KR20200116803A - Method and Apparatus for Decomposition of Quaternion for Minimizing Zero Crossing - Google Patents

Abstract

Disclosed are a quaternion decomposition method for minimizing zero crossing and an apparatus therefor. According to an embodiment of the present invention, a quaternion decomposition apparatus may comprise a data collection unit for obtaining input data, a quaternion data conversion unit for calculating a quaternion vector and a rotation angle based on some information of the input data and a nibble time, a quaternion rotation processing unit for selecting one complex plane among super-complex planes based on the nibble time, etc.

Description

Quaternion decomposition method for minimizing zero crossing and apparatus therefor {Method and Apparatus for Decomposition of Quaternion for Minimizing Zero Crossing}

The present invention relates to a method and apparatus for disassembling quaternions to minimize zero crossing.

The content described in this section merely provides background information on the embodiments of the present invention and does not constitute the prior art.

A quaternion is a hyper-complex number that extends a complex number, and a quaternion q is expressed as qw + iqx + jqy +kqz, which is a real part qw and four imaginary parts i, j, k. It consists of ingredients. Using quaternions, compared to using matrices, it is possible to concisely represent the rotation of an object in space, and because it enables fast calculations, computer graphics, 　 control theory, 　 signal processing, 　attitude control, 　 physics, 　 bioinformatics, It is used in molecular dynamics, computer simulation, orbital mechanics.

Recently, researches on communication systems have been studied in satellite communication, optical communication, and mobile communication areas, such as quaternion modulation, which is transmitted with a dual polarized antenna using a multidimensional modulation method using quaternions. In particular, in mobile communication, methods of transmitting a quaternion modulated signal through a multiple input multiple output (MIMO) antenna after Caley-Dickson decomposition have been proposed.

However, this method divides the super-complex number into two complex numbers and maps them to two different complex planes, and then two QPSK (Quadrature Phase Shift Keying) symbols using two different polarization antennas. It does not have any peculiar advantages when applied to a communication system other than transmitting signals.

On the other hand, in a system operated with limited power such as an Internet of Things (IoT) terminal, a mobile communication terminal, or a satellite communication device, the specification of the high power amplifier (HPA), which consumes the most power, has a linear operating point. It is determined based on the back-off that is determined. Since the installed HPA device affects the transmission power even if the amount of transmitted data is small or the data transmission speed is slow, it is very important to analyze the peak to average power ratio (PAPR) at the design time. As the back-off value increases, the linearity increases, while the power efficiency of HPA decreases. As the back-off value decreases, the power efficiency increases but the nonlinearity increases. The nonlinear characteristic is also important not only from the terminal but also from the system side as it increases the spurious emission of OOB (Out Of Band) and deteriorates the overall system performance. The use of DFT-s-OFDM (Discrete Fourier Transform-spread-Orthogonal Frequency Division Multiplexing) in 4G LTE and 5G is to complement the shortcomings of Cyclic Prefix (CP) OFDM in terms of PAPR and to improve overall system performance.

The present invention rotates a quaternion in a quaternion space to project it onto a complex number plane, and rotates a complex number projected from the complex number plane again in different directions twice to calculate a pair of complex numbers having a predetermined sequence. The main object is to provide a quaternion decomposition method and an apparatus therefor.

) 및 상기 회전각을 기반으로 투영된 제1 복소수(

)를 계산하는 쿼터니언 회전 처리부; 제1 평면 회전자를 기준으로 상기 제1 복소수(

)를 서로 다른 방향으로 회전시켜 제1 복소 쌍을 산출하는 제1 평면 복소수 계산부; 제2 평면 회전자를 기준으로 상기 제1 복소수(

)를 서로 다른 방향으로 회전시켜 제2 복소 쌍을 산출하는 제2 평면 복소수 계산부; 및 상기 제1 복소 쌍 및 상기 제2 복소 쌍 중 적어도 하나를 선택하여 쿼터니언 분해 심볼(

,

)이 전송되도록 하는 멀티플렉서부를 포함할 수 있다. According to an aspect of the present invention, a quaternion decomposition apparatus for achieving the above object comprises: a data collection unit for obtaining input data; A quaternion data conversion unit that calculates a quaternion vector and a rotation angle based on some information of the input data and a nibble time; Based on the nibble time, one of the super complex planes is selected, and the quaternion vector (

) And a first complex number projected based on the rotation angle (

) A quaternion rotation processing unit that calculates; The first complex number based on the first plane rotor (

A first planar complex number calculator configured to calculate a first complex pair by rotating) in different directions; The first complex number (

A second planar complex number calculating unit for calculating a second complex pair by rotating) in different directions; And a quaternion decomposition symbol by selecting at least one of the first complex pair and the second complex pair (

,

) May include a multiplexer to be transmitted.

) 및 상기 회전각을 기반으로 투영된 제1 복소수(

)를 계산하는 쿼터니언 회전 처리 단계; 제1 평면 회전자를 기준으로 상기 제1 복소수(

)를 서로 다른 방향으로 회전시켜 제1 복소 쌍을 산출하는 제1 평면 복소수 계산 단계; 제2 평면 회전자를 기준으로 상기 제1 복소수(

)를 서로 다른 방향으로 회전시켜 제2 복소 쌍을 산출하는 제2 평면 복소수 계산 단계; 및 상기 제1 복소 쌍 및 상기 제2 복소 쌍 중 적어도 하나를 선택하여 쿼터니언 분해 심볼(

,

)이 전송되도록 하는 멀티플렉서 처리 단계를 포함할 수 있다. In addition, according to another aspect of the present invention, a quaternion decomposition method for achieving the above object includes a data collection step of obtaining input data; A quaternion data conversion step of calculating a quaternion vector and a rotation angle based on some information of the input data and a nibble time; Based on the nibble time, one of the super complex planes is selected, and the quaternion vector (

) And a first complex number projected based on the rotation angle (

A quaternion rotation processing step of calculating ); The first complex number based on the first plane rotor (

A first plane complex number calculation step of calculating a first complex pair by rotating) in different directions; The first complex number (

A second plane complex number calculation step of calculating a second complex pair by rotating) in different directions; And a quaternion decomposition symbol by selecting at least one of the first complex pair and the second complex pair (

,

) May include a multiplexer processing step to be transmitted.

As described above, in the present invention, the quaternion is rotated in the quaternion space to be projected onto one complex plane, and the complex number projected from the complex number plane is rotated twice in different directions to perform predetermined By calculating complex pairs having a sequence, zero crossing is restricted to reduce the peak to average power ratio (PAPR), which is a major performance indicator of a terminal (not shown), thereby extending battery usage time. There is an effect that can be done.

In addition, the present invention has the effect of having a quaternion partitioning method and being able to be used in parallel like various existing PAPR reduction methods.

1 is a diagram schematically showing a quaternion disassembly device according to an embodiment of the present invention.
2 is a flowchart illustrating a quaternion decomposition method according to an embodiment of the present invention.
3 is a flowchart illustrating a demodulation operation according to quaternion decomposition according to an embodiment of the present invention.
4 is a view showing a quaternion rotor according to an embodiment of the present invention.
5 shows a three-dimensional quaternion space according to an embodiment of the present invention.
6 is a view for explaining that two complex number pairs are formed based on a quaternion vector according to an embodiment of the present invention.
7 is a diagram illustrating an operation of generating pairs of complex numbers in different orders from the same projection point according to an embodiment of the present invention.
8 is an exemplary diagram showing the configuration of a 2X2 MIMO diversity antenna according to an embodiment of the present invention.
9 is a diagram schematically showing a quaternion decomposition apparatus applied to an 8-phase shift method according to an embodiment of the present invention.
10 is a diagram schematically showing a quaternion decomposition apparatus applied to a DFT-S-OFDM according to an embodiment of the present invention.
11A and 11B are diagrams showing a constellation diagram and a trajectory diagram in a phase space of QDMZC and QPSK according to an embodiment of the present invention.
12A and 12B are diagrams showing results of a PAPR simulation according to an embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In describing the present invention, when it is determined that a detailed description of a related known configuration or function may obscure the subject matter of the present invention, a detailed description thereof will be omitted. In addition, a preferred embodiment of the present invention will be described below, but the technical idea of the present invention is not limited thereto or is not limited thereto, and may be modified and variously implemented by a person skilled in the art. Hereinafter, a quaternion decomposition method for minimizing zero crossing proposed in the present invention and an apparatus therefor will be described in detail with reference to the drawings.

In the present invention, a quaternion is rotated in a quaternion space to project a complex number onto a complex plane, and a complex number projected from the complex number plane is rotated twice in different directions to form a complex number pair having a predetermined sequence. Calculate. Here, two rotations limit the zero crossing (passing through zero) during this sequence by two complex numbers (two QPSK symbols), and the peak to average power ratio (PAPR), which is the main performance indicator of the terminal (not shown). Ratio) to extend the battery usage time.

In addition, the present invention may consider expansion of various types of modulation constellations by using quaternion rotation. For example, when each complex plane is configured in the form of 8 QPSK symbols, one rotated by 8 QPSK symbols and the other rotated by 45 degrees, 2 8PSK symbols (4D TCM 8PSK and 8PSK are standard for satellite communication). It can be configured as a modulation method). In addition, when a MIMO (Multiple Input Multiple Output) antenna is used, 16 symbols may be distinguished through QPSK modulation using a diversity antenna or 8PSK modulation according to a configuration of input information. In the case of DFT-s-OFDM, 16 symbols can be distinguished using different sub-carriers according to the configuration of the input information. Therefore, the present invention can be used in modulation methods (4G, 5G, WiFi, satellite communication, etc.) set by the current standard, and at the same time, by providing a low PAPR, it is possible to extend the battery use time and, like various conventional PAPR reduction methods It can be used in parallel.

In addition, the present invention is a new quaternion decomposition method in which two complex numbers having a certain sequence are decomposed and zero crossing is limited during this sequence, unlike the conventional Kayley-Dixon decomposition, QPSK modulation using antenna diversity, or 16 symbols can be distinguished through 8PSK modulation. Compared to OCQPSK (orthogonal spread modulation), which is the standard modulation method of conventional 3G CDMA, it shows equivalent performance in terms of PAPR. However, in terms of PAPR effectiveness, OCQPSK minimizes zero crossing between two QPSK chip symbols after extending one and the same QPSK data to the chip level. In contrast, the QDMZC (Quaternion Decomposition Minimizing Zero Crossing) method of the present invention is different from the OCQPSK method in that it minimizes zero crossing (zero point passing) between two bit-level QPSK symbols or 8PSK symbols, and is called the same constellation point. Even so, it is different from the OCQPSK method in that different rotation sequences of each complex number mean separate QPSK symbols. In addition, the present invention has a difference in that information required for demodulation is inserted into an Alamouti Code of a MIMO system and transmitted.

1 is a diagram schematically showing a quaternion disassembly device according to an embodiment of the present invention.

The quaternion decomposition apparatus 10 according to the present embodiment includes a data collection unit 100, a quaternion data conversion unit 200, a quaternion rotation processing unit 300, a first plane complex number calculation unit 400, and a second plane complex number calculation unit. 500, a multiplexer unit 600 and an output unit 700. The quaternion disassembly device 10 of FIG. 1 is according to an embodiment, and not all blocks shown in FIG. 1 are essential components, and some blocks included in the quaternion disassembly device 10 in other embodiments are added or changed. Or it can be deleted.

The quaternion decomposition device 10 converts the input data into a quaternion, rotates the quaternion in the quaternion space to project it onto one complex number plane, and rotates the complex number projected from the complex number plane twice in different directions to perform a predetermined sequence. Performs the operation of computing a pair of complex numbers with.

The data collection unit 100 acquires input data and transmits the acquired input data to the quaternion data conversion unit 200. It is preferable that the data collection unit 100 acquires 4 bits of input data. Here, the input data may be 4-bit data composed of (b ₀ , b ₁ , b ₂ , b ₃ ), and each bit information may be composed of 1 or -1. The data collection unit 100 may receive input data from an external server or terminal.

The quaternion data conversion unit 200 acquires input data from the data collection unit 100 and calculates a quaternion vector and a rotation angle using some information using the input data. Specifically, the quaternion data conversion unit 200 calculates a quaternion vector and a rotation angle based on some information of the input data and a nibble time based on a temporal index of the input data.

The quaternion data conversion unit 200 according to the present embodiment includes a quaternion vector conversion unit 210, a rotation angle calculation unit 220, and a nibble time selection unit 230. Hereinafter, each of the components included in the quaternion data conversion unit 200 will be described.

)를 생성한다. 쿼터니언 벡터 변환부(210)는 입력 데이터에 포함된 3 비트 정보(b₁, b₂, b₃)를 이용하여 쿼터니언 벡터(

)를 생성한다. The quaternion vector conversion unit 210 sets the value of the real part to 0, and sets three bit information of the input data as the value of the imaginary part to set the quaternion vector (

). The quaternion vector conversion unit 210 uses 3-bit information (b ₁ , b ₂ , b ₃ ) included in the input data to provide a quaternion vector (

).

)를 생성할 수 있다. The quaternion vector conversion unit 210 uses [Equation 1] to provide a quaternion vector (

) Can be created.

: 쿼터니언 벡터, b₁, b₂, b₃: 입력 데이터에 포함된 3 비트 정보)(

: Quaternion vector, b ₁ , b ₂ , b ₃ : 3-bit information included in input data)

)을 계산한다. 구체적으로, 회전각 계산부(220)는 두 개의 연속된 복소수를 생성한다고 할 때 입력 데이터 중 두 개의 비트정보(b₁, b₃)를 곱한 값(R)과 니블 시간이 짝수 니블 시간 또는 홀수 니블 시간인지 여부에 따라 회전각을 계산한다. 회전각 계산부(220)는 [수학식 2]를 이용하여 회전각을 계산할 수 있다. The rotation angle calculation unit 220 uses some information of the input data and the nibble time selected by the nibble time selection unit 230 to select a rotation angle (

) Is calculated. Specifically, when the rotation angle calculation unit 220 generates two consecutive complex numbers, a value (R) obtained by multiplying two bit information (b ₁ , b ₃ ) of the input data and a nibble time is an even nibble time or an odd number. Calculate the rotation angle according to whether it is nibble time. The rotation angle calculation unit 220 may calculate the rotation angle using [Equation 2].

: 회전각, b₁, b₃: 입력 데이터에 포함된 2 비트 정보, R: b₁b₃)(

: Rotation angle, b ₁ , b ₃ : 2-bit information included in the input data, R: b ₁ b ₃ )

로 계산하고, 입력 데이터가 짝수 니블 시간에 획득되고, 두 개의 비트정보(b₁, b₃)를 곱한 값이 0 미만인 경우 회전각을

로 계산할 수 있다. 또한, 회전각 계산부(220)는 입력 데이터가 홀수 니블 시간에 획득되고, 두 개의 비트정보(b₁, b₃)를 곱한 값이 0을 초과하는 경우 회전각을

로 계산하고, 입력 데이터가 홀수 니블 시간에 획득되고, 두 개의 비트정보(b₁, b₃)를 곱한 값이 0 미만인 경우 회전각을

로 계산할 수 있다.For example, the rotation angle calculation unit 220 calculates the rotation angle when the input data is acquired at an even nibble time and the product of the two bit information (b ₁ , b ₃ ) exceeds 0.

If the input data is obtained at the even nibble time and the product of two bit information (b ₁ , b ₃ ) is less than 0, the rotation angle is

Can be calculated as Further, the rotation angle calculation unit 220 calculates the rotation angle when the input data is acquired at odd nibble times and the product of the two bit information (b ₁ , b ₃ ) exceeds 0.

If the input data is obtained at odd nibble time and the product of two bit information (b ₁ , b ₃ ) is less than 0, the rotation angle is

Can be calculated as

The nibble time selector 230 determines a nibble time based on a time index for input data. The nibble time selector 230 checks the time index at which the input data is obtained, and defines the checked time index as the nibble time. Here, it is preferable that the nibble time is a 4-bit unit time. For example, the nibble time selection unit 230 k = 0, 1, 2, 3, ... Classify the time index of the input data expressed as even nibble time (k=0,2,4…) and odd nibble time (k=1,3,5… ), and even nibble for the time when the input data was acquired. Choose between time and odd nibble time.

)를 투영시켜 제1 복소수(

)를 계산한다. The quaternion rotation processing unit 300 selects one of the super complex planes based on the nibble time, and the quaternion vector (

) By projecting the first complex number (

) Is calculated.

)를 회전시켜 제1 복소수(

)를 계산한다. 쿼터니언 회전 처리부(300)는 [수학식 3] 내지 [수학식 5] 각각에 의해 정의된 j 축 회전자, k 축 회전자, i축 회전자 중 하나의 회전자를 이용하여 제1 복소수(

)를 계산한다. 본 실시예에 따른 쿼터니언 회전 처리부(300)는 j 축 회전자를 이용하여 제1 복소수(

)를 계산한다.The quaternion rotation processing unit 300 is a quaternion vector based on one of a j-axis rotor, a k-axis rotor, and an i-axis rotor.

) By rotating the first complex number (

) Is calculated. The quaternion rotation processing unit 300 uses one of the j-axis rotor, k-axis rotor, and i-axis rotor defined by [Equation 3] to [Equation 5], respectively, using a first complex number (

) Is calculated. The quaternion rotation processing unit 300 according to this embodiment uses a j-axis rotor to provide a first complex number (

) Is calculated.

: j 축 회전자,

: 회전각)(

: j-axis rotor,

: Rotation angle)

: k 축 회전자,

: 회전각)(

: k-axis rotor,

: Rotation angle)

: i 축 회전자,

: 회전각)(

: i-axis rotor,

: Rotation angle)

)를 계산하고, 짝수 니블 시간 또는 홀수 니블 시간인지 여부에 따라 서로 다른 평면으로 투영하는 것이 바람직하다. 쿼터니언 회전 처리부(300)는 [수학식 6]을 이용하여 제1 복소수(

)를 계산할 수 있다. The quaternion rotation processing unit 300 uses a j-axis rotor to provide a first complex number (

) Is calculated and projected onto different planes depending on whether it is an even nibble time or an odd nibble time. The quaternion rotation processing unit 300 uses [Equation 6] to perform a first complex number (

) Can be calculated.

: 제1 복소수,

: j 축 회전자,

:

의 켤레 복소수)(

: First complex number,

: j-axis rotor,

:

Complex conjugate of

)를 제1 평면(I-J Plane)으로 투영하여 제1 복소수(

)를 계산하며, 제1 평면(I-J Plane)으로 투영된 제1 복소수(

)는 제1 평면 복소수(

)으로 정의될 수 있다. 즉, 쿼터니언 회전 처리부(300)는 짝수 니블 시간에 해당하는 경우 쿼터니언 벡터(

)를 제1 평면(I-J Plane)으로 투영시킨 제1 평면 복소수(

) 을 출력한다. When the quaternion rotation processing unit 300 corresponds to the even nibble time, the quaternion vector (

) To the first plane (IJ Plane) to project the first complex number (

) Is calculated, and the first complex number projected onto the first plane (IJ Plane) (

) Is the first plane complex number (

) Can be defined. That is, when the quaternion rotation processing unit 300 corresponds to an even nibble time, the quaternion vector (

) Projected onto the first plane (IJ Plane)

) Is displayed.

)를 제2 평면(K-J Plane)으로 투영하여 제1 복소수(

)를 계산하며, 제2 평면(K-J Plane)으로 투영된 제1 복소수(

)는 제2 평면 복소수(

)으로 정의될 수 있다. 즉, 쿼터니언 회전 처리부(300)는 홀수 니블 시간에 해당하는 경우 쿼터니언 벡터(

)를 제2 평면(K-J Plane)으로 투영시킨 제2 평면 복소수(

)을 출력한다.Meanwhile, when the quaternion rotation processing unit 300 corresponds to an odd nibble time, the quaternion vector (

) To the second plane (KJ Plane) to project the first complex number (

) Is calculated, and the first complex number projected onto the second plane (KJ Plane) (

) Is the second plane complex number (

) Can be defined. That is, when the quaternion rotation processing unit 300 corresponds to an odd nibble time, the quaternion vector (

) Projected onto the second plane (KJ Plane)

) Is displayed.

The first planar complex number calculation unit 400 includes at least two first axis rotation units 410 and 420 that rotate the complex number based on the first axis rotor.

)를 서로 다른 방향으로 회전시켜 제1-1 평면 복소수(

) 및 제1-2 평면 복소수(

)를 포함하는 제1 복소 쌍(

,

)을 계산한다. 여기서, 제1 축 회전자는 K 축 회전자를 의미하며, K 축 회전자는 [수학식 4]에 의해 정의된다. The first planar complex number calculation unit 400 includes a first planar complex number based on the first axis rotator through each of the at least two first axis rotation units 410 and 420.

) To rotate in different directions to create the 1-1th plane complex number (

) And 1-2 plane complex numbers (

A first complex pair (

,

) Is calculated. Here, the first shaft rotor means a K-axis rotor, and the K-axis rotor is defined by [Equation 4].

)를 각각 다른 방향으로 두 번 회전시켜 제1 복소 쌍(

,

)을 계산하며, 제1 복소 쌍(

,

)은 [수학식 7] 및 [수학식 8]을 통해 계산될 수 있다. [수학식 7] 및 [수학식 8]에 포함된 제1 축 회전자 각각은 서로 다른 방향을 갖는다. The first planar complex number calculation unit 400 uses at least two first axis rotation units 410 and 420 to provide a first planar complex number (

) Is rotated twice in different directions, so that the first complex pair (

,

), and the first complex pair (

,

) Can be calculated through [Equation 7] and [Equation 8]. Each of the first shaft rotors included in [Equation 7] and [Equation 8] has a different direction.

: 제1 복소 쌍 중 제1-1 평면 복소수,

: 제1 평면 복소수,

: 제1 축 회전자,

: 제1 축 회전자의 켤레 복소수)(

: The 1-1 plane complex number of the first complex pair,

: First plane complex number,

: 1st shaft rotor,

: Complex conjugate of the first axis rotor)

: 제1 복소 쌍 중 제1-2 평면 복소수,

: 제1 평면 복소수,

: 제1 축 회전자,

: 제1 축 회전자의 켤레 복소수)(

: 1-2 plane complex number of the first complex pair,

: First plane complex number,

: 1st shaft rotor,

: Complex conjugate of the first axis rotor)

,

)을 멀티플렉서부(600)로 전달한다. The first planar complex number calculation unit 400 includes the calculated first complex pair (

,

) Is transferred to the multiplexer unit 600.

The second planar complex number calculation unit 500 includes at least two second axis rotation units 510 and 520 that rotate the complex number based on the second axis rotor.

)를 서로 다른 방향으로 회전시켜 제2-1 평면 복소수(

) 및 제2-2 평면 복소수(

)를 포함하는 제2 복소 쌍(

,

)을 계산한다. 여기서, 제2 축 회전자는 I 축 회전자를 의미하며, I 축 회전자는 [수학식 5]에 의해 정의된다. The second planar complex number calculation unit 500 includes a second planar complex number based on the second axis rotator through each of the at least two second axis rotation units 510 and 520.

) To rotate in different directions to create a complex 2-1 plane (

) And 2-2 plane complex numbers (

A second complex pair containing (

,

) Is calculated. Here, the second axis rotor means an I axis rotor, and the I axis rotor is defined by [Equation 5].

)를 각각 다른 방향으로 두 번 회전시켜 제2 복소 쌍(

,

)을 계산하며, 제2 복소 쌍(

,

)은 [수학식 9] 및 [수학식 10]을 통해 계산될 수 있다. [수학식 9] 및 [수학식 10]에 포함된 제2 축 회전자 각각은 서로 다른 방향을 갖는다. The second planar complex number calculation unit 500 uses at least two second axis rotation units 510 and 520 to provide a first planar complex number (

) Is rotated twice in different directions, so that the second complex pair (

,

), and the second complex pair (

,

) Can be calculated through [Equation 9] and [Equation 10]. Each of the second shaft rotors included in [Equation 9] and [Equation 10] has a different direction.

: 제2 복소 쌍 중 제2-1 평면 복소수,

: 제2 평면 복소수,

: 제2 축 회전자,

: 제2 축 회전자의 켤레 복소수)(

: 2-1 plane complex number of the second complex pair,

: Second plane complex number,

: 2nd shaft rotor,

: Complex conjugate of the 2nd axis rotor)

: 제2 복소 쌍 중 제2-2 평면 복소수,

: 제2 평면 복소수,

: 제2 축 회전자,

: 제2 축 회전자의 켤레 복소수)(

: 2-2 plane complex number of the second complex pair,

: Second plane complex number,

: 2nd shaft rotor,

: Complex conjugate of the 2nd axis rotor)

,

)을 멀티플렉서부(600)로 전달한다. The second planar complex number calculation unit 500 is the calculated second complex pair (

,

) Is transferred to the multiplexer unit 600.

,

) 및 제2 복소 쌍(

,

) 중 적어도 하나를 선택하여 소정의 시퀀스를 갖는 쿼터니언 분해 심볼(

,

)을 출력부(700)로 전달한다. 여기서, 쿼터니언 분해 심볼(

,

)은 쿼터니언 심볼을 두 개의 복소수 쌍으로 분해한 QDMZC(Quaternion Decomposition Minimizing Zero Crossing) 심볼을 의미하며, 쿼터니언 분해 심볼에 포함된

및

은 소정의 시퀀스(순서)를 갖는다. 즉, 쿼터니언 분해 심볼(

,

)와 쿼터니언 분해 심볼(

,

)은 서로 다른 데이터를 의미한다.The multiplexer 600 is based on the nibble time, the first complex pair (

,

) And the second complex pair (

,

) By selecting at least one of the quaternion decomposition symbols having a predetermined sequence (

,

) To the output unit 700. Here, the quaternion decomposition symbol (

,

) Means a QDMZC (Quaternion Decomposition Minimizing Zero Crossing) symbol obtained by decomposing a quaternion symbol into two complex number pairs, and is included in the quaternion decomposition symbol.

And

Has a predetermined sequence (sequence). That is, the quaternion decomposition symbol (

,

) And the quaternion decomposition symbol (

,

) Means different data.

,

)을 획득하고, 쿼터니언 분해 심볼(

,

)을 출력한다. The output unit 700 is a quaternion decomposition symbol from the multiplexer unit 600 (

,

), and the quaternion decomposition symbol (

,

) Is displayed.

In FIG. 1, the output unit 700 is shown as a diversity antenna unit, but this is according to an exemplary embodiment and is not limited thereto. For example, the output unit 700 may be implemented as a diversity antenna unit as shown in FIG. 8, but is not limited thereto, and the phase shift modulation conversion unit 900 based on the 8PSK (Phase Shift Keying) modulation method of FIG. 9 Alternatively, it may be implemented with the DFT-S-OFDM (DFT spread OFDM) system 1000 of FIG. 10.

Tables 1 and 2 show the combination of three bits (b ₁ , b ₂ , b ₃ ) of input data and the sign R for the rotation angle of [Equation 2]. Among the bits included in the input data, b ₀ determines a complex array configuration for MIMO antenna diversity. That is, the information of bit b ₀ is inserted into the Alamouti code of the MIMO system and transmitted.

,

))를 보여준다. 즉, 1^st Sequence 는

이며 2^nd Sequence는

이다. In-Phase는 동위상, Q-Phase는 직교 위상을 나타낸다.Table 1 shows the results calculated through [Equation 7] and [Equation 8] at the even nibble time (the first complex pair (

,

)). That is, 1 ^st Sequence is

^{And the} 2nd Sequence is

to be. In-Phase represents in-phase and Q-Phase represents orthogonal phase.

,

))를 보여준다. 즉, 1^st Sequence 는

이며 2^nd Sequence는

이다. In-Phase는 동위상, Q-Phase는 직교 위상을 나타낸다. Table 2 shows the results calculated through [Equation 9] and [Equation 10] at odd nibble times (the second complex pair (

,

)). That is, 1 ^st Sequence is

^{And the} 2nd Sequence is

to be. In-Phase represents in-phase and Q-Phase represents orthogonal phase.

Each of the complex number sequences in Tables 1 and 2 shows that the change in the sequence of the first complex number and the second complex number corresponds to different quaternions and is divided into 16 QPSK symbols. In addition, by limiting Zero Crossing (Zero Passing) during two QPSK symbol sequences through QDMZC decomposition in all 16 cases, it reduces the peak power-to-average power ratio (PAPR), which is the main performance indicator of the terminal, to extend the battery use time. You will be able to.

2 is a flowchart illustrating a quaternion decomposition method according to an embodiment of the present invention.

The quaternion decomposition device 10 acquires input data (S210). Here, the input data may be 4-bit data composed of (b ₀ , b ₁ , b ₂ , b ₃ ), and each bit information may be composed of 1 or -1.

)를 생성한다(S220). 쿼터니언 분해장치(10)는 입력 데이터에 포함된 3 비트 정보(b₁, b₂, b₃)를 이용하여 쿼터니언 벡터(

)를 생성한다.The quaternion decomposition device 10 uses the input data to provide a quaternion vector (

) Is generated (S220). The quaternion decomposition device 10 uses 3-bit information (b ₁ , b ₂ , b ₃ ) included in the input data, and uses the quaternion vector (

).

The quaternion decomposition apparatus 10 checks the nibble time zone from which the input data was acquired (S230), and calculates a rotation angle (*?*φ) to rotate the complex number plane based on some information of the input data and the nibble time zone (S240). ). Specifically, when the quaternion decomposition device 10 generates two consecutive complex numbers, whether the value obtained by multiplying two bit information (b ₁ , b ₃ ) of the input data and the nibble time is an even nibble time or an odd nibble time Calculate the rotation angle according to.

)을 계산한다(S240). 구체적으로, 쿼터니언 분해장치(10)는 두 개의 연속된 복소수를 생성한다고 할 때 입력 데이터 중 두 개의 비트정보(b₁, b₃)를 곱한 값과 니블 시간이 짝수 니블 시간 또는 홀수 니블 시간인지 여부에 따라 회전각을 계산한다.The quaternion decomposition device 10 checks the nibble time zone in which the input data was acquired (S230), and a rotation angle to rotate the complex number plane based on some of the input data and the nibble time zone (

) Is calculated (S240). Specifically, when the quaternion decomposition device 10 generates two consecutive complex numbers, whether the value obtained by multiplying two bit information (b ₁ , b ₃ ) of the input data and the nibble time is an even nibble time or an odd nibble time Calculate the rotation angle according to.

)와 계산된 회전각(

)을 이용하여 회전시킬 복소 평면을 선택하고, 선택된 복소 평면에 쿼터니언 벡터(

)를 투영시킨다(S250). 쿼터니언 분해장치(10)는 니블 시간에 근거하여 초 복소평면 중 하나의 복소 평면을 선택하고, 선택된 복소 평면에 회전각을 기반으로 쿼터니언 벡터(

)를 투영시켜 제1 복소수(

)를 계산한다.The quaternion decomposition device 10 is a quaternion vector (

) And the calculated rotation angle (

) To select a complex plane to be rotated, and a quaternion vector (

) Is projected (S250). The quaternion decomposition device 10 selects one of the super-complex planes based on the nibble time, and the quaternion vector (

) By projecting the first complex number (

) Is calculated.

)를 계산하고, 짝수 니블 시간 또는 홀수 니블 시간인지 여부에 따라 서로 다른 평면으로 투영한다. 쿼터니언 분해장치(10)는 짝수 니블 시간에 해당하는 경우 쿼터니언 벡터(

)를 제1 평면(I-J Plane)으로 투영시킨 제1 평면 복소수(

)를 출력하고, 홀수 니블 시간에 해당하는 경우 쿼터니언 벡터(

)를 제2 평면(K-J Plane)으로 투영시킨 제2 평면 복소수(

)를 출력한다.The quaternion decomposition device 10 uses a j-axis rotor to provide a first complex number (

) Is calculated and projected onto different planes depending on whether it is an even nibble time or an odd nibble time. When the quaternion decomposition device 10 corresponds to the even nibble time, the quaternion vector (

) Projected onto the first plane (IJ Plane)

), and the quaternion vector (

) Projected onto the second plane (KJ Plane)

) Is displayed.

)을 서로 다른 방향으로 회전시켜 제1-1 평면 복소수(

) 및 제1-2 평면 복소수(

)를 포함하는 제1 복소 쌍(

,

)을 계산한다(S270, S272).In the case of an even number of nibble times (S260), the quaternion decomposition device 10 has a complex number of first planes (

) By rotating in different directions,

) And 1-2 plane complex numbers (

A first complex pair (

,

) Is calculated (S270, S272).

)를 서로 다른 방향으로 회전시켜 제2-1 평면 복소수(

) 및 제2-2 평면 복소수(

)를 포함하는 제2 복소 쌍(

,

)을 계산한다(S280, S282).On the other hand, in the case of an odd nibble time (S260), the quaternion decomposition device 10 has a second planar complex number (

) To rotate in different directions to create a complex 2-1 plane (

) And 2-2 plane complex numbers (

A second complex pair containing (

,

) Is calculated (S280, S282).

,

) 및 제2 복소 쌍 (

,

) 중 적어도 하나를 선택하여 쿼터니언 분해 심볼(

,

)을 출력부를 통해 출력되도록 한다(S290).The quaternion decomposition device 10 is a first complex pair (

,

) And the second complex pair (

,

) By selecting at least one of the quaternion decomposition symbols (

,

) To be output through the output unit (S290).

In FIG. 2, it is described that each step is sequentially executed, but is not limited thereto. In other words, since it is possible to change and execute the steps illustrated in FIG. 2 or execute one or more steps in parallel, FIG. 2 is not limited to a time-series order.

The quaternion decomposition method according to this embodiment illustrated in FIG. 2 may be implemented as an application (or program) and recorded on a recording medium that can be read by a terminal device (or computer). The application (or program) for implementing the quaternion decomposition method according to the present embodiment is recorded, and the recording medium that can be read by the terminal device (or computer) is any type of recording device that stores data that can be read by the computing system or Includes the medium.

3 is a flowchart illustrating a demodulation operation according to quaternion decomposition according to an embodiment of the present invention.

3 illustrates a demodulation operation for estimating a quaternion vector based on a transmission signal modulated by a quaternion decomposition method. Here, the demodulation operation will be described by taking the MIMO system of FIG. 8 as an example.

The receiving device checks the nibble time zone through the synchronized internal clock or pilot signal (S310). The receiving device checks the even QDMZC symbol time zone and the odd QDMZC symbol time zone.

Thereafter, the receiving device estimates b ₀ (S320).

,

로 정의한다. RX₁과 RX₂는 수신 안테나 1 과 2로 정의한다.8, the channel parameters of RX ₁ and RX ₂

,

Is defined as RX ₁ and RX ₂ are defined as receiving antennas 1 and 2.

, 노이즈 성분을

로 정의하고, 두 번째 수신 신호를

, 노이즈 성분을

로 정의한다. The first received signal received from the receiving device

, The noise component

And the second received signal

, The noise component

Is defined as

그리고 두 번째 안테나 송신 심볼을

로 정하면, 잡음을 고려 안 할 때 RX₁의 첫 번째 수신 신호를

및 RX₂의 첫 번째 수신 신호를

로 가정할 수 있다. When the bit information (b ₀ ) is inserted in the Alamouti code of the MIMO system, the first antenna transmission symbol is

And the second antenna transmit symbol

If it is set to, the first received signal of RX ₁ is

And the first received signal of RX ₂

Can be assumed.

및 RX₂의 두 번째 수신 신호를

로 가정 할 수 있다. 이를 안테나 별 수신 신호 모델로 표현하면 수신 장치에서 첫 번째 수신 신호를

로 두 번째 수신 신호는

로 표현 할 수 있다.Also, when noise is not considered, the second received signal of RX ₁ is

And the second received signal of RX ₂

Can be assumed If this is expressed as a received signal model for each antenna, the first received signal is

The second received signal is

It can be expressed as

)과 안테나(TX₂)의 두 번째 수신 심볼 (

)복소수 곱셈을 하면 [수학식 11]과 같이 b₀의 부호를 추정할 수 있다. 또한 수신 장치는 안테나(TX₁)의 두 번째 수신 심볼(

)과 안테나(TX₂)의 첫 번째 수신 심볼 (

) 복소수 곱셈을 하면 - b₀의 부호를 추정할 수 있다. sgn 함수는 부호 함수이다.The receiving device is the first receiving symbol of the antenna (TX ₁ ) (

) And the second received symbol of the antenna (TX ₂ ) (

) By performing complex multiplication, the sign of b ₀ can be estimated as shown in [Equation 11]. In addition, the reception apparatus receives the second symbol of the antenna (TX ₁₎ (

) And the first received symbol of the antenna (TX ₂ ) (

) By multiplying a complex number, the sign of-b ₀ can be estimated. The sgn function is a sign function.

,

)을 추정한다(S330).The receiving device is the received quaternion decomposition symbol (

,

) Is estimated (S330).

Channel parameters can be defined as in [Equation 12].

는 노이즈 성분이며,

은 b₀의 추정치이다.The received signal model considering b ₀ is expressed by [Equation 13]. From here

Is the noise component,

Is an estimate of b ₀ .

,

)은 [수학식 14]으로 표현된다.The estimated quaternion decomposition symbol based on the received signal model (

,

) Is expressed by [Equation 14].

)를 추정한다(S320,S340). The receiving device is the sign of R, b ₀ , b ₁ , b ₂ , b ₃ (

) Is estimated (S320, S340).

Rb is set as a variable for estimating R in [Equation 2].

데이터에서 직교 위상 성분의 norm이 동위상 성분의 norm 보다 크면,

인 것으로 추정하고,

데이터에서 동위상 성분의 norm이 직교 위상 성분의 norm 보다 크면,

인 것으로 추정한다. 또한, 수신 장치는

데이터와,

데이터로부터 다음의 비트들의 부호를 추정할 수 있다.The receiving device is

If the norm of the quadrature component in the data is greater than the norm of the in-phase component,

Is assumed to be

If the norm of the in-phase component in the data is greater than the norm of the quadrature component,

Is assumed to be. Also, the receiving device

With data,

The signs of the following bits can be estimated from the data.

을 추정하고

과

의 곱을 통하여 회전각의 부호

을 추정한다.The receiving device is the sign of b ₂ through the sign of the orthogonal phase component.

To estimate

and

The sign of the rotation angle through the product of

Estimate

을, 홀수 QDMZC 심볼 시간대면 b₃의 부호

을 추정한다.In addition, the receiving device uses the code of the in-phase component, the code of b _{1 in} the even QDMZC symbol

The sign of b _{3 in} the time zone of odd QDMZC symbols

Estimate

을 통하여 b₁b₃ 부호의 추정치

을 구할 수 있다.In addition, the receiving device is [Equation 2] and

The estimate of the sign of b ₁ b ₃ through

Can be obtained.

, 홀수 QDMZC 심볼 시간대면

을 추정하였으므로 추정치

을 통하여 남은 비트를 추정할 수 있는데, 이들은 [수학식 7], [수학식 8], [수학식 9] 및 [수학식 10]의 회전자에서 사용되는 부호들 즉, 짝수 QDMZC 심볼 시간대면

을, 홀수 QDMZC 심볼 시간대면

을 추정한다.Receiving device time zone with even QDMZC symbols

, Odd QDMZC symbol time-to-face

Is estimated, so the estimate

The remaining bits can be estimated through Equation 7, Equation 8, Equation 9, and Equation 10, that is, the even QDMZC symbol time-to-face

, Odd QDMZC symbol time-to-face

Estimate

을 [수학식 15]와 같이 추정 한다(S350). [수학식 15]는 [수학식 14]으로부터 추정된

와

으로부터 정의된다. The receiving device is

Is estimated as in [Equation 15] (S350). [Equation 15] is estimated from [Equation 14]

Wow

Is defined from

을 추정한다(S360).

은 짝수 QDMZC 심볼 시간 대일 경우 [수학식 16]를 통해 추정되고, 홀수 QDMZC 심볼 시간 대일 경우 [수학식 17]을 통해 추정한다. Thereafter, the receiving device

Is estimated (S360).

In the case of the even QDMZC symbol time zone, it is estimated through [Equation 16], and in the case of the odd QDMZC symbol time zone, it is estimated through [Equation 17].

를 통하여 각 비트들의 크기 값을 추정하고, 추정된 부호들을 검증할 수 있다. 따라서 (S340)에서 R이 추정되면 [수학식 15], [수학식 16], 및 [수학식 17]을 통하여 바로

,

을 추정할 수도 있다.The receiving device is an estimated quaternion vector

The size value of each bit can be estimated through and the estimated codes can be verified. Therefore, if R is estimated in (S340), immediately through [Equation 15], [Equation 16], and [Equation 17]

,

Can also be estimated.

라 하면, 전송 다이버시티 이득은 Alamouti type codeword in which a specific bit is inserted

If d, the transmit diversity gain is

이다.

이므로

로 표현되고 전송 다이버시티 이득 2가 확인 된다.

는 C의 Hermitian 행렬, I₂는 2x2 단위 행렬이다.

to be.

Because of

And the transmit diversity gain 2 is confirmed.

Is a Hermitian matrix of C, and I ₂ is a 2x2 identity matrix.

4 is a view showing a quaternion rotor according to an embodiment of the present invention.

4 shows the rotors that rotate three (I, J, K) axes.

또는

으로 정의될 수 있고, k 축 회전자는

또는

으로 정의될 수 있다. 또한, i 축 회전자는

또는

으로 정의될 수 있다.When expressing the predetermined point shown in Fig. 4, the j-axis rotor is

or

Can be defined as, and the k-axis rotor is

or

Can be defined as Also, the i-axis rotor is

or

Can be defined as

5 shows a three-dimensional quaternion space according to an embodiment of the present invention.

As shown in FIG. 5, the I-J Plane 510 and the K-J Plane 520 are formed at right angles to each other and represent a three-dimensional quaternion space composed of two complex planes.

The quaternion decomposition device 10 rotates the quaternion in a three-dimensional quaternion space to project it onto a complex number plane, and rotates the complex number projected from the complex number plane twice in different directions to calculate a complex number pair having a predetermined sequence. Perform the action

6 is a view for explaining that two complex number pairs are formed based on a quaternion vector according to an embodiment of the present invention.

)로부터 두 복소수 쌍이 형성 되는 것을 나타낸다. 예를 들어, 입력 데이터의 (b₁, b₂, b₃)가 (1, 1, 1)일 경우, I-J 복소 평면으로 45도 회전하여 ①에 투영되어 제1 복소수(

)가 계산되고, 제1 복소수(

)를 쿼터니언 회전자를 통하여 서로 다른 방향으로 두 번의 회전을 하여 ②와 ③에 해당하는 복소수 쌍(

,

)이 각각 계산된다. 여기서, 복소수 쌍은 쿼터니언 분해 심볼일 수 있다. 6 shows a quaternion vector in the super complex plane (

It indicates that two pairs of complex numbers are formed from ). For example, if (b ₁ , b ₂ , b ₃ ) of the input data is (1, 1, 1), it is rotated 45 degrees to the IJ complex plane and projected to ①, and the first complex number (

) Is calculated, and the first complex number (

) Is rotated twice in different directions through the quaternion rotor, and a pair of complex numbers corresponding to ② and ③ (

,

) Are each calculated. Here, the complex number pair may be a quaternion decomposition symbol.

7 is a diagram illustrating an operation of generating pairs of complex numbers in different orders from the same projection point according to an embodiment of the present invention.

)를 계산한다. 여기서, 쿼터니언 분해장치(10)는 제1 복소수(

)를 이용하여 서로 다른 순서의 복소수 쌍을 생성할 수 있다. Referring to FIG. 7, the quaternion decomposition device 10 projects a first complex number (

) Is calculated. Here, the quaternion decomposition device 10 is a first complex number (

) Can be used to generate pairs of complex numbers in different orders.

)가 계산되고, 제1 복소수(

)를 k 축 회전자를 통하여 서로 다른 방향으로 두 번의 회전을 하여 ②와 ③에 해당하는 복소수 쌍 (0, 1), (1, 0)이 각각 계산된다. In Fig. 7 (a), when (b ₁ , b ₂ , b ₃ ) of the input data is (1, 1, 1), the quaternion decomposition device 10 rotates 45 degrees to the IJ complex plane and is projected to ①. The first complex number (

) Is calculated, and the first complex number (

) Is rotated twice in different directions through the k-axis rotor to calculate the complex number pair (0, 1) and (1, 0) corresponding to ② and ③, respectively.

)가 계산되고, 제1 복소수(

)를 k 축 회전자를 통하여 서로 다른 방향으로 두 번의 회전을 하여 ②와 ③에 해당하는 복소수 쌍 (1, 0), (0, 1)이 각각 계산된다. On the other hand, in (b) of FIG. 7, when (b ₁ , b ₂ , b ₃ ) of the input data is (1, 1, -1), the IJ complex plane is rotated by -45 degrees. It is projected onto ① and is the first complex number (

) Is calculated, and the first complex number (

) Is rotated twice in different directions through the k-axis rotor to calculate the complex number pair (1, 0) and (0, 1) corresponding to ② and ③, respectively.

8 is an exemplary diagram showing the configuration of a 2X2 MIMO diversity antenna according to an embodiment of the present invention.

,

)을 획득하고, 획득된 쿼터니언 분해 심볼(

,

)을 조합하여 출력한다. 도 8에서는 입력 데이터에 포함된 특정 비트 b₀를 이용한 MIMO 다이버시티 안테나의 동작을 설명하도록 한다. When the output unit 700 according to the present embodiment is configured as a MIMO diversity antenna, the quaternion decomposition symbol (

,

), and the obtained quaternion decomposition symbol (

,

) And output. In FIG. 8, an operation of a MIMO diversity antenna using a specific bit b ₀ included in input data will be described.

,

) 및 제2 복소 쌍(

,

) 중 적어도 하나를 선택하여 쿼터니언 분해 심볼(

,

)로 정의하고,

가

보다 시간적으로 앞선 복소수라 할 때, 알라무티 코드(Alamouti Code)에 의거하여 하나의 안테나(TX₁)이 두 심볼

,

를 전송하면, 다른 안테나(TX₂)는

,

를 전송한다.In the 2x2 MIMO system shown in FIG. 8, the quaternion decomposition device 10 includes a first complex pair calculated by the first plane complex number calculation unit 400 and the second plane complex number calculation unit 500 (

,

) And the second complex pair (

,

) By selecting at least one of the quaternion decomposition symbols (

,

), and

end

In the case of a complex number that is more temporally advanced, one antenna (TX ₁ ) is two symbols based on the Alamouti Code.

,

When is transmitted, the other antenna (TX ₂ ) is

,

Transmit.

)과 안테나(TX₂)의 두 번째 수신 심볼 (

)복소수 곱셈을 하면 [수학식 11]과 같이 b₀의 부호를 추정할 수 있다.The first received symbol of the bit b ₀ of the input data and is simply possible to estimate, in particular an antenna (TX ₁₎ (

) And the second received symbol of the antenna (TX ₂ ) (

) By performing complex multiplication, the sign of b ₀ can be estimated as shown in [Equation 11].

Accordingly, in a 2x2 MIMO system to which the quaternion decomposition device 10 is applied, it is possible to demodulate so that all 16 bit combinations composed of 4 bits can be distinguished.

9 is a diagram schematically showing a quaternion decomposition apparatus applied to an 8-phase shift method according to an embodiment of the present invention.

The output unit 700 according to the present embodiment may include a phase shift modulation conversion unit 900 as shown in FIG. 9.

The phase shift modulation conversion unit 900 operating based on the 8PSK (Phase Shift Keying) modulation method transmits the signal output from the multiplexer unit 600 according to the input bit b ₀ without a phase change or rotates the phase by 45 degrees. Transmit after changing. For example, the phase shift modulation conversion unit 900

,

) 및 제2 복소 쌍(

,

) 중 적어도 하나를 선택하여 출력된 쿼터니언 분해 심볼(

,

)을 비트 b₀에 따라 +45도 혹은 -45도 회전시켜 출력 할 수 있다. 이 경우 비트 b₀가 1일 경우에는 회전하지 않고, 비트 b₀가 -1일 경우에는 45도 회전시키거나 이 반대로 구성될 수 있다. The first complex pair calculated by the first planar complex number calculation unit 400 and the second planar complex number calculation unit 500 (

,

) And the second complex pair (

,

) At least one of the output quaternion decomposition symbols (

,

) Can be output by rotating +45 degrees or -45 degrees according to bit b ₀ . In this case, when the bit b ₀ is 1, it does not rotate, and when the bit b ₀ is -1, it can be rotated 45 degrees or vice versa.

10 is a diagram schematically showing a quaternion decomposition apparatus applied to a DFT-S-OFDM according to an embodiment of the present invention.

When the output unit 700 according to the present embodiment is configured as the DFT-S-OFDM system 1000, as shown in FIG. 10, after performing QDMZC conversion mapping 1010 on the input data bits, M point DFT ( 1020).

10 shows a configuration in which the QDMZC transform mapping unit 1010 applied to the DFT-S-OFDM system is located in front of the M point DFT 1020. In this case, the subcarrier allocation can be configured differently according to the code of bit b ₀ .

11A and 11B are diagrams showing a constellation diagram and a trajectory diagram in a phase space of QDMZC and QPSK according to an embodiment of the present invention.

FIG. 11A shows the constellation points of the QDMZC method and the conventional QPSK method according to the present invention, and FIG. 11B shows the trajectory of the QDMZC method and the conventional QPSK method according to the present invention. In each figure, the x-axis shows in-phase and the y-axis shows quadrature.

It can be seen from FIGS. 11A and 11B that the QDMZC scheme according to the present invention has a smaller number of zero pass frequencies compared to the conventional QPSK.

12A and 12B are diagrams showing results of a PAPR simulation according to an embodiment of the present invention.

12A and 12B show results of a PAPR experiment according to the QDMZC method according to the present invention and the conventional QPSK method.

Referring to FIG. 12A, it can be seen that the QDMZC method 1220 according to the present invention has much better PAPR than the conventional QPSK method 1210. The x-axis of FIG. 12A shows the probability that the peak exceeds the average, and the y-axis shows the probability that the peak exceeds the average, and the smaller the number, the better the performance. In general, when HPA is selected, the back off decision is based on 0.001%. 12A, it can be seen that the QDMZC according to the present invention is 1.8 dB or more better than the conventional QPSK. This means that small capacity HPA can be selected when designing, which means that power efficiency is improved that much.

12B is a result of application to the DFT-s-OFDM system, and 64 point DFT and 256 subcarriers were used. Based on 0.001%, it can be seen that the QDMZC method 1240 according to the present invention is more than 1.1 dB better than the conventional QPSK method 1230.

Currently, the battery life of IoT terminals (based on two AA sizes) is aimed at 20 years, which means that the amount of transmitted data must be very small, and it is important to select an HPA with good power efficiency.

The above description is merely illustrative of the technical idea of the embodiments of the present invention, and those of ordinary skill in the technical field to which the embodiments of the present invention belong to, various modifications and modifications without departing from the essential characteristics of the embodiments of the present invention Transformation will be possible. Accordingly, the embodiments of the present invention are not intended to limit the technical idea of the embodiments of the present invention, but to explain, and the scope of the technical idea of the embodiments of the present invention is not limited by these embodiments. The scope of protection of the embodiments of the present invention should be interpreted by the following claims, and all technical ideas within the scope equivalent thereto should be construed as being included in the scope of the rights of the embodiments of the present invention.

10: Quaternion disassembly device
100: data collection unit 200: quaternion data conversion unit
300: quaternion rotation processing unit 400: first plane complex number calculation unit
500: second plane complex number calculation unit 600: multiplexer unit
700: output

Claims (17)

A data collection unit for obtaining input data;
A quaternion data conversion unit that calculates a quaternion vector and a rotation angle based on some information of the input data and a nibble time;
Based on the nibble time, one of the super complex planes is selected, and the quaternion vector (

) And a first complex number projected based on the rotation angle (

) A quaternion rotation processing unit that calculates;
The first complex number based on the first plane rotor (

A first planar complex number calculator configured to calculate a first complex pair by rotating) in different directions;
The first complex number (

A second planar complex number calculating unit for calculating a second complex pair by rotating) in different directions; And
By selecting at least one of the first complex pair and the second complex pair, a quaternion decomposition symbol (

,

) To be transmitted
Quaternion disassembly device comprising a. The method of claim 1,
The quaternion data conversion unit,
A quaternion vector converter configured to generate the quaternion vector by setting a value of the real part to 0 and setting three bit information of the input data to the value of the imaginary part;
A nibble time selector for selecting one of an even nibble time and an odd nibble time based on a time index of the input data; And
A rotation angle calculator configured to calculate the rotation angle using the partial information and the nibble time; And
Quaternion disassembly device comprising a. The method of claim 2,
The rotation angle calculation unit,
And determining the rotation angle according to a value obtained by multiplying two bit information of the input data and whether the nibble time is an even number or an odd number. The method of claim 1,
The quaternion rotation processing unit,
The first complex number is rotated using the third axis rotor (j axis rotor)

) Is calculated, and projected onto different planes according to whether it is an even nibble time or an odd nibble time, and the first complex number (

), characterized in that the quaternion disassembly device. The method of claim 4,
The quaternion rotation processing unit,
In the case of the even nibble time, the quaternion vector (

) Projected onto the first plane (IJ Plane)

), and if it corresponds to the odd nibble time, the quaternion vector (

) Projected onto the second plane (KJ Plane)

Quaternion disassembly device, characterized in that outputting ). The method of claim 5,
The first plane complex number calculation unit,
It includes at least two first shaft rotating parts for rotating a complex number based on a first shaft rotor (k-axis rotor), and the first plane complex number through each of the at least two first shaft rotating parts (

) In different directions to rotate the first complex pair (

,

) Quaternion decomposition device, characterized in that to calculate. The method of claim 5,
The second planar complex number calculation unit,
It includes at least two second axis rotating parts for rotating a complex number based on a second axis rotor (i-axis rotor), and the second plane complex number through each of the at least two second axis rotating units (

) To rotate in different directions to make the second complex pair (

,

) Quaternion decomposition device, characterized in that to calculate. The method according to any one of claims 6 and 7,
The multiplexer unit,
Based on the nibble time, the first complex pair (

,

) And the second complex pair (

,

) The quaternion decomposition symbol having a predetermined sequence by selecting at least one complex pair (

,

), and the determined quaternion decomposition symbol (

,

Quaternion disassembly device, characterized in that to be output through the output unit. The method of claim 1,
In consideration of specific bit information among the input data, the quaternion decomposition symbol (

,

Quaternion decomposition device, characterized in that it further comprises an output unit for converting and outputting ). The method of claim 9,
The output unit,
The quaternion decomposition symbol so that the specific bit information is inserted into an Alamouti Code of a MIMO (Multiple Input Multiple Output) system and transmitted.

,

) To convert and output the quaternion decomposition device. The method of claim 9,
The output unit,
The quaternion decomposition symbol at a certain angle according to the sign of the specific bit information (

,

Quaternion decomposition device, characterized in that to configure a phase shift (Phase Shift Keying) signal by rotating. The method of claim 9,
The output unit,
Applied to an orthogonal frequency division system, a subcarrier is selected according to the specific bit information, and the quaternion decomposition symbol (

,

) To convert and output the quaternion decomposition device. In the method for the quaternion decomposition device to decompose the quaternion,
A data collection step of obtaining input data;
A quaternion data conversion step of calculating a quaternion vector and a rotation angle based on some information of the input data and a nibble time;
Based on the nibble time, one of the super complex planes is selected, and the quaternion vector (

) And a first complex number projected based on the rotation angle (

A quaternion rotation processing step of calculating );
The first complex number based on the first plane rotor (

A first plane complex number calculation step of calculating a first complex pair by rotating) in different directions;
The first complex number (

A second plane complex number calculation step of calculating a second complex pair by rotating) in different directions; And
By selecting at least one of the first complex pair and the second complex pair, a quaternion decomposition symbol (

,

) To be transmitted
Quaternion decomposition method comprising a. The method of claim 13,
The quaternion rotation processing step,
The first complex number (

) Is calculated, and projected onto different planes according to whether it is an even nibble time or an odd nibble time, and the first complex number (

), characterized in that the quaternion decomposition method. The method of claim 14,
The quaternion rotation step,
In the case of the even nibble time, the quaternion vector (

) Projected onto the first plane (IJ Plane)

), and if it corresponds to the odd nibble time, the quaternion vector (

) Projected onto the second plane (KJ Plane)

Quaternion decomposition method, characterized in that outputting ). The method of claim 15,
The step of calculating the first complex plane number,
It includes at least two first shaft rotation units for rotating a complex number with respect to a first axis rotor, and the first plane complex number through each of the at least two first axis rotation units (

) In different directions to rotate the first complex pair (

,

) Quaternion decomposition method, characterized in that to calculate. The method of claim 15,
The step of calculating the second planar complex number,
It includes at least two second shaft rotation units for rotating a complex number with respect to the second axis rotor, and the second plane complex number through each of the at least two second axis rotation units (

) To rotate in different directions to make the second complex pair (

,

) Quaternion decomposition method, characterized in that to calculate.

Images