Method and apparatus for constellation design based on stepped hierarchical modulation

Abstract

Disclosed are a method and an apparatus for a constellation design based on stepped hierarchical modulation. According to the present invention, there is provided an apparatus for a constellation design based on stepped hierarchical modulation comprising a processor and a memory connected to the processor, wherein the memory stores program instructions to be executed by the processor so as to generate an initial constellation including M (M is a natural number) signal points based on stepped θ-QAM, set a constellation parameter to control a degree of data protection, move signal points located in an m-th quadrant by a preset distance in a preset direction by applying the constellation parameter to the initial constellation, and map information bits encoded in the moved signal points.

Claims

1. An apparatus for a constellation design based on stepped hierarchical modulation, the apparatus comprising: a processor; and a memory connected to the processor, wherein the memory stores program instructions to be executed by the processor so as to: generate an initial constellation including M signal points based on stepped θ-QAM, wherein M is a natural number; set a constellation parameter to control a degree of data protection; move signal points located in an m-th quadrant by a preset distance in a preset direction by applying the constellation parameter to the initial constellation, wherein m is 1, 2, 3 or 4; and map information bits encoded in the moved signal points, wherein the constellation parameter is determined according to the following Equation: $a=\frac{d_h}{d_l},$ wherein α is a constellation parameter of α≥1, 2d.sub.h is a minimum distance between two signal points located in adjacent quadrants, and 2d.sub.l is a minimum distance between two signal points located in the same quadrant.

2. The apparatus of claim 1, wherein the encoded information bits mapped to the signal points have two high-priority (HP) bits.

3. The apparatus of claim 2, wherein the two HP bits are allocated to the most significant bit as 00, 10, 11, and 01 at signal points located in each quadrant 1, 2, 3, or 4, respectively.

4. The apparatus of claim 3, wherein in the program instructions, the remaining bits except for the most significant bit are mapped through a layer labeling algorithm, which is a suboptimal algorithm for minimizing a Hamming distance between the signal points.

5. An apparatus for a constellation design based on stepped hierarchical modulation, the apparatus comprising: a processor; and a memory connected to the processor, wherein the memory stores program instructions to be executed by the processor so as to: generate an initial constellation including M signal points based on stepped θ-QAM, wherein M is a natural number; set a constellation parameter to control a degree of data protection; move signal points located in an m-th quadrant by a preset distance in a preset direction by applying the constellation parameter to the initial constellation, wherein m is 1, 2, 3 or 4; and map information bits encoded in the moved signal points, wherein the signal points located in the m-th quadrant are moved by (λ.sub.x(m), λ.sub.y(m)) by the constellation parameter, wherein (λ.sub.x(m), λ.sub.y(m)) is determined according to the following Equation:
(λ.sub.x(m),λ.sub.y(m))=((−1).sup.└m/2┘λ,(−1).sup.└(m+1)/2┘+1λ),m=1,2,3,4, wherein, λ is a shifting factor of λ≥0 and └⋅┘ is a floor function.

6. The apparatus of claim 5, wherein the constellation parameter is determined differently according to θ in the same λ and d.sub.l (2d.sub.l is a minimum distance between two signal points located in the same quadrant).

7. A method for designing a constellation based on stepped hierarchical modulation in an apparatus comprising a processor and a memory, the method comprising: generating an initial constellation including K signal points based on stepped θ-QAM, wherein K is a natural number; setting a constellation parameter to control a degree of data protection; moving signal points located in an m-th quadrant by a preset distance in a preset direction by applying the constellation parameters to the initial constellation, wherein m is 1, 2, 3 or 4; and mapping information bits encoded in the moved signal points, wherein the constellation parameter is determined according to the following Equation: $a=\frac{d_h}{d_l},$ wherein α is a constellation parameter of α≥1, 2d.sub.h is a minimum distance between two signal points located in adjacent quadrants, and 2d.sub.l is a minimum distance between two signal points located in the same quadrant.

8. The method of claim 7, wherein the encoded information bits mapped to the signal points have two high-priority (HP) bits.

9. A non-transitory computer readable medium configured to store a program for performing the method according to claim 7.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other features of the present invention will now be described in detail with reference to certain exemplary embodiments thereof illustrated the accompanying drawings which are given hereinbelow by way of illustration only, and thus are not limitative of the present invention.

(2) FIG. 1 is a diagram illustrating a configuration of an apparatus for a constellation design based on stepped hierarchical modulation according to a preferred embodiment of the present invention.

(3) FIG. 2 is a diagram illustrating signal points and coordinate pairs of a 64-ary stepped θ-QAM.

(4) FIGS. 3A-3D are diagrams illustrating a stepped θ-based constellation designed according to a modulation order M when α=2, θ=60°.

(5) FIG. 4 is a diagram illustrating bit mapping of 4/64-stepped θ-QAM when α=2, θ=60°.

(6) It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various preferred features illustrative of the basic principles of the invention. The specific design features of the present invention as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes will be determined in part by the particular intended application and use environment.

(7) In the figures, reference numbers refer to the same or equivalent parts of the present invention throughout the several figures of the drawing.

DETAILED DESCRIPTION

(8) In the present invention, various modifications may be made and various embodiments may be provided, and specific embodiments will be illustrated in the drawings and described in detail.

(9) However, it is not intended to limit the present invention to a specific embodiment, and it is to be understood to cover all changes, equivalents, and substitutes included in the spirit and scope of the present invention.

(10) Stepped hierarchical quadrature amplitude modulation (stepped θ-QAM, hereinafter referred to as stepped hierarchical modulation) is known to exhibit superior performance to SQAM in terms of average symbol energy and error probability.

(11) The present invention proposes a scheme for designing a constellation and transmitting data based on such stepped hierarchical modulation.

(12) FIG. 1 is a diagram illustrating a configuration of an apparatus for a constellation design based on stepped hierarchical modulation according to a preferred embodiment of the present invention.

(13) As illustrated in FIG. 1, the apparatus according to the present embodiment may include a processor 100 and a memory 102.

(14) The processor 100 may include a central processing unit (CPU) capable of executing a computer program or other virtual machines.

(15) The memory 102 may include a nonvolatile storage device such as a fixed hard drive or a removable storage device. The removable storage device may include a compact flash unit, a USB memory stick, or the like. The memory 102 may also include volatile memories such as various random access memories.

(16) Program instructions executable by the processor 100 are stored in such a memory 102.

(17) The program instructions according to the embodiment generate an initial constellation including K (K is a natural number) signal points based on stepped θ-QAM, set a constellation parameter to control a degree of data protection, move signal points located in an m-th quadrant by a preset distance in a preset direction by applying the constellation parameter to the initial constellation, and map information bits encoded in the moved signal points.

(18) According to the embodiment, the encoded information bits mapped to the signal points have two high-priority (HP) bits, and in this case, the two HP bits may be allocated to the most significant bit as 00, 10, 11, and 01 at signal points located in each quadrant 1, 2, 3, or 4, respectively.

(19) Hereinafter, a process of designing a constellation based on stepped hierarchical modulation according to the embodiment will be described in detail with reference to the drawings and Equations.

(20) First, a set of signal points located in an m-th quadrant is assumed as S.sub.m.

(21) Here, an initial value of S.sub.m is set as a signal point according to the stepped θ-QAM-based constellation, and respective signal points are denoted as S.sub.m.sup.1, S.sub.m.sup.2, . . . , S.sub.m.sup.p in order of from left to right and from top to bottom.

(22) The stepped θ-QAM-based constellation has p=M/4 due to the same number of signal points in each quadrant, and coordinate pairs of an arbitrary signal point s.sub.m.sup.q are denoted as (x.sub.m.sup.q, y.sub.m.sup.q).

(23) FIG. 2 is a diagram illustrating signal points and coordinate pairs of 64-ary stepped θ-QAM.

(24) According to the embodiment, a constellation parameter α for controlling a relative degree of data protection is set.

(25) The constellation parameter according to the embodiment is defined as follows.

(26) $\begin{array}{cc}a=\frac{d_h}{d_l}& \left[\mathrm{Equation}1\right]\end{array}$

(27) Wherein, 2d.sub.h is a minimum distance between two signal points located in adjacent quadrants, 2d.sub.l is a minimum distance between two signal points located in the same quadrant, and α is a constant of α≥1.

(28) According to the embodiment, a constellation based on stepped quadrature amplitude modulation (QAM) to which the constellation parameter as described above is applied is designed.

(29) To this end, the signal points located in the m-th quadrant are moved by (λ.sub.x(m), λ.sub.y(m)), wherein (λ.sub.x(m), λ.sub.y(m)) is calculated as follows.
(λ.sub.x(m),λ.sub.y(m))=((−1).sup.└m/2┘λ,(−1).sup.└(m+1)/2┘+1λ),m=1,2,3,4  [Equation 2]

(30) λ is a shifting factor of λ≥0 and └⋅┘ is a floor function.

(31) In the case of the stepped θ-QAM, a lattice structure of the constellation forms a triangle, and according to the embodiment, the constellation parameter is determined differently according to θ in the same λ and d.sub.l (2d.sub.l is a minimum distance between two signal points located in the same quadrant).

(32) This is generalized as follows according to the constellation design parameter θ.

(33) $\begin{array}{cc}a=\{\begin{array}{cc}\frac{\sqrt{d_l^2+2\lambda d_l\sin \left(\theta /2\right)+{\lambda }^2}}{d_l},& 0<\theta \le \frac{\pi }{3}\\ \frac{\sqrt{d_l^2(1-\cos \left(\theta \right)+2\lambda d_l(1-\cos \left(\theta \right)+{\lambda }^2}}{d_l},& \frac{\pi }{3}<\theta \le f\left(d_i,\lambda \right)\\ \frac{\sqrt{d_l^2+2\lambda d_l\sin \theta +{\lambda }^2}}{d_l},& f\left(d_i,\lambda \right)<\theta \le \frac{\pi }{2}\end{array}& \left[\mathrm{Equation}3\right]\end{array}$

(34) Wherein, f(d.sub.l;λ) is calculated as follows.

(35) $\begin{array}{cc}f\left(d_i,\lambda \right)={\sin }^{-1}\left[\frac{\lambda d_l+2{\lambda }^2+\left(d_l+\lambda \right)\sqrt{3d_l^2+4\lambda d_l+4{\lambda }^2}}{2\left(d_l^2+2\lambda d_l+2{\lambda }^2\right)}\right]& \left[\mathrm{Equation}4\right]\end{array}$

(36) According to the embodiment, as α is increased, the degree of protection for the base layer is increased.

(37) FIGS. 3A-3D are diagrams illustrating a stepped θ-based constellation designed according to a modulation order M when α=2, θ=60°, and illustrate cases of K=64, 256, 1024, and 4096, respectively.

(38) As illustrated in FIGS. 3A-3D, the stepped θ-QAM-based constellation has 4-QAM as a base layer, and as the modulation order M increases, the shape of the constellation becomes stepped.

(39) According to the embodiment, since the encoded information bits mapped to the signal points are set to have two high priority (HP) bits, it is referred to as 4/M-stepped θ-QAM.

(40) In order to use the designed constellation for data transmission, bits need to be mapped to each symbol in an appropriate method.

(41) Optimal bit mapping may be derived by finding the bit mapping with a minimum average Hamming distance through enumeration survey, but since the optimal bit mapping includes the number of M cases, it is impossible to be actually implemented as the modulation order increases.

(42) Accordingly, according to an embodiment of the present invention, the bit mapping of 4/M-stepped θ-QAM is derived by applying a layer labeling algorithm, which is a suboptimal algorithm for minimizing a Hamming distance between adjacent symbols.

(43) Since the 4/M-stepped θ-QAM has 4-QAM as the base layer, first, two bits are allocated to the most significant bit so as to be gray-mapped.

(44) That is, 00, 10, 11, and 01 are allocated to the most significant bit in each quadrant 1, 2, 3, or 4.

(45) Next, log.sub.2 M−2 bits are mapped to each signal point (symbol) over four steps.

(46) In the bit mapping, N.sub.b is defined as the number of bits per symbol, N.sub.Q=floor(N.sub.b/2), N.sub.I=N.sub.b−N.sub.Q.

(47) First, the maximum number of 2.sup.N.sup.Q symbols close to a quadrature axis (vertical axis) is selected from each row of 2.sup.N.sup.Q close to an in-phase axis (horizontal axis).

(48) Second, the same bit is mapped to symbols having the same quadrature value for front N.sub.Q−2 bits of the selected symbols, and gray-mapped between symbols of adjacent rows.

(49) Third, the gray mapping is performed between symbols having the same quadrature value and between symbols of adjacent rows for upper N.sub.I bits of the previously selected symbols.

(50) Fourth, bits are mapped to the remaining symbols so that the Hamming distance between adjacent symbols is minimized.

(51) FIG. 4 illustrates bit mapping of 4/64-stepped θ-QAM when α=2, θ=60°.

(52) The above-described embodiments of the present invention are disclosed for the purpose of illustration, and it should be understood to those skilled in the art that various modifications, changes, and additions will be made within the spirit and scope of the present invention, and these modifications, changes and additions belong to the appended claims.