Abstract:
Disclosed is a bits-to-symbol mapping method of 4+12+16 amplitude phase shift keying (APSK) having excellent performance against the non-linearity of a high power amplifier. According to the present invention A bits-to-symbol mapping method of 4+12+16 APSK modulation, comprising: representing 32 symbols of the 4+12+16 APSK modulation by a polar coordinate and arranging the 32 symbols by a size of θ while giving priority to a symbol having a small signal size when the size of θ of two or more symbols are same; grouping the arranged 32 symbols into 4 groups according to quadrant regions where the symbols are located; and allocating bits so that the same bits are allocated to the symbols belonging to the same region for each region with respect to each of the first to fifth bits of the symbols grouped into four regions.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2009-0127731, filed on Dec. 21, 2009, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference in its entirety. 
     TECHNICAL FIELD 
     The present disclosure relates to a bits-to-symbol mapping method for 4+12+16 amplitude phase shift keying (APSK) modulation, and more particularly, to a bits-to-symbol mapping algorithm for the 4+12+16 APSK having excellent performance against non-linearity of a high power amplifier. 
     BACKGROUND 
     In a digital video broadcasting-satellite 2 (DVB-S2) standard for a broadband satellite communication broadcast convergence service suitable for a Ka band, bits-to-symbol mapping for 4+12+16 APSK modulation is as shown in  FIG. 1 . 
     In the bits-to-symbol mapping, mapping regions for each bit (b h , h=1, 2, . . . , 5) are shown in  FIGS. 2A to 2E . At this time the left-most bit is a first bit (b 1 ), that is, a most significant bit (MSB). 
     The above-mentioned related art has several problems. Since the 4+12+16 APSK modulation of the DVB-S2 is impossible to perform a gray bits-to-symbol mapping, the bit error probability performance may be varied according to the bits-to-symbol mapping algorithm and since signal constellation is formed of three different amplitudes, the bit error performance is changed due to an effect on non-linearity of the high power amplifier. 
     As can be appreciated from  FIGS. 2A to 2E , the bits-to-symbol mapping proposed in the existing standards applies a decision region-based bits-to-symbol algorithm to each bit. However, the bits-to-symbol mapping type of each bit is not symmetrical to I/Q axes and a Hamming distance between adjacent symbols is up to 3 as can be appreciated from  FIG. 1 . As shown in  FIG. 3 , when a set of signal constellations on an inner circle is s I ={s 4 , s 12 , s 20 , s 28 }, a set of signal constellations on an intermediate circle is s M ={s 2 , s 5 , s 8 , . . . , s 32 }, and a set of signal constellations on an outer circle is s O ={s 1 , s 3 , s 6 , . . . , s 31 }, the maximum Hamming distance according to the standard bits-to-symbol algorithm shown in  FIG. 1  depends on the following Equation 1.
 
 H   —   d ( s   5   ,s   6 )= H   —   d ( s   21   ,s   22 )=3  [Equation 1]
 
     Since the bit error probability is inversely proportional to the Hamming distance between adjacent symbols, the Hamming distance of 3 is a direct factor of the error performance deterioration.  FIG. 3  shows the signal constellations according to the 4+12+16 APSK modulation using input backoff of 9 dB and the effect of the non-linear high power amplifier (HPA), and the change in the signal constellation and the decision boundary accordingly. When there is non-linearity due to the AM/AM and AM/PM distortions of the high power amplifier, it can be appreciated from  FIG. 3  that the positions of the signal constellations are changed. In other words, it can be appreciated that the signal constellations of the intermediate circle approaches the signal constellations of the outer circle. This means that a Euclidean distance is short and the shortened Euclidean distance causes the degradation of the error performance. In particular, reviewing the Euclidean distance of the signal constellations having the above-mentioned Hamming distance at maximum of 3, it can be appreciated that the Euclidean distance thereof is closest. This is a main factor of the deterioration of the entire bit error performance. 
     SUMMARY 
     The present invention proposes to solve the above problem. It is an object of the present invention to improve bit error performance by performing bits-to-symbol mapping so that a Hamming distance between signal constellations approaching each other due to non-linear characteristic of HPA becomes minimal. 
     In order to achieve the above-mentioned objects, there is provided a bits-to-symbol mapping method of 4+12+16 APSK modulation, including: representing 32 symbols of the 4+12+16 APSK modulation by a polar coordinate and arranging the 32 symbols by a size of θ while giving priority to a symbol having a small signal size when the size of θ of two or more symbols are same; grouping the arranged 32 symbols into 4 groups according to quadrant regions where the symbols are located; and allocating bits so that the same bits are allocated to the symbols belonging to the same region for each region with respect to each of the first to fifth bits of the symbols grouped into four regions. 
     Preferably, when allocating the bits, bits may be allocated so that the bits-to-symbol mapping of the third to the fifth bits of each symbol are symmetrical to Quadrature axis and In-phase axis, the bit difference between all the adjacent symbols forming a decision boundary is 1 bit or 2 bits, and a Hamming distance between all the adjacent symbols is a minimum value. 
     According to an exemplary embodiment of the present invention, the bit error performance can be improved by performing the bits-to-symbol mapping so that the Hamming distance between the signal constellations approaching each other due to the non-linear characteristic of the HPA becomes minimal. 
     According to an exemplary embodiment of the present invention, the bit difference between all the adjacent symbols forming the decision boundary in the bits-to-symbol mapping of the 4+12+16 APSK modulation is only 1 bit or 2 bits and in particular, the Hamming distance of two pairs of signals positioned on a diagonal line having a large Hamming distance is 1, which is the minimum distance. 
     In addition, the mapping type of the third, fourth, and fifth bits meets the I/Q symmetry, thereby making it possible to further simplify the structure of the receiver and reduce the load of the receiver. 
     Other features and aspects will be apparent from the following detailed description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing bits-to-symbol mapping of 4+12+16 APSK proposed in a DVB-S2 standard; 
         FIGS. 2A to 2E  are diagrams showing a bits-to-symbol algorithm proposed in the DVB-S2 standard; 
         FIG. 3  is a diagram showing signal constellations of the 4+12+16 APSK modulation and an effect of a non-linear high power amplifier (HPA), and the change in the signal constellations and the decision boundary accordingly; 
         FIGS. 4A to 4F  are diagrams showing a bits-to-symbol mapping algorithm according to an exemplary embodiment of the present invention; 
         FIG. 5  is a diagram showing bits-to-symbol mapping according to an exemplary embodiment of the present invention; and 
         FIG. 6  is a graph showing BER performance of the 4+12+16 APSK modulation according to an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience. The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. Accordingly, various changes, modifications, and equivalents of the methods, apparatuses, and/or systems described herein will be suggested to those of ordinary skill in the art. Also, descriptions of well-known functions and constructions may be omitted for increased clarity and conciseness. 
     Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings. 
     According to the present invention, bit error performance is improved by performing bit-to-symbol mapping so that a Hamming distance between the signal constellations approaching each other due to non-linear characteristic of HPA becomes minimal. 
     In  FIG. 3 , 32 symbols of 4+12+16 APSK modulation are marked in a polar coordinate system, and it can be expressed as the following Equation 2 when the symbols are arranged by a size of θ.
 
 s=[s   1   , s   2   , . . . , s   32   ], s   i   =r   i   e   jθ     i     , i= 1, 2, . . . , 32  s. t. θ   i ≦θ i+1 , 0≦θ&lt;2π  [Equation 2]
 
     Herein, if the θ sizes of the symbols are equal to each other, the symbol having a small signal size r i  is given a priority. 
     Next, the 32 symbols of a defined order which are in the possible same quadrant are grouped into 8, which are divided into four regions (R k ,k=1,2,3,4), such as illustrated in  FIG. 4F , according to the following Equation 3.
 
 R   k   =[s   8k-7    s   8k-6    s   8k-5    s   8k-4    s   8k-3    s   8k-2    s   8k-1    s   8k   ], k= 1, . . . , 4  [Equation 3]
 
     Here, R k  represents a region having 8 symbols grouped as positioned in a k-quadrant. 
     Next, bits are allocated to symbols grouped into four regions, respectively.  FIGS. 4A to 4F  show the bit-to-symbol mapping according to the exemplary embodiment of the present invention by using the decision boundary. As shown in  FIGS. 4A to 4F , each bit is allocated by dividing the region. 
     For the first bit (b i,1 ), bit  0  is allocated to symbols in a R 1 , R 2  region and bit  1  to symbols in a R 3 , R 4  region as shown in  FIG. 4A . For the second bit (b i,2 ), bit  0  is allocated to symbols in a R 1 , R 4  region and bit  1  to symbols in a R 2 , R 3  region as shown in  FIG. 4B . Herein, b i,h  represents a h-th bit of a i-th symbol. This is represented by the following Equations 4 and 5.
         First bit (h=1)
 
 b   i,h =0, if  s   i    ∈{R   1    ∪R   2   }, i= 1, 2, . . . , 32
 
 b   i,h =1, if  s   i   ∈{R   3    ∪R   4   }, i= 1, 2, . . . , 32  [Equation 4]
   Second bit (h=2)
 
 b   i,h =0, if  s   i    ∈{R   1    ∪R   4   }, i= 1, 2, . . . , 32
 
 b   i,h =1, if  s   i    ⊂{R   2    ∪R   3   },i= 1, 2, . . . , 32  [Equation 5]
       

     After the third bit (b i,3 ), bits are allocated based on the element size of the signal set R 1 . When the set rearranged by the size r i  of the signals belonging to R 1  in an ascending order is A=[α 1  α 2  . . . α 8 ], 0 is allocated to the third bit when the size r i  of a signal belongs to the set {α 1  . . . α 4 } of smaller size and 1 is allocated 1 when the size r i  of a signal belongs to the set {α 5  . . . α 8 } of a larger size. The mapping for the third bit is shown in  FIG. 4C  and is represented by the following Equation 6.
         Third bit (h=3)
 
 A =sort ( r   i   |r   i    ∈ R   1 )=[α 1  α 2  . . . α 8   ] b   i,h =0, if  r   i  ∈ {α 1  . . . α 4   }, i= 1, 2, . . . , 32  b   i,h =1, otherwise  [Equation 6]
       

     For the fourth bit (b i,4 ) and the fifth bit (b i,5 ), bits are allocated to each symbol so that the allocated bits-to-symbol mapping is symmetrical as shown in  FIGS. 4D and 4E . The bits-to-symbol mapping of the fourth bit is performed by comparing the Quadrature axis size (r i     —     Q ) of all the signals with the size r i  (r i     —     I , r i     —     Q ) of signals belonging to R 1  and the bits-to-symbol mapping of the fifth bit is performed by comparing an In-phase axis size (r i     —     I ) of all the signals with the size r i  (r i     —     I , r i     —     Q ) of the signals belonging to R 1 . 
     In other words, when the set rearranged by the Quadrature axis size r i     —     Q  of the signals belonging to R 1  in an ascending order is B=[b 1  b 2  . . . b 8 ], 0 is allocated to the fourth bit when the Quadrature axis size r i     —     Q  of a signal belongs to the set {b 5  . . . b 8 } of a larger size, and otherwise, 1 is allocated. 
     The fifth bit is allocated in a manner similar to the fourth bit. When the set rearranged by the in-phase axis size r i     —     I  of the signals belonging to R 1  in an ascending order is c=[c 1  c 2  . . . c 8 ], 0 is allocated when the In-phase axis size r i     —     I  of a signal belonging to the set {c 4  . . . c 7 } of a larger size other than the largest In-phase axis size, and otherwise, 1 is allocated. 
     The mapping for the fourth bit and the fifth bit is represented by the following Equations 7 and 8.
         Fourth bit (h=4)
 
 B =sort ( r   i     —     Q   |r   i    ∈ R   1 )=[ b   1    b   2    . . . b   8   ] b   i,h =0, if  r   i     —     Q    ∈ {b   5    . . . b   8   }, i= 1, 2, . . . , 32  b   i,h =1, otherwise  [Equation 7]
   Fifth bit (h=5)
 
 C =sort ( r   i     —     I   |r   i    ∈R   1 )=[ c   1    c   2    . . . c   8   ] b   i,h =0, if r i     —     I    ∈ {c   4    . . . c   7   }, i= 1, 2, . . . , 32  b   i,h =1, otherwise  [Equation 8]
       

     The bits-to-symbol mapping structure allocated to each signal according to the above-mentioned manner is shown in  FIG. 5 . As can be appreciated from  FIG. 5 , in the bits-to-symbol mapping of the 4+12+16 APSK modulation according to the exemplary embodiment of the present invention, the bit difference between all the adjacent symbols forming the decision boundary is only 1 bit or 2 bits, and in particular, the Hamming distance of two pairs of signals having a large Hamming distance is 1, which is the minimum distance as in the following Equation 9.
 
 H   —   d  ( s   5   ,s   6 )= H   —   d  ( s   21   , s   22 )=1  [Equation 9]
 
     In the standard bits-to-symbol mapping, only the second bit (b 2 ) meets the I/Q symmetry as shown in  FIG. 2B , while in the bits-to-symbol mapping according to the exemplary embodiment of the present invention, the mapping type of the third, fourth, and fifth bits b 3 , b 4 , and b 5  meet the I/Q symmetry as shown in  FIGS. 4C to 4E . The I/Q symmetry can further simplify the structure of the receiver and reduce the load of the receiver at the time of the signal demodulation. 
       FIG. 6  is a graph showing the bit error performances of the existing standard and an exemplary embodiment of the present invention are applied. At this time, the IBO of the high power amplifier considers 8, 9, 10 dB based on 9 dB proposed in the DVB-S2 and compares the numerical results and the simulation results. 
     As can be appreciated from  FIG. 6 , the bits-to-symbol mapping according to the exemplary embodiment of the present invention has superior bit error performance iii all cases than that of the existing standard regardless of the linear amplifier and the non-linear amplifier. In particular, it can be appreciated that the bit error performance is far better at the IBO of about 9 -10 dB. 
     Therefore, when the bits-to-symbol mapping algorithm of the 4+12+16 APSK according to the exemplary embodiment of the present invention is applied to the DVB-S2 system, it can reduce performance deterioration for non-linearity of the high power amplifier and can further simplify the structure of the receiver to reduce the load as compared to the existing system, such that it is expected to be usefully used in a system for satellite communication and space communication. 
     The bits-to-symbol mapping of the 4+12+16 APSK according to the exemplary embodiment of the present invention can be implemented as computer readable codes in a recording medium readable by a computer. The computer-readable recording media includes all types of recording apparatuses in which data readable by a computer system is stored. Examples of the computer-readable recording media include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage, etc., and in addition, include a recording medium implemented in the form of a carrier wave (for example, transmission through the Internet). The computer-readable recording media are distributed on computer systems connected through the network, and thus the computer-readable recording media may be stored and executed as the computer-readable code by a distribution scheme. 
     A number of exemplary embodiments have been described above. Nevertheless, it will be understood that various modifications may be made. For example, suitable results may be achieved if the described techniques are performed in a different order and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Accordingly, other implementations are within the scope of the following claims.