoint symbol of the (n) -level subset;
(N) determining the location of the midpoint symbol of the (N) -level subset and the (N) -level subset by increasing the number of levels (n) Repeating the steps (b) to (e) until the determination is made; And
(i) determining a symbol of a position from the position of the midpoint symbol of the 1-level subset to the position of the midpoint symbol of the (N) -level subset as a solution of ML detection,
, Wherein the N

, And n is

. ≪ / RTI > The method according to claim 1,
M is equal to or greater than 4, and the M symbols are square M-ary Quadrature Amplitude Modulation (QAM) symbols. The method according to claim 1,
Level subsets of the (M-1) -level subset among the (M-1) -level subsets in the step (c) Detection method. The method of claim 3,
The determining of the position of the midpoint symbol of the (n) -level subset in step (c) may include determining the position of the symbol closest to the origin among the symbols of the selected (n) level subset of the (n-1) -level subset as a median point symbol of the (n) -level subset, the symbol at a location averaging the location of the smallest distance from the decision variable of the (n-1) -level subset. 5. The method of claim 4,
The ML detection solution determined in the step (i) is determined based on the following expression (11)
&Quot; (11) "

Is the solution of ML detection,

Is determined based on the following equation (12) as the position of the midpoint symbol of the (n) -level subset,
&Quot; (12) "

here

ego,

Is a (n-1) -level subset of the decision variable,

Is a function for determining the phase of the decision variable z according to the following equation (13).
&Quot; (13) "

6. The method of claim 5,
(n) - the position of the midpoint symbol of the level subset

Is determined based on Equation (14) below,
&Quot; (14) "

remind

(Y) received at the receiver and the estimated channel coefficient

The initial decision variable being determined based on the initial decision variable. 6. The method of claim 5,
The step (i) may further comprise the step of determining the phase of the decision variable based on Equation (13)
When the real part of the decision variable is over 0 and the imaginary part is over 0, the phase of the decision variable is

, When the real part of the decision variable is 0 or less and the imaginary part is over 0, the phase of the decision variable is

, When the real part of the decision variable is less than 0 and the imaginary part is less than or equal to 0,

, When the real part of the decision variable is 0 or more and the imaginary part is less than 0,

. ≪ / RTI > 3. The method of claim 2,
Wherein the average symbol power of the M symbols is one. A receiver for performing Maximum Likelihood (ML) detection,
A signal receiving unit for receiving a signal;
A channel estimator for estimating a channel coefficient by selecting M symbols from the received signal;
A decision variable generator for determining an initial decision variable based on the estimated channel coefficient; And
An ML detector for performing ML detection on the M symbols,
, ≪ / RTI &
Wherein the ML detection unit comprises:
(B) and (i) of claim 1,
N is

And n is

≪ / RTI > 10. The method of claim 9,
M is equal to or greater than 4, and the M symbols are square M-ary Quadrature Amplitude Modulation (QAM) symbols. 10. The method of claim 9,
In step (c), the ML detector selects a subset to which the symbol having the smallest distance from the decision variable of the (n-1) -level subset among the M symbols among the (n) Receiver. 12. The method of claim 11,
In the step (c), the ML detector detects the position of a symbol closest to the origin among the symbols of the selected (n) -level subset and the determination variable of the (n-1) And determines a symbol of a position averaging a position of a symbol having the smallest distance as a midpoint symbol of the (n) -level subset. 13. The method of claim 12,
The ML detection solution determined in the step (i) is determined based on the following expression (15)
&Quot; (15) "

Is the solution of ML detection,

Is determined based on the following equation (16) as the position of the midpoint symbol of the (n) -level subset,
&Quot; (16) "

here

ego,

Is a (n-1) -level subset of the decision variable,

Is a function for determining the phase of the decision variable z according to the following equation (17).
&Quot; (17) "

14. The method of claim 13,
(n) - the position of the midpoint symbol of the level subset

Is determined based on Equation (18) below,
&Quot; (18) "

remind

(Y) received at the receiver and the estimated channel coefficient

The initial decision variable being determined based on the initial decision variable. 14. The method of claim 13,
The ML detector determines the phase of the decision variable based on Equation (17) in the step (i)
Wherein the ML detector detects the phase of the decision variable when the real part and imaginary part of the decision variable are equal to or larger than 0

, When the real part of the decision variable is less than 0 and the imaginary part is 0 or more,

If the real part and the imaginary part of the decision variable are less than 0, the phase of the decision variable is

, When the real part of the decision variable is 0 or more and the imaginary part is less than 0,

≪ / RTI > 11. The method of claim 10,
Wherein the average symbol power of the M symbols is one. 9. A computer-readable recording medium storing a program for causing a computer to execute the method according to any one of claims 1 to 8.

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