Abstract:
The present invention relates to a method and a device for transmitting a pay load sequence, and provides in one embodiment a transmitter comprising a first signal converter for converting a ternary payload sequence composed of elements −1, 0, or 1 into a first signal, wherein the first signal converter comprises: a ternary sequence mapper for generating the ternary payload sequence by mapping a pre-designed sequence into a binary data sequence; and a converter for converting the ternary payload sequence into the first signal.

Description:
TECHNICAL FIELD 
       [0001]    The following example embodiments relate to a method and apparatus for transmitting a payload sequence. 
       RELATED ART 
       [0002]    In general, a modulation scheme of a digital wireless communication system may be classified into a noncoherent modulation scheme and a coherent modulation scheme. The noncoherent modulation scheme may be suitable for a noncoherent receiver having a low power consumption and a low complexity, and the coherent modulation scheme may be suitable for a coherent receiver having relatively small constraints on a power consumption and a complexity and also having an excellent performance. 
       SOLUTIONS 
       [0003]    A transmitter according to an example embodiment includes a first signal converter configured to convert a ternary payload sequence including elements of −1, 0, or 1, to a first signal, wherein the first signal converter includes a ternary sequence mapper configured to generate the ternary payload sequence by mapping a pre-designed sequence to a binary data sequence; and a converter configured to convert the ternary payload sequence to the first signal. 
         [0004]    The ternary sequence mapper may be configured to divide a binary data sequence including elements of 0 or 1 based on a predetermined length, and to map the pre-designed ternary sequence to the divided binary data sequence. 
         [0005]    The first signal converter may include a pulse shaping filter figured to adjust a transmit power spectrum of the first signal. 
         [0006]    The transmitter may further include a second signal converter configured to convert the first signal to the second signal by converting each section of the first signal based on the element. 
         [0007]    The second signal converter may include a zero-value converter configured to convert a section corresponding to the element of 0 in the first signal; and an absolute one value converter configured to convert a section corresponding to the element of 1 and a section corresponding to the element of −1 in the first signal. 
         [0008]    The zero-value converter may include a zero-value detector configured to detect the section corresponding to the element of 0 in the first signal. 
         [0009]    The zero-value converter may include an ON-OFF controller configured to turn OFF an output of the section corresponding to the element of 0. 
         [0010]    The absolute one value converter may include an absolute value detector configured to detect a section corresponding to an absolute one value in the first signal; and a sign detector configured to detect a sign of the element of the absolute one value, and to classify the section corresponding to the element of the absolute one value into the section corresponding to the element of 1 and the section corresponding to the element of −1. 
         [0011]    The absolute one value converter may include a frequency shifter configured to shift a frequency of the section corresponding to the element of 1 to a first frequency, and to shift a frequency of the section corresponding to the element of −1 to a second frequency, in the first signal. 
         [0012]    The absolute one value converter may include a phase shifter configured to shift a phase of the section corresponding to the element of 1 to a first phase, and to shift a phase of the section corresponding to the element of −1 to a second phase, in the first signal. 
         [0013]    The absolute one value converter may include a frequency shifter configured to shift a frequency of the section corresponding to the element of 1 to a first frequency and to shift a frequency of the section corresponding to the element of −1 to a second frequency, in the first signal; and a phase shifter configured to shift a phase of the section corresponding to the element of 1 and to shift a phase of the section corresponding to the element of −1 to a second phase, in the first signal. 
         [0014]    The second signal converter may include an amplifier configured to amplify an amplitude of die second signal. 
         [0015]    The ternary sequence mapper may be configured to extract, from the following Table 1, a ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence, and in the following Table 1, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by in where m denotes an integer between 1 and 7. 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
                 000 
                 0 
                 c 0   
               
               
                   
                 100 
                 1 
                 c 1   
               
               
                   
                 110 
                 2 
                 c 2   
               
               
                   
                 010 
                 3 
                 c 3   
               
               
                   
                 011 
                 4 
                 c 4   
               
               
                   
                 111 
                 5 
                 c 5   
               
               
                   
                 101 
                 6 
                 c 6   
               
               
                   
                 001 
                 7 
                 c 7   
               
               
                   
                   
               
             
          
         
       
     
         [0016]    The ternary sequence mapper may be configured to extract, from the following Table 2, a ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence, and in the following Table 2, C 0  denotes a sequence of [−1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by m where m denotes an integer between 1 and 31. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
         [0017]    A transmitter according to an example embodiment includes a ternary sequence mapper configured to generate a ternary payload sequence including elements of −1 , 0, or 1 by mapping a pre-designed ternary sequence to a binary data sequence; and a converter configured to convert the ternary payload sequence to a signal, wherein the ternary sequence mapper is configured to extract, from the following Table 3, a ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence, and in the following Table, 3, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and C, denotes a sequence acquired by cyclic shifting C 0  to right by in where m denotes an integer between 1 and 7. 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Biliary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
                 000 
                 0 
                 c 0   
               
               
                   
                 100 
                 1 
                 c 1   
               
               
                   
                 110 
                 2 
                 c 2   
               
               
                   
                 010 
                 3 
                 c 3   
               
               
                   
                 011 
                 4 
                 c 4   
               
               
                   
                 111 
                 5 
                 c 5   
               
               
                   
                 101 
                 6 
                 c 6   
               
               
                   
                 001 
                 7 
                 c 7   
               
               
                   
                   
               
             
          
         
       
     
         [0018]    A transmitter according to an example embodiment includes a ternary sequence mapper configured to generate a ternary payload sequence including elements of −1, 0, or 1 by mapping a pre-designed ternary sequence to a binary data sequence; and a converter configured to convert the ternary payload sequence to a signal, wherein the ternary sequence mapper is configured to extract, from the following Table 4, a ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence, and in the following Table 4, C 0  denotes a sequence of [−1 0010 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by m where m denotes an integer between 1 and 31. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
         [0019]    A receiver according to an example embodiment includes an envelope detector configured to detect an amplitude value of an envelope of a received signal that is converted from a ternary payload sequence including elements of −1, 0, or 1; and a binary data sequence detector configured to detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between the detected amplitude value of the envelope and desired binary sequences. 
         [0020]    The receiver may further include a filter configured to filter the received signal using a first frequency. The envelope detector may be configured to detect an envelope of the filtered received signal. 
         [0021]    The first frequency may be a frequency between a second frequency denoting a frequency and a third frequency, the second frequency denoting a frequency of a section of the received signal converted from the element of 1 in the ternary payload sequence and the third frequency denoting a frequency of a section of the received signal converted from the element of −1 in the ternary payload sequence. 
         [0022]    The binary data sequence detector may be configured to detect a bit sequence corresponding to a binary sequence having a highest correlation with the detected amplitude value of the envelope among the binary sequences as the binary data sequence. 
         [0023]    A receiver according to an example embodiment includes an entire envelope detector configured to detect an amplitude value of an envelope of a received signal converted from a ternary payload sequence including elements of −1, 0, or 1 and a binary data sequence detector configured to detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between the detected amplitude value of the envelope and desired ternary sequences. 
         [0024]    The entire envelope detector may include a first filter configured to filter the received signal using a first frequency; a second filter configured to filter the received signal using a second frequency; a first envelope detector configured to detect a first envelope that indicates an envelope of the received signal filtered using the first frequency; a second envelope detector configured to detect a second envelope that indicates an envelope of the received signal filtered using the second frequency; and a calculator configured to extract a third envelope based on a difference between the first envelope and the second envelope. 
         [0025]    The binary data sequence detector may be configured to detect a bit sequence corresponding to a ternary sequence having a highest correlation with the third envelope among the ternary sequences as the binary data sequence. 
         [0026]    A receiver according to an example embodiment includes a correlation detector configured to detect a correlation between a received signal converted from a ternary payload sequence including elements of −1, 0, or 1 and a reference signal; and a binary data sequence detector configured to detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between a result value of the correlation and desired ternary sequences. 
         [0027]    The binary data sequence detector may be configured to detect a bit sequence corresponding to a ternary sequence having a highest correlation with the result value of the correlation among the ternary sequences as the binary data sequence. 
         [0028]    A receiver according to an example embodiment includes a signal receiver configured to receive a signal modulated from a ternary payload sequence generated by mapping a pre-designed ternary sequence to a binary data sequence and including elements of −1, 0, or 1; and a detector configured to detect the pre-designed ternary sequence and the binary data sequence by referring to the following Table 5. In the following Table 5, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and C, denotes a sequence acquired by cyclic shifting C 0  to right by m where in denotes an integer between 1 and 7. 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
                 000 
                 0 
                 c 0   
               
               
                   
                 100 
                 1 
                 c 1   
               
               
                   
                 110 
                 2 
                 c 2   
               
               
                   
                 010 
                 3 
                 c 3   
               
               
                   
                 011 
                 4 
                 c 4   
               
               
                   
                 111 
                 5 
                 c 5   
               
               
                   
                 101 
                 6 
                 c 6   
               
               
                   
                 001 
                 7 
                 c 7   
               
               
                   
                   
               
             
          
         
       
     
         [0029]    A receiver according to an example embodiment includes a signal receiver configured to receive a signal modulated from a ternary payload sequence generated by mapping a pre-designed ternary sequence to a binary data sequence and including elements of −1, 0, or 1; and a detector configured to detect the pre-designed ternary sequence and the binary data sequence by referring to the following Table 6. In the following Table 6, C 0  denotes a sequence of [−1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by in where m denotes an integer between 1 and 31. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0030]      FIG. 1  is a diagram illustrating a wireless communication system according to an example embodiment; 
           [0031]      FIG. 2  illustrates a format of a transmission frame according to an example embodiment; 
           [0032]      FIG. 3  is a block diagram illustrating a transmitter according to an example embodiment; 
           [0033]      FIGS. 4 through 6  are block diagrams illustrating examples of a transmitter according to another example embodiment; 
           [0034]      FIGS. 7 through 9  illustrate examples of a transmission signal according to an example embodiment; 
           [0035]      FIGS. 10 through 12  are block diagram illustrating examples of a receiver according to an example embodiment; 
           [0036]      FIGS. 13 through 15  illustrate examples of detecting a binary data sequence according to an example embodiment; 
           [0037]      FIG. 16  is a block diagram illustrating a transmitter according to another example embodiment; 
           [0038]      FIG. 17  is a block diagram illustrating a receiver according to another example embodiment; 
           [0039]      FIG. 18  is a flowchart illustrating a transmission method according to an example embodiment; 
           [0040]      FIG. 19  is a flowchart illustrating a transmission method according to another example embodiment; and 
           [0041]      FIGS. 20 through 23  are flowcharts illustrating a reception method according to an example embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0042]    Hereinafter, example embodiments will be described with reference to the accompanying drawings. Like reference numerals illustrated in the respective drawings refer to like elements throughout. 
         [0043]    In the following example embodiments, various modifications may be made thereto. The following example embodiments are not construed as limited to the example embodiments and should be understood to include all changes, equivalents, and replacements within the technical scope of the example embodiments. 
         [0044]    The terminology used herein is for the purpose of describing particular example embodiments only and is not to be used to limit the example embodiments. As used herein, the terms “a” and “the” are identical to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the terms “include,” “comprise,”, and “have” specify the presence of stated features, numbers, operations, elements, components, and/or combinations thereof, but do not preclude the presence or addition of one or more other features, numbers, operations, elements, components, and/or combinations thereof. 
         [0045]    Unless otherwise defined, all terms, including technical and scientific terms, used herein have the same meaning as commonly understood by one of ordinary skill in the art to which these example embodiments pertain. Terms, such as those defined in commonly used dictionaries, are to be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art, and are not to be interpreted in an idealized or overlay formal sense unless expressly so defined herein. 
         [0046]    Also, when describing with reference to the accompanying drawings, like reference numerals are assigned to like constituent elements and a repeated description related thereto is omitted. When it is determined that a detailed description related to a relevant known art may make the purpose of the example embodiments unnecessarily ambiguous, the detailed description will be omitted here. 
         [0047]      FIG. 1  is a diagram illustrating a wireless communication system according to an example embodiment. 
         [0048]    Referring to  FIG. 1 , the wireless communication system may include a coherent transmitter  110 , noncoherent receivers  120  and  130 , and a coherent receiver  140 . The noncoherent receiver may be classified into a low selectivity noncoherent receiver  120  and a high selectivity noncoherent receiver  130 . 
         [0049]    The coherent transmitter  110  may transmit data based on a packet unit. A packet may include payload or Physical Service Data Unit (PSDU) of the coherent transmitter  110  and the receivers  120 ,  130 , and  140 . The payload may include data and a Cyclical Redundancy Check (CRC) that the coherent transmitter  110  is to transmit. 
         [0050]    The coherent transmitter  110  may modulate the payload using a coherent modulation scheme. When a binary bit sequence is to be transmitted to the receivers  120 ,  130 , and  140  using the coherent modulation scheme, the coherent transmitter  110  may map different bit sequences with a constant length to different code sequences and may transmit the mapped code sequences. Here, a length of a code sequence or a number of elements or alphabets of the code sequence may be greater than a length of a bit sequence. Also, the code sequence may include elements {−1, 0, +1}. According to an example embodiment, a sequence including elements {−1, 0, +1]} may be represented as a ternary sequence, a sequence including elements {0, +1} may be represented as a unipolar sequence, and a sequence including elements {−1, 1} may be represented as a bipolar sequence. Here, if a frequency of a carrier signal corresponding to the element +1 and a frequency of a carrier signal corresponding to the element −1 differ from each other, the element +1 may indicate setting a phase value of the carrier signal as zero degree, the element 0 may indicate setting OFF the carrier signal, and the element −1 may indicate setting the phase value of the carrier signal to be 180 degrees. Hereinafter, the term “phase” may be represented as an angular frequency. When the low selectivity noncoherent receiver  120  receives a packet from the coherent transmitter  110 , the low selectivity noncoherent receiver  120  may demodulate the payload based on a noncoherent demodulation scheme and thus, may not distinguish different phases of carrier signals. Since the low selectivity noncoherent receiver  120  may not distinguish the elements +1 and −1 from each other, the low selectivity noncoherent receiver  120  may recognize a ternary sequence as a unipolar sequence. The high selectivity noncoherent receiver  130  may distinguish different frequencies of carrier signals using a filter having a relatively high frequency selectivity or a relatively high Q-factor filter. Thus, the high selectivity noncoherent receiver  130  may distinguish elements +1 and −1 of a ternary sequence and may recognize the ternary sequence. 
         [0051]    When the coherent receiver  140  receives a packet from the coherent transmitter  110 , the coherent receiver  140  may demodulate a payload using a coherent demodulation scheme, may distinguish different phases of received signals, and may recognize a ternary sequence, which differs from the low selectivity noncoherent receiver  120 . 
         [0052]    Hereinafter, a method of designing a ternary sequence applicable e noncoherent receivers  120  and  130  and the coherent receiver  140  will be described. 
         [0053]    Also, a method of transmitting and receiving a payload using the designed ternary sequence will be described with reference to  FIGS. 2 through 15 . 
         [0054]    &lt;Design of Ternary Sequence&gt; 
         [0055]    System 
         [0056]    During a process of designing a ternary sequence, the system may include a coherent transmitter, a coherent receiver, and a noncoherent receiver. The system may use the following elements. 
         [0057]    a) Unipolar binary element (alphabet) {0, 1} 
         [0058]    b) Ternary element {0, ±1} 
         [0059]    A sequence/codeword including a ternary element may be represented as a ternary sequence/codeword. A sequence/codeword including a unipolar binary element may be represented as a unipolar binary sequence/codeword. 
         [0060]    According to an example embodiment, a transmitter may extract a symbol from an M-ary element S. Here, S may denote S={0, 1, . . . , 2 k −1}, k=log 2 (M). Accordingly, an information rate may be k-bits/symbol. Before the transmitter performs transmission, each symbol extracted from S may be mapped to one of M possible waveforms or codewords from a spreading code C. Here, the term “spreading code” may also indicate a spreading factor or coefficient. That is, mapping of a symbol may be represented as m∈S         c m ∈C={c 0 , . . . , c M−1 }. If N denotes a length of a codeword, an effective rate of a code or a spreading code may be represented as 
         [0000]    
       
         
           
             r 
             = 
             
               
                 k 
                 N 
               
               . 
             
           
         
       
     
         [0061]    According to an example embodiment, a transmitted waveform corresponding to symbol m∈S, equivalently, c m ∈C may be represented as Equation 1. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       c 
                       m 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         Λ 
                         - 
                         1 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           c 
                           m 
                         
                          
                         
                           [ 
                           n 
                           ] 
                         
                       
                        
                       
                         
                           g 
                            
                           
                             ( 
                             
                               t 
                               - 
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 
                                   T 
                                   c 
                                 
                               
                             
                             ) 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
         [0062]    In Equation 1, git denotes a chip waveform, !; denotes a chip, and T denotes a symbol section. 
         [0063]    Under presumption of a constant weight code, or equal energy waveforms, a symbol detected at the receiver through matched filtering or correlation may be represented as Equation 2. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       m 
                       ^ 
                     
                     = 
                     
                       
                         argmax 
                         
                           m 
                           ∈ 
                           
                             { 
                             
                               0 
                               , 
                               1 
                               , 
                               … 
                                
                               
                                   
                               
                               , 
                               M 
                             
                             } 
                           
                         
                       
                        
                       
                           
                       
                        
                       
                         C 
                         m 
                       
                     
                   
                   ; 
                   
                     
                       where 
                        
                       
                           
                       
                        
                       
                         C 
                         m 
                       
                     
                     = 
                     
                       
                         ∫ 
                         0 
                         T 
                       
                        
                       
                         
                           y 
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                         
                           
                             c 
                             m 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
         [0064]    In Equation 2, y(t) denotes a received waveform. y(t) may be deformed by additive white Gaussian noise (AWGN). {circumflex over (m)} may be defined as a symbol estimated at the receiver. 
         [0065]    A symbol detection at the receiver may be carried out by performing correlation using a bank of M correlators that match M waveforms, respectively. 
         [0066]    Code Design Condition: 
         [0067]    When a ternary sequence/codeword is transmitted, the coherent receiver may recognize polarities of chips and may recognize the ternary sequence/codeword. On the contrary, the noncoherent receiver, for example, the receiver based on energy detection may recognize the ternary sequence/codeword as a unipolar binary sequence/codeword due to lack of phase information. 
         [0068]    According to an example embodiment, a spreading code is to satisfy the followings. 
         [0069]    1) Sequences of a ternary code set C may be maximally separated. 
         [0070]    2) Sequences corresponding to a binary set |C| may be maximally separated. 
         [0071]    Spreading Code Design for Ultra Low Power (ULF): 
         [0072]    Due to a difference between a design of a coherent spreading code and a design of a noncoherent spreading code, the spreading code design for TAP may show aspects different from the aforementioned description. Hereinafter, an efficient spreading code design will he described. 
         [0073]    Basic Definition and Concept: 
         [0074]    Spreading codes for ULP may be acquired using two-level autocorrelation sequences. The two-level autocorrelation sequences may be used as a basis to acquire a coherent ternary code and a noncoherent binary code or an optical orthogonal code (OOC). 
         [0075]    Ternary Sequence Having Perfect Periodic Autocorrelation: 
         [0076]    A ternary sequence having perfect periodic autocorrelation and a length of N may have autocorrelation as expressed by Equation 3: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         ^ 
                       
                       
                         x 
                         , 
                         x 
                       
                     
                      
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           N 
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               
                                 k 
                                 _ 
                               
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               
                                 λ 
                                 ″ 
                               
                             
                             ≠ 
                             
                               0 
                                
                               
                                 mod 
                                  
                                 N 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
         [0077]    Two-Level Autocorrelation Sequence: 
         [0078]    A binary sequence may be represented as {x 1 , x 2 , . . . , x N }, where x 1 ∈{0,1}. If the following condition of Equation 4 is met, the binary sequence may have two-level autocorrelation: 
         [0000]      [Equation 4] 
         [0000]    
       
         
           
             
               
                 
                   R 
                   ^ 
                 
                 
                   x 
                   , 
                   x 
                 
               
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     N 
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         k 
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     A 
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         k 
                       
                       ≠ 
                       
                         0 
                          
                         
                           mod 
                            
                           N 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0079]    In Equation 4, an autocorrelation function may be defined as 
         [0000]    
       
         
           
             
               
                 R 
                 ^ 
               
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   N 
                   - 
                   1 
                 
               
                
               
                   
               
                
               
                 
                   
                     ( 
                     
                       - 
                       1 
                     
                     ) 
                   
                   
                     
                       x 
                       j 
                     
                     ⊕ 
                     
                       x 
                       
                         
                           ( 
                           
                             j 
                             + 
                             k 
                           
                           ) 
                         
                          
                         modN 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    If A=1, the binary sequence may be an ideal two-level autocorrelation sequence. Such sequences may serve as a bridge between a coherent ternary sequence and a noncoherent binary sequence. Many of the sequences may correspond to an m-sequence having a length of N=1 m −1 where m denotes an integer. 
         [0080]    Cyclic Difference Set: 
         [0081]    A difference set of A(n, k, λ) may be represented as D={d 1 , d 2 , . . . , d k }. Here, k denotes an integer. A number of solution pairs (d i , d j ) of elements of the difference set D may be λ, and a relationship between d i  and d j  may be represented as d 1 −d j ≡t(mod N). Here, t may be represented as 1≦t≦N−1. 
         [0082]    The cyclic difference set may correspond to two-level autocorrelation sequences in one-to-one manner. Accordingly, the cyclic difference set may be used to design ternary sequences having the perfect autocorrelation. 
         [0083]    Spreading Code for ULP: 
         [0084]    The best method for completely synchronizing the system may include selecting sequences having an excellent autocorrelation attribute and assigning different cyclic shifts to different symbols. 
         [0085]    Hereinafter, a method of designing shift equivalent codes of spreading codes 8, 16, and 32 will be described. 
         [0086]    1. Select an m-sequence with the period of N−1. Here, N denotes a target spreading code of a ternary code. 
         [0087]    2. Acquire the auric period of a ternary sequence from the m-sequence by converting elements of 1 and by maintaining elements of 0. It may be represented as a procedure A. 
         [0088]    3. Add the element 0 or 1 to a sequence in order to prevent damage to correlation of the sequence. 
         [0089]    4. The following two cases are possible based on the m-sequence and zero padding: 
         [0090]    i) Balanced ternary sequence (from the m-sequence of weight N/2 or (N−2)/2) 
         [0091]    ii) Unbalanced ternary sequence (all weights are (N−2)/2 or N/2+1) 
         [0092]    The acquired ternary sequences may be characterized based on excellent correlation attributes. A set of spreading sequences to which different symbols are allocated may be acquired based on cyclic shifts of the acquired ternary sequences. According to an example embodiment, spreading codes 8, 16, and 32 may correspond to symbol sizes 3, 4, and 5, respectively. 
         [0093]    Balanced Sequences Acquired from M-Sequences with the Weight of N/2 
         [0094]    The following procedure may refer to a procedure of acquiring the balanced ternary sequence with the weight of N/2 from the m-sequence with the weight of N/2. 
         [0095]    1. Select the m-sequence with the weight of N/2. 
         [0096]    2. Acquire a tertiary sequence with the period of N−1 from the m-sequence with the period of N−1 using the procedure A if N=perfect square. 
         [0097]    3. Add the element of 0 to the acquired ternary sequence to minimize Mean Squared AutoCorrelation (MSAC). Here, the MSAC may be defined as Equation 5. 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     MSAC 
                   
                   = 
                   
                     
                       1 
                       
                         ( 
                         
                           N 
                           - 
                           1 
                         
                         ) 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           τ 
                           = 
                           1 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           R 
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
         [0098]    In Equation 5, R(τ) denotes autocorrelation normalized at the period of a sequence in delay τ, and may be defined as Equation 6. 
         [0000]      [Equation 6] 
         [0000]    
       
         
           
             
               R 
                
               
                 ( 
                 τ 
                 ) 
               
             
             = 
             
               
                 1 
                 / 
                 w 
               
                
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                   
                     C 
                     n 
                   
                    
                   
                     C 
                     
                       n 
                       + 
                       τ 
                     
                   
                 
               
             
           
         
       
     
         [0099]    In Equation 6, w denotes a hamming weight of a sequence. Balanced sequences acquired from a representative m-sequence with the weight of N/2 may be represented as Table 1. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Period 
                 Basic Ternary spreading sequence 
                 Base sequence 
                 μ coherent   
                 μ non-coherent   
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 8 
                 1 
                 1 
                 −1 
                 0 
                 1 
                 1 
                 −1 
                 0 
                 0 
                 1 
                 0 
                   
                 0.0536 
                 0.1964 
               
               
                   
                 0 
                 1 
                 0 
                 0; 0 
               
               
                   
                 1 
                 1 
                 −1 
                 0 
               
               
                   
                 0 
                 1 
                 0; 1 
                 0 
               
               
                   
                 1 
                 1 
                 −1 
                 0 
               
               
                   
                 0 
                 0; 0 
                 1 
                 0 
               
               
                   
                 1 
                 1 
                 −1 
                 0 
               
               
                   
                 0; 0 
                 0 
                 1 
                 0 
               
               
                   
                 1 
                 1 
                 −1 
                 0 
               
               
                 16 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                   
                 −1 
                   
                 1 
                   
                 0.0250/ 
                 0.2250/ 
               
               
                   
                 −1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                   
                 0 
                   
                 0.0375 
                 0.2208 
               
               
                   
                 1 
                 1 
                 −1 
                 1 
                 0 
                 −1 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 0; 0 
               
               
                   
                 1 
                 1 
                 −1 
                 1 
               
               
                   
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 1 
                 0 
                 0 
                 −1 
               
               
                   
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                   
                 1 
                 0 
                 −1 
                 0.0125 
                 0.2208 
               
               
                   
                 1 
                 0 
                 −1 
                 0 
                 0 
                 1 
                 −1 
                 0 
                 0 
                 1 
                 0 
                 0 
               
               
                   
                 1 
                 −1 
                 0 
                 0 
               
               
                   
                 1 
                 0 
                 0 
                 0 
               
               
                 32 
                 1 
                 1 
                 −1 
                 1 
                 −1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0.0111 
                 0.2359 
               
               
                   
                 −1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 −1 
                 1 
                 −1 
                 0 
                 0 
               
               
                   
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 −1 
                 −1 
                 0 
               
               
                   
                 −1 
                 −1 
                 0 
                 1 
                 1 
                 0 
                 −1 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 −1 
                 0 
                 0 
               
               
                   
                 0 
                 0 
                 −1 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 1 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
         
       
     
         [0100]    According to an example embodiment, other m-sequences may be replaced with base sequences. 
         [0101]    Balanced Sequences Acquired from M-Sequences with the Weight of (N−2)/2 
         [0102]    The following procedure may refer to a procedure of acquiring the balanced ternary sequence with the weight of N/2 from the m-sequence with the weight of (N−2)/2. 
         [0103]    1. Acquire a ternary sequence with the period of N−1 from the m-sequence. A perfect ternary sequence with the weight of (N−2)/2 may be absent. Accordingly, a procedure B may be employed to deduce a ternary sequence having an excellent correlation attribute from a ternary element. 
         [0104]    2. Add the element of 1 to the acquired ternary sequence to minimize MSAC. 
         [0105]    3. Result sequences may be characterized by the weight of N/2. 
         [0106]    Balanced sequences acquired from the representative in-sequence with the weight of (N−2)/2 may be represented as Table 2. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Period 
                 Basic Ternary spreading sequence 
                 Base sequence 
                 μ coherent   
                 μ non-coherent   
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 8 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 −1 
                 0 
                 1 
                   
                   
                   
                 0.0536 
                 0.1964 
               
               
                   
                 −1 
                 0 
                 1 
                 1; 1 
               
               
                   
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 −1 
                 0 
                 1 
               
               
                 16 
                 −1 
                 0 
                 0 
                 0 
                 −1 
                   
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 −1 
                 0 
                 0.0125 
                 0.2208 
               
               
                   
                 0 
                 1 
                 0 
                 −1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 0 
                 1 
                 1 
                 1; 1 
               
               
                   
                 −1 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 −1 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 0 
                 1 
                 1; 1 
                 1 
               
               
                   
                 −1 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 −1 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 0 
                 1 
               
               
                 32 
                 −1 
                 0 
                 0 
                 1 
                 0 
                 −1 
                   
                 −1 
                 1 
                   
                 −1 
                 0 
                 1 
                 0 
                 0.0131 
                 0.2359 
               
               
                   
                 0 
                 1 
                 −1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 −1 
               
               
                   
                 −1 
                 −1 
                 1 
                 −1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                   
                 −1 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 −1 
               
               
                   
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 −1 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
               
             
          
         
       
     
         [0107]    According to an example embodiment, other m-sequences may be replaced with base sequences. 
         [0108]    Consolidated List 
         [0109]    To deduce sequences of Table 3, a sequence in which elements of 0 and elements aside from 0 are uniformly distributed may be selected from Table 1 and Table 2. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Basic Ternary 
                   
                   
                   
               
               
                 Period 
                 spreading sequence 
                 Base sequence 
                 μ coherent   
                 μ non-coherent   
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 8 
                 0 
                 0 
                 0 
                 1 
                 −1 
                 0 0 0 1 −1 0 1 
                 0.0536 
                 0.1964 
               
               
                   
                 0 
                 1  
                 1 
               
               
                 16 
                 1 
                 −1 
                 0 
                 0 
                 0 
                 −1 0 0 0 0 1 0 
                 0.0125 
                 0.2208 
               
               
                   
                 0 
                 1 
                 0 
                 −1 
                 0 
                 −1 0 0 1 1 0 
               
               
                   
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 1 
               
               
                   
                 1 
               
             
          
           
               
                 32 
                 −1 
                 0 
                 0 
                 1 
                 0 −1 −1 1 −1 0 
                 0.0131 
                 0.2359 
               
             
          
           
               
                   
                 0 
                 1 
                 −1 
                 0 
                 −1 
                 1 0 1 0 0 0 1 0 
               
             
          
           
               
                   
                 −1 
                 1 
                 −1 
                 0 
                 0 1 1 −1 0 0 0 
               
             
          
           
               
                   
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 0 1 −1 0 0 1 
               
               
                   
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 1 −1 
               
               
                   
                 1 
                 −1 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                   
               
             
          
         
       
     
         [0110]    Base ternary spreading sequences of Table 3 may be used to encode data symbols for transmission through a wireless channel. Spreading sequences to encode data symbols may be acquired through a cyclic shift of a single base ternary spreading sequence of Table 3. Accordingly, a number of distinct spreading sequences may be equal to a spreading code. Spreading sequences of a spreading code M may be used to encode data symbols with the size of k=log 2  M. For example, a spreading sequence of the spreading code M=8 may be used to encode a data symbol with the size of k=log 2  8=3. 
         [0111]    Also, spreading sequences of spreading codes 16 and 32 may be used to encode data symbols with the sizes of 4 and 5, respectively. In Table 3, the basic ternary spreading sequences may be represented as 3/8-OOK, 4/16-OOK, and 5/32-OOK, respectively. Table 4 shows an example in which the basic ternary sequences of Table 3 are classified into 3/8-OOK, 4/16-OOK, and 5/32-OOK. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                   
                   
                   
                 Basic Ternary 
                   
               
               
                   
                 k 
                 M 
                 Nomenclature 
                 spreading sequence 
                   
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 3 
                 8 
                 ⅜-OOK 
                 0 
                 0  
                 0  
                 1 
               
               
                   
                   
                   
                   
                 −1 
                 0 
                 1 
                 1 
               
               
                   
                 4 
                 16 
                  4/16-OOK 
                 1 
                 −1 
                 0 
                 0 
               
               
                   
                   
                   
                   
                 0 
                 0 
                 1 
                 0 
               
               
                   
                   
                   
                   
                 −1 
                 0 
                 0 
                 1 
               
               
                   
                   
                   
                   
                 1 
                 0 
                 1 
                 1 
               
               
                   
                 5 
                 32 
                  5/32-OOK 
                 −1 
                 0 
                 0 
                 1 
               
               
                   
                   
                   
                   
                 0 
                 1 
                 −1 
                 0 
               
               
                   
                   
                   
                   
                 −1 
                 −1 
                 1 
                 −1 
               
               
                   
                   
                   
                   
                 0 
                 1 
                 0 
                 1 
               
               
                   
                   
                   
                   
                 0 
                 0 
                 0 
                 1 
               
               
                   
                   
                   
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                   
                   
                   
                 −1 
                 0 
                 0 
                 0 
               
               
                   
                   
                   
                   
                 0 
                 0 
                 1 
                 1 
               
               
                   
                   
               
             
          
         
       
     
         [0112]    According to an example embodiment, data symbols may be allocated to spreading codes based on a customized logic, for example, grey coding. Table 5 shows a representative example in which data symbols corresponding to k=3 and M=8 are allocated to spreading codes. Here, a cyclic shift of an original sequence may be a decimal equivalent of a binary data symbol. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                   
                 Cyclic shift 
                   
               
               
                   
                 (Decimal 
               
               
                 Data-symbol 
                 equivalent) 
                 Spreading sequence 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 000 
                 0 
                 0 
                 0 
                 0 
                 1 
                 −1 
                 0 
                 1 
                 1 
               
               
                 001 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 −1 
                 0 
                 1 
               
               
                 010 
                 2 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 −1 
                 0 
               
               
                 011 
                 3 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 −1 
               
               
                 100 
                 4 
                 −1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                 101 
                 5 
                 1 
                 −1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
               
               
                 110 
                 6 
                 0 
                 1 
                 −1 
                 0 
                 1 
                 1 
                 0 
                 0 
               
               
                 111 
                 7 
                 0 
                 0 
                 1 
                 −1 
                 0 
                 1 
                 1 
                 0 
               
               
                   
               
               
                 *Maximum length shift register sequence (m-sequence) 
               
             
          
         
       
     
         [0113]    An m-sequence or a maximum length sequence may belong to a general grade of a two-level autocorrelation sequence and may be present for all of N=2 m −1 where in denotes an integer. The m-sequence may be generated using a linear feedback shifter register (LFSR) having a primitive polynomial feedback. Such sequence may correspond to a maximum period acquired from a given length LFSR. 
         [0114]    Advantages in the Case of Applying an M-Sequence to a Sequence Design: 
         [0115]    Using the m-sequence to design spreading sequences may be advantageous for all of coherent and noncoherent. 
         [0116]    In view of the noncoherent, using the m-sequence may have the following advantages: 
         [0117]    1) The m-sequence may correspond to a cyclic difference set in a form of □m−1, 2m−1, 2m−2}. 
         [0118]    2) It may indicate a constant in phase autocorrelation of (N+1)/4 of a unipolar binary element {0, 1}. 
         [0119]    In view of the coherent, using the m-sequence may have the following advantages: 
         [0120]    1) If m-sequence=perfect square, a perfect sequence of elements {0, −1, 1} may he generated from the m-sequence, for example, the procedure A to maintain the element of 0. 
         [0121]    2) Perfect sequences with the periods of 7 and 31 may be acquired. 
         [0122]    3) Such sequence may be expanded based on zero padding and a correlation attribute may not be damaged. The result thereof may be represented as sequences with the periods of 8 and 32. A ternary sequence close to perfection may be acquired for a spreading code 15 through the procedure B by the aforementioned method. 
         [0123]    Procedure A: Acquires a Perfect Ternary Sequence from an M-Sequence: 
         [0124]    If x and y are two ideal two-level autocorrelation sequences, u sequence {θ(x,y)+1} may be a perfect sequence including an element of 0 in phase autocorrection. Here, θ(x,y) denotes a cross-correlation sequence between sequences x and y. If two sequences are selected as a preferred pair among m-sequences, a result thereof, that is, {θ(x,y)+1} may be ternary. For example, if preferred pair= 
         [0000]    
       
         
           
             
               
                 θ 
                  
                 
                   ( 
                   
                     x 
                     , 
                     y 
                   
                   ) 
                 
               
               ∈ 
               
                 { 
                 
                   
                     - 
                     1 
                   
                   , 
                   
                     
                       - 
                       1 
                     
                     + 
                     
                       2 
                       
                         
                           n 
                           + 
                           1 
                         
                         2 
                       
                     
                   
                   , 
                   
                     - 
                     1 
                   
                   , 
                   
                     - 
                     
                       2 
                       
                         
                           n 
                           + 
                           1 
                         
                         2 
                       
                     
                   
                 
                 } 
               
             
             , 
           
         
       
     
         [0000]    it may be represented as 
         [0000]    
       
         
           
             
               
                 θ 
                  
                 
                   ( 
                   
                     x 
                     , 
                     y 
                   
                   ) 
                 
               
               + 
               1 
             
             ∈ 
             
               
                 { 
                 
                   0 
                   , 
                   
                     ± 
                     
                       2 
                       
                         
                           n 
                           + 
                           1 
                         
                         2 
                       
                     
                   
                 
                 } 
               
               . 
             
           
         
       
     
         [0000]    A result acquired by dividing 
         [0000]    
       
         
           
             
               { 
               
                 
                   θ 
                    
                   
                     ( 
                     
                       x 
                       , 
                       y 
                     
                     ) 
                   
                 
                 + 
                 1 
               
               } 
             
              
             
                 
             
              
             by 
              
             
                 
             
              
             
               2 
               
                 
                   n 
                   + 
                   1 
                 
                 2 
               
             
           
         
       
     
         [0000]    may be represented as a sequence including elements {0, ±1}. 
         [0125]    Procedure B: Acquires a Ternary Sequence Close to Perfection from an M-Sequence. 
         [0126]    A perfect ternary sequence may be present if a weight of a sequence is a perfect square. Accordingly, a perfect ternary sequence having a period of 15 may be absent. In this case, a ratio between elements of −1 and elements of +1 in the perfect ternary sequence may be a value between 1/3 and 2/3. Accordingly, the ternary sequence close to perfection may be acquired based on the ratio. A sequence having a smallest MSAC value may be selected. The MSAC may be defined as Equation 7. 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     MSAC 
                   
                   = 
                   
                     
                       1 
                       
                         ( 
                         
                           N 
                           - 
                           1 
                         
                         ) 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           τ 
                           = 
                           1 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           R 
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
         [0127]    In Equation 7, R(τ) denotes periodic autocorrelation of a sequence in delay τ. 
         [0128]    &lt;Transmission and Reception of Ternary Payload Sequence&gt; 
         [0129]      FIG. 2  illustrates a format of a transmission frame according to an example embodiment. 
         [0130]    Referring to  FIG. 2 , a transmission frame  200  may include a preamble  210 , a start frame delimiter (SFD)  220 , a physical layer header (PHR)  230 , and a physical service data unit (PSDU)  240 . In one example embodiment, a packet may be used as the same meaning as the transmission frame  200 . 
         [0131]    The preamble  210  may be a bitstream recorded at the head of the transmission frame  200 . The preamble  210  may include a specific bit-pattern for time synchronization. 
         [0132]    The SFD  220  may identify a beginning of a frame, and may identify reconfirmation of synchronization. Also, the SFD  220  may indicate a field for acquiring frame synchronization. 
         [0133]    The PHR  230  may be a field that indicates useful information associated with a physical layer For example, information may be information about a length indicator, a used modulation scheme, and a used encoding scheme. Also, the PHR  230  may include a header check sequence (WS) and a field about a format of the PSDU  240 . Here, the HCS may he used to determine whether an error has occurred in the PHR  230 . 
         [0134]    The PSDU  240  may be a unit of data transferred from an upper layer of the physical layer and not encoded in a format of bits. The PSDU  240  may include data that is substantially transmitted and received in the upper layer of the physical layer. The PSDU  240  may be expressed as a payload. 
         [0135]      FIG. 3  is a block diagram illustrating a transmitter according to an example embodiment. 
         [0136]    Referring to  FIG. 3 , a transmitter  300  may include a first signal converter  310  and a second signal converter  320 . Here, the transmitter  300  may indicate the coherent transmitter  110  of  FIG. 1 . Hereinafter, a scheme in which a transmitter converts a binary data sequence to a first signal and a second signal may also be referred to as a ternary amplitude shift keying (TASK) scheme, a ternary frequency shift keying (TFSK) scheme, or an ON-OFF FSK scheme. 
         [0137]    The first signal converter  310  may convert a ternary payload sequence including elements of −1, 0, or 1 to the first signal. In one example embodiment, elements may be represented using an alphabet or a chip. 
         [0138]    The first signal converter  310  may include a ternary sequence mapper and a converter. The ternary sequence mapper may generate a ternary payload sequence by mapping a pre-designed ternary sequence to a binary data sequence. In one example embodiment, the ternary sequence mapper may generate a ternary payload sequence by dividing a binary data sequence including elements of 0 or 1 based on a predetermined length, and by mapping a pre-designed ternary sequence to the divided binary data sequence. Here, the pre-designed ternary sequence may indicate a ternary sequence extracted during the aforementioned ternary sequence design process. Also, the pre-designed ternary sequence may be pre-stored in the transmitter  300 . For example, the pre-designed ternary sequence may be stored in a lookup table. 
         [0139]    According to an example embodiment, in the case of using a 3/8 TASK modulation scheme, a ternary sequence mapped to a binary data sequence may be shown as in Table 6. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
               
             
             
               
                 000 
                 0 
                 c 0   
               
               
                 100 
                 1 
                 c 1   
               
               
                 110 
                 2 
                 c 2   
               
               
                 010 
                 3 
                 c 3   
               
               
                 011 
                 4 
                 c 4   
               
               
                 111 
                 5 
                 c 5   
               
               
                 101 
                 6 
                 c 6   
               
               
                 001 
                 7 
                 c 7   
               
               
                   
               
             
          
         
       
     
         [0140]    In Table 6, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, m denotes an integer between 1 and 7. For example, C 1  may denote a sequence of [1 0 0 0 1 −1 0 1] and C 2  may denote a sequence of [1 1 0 0 0 1 −1 0]. 
         [0141]    In the case of using a 5/32 TASK modulation scheme, a ternary sequence mapped to a binary data sequence may be shown as in Table 7. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
         [0142]    In Table 7, C 0  denotes a sequence of [−1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1] and (̂ denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, m denotes an integer between 1 and 31. 
         [0143]    According to an example embodiment, the ternary sequence mapper may search Table 6 or Table 7 for a ternary sequence corresponding to a binary data sequence, may extract the retrieved ternary sequence as a pre-designed ternary sequence, and may map the pre-designed ternary sequence to the binary data sequence. 
         [0144]    The converter may modulate a ternary payload sequence using a TASK modulation scheme, and may convert the ternary payload sequence, or a chip sequence of a payload, or a chip sequence of a PPM, to a first signal. 
         [0145]    According to an example embodiment, the converter may modulate a ternary payload sequence using an amplitude shift keying (ASK) modulation scheme. Here, the converter may map the ternary payload sequence as shown in Equation 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     A 
                     n 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             + 
                             A 
                           
                         
                         
                           
                             
                               when 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                             = 
                             
                               + 
                               1 
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             
                               when 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           
                             - 
                             A 
                           
                         
                         
                           
                             
                               when 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                             = 
                             
                               - 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
         [0146]    In Equation 8, {d(n)} denotes the ternary payload sequence, A n  denotes an amplitude of an n th  element or chip, and A denotes a transmission voltage level. Gaussian pulse shaping may be employed for the ASK modulation scheme. The respective elements of the ternary payload sequence may be generated at rates of 1 Mchip/s for 2.4 GHz band; 600 Kchips/s for 780 MHz, 863 MHz, 900 MHz and 950 MHz bands; and 250 Kchips/s for 433 MHz and 470 MHz bands. 
         [0147]    Also, the first signal converter  310  may include a pulse shaping filter. The pulse shaping filter may sequentially receive elements of the ternary payload sequence, thereby enabling a shape of the first signal of a baseband to be smoothly changed instead of being suddenly changed on a time axis. Accordingly, the pulse shaping filter may adjust a frequency hand of the first signal not to be widely distributed. 
         [0148]    According to an example embodiment, the pulse shaping filter may adjust a transmit power spectrum. The pulse shaping filter may approximate an ideal Gaussian pulse having a section of T and BT of 0.3 to 0.5. An impulse response of the pulse shaping filter may be represented as Equation 9. 
         [0000]    
       
         
           
             
               
                 
                   
                     g 
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     B 
                      
                     
                       
                         
                           2 
                            
                           π 
                         
                         
                           ln 
                            
                           
                             ( 
                             2 
                             ) 
                           
                         
                       
                     
                      
                     
                        
                       
                         - 
                         
                           ( 
                           
                             
                               2 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 B 
                                 2 
                               
                                
                               
                                 t 
                                 2 
                               
                             
                             
                               l 
                                
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
         [0149]    Also, the first signal modulated from the ternary payload sequence may be represented as Equation 10. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       x 
                       BB 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     A 
                      
                     
                       
                         ∑ 
                         
                           
                             
                               n 
                               = 
                             
                             ] 
                           
                           ⌊ 
                         
                         
                           
                             W 
                             pp 
                           
                            
                           DU 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           d 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                         
                           g 
                            
                           
                             ( 
                             
                               t 
                               - 
                               
                                 nT 
                                 chip 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
         [0150]    In Equation 10, d(n)∈{−1, 0, 1} denotes an element of the ternary payload sequence, T chip  denotes a section of the first signal corresponding to the element, and N PPDU  denotes a number of elements of the ternary payload sequence. Elements of the ternary payload sequence may be represented as Equation 11. 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         d 
                          
                         
                           ( 
                           1 
                           ) 
                         
                       
                       , 
                       … 
                        
                       
                           
                       
                       , 
                       
                         d 
                          
                         
                           ( 
                           
                             N 
                             PPDU 
                           
                           ) 
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       [ 
                       
                         
                           { 
                           
                             
                               
                                 c 
                                 pre 
                               
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 c 
                                 pre 
                               
                                
                               
                                 ( 
                                 
                                   N 
                                   p 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                         , 
                         
                           { 
                           
                             
                               
                                 c 
                                 SFD 
                               
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 c 
                                 SFD 
                               
                                
                               
                                 ( 
                                 
                                   N 
                                   S 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                         , 
                         
                           { 
                           
                             
                               
                                 c 
                                 PHR 
                               
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               
                                 c 
                                 PHR 
                               
                                
                               
                                 ( 
                                 
                                   N 
                                   R 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                         , 
                         
                           { 
                           
                             
                               c 
                                
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             , 
                             … 
                              
                             
                                 
                             
                             , 
                             
                               c 
                                
                               
                                 ( 
                                 
                                   N 
                                   D 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
         [0151]    In Equation 11, 
         [0000]    
       
         
           
             { 
             
               
                 
                   c 
                   bLG 
                 
                  
                 
                   ( 
                   ! 
                   ) 
                 
               
               , 
               
                 … 
                  
                 
                     
                 
                  
                  
                 
                     
                 
                  
                 
                   ( 
                   ) 
                 
               
             
             } 
           
         
       
     
         [0000]    denotes a chip sequence that configures a preamble field, 
         [0000]    
       
         
           
             { 
             
               
                 c 
                 
                   SFD 
                    
                   
                       
                   
                    
                 
               
               , 
               … 
                
               
                   
               
                
               
                 , 
                 cSFD 
               
                
               
                 
                   ( 
                   
                     N 
                     s 
                   
                   ) 
                 
                 } 
               
             
           
         
       
     
         [0000]    denotes a chip sequence that configures a spreading SFD field, {C PHR (1), . . . , C PHR (iŶ)} denotes a chip sequence that configures a spreading PHR field, and {c(1), . . . , c(N D )} denotes a chip sequence that configures an encoded ternary sequence spreading PSDU field. 
         [0152]    A pass band of the first signal modulated from the ternary payload sequence may be represented as Equation 12. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       x 
                       PB 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         A 
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               1 
                             
                             
                               N 
                               PPDU 
                             
                           
                            
                           
                               
                           
                            
                           
                             
                               d 
                                
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                              
                             
                               g 
                                
                               
                                 ( 
                                 
                                   t 
                                   - 
                                   
                                     nT 
                                     chip 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             
                               ω 
                               c 
                             
                              
                             t 
                           
                           + 
                           φ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
         [0153]    In Equation 12, ω c  denotes an angular frequency of a carrier signal and φ∈[0,2π] denotes a random phase. 
         [0154]    Also, the second signal converter  320  may convert the first signal to a second signal by converting each section of the first signal based on an element of the ternary payload sequence. The second signal converter  320  may include a zero-value converter configured to convert a section corresponding to an element of 0 in the first signal and an absolute one value converter configured to convert a section corresponding to an element of 1 and a section corresponding to element of −1 in the first signal. 
         [0155]    The zero-value converter may convert the section corresponding to the element of 0 in the first signal using a zero-value detector and an ON-OFF controller. The zero-value detector may detect the section corresponding to the element of 0 in the first signal. For example, the zero-value detector may detect a section in which an amplitude of the first signal is close to 0 as the section corresponding to the element of 0. The ON-OFF controller may turn OFF an output of the section corresponding to the element of 0 detected at the zero-value detector. Accordingly, an amplitude value of a section corresponding to the element of 0 in the second signal may be zero. 
         [0156]    Further, the absolute one value converter my detect the section corresponding to the element of 1 and the section corresponding to the element of −1 in the first signal, and may convert the section corresponding to the element of 1 and the section corresponding to the element of −1 by applying different conversion schemes. 
         [0157]    According to an example embodiment, the absolute one value converter may detect the section corresponding to the element of 1 and the section corresponding to the element of −1 in the first signal using an absolute value detector and a sign detector. The absolute value detector may detect a section corresponding to an element of an absolute one value in the first signal, for example, a section in which an amplitude of the first signal is greater than or equal to a threshold value, as the section corresponding to the element of the absolute one value. The sign detector may detect a signal of the element of the absolute one value and may classify the section corresponding to the element of the absolute one value into the section corresponding to the element of 1 and the section corresponding to the element of −1. For example, the sign detector may detect a section corresponding to a phase of zero degrees as the section corresponding to the element of 1 and a section corresponding to a phase of 180 degrees as the section corresponding to the element of −1, in the section corresponding to the element of the absolute one value. 
         [0158]    Also, the absolute one value converter may convert the selection corresponding to the element of and the section corresponding to the element of −1 using a frequency shifter or/and a phase shifter. For example, when transmitting a second signal to a noncoherent receiver, the absolute one value converter may convert the section corresponding to the element of 1 and the section corresponding to the element of −1 using the frequency shifter. When transmitting a second signal to a coherent receiver, the absolute one value converter may convert the section corresponding to the element of 1 and the section corresponding to the element of −1 using all of the frequency shifter and the phase shifter. 
         [0159]    The frequency shifter may shift a frequency of the section corresponding to the element of 1 in the first signal to a frequency f 1 , and may shift a frequency of the section corresponding to the element of −1 in the first signal to a frequency f 2 . 
         [0160]    For example, when converting the section corresponding to the element of 1 in the first signal, the frequency shifter may shift a frequency of a carrier signal adjusted by voltage controlled oscillation (VCO) to a frequency and the absolute one value converter may multiply the carrier signal shifted to the frequency f 1  by an absolute value of an amplitude of the section corresponding to the element of 1. Also, the frequency shifter may shift, to the frequency f 1 , a frequency of a carrier signal having an envelope corresponding to a value that is proportional to the absolute value of the amplitude of the section corresponding to the element of 1. As another example, when converting the section corresponding to the element of −1 in the first signal, the frequency shifter may shift a frequency of a carrier signal adjusted by VCO to a frequency f 2 , and the absolute one value converter may multiply the carrier signal shifted to the frequency f 2  by an absolute value of an amplitude of the section corresponding to the element of −1. Also, the frequency shifter may shift, to the frequency f 2 , a frequency of a carrier signal having an envelope corresponding to a value that is proportional to the absolute value of the amplitude of the section corresponding to the element of −1. According to an example embodiment, the frequency f 1  and the frequency f 2  may have different frequency bands. For example, the frequency f 2  may be mater than the frequency f 1 . 
         [0161]    Also, the phase shifter may shift a phase of the section corresponding to the element of 1 in the first signal to a phase θ 1 , and may shift a phase of the section corresponding to the element of −1 to a phase θ 2 . For example, the phase shifter may shift a phase of a carrier signal to zero degrees, and the absolute one value converter may multiply the carrier signal shifted to zero degrees by an absolute value of an amplitude of the section corresponding to the element of 1. Also, the phase shifter may shift, to zero degrees, a phase of a carrier signal having an envelope corresponding to a value that is proportional to the absolute value of the amplitude of the section corresponding to the element of 1. As another example, the phase shifter may shift a phase of a carrier signal to 180 degrees, and the absolute one value converter may multiply the carrier signal shifted to 180 degrees by an absolute value of an amplitude of the section corresponding to the element of −1. Also, the phase shifter may shift, to 180 degrees, a phase of a carrier signal having an envelope corresponding to a value that is proportional to the absolute value of the amplitude of the section corresponding to the element of −1. 
         [0162]    According to an example embodiment, the phase shifter may shift, to the phase θ 1 , a phase of the section corresponding to the element of 1 shifted to the frequency f 1  by the frequency shifter, and may shift, to the phase θ 2 , a phase of the section corresponding to the element of −1 shifted to the frequency f 2  by the frequency shifter. 
         [0163]    Also, the second signal converter  320  may include an amplifier. The amplifier may amplify an amplitude of the converted second signal. The transmitter  300  may transmit the amplified second signal to the noncoherent receiver or the coherent receiver via an antenna. 
         [0164]      FIGS. 4 through 6  are block diagrams illustrating examples of a transmitter according to another example embodiment. 
         [0165]    Referring to  FIG. 4 , a transmitter  400  may transmit data to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. The transmitter  400  may include a first signal converter  410  and a second signal converter  420 . The first signal converter  410  may include a ternary sequence mapper  411  and a pulse shaping filter  412 . 
         [0166]    The ternary sequence mapper  411  may generate a ternary payload sequence by dividing a binary data sequence including elements of 0 or 1 based on a predetermined length, and by mapping a pre-designed ternary sequence to the divided binary data sequence. For example, if a binary data sequence of [1 0 1 0 0 1 1 1 0] is input to the ternary sequence mapper  411 , the ternary sequence mapper  411  may divide the binary data sequence into [1 0 1], [0 0 1], and [1 1 0]. The ternary sequence mapper  411  may map the pre-designed ternary sequence to the divided binary data sequence. For example, if a pre-designed ternary sequence corresponding to a divided binary data sequence [1 0 1] is [0 1 −1 0 1 1 0 0], the ternary sequence mapper  411  may generate a ternary payload sequence [0 1 −1 0 1 1 0 0] by mapping the ternary sequence [0 1 −1 0 1 1 0 0] to the divided binary sequence [1 0 1]. Also, the ternary sequence mapper  411  may modulate a ternary payload sequence to a first signal. 
         [0167]    Also, the ternary sequence mapper  411  may modulate the ternary payload sequence using an ASK modulation scheme. According to an example embodiment, the ternary sequence mapper  411  may include the converter of  FIG. 3 . For example, when modulating a ternary payload sequence [0 1 −1 0 1 1 0 0] to a first signal, an amplitude of a section of the first signal corresponding to 0 of the ternary payload sequence may be zero, an amplitude of a section of the first signal corresponding to 1 may have a positive value, and an amplitude of a section of the first signal corresponding to −1 may have a negative value. 
         [0168]    The pulse shaping filter  412  may sequentially receive elements of the ternary payload sequence and may adjust a frequency band of the first signal not to be widely distributed. 
         [0169]    The second signal converter  420  may include a zero-value converter  430 , an absolute one value converter  440 , and an amplifier  450 . 
         [0170]    The zero-value converter  430  may include a zero-value detector  431  and an ON-OFF controller  432 . The zero-value detector  431  may detect a section in which an amplitude of the first signal is less than a threshold value as a section corresponding to an element of 0. Here, the threshold value may denote a magnitude of noise of the first signal. The ON-OFF controller  432  may turn OFF output of the section corresponding to the element of 0 detected at the zero-value detector  431 . 
         [0171]    The absolute one value converter  440  may include an absolute value detector  441 , a sign detector  442 , a VCO  443 , a frequency shifter  444 , and a calculator  445 . 
         [0172]    The absolute value detector  441  may detect a section in which an amplitude of the first signal is greater than or equal to a threshold value as a section corresponding to an element of an absolute one value. The sign detector  442  may detect a signal of the element of the absolute one value and may classify the section corresponding to the element of the absolute one value into the section corresponding to the element of 1 and the section corresponding to the element of −1. For example, the sign detector  442  may detect a section corresponding to a phase of zero degrees in the section corresponding to the element of the absolute one value as the section corresponding to the element of 1, and may detect the section corresponding to a phase of 180 degrees as the section corresponding to the element of −1. 
         [0173]    The VCO  443  may adjust a frequency of a carrier signal. The frequency shifter  444  may shift a frequency of a carrier signal of the section corresponding to the element of 1 to a frequency f 1 , and may shift a frequency of a carrier signal of the section corresponding to the element of −1 to a frequency f 2 . 
         [0174]    The calculator  445  may generate a second signal by multiplying carrier signal shifted to the frequency f 1  by an absolute value of an amplitude of the section corresponding to the element of 1 and by multiplying the carrier signal shifted to the frequency f 2  by an absolute value of an amplitude of the section corresponding to the element of −1. 
         [0175]    The amplifier  450  may amplify an amplitude of the second signal. The transmitter  400  may transmit the amplified second signal to the noncoherent receiver or the coherent receiver via an antenna. 
         [0176]    Referring to  FIG. 5 , a transmitter  500  may transmit data to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. The transmitter  500  may include a first signal converter  510  and a second signal converter  520 . The first signal converter  510  may include a ternary sequence mapper  511  and a pulse shaping filter  512 . 
         [0177]    The ternary sequence mapper  511  may generate a ternary payload sequence by receiving a binary data sequence including elements of 0 or 1, by dividing the binary data sequence based on a predetermined length, and by mapping a pre-designed ternary sequence to the divided binary data sequence. 
         [0178]    Also, the first signal converter  510  may generate a first signal by modulating the ternary payload sequence. According to an example embodiment, the ternary sequence mapper  511  may include the converter of  FIG. 3 . 
         [0179]    The pulse shaping filter  512  may sequentially receive elements of the ternary payload sequence and may adjust a frequency band of the first signal not to be widely distributed. 
         [0180]    The second signal converter  520  may include a zero-value converter  530 , an absolute one value converter  540 , and an amplifier  550 . 
         [0181]    The zero-value converter  530  may include a zero-value detector  531  and an ON-OFF controller  532 . The zero-value detector  531  may detect a section in which an amplitude of the first signal is less than a threshold value as a section corresponding to an element of 0. Here, the threshold value may denote a magnitude of noise of the first signal. The ON-OFF controller  532  may turn OFF output of the section corresponding to the element of 0 detected at the zero-value detector  531 . 
         [0182]    The absolute one value converter  540  may include an absolute value detector  541 , a sign detector  542 , a phase shifter  543 , and a calculator  544 . 
         [0183]    The absolute value detector  541  may detect a section in which an amplitude of the first signal is greater than or equal to a threshold value as a section corresponding to an element of an absolute one value. The sign detector  542  may detect a sign of the element of the absolute one value and may classify the section corresponding to the element of the absolute one value into a section corresponding to an element of 1 and a section corresponding to an element of −1. 
         [0184]    The phase shifter  543  may shift a phase of a carrier signal of the section corresponding to the element of 1 to a first phase and may shift a phase of a carrier signal of the section corresponding to the element of −1 to a second phase, in the first signal. 
         [0185]    The calculator  544  may generate a second signal by multiplying the carrier signal shifted to the first phase by an absolute value of an amplitude of the section corresponding to the element of 1 and by multiplying the carrier signal shifted to the second phase by an absolute value of an amplitude of the section corresponding to the element of −1. 
         [0186]    The amplifier  550  may amplify an amplitude of the second signal. The transmitter  500  may transmit the amplified second signal to the noncoherent receiver or the coherent receiver via an antenna. 
         [0187]    Referring to  FIG. 6 , a transmitter  600  may transmit data to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. The transmitter  600  may include a first signal converter  610  and a second signal converter  620 . The first signal converter  610  may include a ternary sequence mapper  611  and a pulse shaping filter  612 . 
         [0188]    The ternary sequence mapper  611  may generate a ternary payload sequence by receiving a binary data sequence including elements of 0 or 1, by dividing the ternary payload sequence based on a predetermined length, and by mapping a pre-designed ternary sequence to the divided binary data sequence. 
         [0189]    Also, the first signal converter  610  may generate a first signal by modulating the ternary payload sequence. According to an example embodiment, the ternary sequence mapper  611  may include the converter of  FIG. 3 . 
         [0190]    The pulse shaping filter  612  may sequentially receive elements of the ternary payload sequence and may adjust a frequency band of the first signal not to be widely distributed. 
         [0191]    The second signal converter  620  may include a zero-value converter  630 , an absolute one value converter  640 , and an amplifier  650 . 
         [0192]    The zero-value converter  630  may include a zero-value detector  631  and an ON-OFF controller  632 . The zero-value detector  631  may detect a section in which an amplitude of the first signal is less than a threshold value as a section corresponding to an element of 0. Here, the threshold value may denote a magnitude of noise of the first signal. The ON-OFF controller  632  may turn OFF output of the section corresponding to the element of 0 detected at the zero-value detector  631 . 
         [0193]    The absolute one value converter  640  may include an absolute value detector  641 , a sign detector  642 , a VCO  643 , a frequency shifter  644 , a phase shifter  645 , and a calculator  646 . 
         [0194]    The absolute value detector  641  may detect a section in which an amplitude of the first signal is greater than or equal to a threshold value as a section corresponding to an element of an absolute one value. The sign detector  642  may detect a sign of the element of the absolute one value and may classify the section corresponding to the element of the absolute one value into a section corresponding to an element of 1 and a section corresponding to an element of −1. 
         [0195]    The VCO  643  may adjust a frequency of a carrier signal. The frequency shifter  644  may shift a carrier signal of the section corresponding to the element of 1 to a frequency f 1 , and may shift a carrier signal of the section corresponding to the element of −1 to a frequency f 2 . The phase shifter  645  may shift, to a phase θ 1 , a phase of the carrier signal shifted to the frequency f 1  at the frequency shifter  644  and may shift, to a phase θ 2 , a phase of the carrier signal shifted to the frequency f 2  at the frequency shifter  644   
         [0196]    The calculator  646  may generate a second signal by multiplying the carrier signal shifted to the frequency f 1  and the phase θ 1  by an absolute value of an amplitude of the section corresponding to the element of 1, and by multiplying the carrier signal shifted to the frequency f 2  and the phase θ 2  by an absolute value of an amplitude of the section corresponding to the element of −1. 
         [0197]    The amplifier  650  may amplify an amplitude of the second signal. The transmitter  600  may transmit the amplified second signal to the low selectivity noncoherent receiver, the high selectivity noncoherent receiver, or the coherent receiver via an antenna. 
         [0198]      FIGS. 7 through 9  illustrate examples of a transmission signal according to an example embodiment. 
         [0199]    Referring to  FIG. 7 , a transmitter may modulate a binary data sequence, and may transmit the modulated binary data sequence to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. When a binary data sequence  710  is transmitted to the transmitter, the transmitter may generate a first signal by mapping, to the binary data sequence  710 , a ternary sequence  720  that is preset to correspond to the binary data sequence  710 , and by modulating the ternary sequence  720 . The transmitter may input the first signal to a pulse shaping filter and may adjust a frequency band of the first signal not to be widely distributed. In a pulse shaping filter output signal  730 , an amplitude of a section corresponding to an element of 1 may have a positive value, an amplitude of a section corresponding to an element of −1 may have a negative value, and an amplitude of a section corresponding to an element of 0 may be zero. 
         [0200]    In the pulse shaping filter output signal  730 , the transmitter may shift a frequency of a carrier signal of the section corresponding to the element of 1 to a frequency f 1 , and may shift a frequency of a carrier signal of the section corresponding to the element of −1 to a frequency f 2 . Here, an amplitude of the second frequency may be greater than an amplitude of the first frequency. Also, the transmitter may generate a second signal by multiplying the carrier signal shifted to the frequency f 1  by an absolute value of an amplitude of the section corresponding to the element of 1 and by multiplying the carrier signal shifted to the frequency f 2  by an absolute value of an amplitude of the section corresponding to the element of −1. The transmitter may amplify the second signal by inputting the second signal to an amplifier. In an amplified second signal  740 , a frequency of the section corresponding to the element of 1 may be distinguished from a frequency of the section corresponding to the element of −1. An output of the section corresponding to the element of 0 may be zero. The transmitter may transmit the amplified second signal  740  to the low selectivity noncoherent receiver and the high selectivity noncoherent receiver. 
         [0201]    Referring to  FIG. 8 , a transmitter may modulate a binary data sequence, and may transmit the modulated binary data sequence to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. When a binary data sequence  810  is input to the transmitter, the transmitter may generate a first signal by mapping, to the binary data sequence  810 , a ternary sequence  820  that is preset to correspond to the binary data sequence  810 , and by modulating the ternary sequence  820 . The transmitter may input the first signal to a pulse shaping filter and may adjust a frequency band of the first signal not to be widely distributed. In a pulse shaping filter output signal  830 , an amplitude of a section corresponding to an element of 1 may have a positive value, an amplitude of a section corresponding to an element of −1 may have a negative value, and an amplitude of a section corresponding to an element of 0 may be zero. 
         [0202]    In the pulse shaping filter output signal  830 , the transmitter may shift a phase θ 2  carrier signal of the section corresponding to the element of 1 to a phase θ 1 , and may shift a phase of a carrier signal of the section corresponding to the element of −1 to a phase θ 2 . Here, a difference between the phase θ 1  and the phase θ 2  may be 180 degrees. Also, the transmitter may generate a second signal by multiplying the carrier signal shifted to the phase θ 1  by an absolute value of an amplitude of the section corresponding to the element of 1 and by multiplying the carrier signal shifted to the phase θ 2  by an absolute value of an amplitude of the section corresponding to the element of −1. The transmitter may amplify the second signal by inputting the second signal to an amplifier. As shown in a section  841  of an amplified second signal  840 , a difference between a phase of the section corresponding to the element of 1 and a phase of the section corresponding to the element of −1 may be 180 degrees. Also, an output of the section corresponding to the element of 0 may be zero. The transmitter may transmit the amplified second signal  840  to the noncoherent receiver and the coherent receiver. 
         [0203]    Referring to  FIG. 9 , a transmitter may modulate a binary data sequence and may transmit the modulated binary data sequence to a low selectivity noncoherent receiver, a high selectivity noncoherent receiver, or a coherent receiver. When a binary data sequence  910  is input to the transmitter, the transmitter may generate a first signal by mapping, to the binary data sequence  910 , a ternary sequence  920  that is preset to correspond to the binary data sequence  910  and by modulating the ternary sequence  920 . The transmitter may input the first signal to a pulse shaping filter and may adjust a frequency band of the first signal not to be widely distributed. In a pulse shaping filter output signal  930 , an amplitude of a section corresponding to an element of 1 may have a positive value, an amplitude of a section corresponding to an element of −1 may have a negative value, and an amplitude of a section corresponding to an element of 0 may be zero. 
         [0204]    In the pulse shaping filter output signal  930 , the transmitter may shift a frequency of a carrier signal of the section corresponding to the element of 1 to a frequency f 1 , and may shift a frequency of a carrier signal of the section corresponding to the element of −1 to a frequency f 2 . Also, the transmitter may shift, to a phase θ 1 , a phase of the carrier signal shifted to the frequency and may shift, to a phase θ 2 , a phase of the carrier signal shifted to the frequency f 2 . Here, an amplitude of the frequency f 2  may be greater than an amplitude of the frequency f 1  and a difference between the phase θ 1  and the phase θ 2  may be 180 degrees. Also, the transmitter may generate a second signal by multiplying the carrier signal shifted to the frequency f 1  and the phase θ 1  by an absolute value of an amplitude of the section corresponding to the element of 1 and by multiplying the carrier signal shifted to the frequency f 2  and the phase θ 2  by an absolute value of an amplitude of the section corresponding to the element of −1. The transmitter may amplify the second signal by inputting the second signal to an amplifier. In a section  941  of an amplified second signal  940 , a difference between the phase of the section corresponding to the element of 1 and the phase of the section corresponding to the element of −1 may be 180 degrees. Also, an output of the section corresponding to the element of 0 may be zero. The transmitter may transmit the amplified second signal  940  to the low selectivity noncoherent receiver, the high selectivity noncoherent receiver, or the coherent receiver. 
         [0205]      FIGS. 10 through 12  are block diagram illustrating examples of a receiver according to an example embodiment. 
         [0206]    Referring to  FIG. 10 , a receiver  1000  may include a filter  1010 , an envelope detector  1020 , and a binary data sequence detector  1030 . According to an example embodiment, the receiver  1000  may indicate a low selectivity noncoherent receiver. 
         [0207]    The receiver  1000  may receive a signal from the transmitter of  FIG. 3 . The received signal may be a signal converted from a ternary payload sequence including elements of −1, 0, or 1. 
         [0208]    The filter  1010  may filter the received signal using a frequency f 0 . Here, the frequency f 0  may be a frequency between a frequency f 1  and a frequency f 2 . The frequency f 1  denotes a frequency of a section of the received signal converted from the element of 1 and the frequency f 2  denotes a frequency of a section of the received signal converted from the element of −1, in the ternary payload sequence. For example, the frequency f 0  may be the arithmetic mean between the frequency f 1  and the frequency f 2 . For example, an amplitude of the frequency f 2  may be greater than an amplitude of the frequency f 1 . The low selectivity noncoherent receiver may not accurately distinguish the frequency f 1  and the frequency f 2 . Accordingly, the filter  1010  may filter the received signal using the frequency f 0  corresponding to the frequency f 0  between the frequency f 1  and frequency f 2 , and may receive the received signal in a wide bandwidth in order to cover all of the frequency f 1  and the frequency f 2 . 
         [0209]    The envelope detector  1020  may detect an amplitude value of an envelope of the filtered received signal. In a section in which an amplitude of the received signal is not zero between the frequency f 1  and the frequency f 2 , the envelope detector  1020  may detect an envelope of which an amplitude is not zero in the corresponding section. In a section in which an amplitude of the received signal is zero between the frequency f 1  and the frequency f 2 , the envelope detector  1020  may detect a signal of which an amplitude is zero in the corresponding section and that contains only noise. Accordingly, if a signal to noise ratio (SNR) value is greater than or equal to a preset value, the frequency f 1  and the frequency f 2  may not be distinguished in an envelope. Thus, the receiver  1000  may not distinguish the element of 1 and the element of −1 of the ternary payload sequence. 
         [0210]    The binary data sequence detector  1030  may detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between the detected amplitude value of the envelope and desired binary sequences. The binary data sequence detector  1030  may include a correlator  1031  and a data decoder  1032 . 
         [0211]    The correlator  1031  may calculate the correlation between the detected amplitude value and desired binary sequences. For example, the correlator  1031  may calculate a correlation between an amplitude value of each section of the envelope detected at the envelope detector  1020  and desired binary sequences. 
         [0212]    The binary data sequence detector  1030  may detect, as the binary data sequence, a bit sequence corresponding to a binary sequence having a highest correlation with the detected amplitude value of the envelope among the binary sequences. 
         [0213]    According to an example embodiment, the binary data sequence detector  1030  may include information regarding Table 6 or Table 7. The binary data sequence detector  1030  may extract desired binary sequences by converting an element of −1 to an absolute value in the ternary sequences of Table 6 or Table 7. The binary data sequence detector  1030  may calculate a correlation between the binary sequences and the detected amplitude value of the envelope, may search for a bit sequence corresponding to the binary sequence having the highest correlation from Table 6 or Table 7, and may detect the retrieved bit sequence as the binary data sequence. 
         [0214]    For example, the correlator  1031  may calculate a correlation between desired binary sequences [0 0 0 1 1 0 1 1], [1 0 0 0 1 1 0 1], [1 1 0 0 0 1 1 0], and [0 0 1 1 0 1 1 0] and an amplitude value of each section of an envelope. In this example, if the binary sequence [1 0 0 0 1 1 0 1] has a highest correlation among the binary sequences, the binary data sequence detector  1030  may extract a bit sequence, for example, [1 0 0], corresponding to the binary sequence [1 0 0 0 1 1 0 1] as a binary data sequence. 
         [0215]    The data decoder  1032  may decode the binary data sequence. 
         [0216]    Referring to  FIG. 11 , a receiver  1100  may include an entire envelope detector  1110  and a binary data sequence detector  1120 . According to an example embodiment, the receiver  1100  may indicate a high selectivity noncoherent receiver. 
         [0217]    The receiver  1100  may receive a signal from the transmitter described with reference to  FIGS. 3 and 5 . The received signal may be a signal converted from a ternary payload sequence including elements of −1, 0, or 1. The entire envelope detector  1110  may detect an amplitude value of an envelope of the received signal. 
         [0218]    The entire envelope detector  1110  may include a first filter  1111 , a first envelope detector  1112 , a second filter  1113 , a second envelope detector  1114 , and a calculator  1115 . 
         [0219]    The first filter  1111  may filter the received signal using a frequency f 1 , and the second filter  1112  may filter the received signal using a frequency f 2 . Here, the frequency f 1  may denote a frequency of a section of the received signal in which the element of 1 in the ternary payload sequence is converted, and the frequency f 2  may denote a frequency of a section of the received signal in which the element of −1 in the ternary payload sequence is converted. For example, an amplitude of the frequency f 2  may be greater than an amplitude of the frequency f 1 . 
         [0220]    The first envelope detector  1112  may detect a first envelope indicating an envelope of the received signal filtered based on the frequency f 1 . In a section in which an amplitude of the received signal is not zero at the frequency f 1 , the first envelope detector  1112  may detect an envelope of which an amplitude is not zero in the corresponding section. In a section in which the amplitude of the received signal is zero at the frequency f 1 , the first envelope detector  1112  may detect a signal of which an amplitude is zero in the corresponding section and that contains only noise. Also, in a section in which the amplitude of the received signal is not zero at the frequency f 2 , the first envelope detector  1112  may detect a signal of which an amplitude is zero in the corresponding section and that contains only noise. 
         [0221]    The second envelope detector  1114  may detect a second envelope indicating an envelope of the received signal filtered based on the frequency In a section in which an amplitude of the received signal is not zero at the frequency f 2 , the second envelope detector  1114  may detect an envelope of which an amplitude is not zero in the corresponding section. In a section in which the amplitude of the received signal is zero at the frequency f 2 , the second envelope detector  1114  may detect a signal of which an amplitude is zero in the corresponding section and that contains only noise. Also, in a section in which the amplitude of the received signal is not zero at the frequency f 1 , the second envelope detector  1114  may detect a signal of which an amplitude is zero in the corresponding section and that contains only noise. 
         [0222]    The calculator  1115  may deduct an envelope output from the second envelope detector  1114  from an envelope output from the first envelope detector  1112 . Accordingly, in the section in which the amplitude of the received signal is not zero at the frequency f 1 , the calculator  1115  may output an envelope having a positive amplitude value in the corresponding section. In the section in which the amplitude of the received signal is not zero at the frequency f 2 , the calculator  1115  may output an envelope having a negative amplitude value in the corresponding section. Also, in the section in which the amplitude of the received signal is zero at the frequency f 1  and the frequency f 2 , the calculator  1115  may output an envelope having zero amplitude value in the corresponding section. 
         [0223]    The binary data sequence detector  1120  may detect the binary data sequence corresponding to the ternary payload sequence based on the correlation between the desired ternary sequences and the amplitude value of the envelope detected at the entire envelope detector  1110 . The binary data sequence detector  1120  may include a correlator  1121  and a data decoder  1122 . 
         [0224]    The correlator  1121  may calculate a correlation between the amplitude value of the envelope and each of the ternary sequences. For example, the correlator  1121  may calculate a correlation between an amplitude value of each section of a third envelope and each of the ternary sequences. 
         [0225]    The binary data sequence detector  1120  may detect, as the binary data sequence, a bit sequence corresponding to a ternary sequence having a highest correlation with the detected amplitude value of the envelope among the ternary sequences. 
         [0226]    According to an example embodiment, the binary data sequence detector  1120  may include information regarding Table 6 or Table 7. The binary data sequence detector  1120  may calculate a correlation between the ternary sequences of Table 6 or Table 7 and the detected amplitude value of the envelope, may search for a bit sequence corresponding to the ternary sequence having the highest correlation from Table 6 or Table 7, and may detect the retrieved bit sequence as the binary data sequence. 
         [0227]    For example, the correlator  1121  may calculate a correlation between desired binary sequences [0 0 0 1 −1 0 1 1], [1 0 0 0 1 −1 0 1], [1 1 0 0 0 1 −1 0], and [0 0 1 −1 0 1 1 0] and an amplitude value of each section of an envelope. In this example, if the binary sequence [1 0 0 0 1 −1 0 1] has a highest correlation among the binary sequences, the binary data sequence detector  1120  may extract a bit sequence, for example, [1 0 0], corresponding to the binary sequence [1 0 0 0 1 −1 0 1] as a binary data sequence. 
         [0228]    The data decoder  1122  may decode the binary data sequence. 
         [0229]    Referring to  FIG. 12 , the receiver  1200  may include a correlation detector  1210  and a binary data sequence detector  1220 . According to an example embodiment, the receiver  1200  may indicate a coherent receiver. 
         [0230]    The receiver  1200  may receive a signal from the transmitter described with reference to  FIGS. 3 and 6 . The received signal may be a signal converted from a ternary payload sequence including elements of −1, 0, or 1. The correlation detector  1210  may detect a correlation between the received signal and a carrier signal. The correlation detector  1210  may include a radio frequency (RF)/analog processor  1211  and a first correlator  1211   
         [0231]    The RF/analog processor  1211  may convert the received signal, received via an antenna, to be processed at the first correlator  1212 . The first correlator  1212  may detect a correlation between a reference signal and the received signal. For example, a phase detector may calculate a correlation between a sinusoidal carrier signal and the received signal. 
         [0232]    The binary data sequence detector  1220  may detect a binary data sequence of the received signal based on a correlation between a result value of the correlation and desired ternary sequences. The binary data sequence detector  1220  may include a second correlator  1221  and a data decoder  1222 . 
         [0233]    The second correlator  1221  may calculate a correlation between a result value of the correlation calculated at the first correlator  1212  and the ternary sequences. The binary data sequence detector  1220  may detect, as the binary data sequence, a bit sequence corresponding to a ternary sequence having a highest correlation with the result value of the correlation calculated at the first correlator  1212  among the ternary sequences. 
         [0234]    According to an example embodiment, the binary data sequence detector  1220  may include information regarding Table 6 or Table 7. The binary data sequence detector  1220  may calculate a correlation between the ternary sequences of Table 6 or Table 7 and the amplitude value of the envelope, may search for a bit sequence corresponding to the ternary sequence having the highest correlation from Table 6 or Table 7, and may detect the retrieved bit sequence as the binary data sequence. 
         [0235]    The data decoder  1222  may decode the binary data sequence. 
         [0236]      FIGS. 13 through 15  illustrate examples of detecting a binary data sequence according to an example embodiment. 
         [0237]    A graph of  FIG. 13  shows a spectrum  1311  of a transmission signal transmitted from a transmitter and a filter frequency response  1312  at a low selectivity noncoherent receiver. In the graph, a horizontal axis denotes a frequency and a vertical axis denotes a spectrum power. 
         [0238]    A frequency f 1  of the spectrum  1311  may denote a frequency of a section of the transmission signal converted from an element of 1 in a ternary payload sequence, and a frequency f 2  may denote a frequency of a section of the transmission signal converted from an element of −1 in the ternary payload sequence. According to an example embodiment, a frequency f 0  may be the arithmetic mean of the frequency f 1  and the frequency f 2 . 
         [0239]    The low selectivity noncoherent receiver may not accurately distinguish the frequency f 1  and the frequency f 2  from each other. Accordingly, to cover all of the frequency f 1  and the frequency f 2 , the low selectivity noncoherent receiver may filter the received signal based on the frequency f 0  that is an intermediate frequency between the frequency f 1  and the frequency f 2  using the filter frequency response  1312 . 
         [0240]    The low selectivity noncoherent receiver may detect an envelope of the filtered received signal. The low selectivity noncoherent receiver may detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between an amplitude value of the envelope and desired binary sequences. 
         [0241]    A graph of  FIG. 14  shows a spectrum  1411  of a transmission signal transmitted from a transmitter and filter frequency responses  1412  and  1413  at a high selectivity noncoherent receiver. In the graph, a horizontal axis denotes a frequency and a vertical axis denotes a spectrum power. 
         [0242]    The transmitter may transmit a transmission signal having the spectrum  1411  to the high selectivity noncoherent receiver. 
         [0243]    A frequency f 1  of the spectrum  1411  may denote a frequency of a section of the transmission signal converted from an element of 1 in a ternary payload sequence, and a frequency f 2  may denote a frequency of a section of the transmission signal converted from an element of −1 in the ternary payload sequence. According to an example embodiment, a frequency f 0  may be the arithmetic mean of the frequency f 1  and the frequency f 2 . 
         [0244]    The high selectivity noncoherent receiver may filter the received signal using a first filter in which the frequency f 1  is set as a center frequency and a second filter in which the frequency f 2  is set as a center frequency. The first filter may filter the received signal based on the frequency f 1  using the filter frequency response  1412 , and the second filter may filter the received signal based on the frequency f 2  using the filter frequency response  1413 . 
         [0245]    The high selectivity noncoherent receiver may detect an envelope of the received signal filtered based on the frequency f 1  and an envelope of the received signal filtered based on the frequency f 2 , and may deduct the envelope of the received signal filtered based on the frequency f 2  from the envelope of the received signal filtered based on the frequency f 1 . Accordingly, a section in which the amplitude of the received signal is not zero at the frequency f 1  may appear as an envelope having a positive amplitude value. A section in which the amplitude of the received signal is not zero at the frequency f 2  may appear as an envelope having a negative amplitude value. A section in which the amplitude of the received signal is zero at the frequency f 1  and the frequency f 2  may appear as an amplitude having zero amplitude value. 
         [0246]    The high selectivity noncoherent receiver may detect a binary data sequence corresponding to the ternary payload sequence based on the correlation between the amplitude value of the amplitude and the desired ternary sequences. 
         [0247]    Referring to  FIG. 15 , coordinates may indicate a phase ̂  1511  of a section corresponding to an element of 1 and a phase θ 2    1512  of a section corresponding to an element of −1 in a ternary payload sequence of a received signal received at a coherent receiver. Here, the phase ̂  1511  may indicate zero degrees and the phase θ 2    1512  my indicate 180 degrees. 
         [0248]    The coherent receiver may detect a correlation between a sinusoidal carrier signal and the received signal. 
         [0249]    Also, the coherent receiver may detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between a correlation result value and a desired ternary sequence. 
         [0250]      FIG. 16  is a bloc diagram illustrating a transmitter according to another example embodiment. 
         [0251]    Referring to  FIG. 16 , a transmitter  1600  may include a ternary sequence mapper  1610  and a converter  1620 . According to an example embodiment, the transmitter  1600  may include the first signal converter  310  of  FIG. 3 . 
         [0252]    The ternary sequence mapper  1610  may generate a ternary payload sequence including elements of −1, 0, or 1 by mapping a pre-designed ternary sequence to a binary data sequence. 
         [0253]    According to an example embodiment, the ternary sequence mapper  1610  may extract, from Table 8, a ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence. In Table 8, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and C m  denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, m denotes an integer between 1 and 7. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
               
             
             
               
                 000 
                 0 
                 c 0   
               
               
                 100 
                 1 
                 c 1   
               
               
                 110 
                 2 
                 c 2   
               
               
                 010 
                 3 
                 c 3   
               
               
                 011 
                 4 
                 c 4   
               
               
                 111 
                 5 
                 c 5   
               
               
                 101 
                 6 
                 c 6   
               
               
                 001 
                 7 
                 c 7   
               
               
                   
               
             
          
         
       
     
         [0254]    According to another example embodiment, the ternary sequence mapper  1610  may extract, from Table 9, the ternary sequence corresponding to the binary data sequence as the pre-designed ternary sequence. In Table 9, C 0  denotes a sequence of [−1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1] and 0, denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, m denotes an integer between 1 and 31. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
         [0255]    The converter  1620  may convert the ternary payload sequence to a signal. 
         [0256]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the transmitter of  FIG. 16 , and a further description related thereto will be omitted. 
         [0257]      FIG. 17  is a block diagram illustrating a receiver according to another example embodiment. 
         [0258]    Referring to  FIG. 17 , a receiver  1700  may include a signal receiver  1710  and a detector  1720 . According to an example embodiment, the receiver  1700  may refer to the receiver  1200 ,  1300 ,  1400  described with reference to  FIGS. 10 through 12 . 
         [0259]    The signal receiver  1710  may receive a signal demodulated from a ternary payload sequence generated by mapping a pre-designed ternary sequence to a binary data sequence and including elements of −1, 0, or 1. 
         [0260]    The detector  1720  may detect the pre-designed ternary sequence and binary data sequence. 
         [0261]    According to an example embodiment, the detector  1720  may detect the pre-designed ternary sequence and the binary data sequence using Table 10. In Table 10, C 0  denotes a sequence of [0 0 0 1 −1 0 1 1] and 0, denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, m denotes an integer between 1 and 7. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                 3-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
               
             
             
               
                 000 
                 0 
                 c 0   
               
               
                 100 
                 1 
                 c 1   
               
               
                 110 
                 2 
                 c 2   
               
               
                 010 
                 3 
                 c 3   
               
               
                 011 
                 4 
                 c 4   
               
               
                 111 
                 5 
                 c 5   
               
               
                 101 
                 6 
                 c 6   
               
               
                 001 
                 7 
                 c 7   
               
               
                   
               
             
          
         
       
     
         [0262]    According to another example embodiment, the detector  1720  may detect the pre-designed ternary sequence and the binary data sequence using Table 11. In Table 11, C 0  denotes a sequence of [−1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1] and 0, denotes a sequence acquired by cyclic shifting C 0  to right by m. Here, no denotes an integer between 1 and 31. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 11 
               
               
                   
                   
               
               
                   
                 Binary data sequence 
                 Data symbol 
                 Ternary sequence 
               
               
                   
                 5-tuple 
                 m ∈            
                 c m  ∈            
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 00000 
                 0 
                 c 0   
               
               
                   
                 10000 
                 1 
                 c 1   
               
               
                   
                 11000 
                 2 
                 c 2   
               
               
                   
                 01000 
                 3 
                 c 3   
               
               
                   
                 01100 
                 4 
                 c 4   
               
               
                   
                 11100 
                 5 
                 c 5   
               
               
                   
                 10100 
                 6 
                 c 6   
               
               
                   
                 00100 
                 7 
                 c 7   
               
               
                   
                 00110 
                 8 
                 c 8   
               
               
                   
                 10110 
                 9 
                 c 9   
               
               
                   
                 11110 
                 10 
                 c 10   
               
               
                   
                 01110 
                 11 
                 c 11   
               
               
                   
                 01010 
                 12 
                 c 12   
               
               
                   
                 11010 
                 13 
                 c 13   
               
               
                   
                 10010 
                 14 
                 c 14   
               
               
                   
                 00010 
                 15 
                 c 15   
               
               
                   
                 00011 
                 16 
                 c 16   
               
               
                   
                 10011 
                 17 
                 c 17   
               
               
                   
                 11011 
                 18 
                 c 18   
               
               
                   
                 01011 
                 19 
                 c 19   
               
               
                   
                 01111 
                 20 
                 c 20   
               
               
                   
                 11111 
                 21 
                 c 21   
               
               
                   
                 10111 
                 22 
                 c 22   
               
               
                   
                 00111 
                 23 
                 c 23   
               
               
                   
                 00101 
                 24 
                 c 24   
               
               
                   
                 10101 
                 25 
                 c 25   
               
               
                   
                 11101 
                 26 
                 c 26   
               
               
                   
                 01101 
                 27 
                 c 27   
               
               
                   
                 01001 
                 28 
                 c 28   
               
               
                   
                 11001 
                 29 
                 c 29   
               
               
                   
                 10001 
                 30 
                 c 30   
               
               
                   
                 00001 
                 31 
                 c 31   
               
               
                   
                   
               
             
          
         
       
     
         [0263]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the receiver of  FIG. 17 , and a further description related thereto will be omitted. 
         [0264]      FIG. 18  is a flowchart illustrating a transmission method according to an example embodiment. 
         [0265]    Referring to  FIG. 18 , in operation  1810 , a transmitter my generate a ternary payload sequence by mapping a pre-designed sequence to a binary data sequence. 
         [0266]    In operation  1820 , the transmitter may convert the ternary payload sequence to a first signal. 
         [0267]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the transmission method of  FIG. 18 , and a further description related thereto will be omitted. 
         [0268]      FIG. 19  is a flowchart illustrating a transmission method according to another example embodiment. 
         [0269]    Referring to  FIG. 19 , in operation  1910 , a transmitter may convert a ternary payload sequence including elements of −1, 0, or 1 to a first signal. 
         [0270]    In operation  1920 , the transmitter may convert the first signal to a second signal by applying a different conversion scheme to each section of the first signal based on an element. 
         [0271]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the transmission method of  FIG. 19 , and a further description related thereto will be omitted. 
         [0272]      FIGS. 20 through 23  are flowcharts illustrating examples of a reception method according to an example embodiment. 
         [0273]    Referring to  FIG. 20 , in operation  2010 , a receiver may detect an amplitude value of an envelope of a received signal converted from a ternary payload sequence including elements of −1, 0, or 1. 
         [0274]    In operation  2020 , the receiver may detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between the detected amplitude value of the envelope and desired binary sequences. 
         [0275]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the reception method of  FIG. 20 , and a further description related thereto will be omitted. 
         [0276]    Referring to  FIG. 21 , in operation  2110 , a receiver may detect an amplitude value of an envelope of a received signal converted from a ternary payload sequence including elements of −1, 0, or 1. 
         [0277]    In operation  2120 , the receiver may detect a binary data sequence corresponding to the ternary payload sequence based on a correlation between the detected amplitude value of the envelope and desired ternary sequences. 
         [0278]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the reception method of  FIG. 21 , and a further description related thereto will be omitted. 
         [0279]    Referring to  FIG. 22 , in operation  2210 , a receiver may detect a correlation between a reference signal and a received signal converted from a ternary payload sequence including elements of −1, 0, or 1. 
         [0280]    In operation  2220 , the receiver may detect a binary data sequence corresponding to the ternary payload sequence based on a result value of the correlation and desired ternary sequences. 
         [0281]    The description made above with reference to  FIGS. 1 through 15  may be applicable to the reception method of  FIG. 22 , and a further description related thereto will be omitted. 
         [0282]    Referring to  FIG. 23 , in operation  2310 , a receiver may receive a signal modulated from a ternary payload sequence generated by mapping a pre-designed ternary sequence to a binary data sequence and including elements of −1, 0, or 1. 
         [0283]    In operation  2320 , the receiver may detect the pre-designed ternary sequence and the binary data sequence. Here, the receiver may detect the pre-designed ternary sequence and the binary data sequence using Table 10 and Table 11. 
         [0284]    The apparatuses described herein may be implemented using hardware components, software components, and/or combination of the hardware components and the software components. For example, the apparatuses and the components may be configured using at least one universal computer or special purpose computer, for example, a processor, a controller and an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array (FPA), a programmable logic unit (PLU), a microprocessor or any other device capable of responding to and executing instructions in a defined manner. The processing device may run an operating system (OS) and one or more software applications that run on the OS. The processing device also may access, store, manipulate, process, and create data in response to execution of the software. For purpose of simplicity, the description of a processing device is used as singular; however, one skilled in the art will appreciated that a processing device may include multiple processing elements and multiple types of processing elements. For example, a processing device may include multiple processors or a processor and a controller. In addition, different processing configurations are possible, such as parallel processors. 
         [0285]    The software may include a computer program, a piece of code, an instruction, or some combination thereof, to independently or collectively instruct and/or configure the processing device to operate as desired, thereby transforming the processing device into a special purpose processor. Software and/or data may be embodied permanently or temporarily in any type of machine, component, physical or virtual equipment, computer storage medium or device, or in a propagated signal wave capable of providing instructions or data to or being interpreted by the processing device. The software also may be distributed over network coupled computer systems so that the software is stored and executed in a distributed fashion. The software and data may be stored by one or more non-transitory computer readable recording mediums. 
         [0286]    The methods according to the above-described example embodiments may be recorded in non-transitory computer-readable media including program instructions to implement various operations of the above-described example embodiments. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The program instructions recorded on the media may be those specially designed and constructed for the purposes of examples, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of non-transitory computer-readable media include magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM discs, DVDs, and/or Blue-ray discs; magneto-optical media such as optical discs; and hardware devices that are specially configured to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory (e.g., USB flash drives, memory cards, memory sticks, etc.), and the like. Examples of program instructions include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. The above-described devices may be configured to act as one or more software modules in order to perform the operations of the above-described example embodiments, or vice versa. 
         [0287]    Although example embodiments are described with reference to some example embodiments and drawings, it will be apparent to one of ordinary skill in the art that various modifications and alterations may be made from the description. 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. 
         [0288]    Therefore, the scope of the example embodiments is defined not by the detailed description, but by the claims and their equivalents, and all variations within the scope of the claims and their equivalents are to be construed as being included in the example embodiments.