Patent Publication Number: US-2012044796-A1

Title: Method for generating signal pattern using modulus or sequence, and device thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority from and the benefit under 35 U.S.C. §119(a) of Korean Patent Application Nos. 10-2009-0031548, 10-2009-0038564, 10-2009-0056705, 10-2009-0056708, and 10-2009-0059978, filed on Apr. 10, 2009, Apr. 30, 2009, Jun. 24, 2009, Jun. 24, 2009, and Jul. 1, 2009, respectively, which are hereby incorporated by reference for all purposes as if fully set forth herein. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     Embodiments of the present invention relate to a method and an apparatus for generating a signal pattern used in a transmission/reception process between a terminal and a base station in a wireless communication system. More particularly, embodiments of the present invention relate to a method and an apparatus for generating a cell-specific Positioning Reference Signal (PRS) pattern, which is a signal pattern used to measure a location of a UE (User Equipment) through a reference signal (or a pilot) in an OTDOA (Observed Time Difference Of Arrival) manner in an OFDM (Orthogonal Frequency Division Multiplexing) based wireless mobile communication system, among signal patterns. 
     2. Discussion of the Background 
     A terminal or a base station transmits and receives a predetermined signal in a specific time and frequency band for a channel estimation, a position estimation, and a transmission/reception of information for control information or a scheduling required for a process of wireless communication between the terminal and the base station. That is, the terminal or the base station may insert a specific signal or symbol into a 2-dimensional domain grid of a time/frequency at regular intervals or irregular intervals. A form in which the specific signal is inserted into a 2-dimensional region of a time/frequency corresponds to a signal pattern. For example, a Reference Signal (RS) is transmitted in a specific time and frequency band for a frequency domain channel estimation, and a rule for the specific time and frequency band in which the reference signal is transmitted corresponds to a reference signal pattern. 
     The present invention relates to a technology of forming the signal patterns by using a modular sonar sequence. More particular, the present invention relates to a technology of forming a cell-specific positioning reference signal pattern, which is a signal pattern used to measure a position of a UE through a reference signal in an OTDOA manner in an OFDM based wireless communication system. 
     SUMMARY 
     Additional features of the invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. 
     Exemplary embodiments of the present invention disclose a method of generating a signal pattern in a wireless communication system including one or more base stations and one or more User Equipments (UEs), each of the base station and UEs including one or more antennas and transmitting and receiving a particular signal including one or more symbols in resource blocks, each of the resource blocks including a plurality of Orthogonal Frequency Division Multiplexing (OFDM) subcarriers and a plurality of OFDM symbols in one time slot within a radio frame, the radio frame including a plurality of subframes, the method including forming a pattern of the particular signal from the second M×N modular sonar sequence and mapping the signal, and an apparatus and a transmission/reception device thereof. 
     Further, a method of using a sequence having the same characteristic as that of the M×N modular sonar sequence in generating signal patterns, and an apparatus and a transmission/reception device thereof. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention, and together with the description serve to explain the principles of the invention. 
         FIG. 1  illustrates an apparatus for forming a Positioning Reference Signal (PRS) pattern by using a M×N modular sonar sequence according to an aspect of the present invention; 
         FIGS. 2 and 3  illustrate an embodiment in a structure of an MBSFN (Multicast Broadcast Single Frequency Network) subframe of an LTE (Long Term Evolution) system according to the aspect of the present invention; 
         FIG. 5  illustrates an embodiment in a structure of a normal subframe having a normal CP (Cyclic Prefix) of an LTE system according to the aspect of the present invention; 
         FIG. 6  illustrates an embodiment in a structure of a normal subframe having an extended CP of an LTE system according to the aspect of the present invention; 
         FIGS. 7 and 8  illustrate another embodiment in the structure of the normal subframe having the extended CP of an LTE system according to the aspect of the present invention; 
         FIG. 9  illustrates an apparatus for forming a PRS pattern by using an M×(N−N′) modular sonar sequence according to another aspect (second aspect) of the present invention; 
         FIGS. 10 and 13  illustrate an embodiment in the structure of the MBSFN subframe of an LTE system according to another aspect of the present invention; 
         FIGS. 11 and 14  illustrate an embodiment in the structure of the normal subframe having the normal CP of an LTE system according to another aspect of the present invention; 
         FIGS. 12 and 15  illustrate an embodiment in the structure of the normal subframe having the extended CP of an LTE system according to another aspect of the present invention; 
         FIG. 16  illustrate structures of a frame, in which a positioning reference signal pattern is formed in one or more subframes, and a subframe according to another embodiment of the present invention; 
         FIG. 17  illustrates a signal generation structure of a downlink physical channel in a wireless communication system to which embodiments of the present invention are applied; 
         FIG. 18  illustrates a structure of a receiver in a wireless communication system; and 
         FIGS. 19 and 20  illustrate an embodiment in a structure a normal subframe having the normal CP and the extended CP of an LTE system according to still another aspect of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS 
     The above and other objects, features and advantages of the present invention will be more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which: 
     Exemplary embodiments now will be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments are shown. This disclosure may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments set forth therein. Rather, these exemplary embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art. Various changes, modifications, and equivalents of the systems, apparatuses, and/or methods described herein will likely suggest themselves to those of ordinary skill in the art. Elements, features, and structures are denoted by the same reference numerals throughout the drawings and the detailed description, and the size and proportions of some elements may be exaggerated in the drawings for clarity and convenience. 
     An object of the present invention is to provide a new effective method of forming patterns of signals transmitted and received by a terminal or a base station in a specific time and frequency band for a channel estimation, a position estimation, and a transmission/reception of information for control information or a scheduling required for a process of wireless communication between the terminal and the base station. 
     Further, an object of the present invention is to provide a new effective method of constructing a reference signal for the positioning in a new resource allocation structure where a communication infrastructure is changed from an existing asynchronous CDMA-based WCDMA method to OFDM-based multiplexing method and access method in detecting a UE (User Equipment) location through a reference signal (or a pilot) for the positioning in an OTDOA (Observed Time Difference Of Arrival) manner in the OFDM (Orthogonal Frequency Division Multiplexing)-based wireless mobile communication system. 
     An object of the present invention is to provide excellent PRS (Positioning Reference Signal) patterns in an aspect of the number of distinct cell-specific patterns and the performance for a more accurate positioning method required by the development of a communication system such as an increase in a movement velocity of a UE, a change in an interference environment between base stations, and an increase in complexity, in the OFDM (Orthogonal Frequency Division Multiplexing)-based wireless mobile communication system. 
     In order to achieve the above objects, the present invention provides a method of generating signal patterns having different patterns specific for each cell in a resource allocation structure by using the modular sonar sequence. Accordingly, greatly more patterns according to system-specific information may be generated in comparison with a conventional method in an aspect of the number of distinct patterns, and although each pattern is cyclic-delayed on a time (a symbol in an OFDM structure) axis or a frequency (a subcarrier in an OFDM structure) axis, errors generated by overlapping with an original pattern may be reduced in comparison with a conventional method in an aspect of distinct performances. 
     The present invention provides a method of generating signal patterns having different patterns specific for each cell by using the modular sonar sequence and allocating the generated signal patterns to one or more subframes. 
     An effect of a method of generating a Positioning Reference Signal (PRS) pattern by using the aforementioned modular sonar sequence, which is one embodiment of the present invention, is described below. 
     According to the method of generating the PRS pattern by using the modular sonar sequence, although each pattern is cyclic-delayed on a time (a symbol in an OFDM structure) axis or a frequency (a subcarrier in an OFDM structure) axis, errors generated by overlapping with an original pattern may be reduced in comparison with a conventional method and positioning reference signal patterns having greatly more different patterns specific for each base station (cell) may be generated in a resource allocation structure in comparison with the conventional method. 
     Positioning methods of providing various location services in a WCDMA (Wideband Code Division Multiple Access) and location information required for communication are largely based on three methods, which are a cell coverage-based positioning method, an OTDOA-IPDL (Observed Time Difference Of Arrival-Idle Period DownLink) method, and a network-assisted GPS method. Each method is complementary to each other rather than competitive, and properly used according to a different objective. 
     Among the three methods, the OTDOA method is based on measuring relative arrival times of reference signals (or pilots) from different base stations (or cells) while moving. A UE (or MS (Mobile Station)) should receive corresponding reference signals (RS) from at least three different base stations (or cells) for a location calculation. In order to make an OTDOA location measurement easy and avoid a near-far problem, the WCKMA standard includes an IPDL (Idle Periods in DownLink). Although a RS (or a pilot) from a serving cell, in which a current UE is located, on the same frequency is strong (or MS), the UE should be able to receive an RS (or a pilot) from a neighbor cell during the idle periods. 
     In a positioning through the OTDOA method, the accuracy of the measurement is based on 1) the number of base stations (or cells), which can receive an RS (or a pilot) discriminated by a UE (or MS) (the number should be more than three and the accuracy may be increased as the number of base stations is increased), 2) a relative location of a base station (the accuracy may be increased when the base station is located in a different direction from a UE), and 3) a line-of-sight (when the UE and the base station are location in line-of-sight from each other, the accuracy may be increased). That is, when a UE or a base station on each network receives a RS (or a pilot) from a neighbor cell, the UE or the base station should be able to discriminate RSs transmitted from neighbor cells to receive the discriminated RSs. When the number of distinct RSs is increased and the performance of the RSs is improved, the three considerations may be satisfied. In other words, as the number of base station (cell)-specific RSs (or pilots), which have distinct excellent performances, is increased, 1) the number of base stations, which can be received, is increased, 2) a possibility that at least three base stations, which are positioned in a relatively better location, can be selected among the base stations is stochastically increased, and 3) a possibility that at least three base stations, which are positioned in a relatively better lint-of-sight, can be selected among the base stations is stochastically increased, so that a correct location information may be obtained through a more accurate OTDOA measurement. 
     An LTE system advanced from WCDMA affiliated with 3GPP is based on an OFDM (Orthogonal Frequency Division Multiplexing) unlike asynchronous CDMA (Code Division Multiple Access) scheme of WCDMA. As the positioning performed through an OTDOA method in the WCDMA, a new LTE system considers the positioning performed based on the OTDOA method. Accordingly, a method is considered in which data regions, which are the remaining regions except control regions for existing Reference Signals (RSs) and control channels, are reserved on a regular period in one of an MBSFN (Multicast Broadcast Single Frequency Network) subframe structure and a normal subframe structure, or each subframe structure of both subframes and then reference signals for the positioning is transmitted to the reserved regions in the subframes. That is, for the positioning in an LTE, which is a new next generation communication method based on the OFDM method, a method of transmitting reference signals for the positioning and constructing the reference signals in a new resource allocation structure should be reconsidered since a communication infrastructure has been changed from an existing asynchronous CDMA-based WCDMA method to OFDM-based multiplexing method and access method. Further, a more accurate positioning method is required by the development of a communication system such as an increase in a movement velocity of a UE, a change in an interference environment between base stations, and an increase in complexity. 
     An embodiment of the present invention provides a method of generating a positioning reference signal pattern by using the modular sonar sequence. 
     In accordance with an aspect of the present invention, there is provided a method of generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the method including generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, converting the generated first M×N modular sonar sequence to a second M×N modular sonar sequence according to system-specific information, and forming a positioning reference signal pattern from the second M×N modular sonar sequence and mapping positioning reference signals. 
     In accordance with another aspect of the present invention, there is provided a method of generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the method including generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, generating a first M×(N−N′) modular sonar sequence by truncating an end part having a length N′ out of the generated first M×N modular sonar sequence having a length N, converting the first M×(N−N′) modular sonar sequence to a second M×(N−N′) modular sonar sequence according to system-specific information, and forming a positioning reference signal pattern from the second M×(N−N′) modular sonar sequence and mapping positioning reference signals. 
     In accordance with another aspect of the present invention, there is provided a method of generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the method including generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, converting the generated first M×N modular sonar sequence to a second M×N modular sonar sequence according to system-specific information, generating a second M×(N−N′) modular sonar sequence by truncating an end part having a length N′ out of the second M×N modular sonar sequence having a length N, and forming a positioning reference signal pattern from the second M×(N−N′) modular sonar sequence and mapping positioning reference signals. 
     In accordance with another aspect of the present invention, there is provided an apparatus for generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the apparatus including an M×N modular sonar sequence generator for generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, and converting the generated first M×N modular sonar sequence to a second M×N modular sonar sequence according to system-specific information, and a positioning reference signal mapper for forming a positioning reference signal pattern from the second M×N modular sonar sequence and mapping positioning reference signals. 
     In accordance with another aspect of the present invention, there is provided an apparatus for generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the apparatus including an M×N modular sonar sequence generator for generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, an M×(N−N′) modular sonar sequence generator for generating a first M×(N−N′) modular sonar sequence by truncating an end part having a length N′ out of the generated first M×N modular sonar sequence having a length N, and converting the first M×(N−N′) modular sonar sequence to a second M×(N−N′) modular sonar sequence according to system-specific information, and a positioning reference signal mapper for forming a positioning reference signal pattern from the second M×(N−N′) modular sonar sequence and mapping positioning reference signals. 
     In accordance with another aspect of the present invention, there is provided an apparatus of generating a positioning reference signal pattern for positioning a User Equipment (UE) in a wireless communication system, the apparatus including an M×N modular sonar sequence generator for generating a first M×N modular sonar sequence based on M and N corresponding to determined modular sonar sequence sizes, an M×(N−N′) modular sonar sequence generator for converting the generated first M×N modular sonar sequence to a second M×N modular sonar sequence according to system-specific information, and generating a second M×(N−N′) modular sonar sequence by truncating an end part having a length N′ out of the second M×N modular sonar sequence having a length N, and a positioning reference signal mapper for forming a positioning reference signal pattern from the second M×(N−N′) modular sonar sequence and mapping positioning reference signals. 
     Specifically, the present invention provides an effective method of constructing a reference signal for the positioning in a new resource allocation structure where a communication infrastructure is changed from an existing asynchronous CDMA-based WCDMA method to OFDM-based multiplexing method and access method in detecting a UE (User Equipment) location through a reference signal (or a pilot) for the positioning in an OTDOA (Observed Time Difference Of Arrival) manner in the OFDM (Orthogonal Frequency Division Multiplexing)-based wireless mobile communication system. Particularly, the present invention provides excellent PRS (Positioning Reference Signal) patterns in an aspect of the number of distinct cell-specific patterns and the performance for more accurate positioning method required by the development of a communication system such as an increase in a movement velocity of a UE, a change in an interference environment between base stations, and an increase in complexity. 
     Accordingly, the present invention considers a method of generating a positioning reference signal according to the requirements based on the modular sonar sequence. 
     The modular sonar sequence described herein is first discussed below. 
     For integers m and n, M={1, 2, . . . , m} and N={1, 2, . . . , n} (where, M is a set including values generated by modulo m of integers). For all integers h, i, and j where 1≦h≦n−1, 1≦i, and j≦n−h, when i=j from f(i+h)−f(i)=f(j+h)−f(j) (mod m), a function f: N→M has a difference property discriminated by a modular (hereinafter, referred to as a “distinct modular differences property”). 
     At this time, an M×N modular sonar sequence corresponds to the function f: N−*M having the “distinct modular differences property”. 
     For example, a sequence {1, 3, 7, 4, 9, 8, 6, 2, 5, 11(=0)} may be a 11×10 modular sonar sequence having a value of “11” as a modular. 
     There are various methods of generating modular sonar sequences. Table 1 below summarizes and illustrates all methods of generating the modular sonar sequence known today according to a length, a range, and modulo value. Detailed methods of generating the modular sonar sequence in each method correspond to from generation method-A to generation method-G. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Constructions 
                 Length (N) 
                 Range 
                 Modulo(M) 
                 method 
               
               
                   
               
             
            
               
                 Quadratic 
                 n = p + 1 
                 {1, 2, . . . , p} 
                 m = p 
                 generation method-A 
               
               
                 Exponential Welch 
                 n = p − 1 
                 {1, 2, . . . , p} 
                 m = p 
                 generation method-B 
               
               
                 Logarithm Welch 
                 n = p − 1 
                 {1, 2, . . . , p − 1} 
                 m = p − 1 
                 generation method-C 
               
               
                 Lempel 
                 n = p{circumflex over ( )}r − 2 
                 {1, 2, . . . , p{circumflex over ( )}r − 1} 
                 m = p{circumflex over ( )}r − 1 
                 generation method-D 
               
               
                 Golomb 
                 n = p{circumflex over ( )}r − 2 
                 {1, 2, . . . , p{circumflex over ( )}r − 1} 
                 m = p{circumflex over ( )}r − 1 
                 generation method-E 
               
               
                 Extended Exponential 
                 n = p 
                 {1, 2, . . . , p} 
                 m = p 
                 generation method-F 
               
               
                 Welch 
               
               
                 Shift Sequence 
                 n = p{circumflex over ( )}r 
                 {1, 2, . . . , p{circumflex over ( )}r − 1} 
                 m = p{circumflex over ( )}r − 1 
                 generation method-G 
               
               
                   
               
            
           
         
       
     
     1) Generation method-A (Quadratic): p is an odd prime number, and, when a, b, and c are integers which are not “0” generated by performing modulo p, a function f: {1, 2, . . . , p+1}→{1, 2, . . . , p} defined as f(i)=ai 2 +bi+c (mod p) corresponds to a p×(p−1) modular sonar sequence. 
     2) Generation method-B (Exponential Welch): when a is a modular primitive element for a prime number p, a function f: {1, 2, . . . , p−1}→{1, 2, . . . , p} defined as f(i)=a i  corresponds to a p×(p−1) modular sonar sequence. 
     3) Generation method-C (Logarithmic Welch): when a is a modular primitive element for a prime number p, a function f: {1, 2, . . . , p−1}→{1, p−1} defined as f(i)=log a i corresponds to a (p−1)×(p−1) modular sonar sequence. 
     4) Generation method-D (Lempel): q=p r &gt;2 is a prime power. When a is a primitive element on GF(p r ), a function f: {1, 2, . . . , p r −2}→{1, 2, . . . , p r −1} defined as a necessary and sufficient condition of a i −a j =1 is a (p r −1)×(p r −2) modular sonar sequence. 
     5) Generation method-E (Golomb): q=p r &gt;2 is a prime power. When a and b are primitive elements on GF(p r ), a function f: {1, 2, . . . , p r −2}→{1, p r −1} defined as a necessary and sufficient condition of f(i)=j and a i +b j =1 corresponds to a (p r −1)×(p r −2) modular sonar sequence. 
     6) Generation method-F (Extended Exponential Welch): when a is a modular primitive element for a prime number p and s is an integer, a function f: {1, 2, . . . , p−1}→{1, 2, . . . , p} defined as f(i)=a i+s  corresponds to a p×p modular sonar sequence. 
     7) Generation method-G (Shift sequence): Suppose p is a prime number and a and b are primitive elements on GF(p 2r ) and GF(p r ), respectively. Here, when p is 2, a function f: {1, 2, . . . , p r }→{1, 2, . . . , p r −1} is defined as f(i)=log b ((a i ) p     λ     r +a i =Tr 2r   r (a i ), and b f(i) =(a i ) p̂r +a i =Tr 2r   r (a i ). When p is an odd number, the function f corresponds to a (p r −1)×p r  modular sonar sequence where the function f is defined similarly as a case when p is 2, but a range of i is {i: −(p r −1)/2≦i≦(p r −1)/2}. 
     The sequence {1, 3, 7, 4, 9, 8, 6, 2, 5, 11} described above as an example is generated by cyclic-shifting a sequence {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} by −1, and the 11×10 modular sonar sequence {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} may be constructed by the Exponential Welch method (a detailed generation method may be drawn from a case where a is 2 in generation method-B (Exponential Welch)) in table 1. As shown in table 1, a modular M has a value of “11” which is a prime number, and a length L has a value of “10” which is obtained by 11−1. 
     M×N modular sonar sequences may be converted to different M×N modular sonar sequences through three transformations. 
     First, when an original generated M×N modular sonar sequence is f(i), 1≦i≦N (or 0≦i≦N−1), a is added to f(i) for modulo m. The above function is represented as equation 1 below. 
         f   +a ( i )= f ( i )+ a  (mod  m )   (1)
 
     Equation 1 indicates that a row of a modular sonar array (representing a modular sonar sequence as a two-dimension having a row and a column) is cyclic-rotated in the unit of a. That corresponds to all cyclic shifts in a frequency side of a sequence pattern one to one in a two-dimension pattern of a time/frequency. 
     Second, when the original generated M×N modular sonar sequence is f(i), 1≦i≦N (or 0≦i≦N−1), u is multiplied by f(i) for modular m. The above function is represented as equation 2 below. 
         f   ×u ( i )= uf ( i ) (mod  m )   (2)
 
     Equation 2 refers to a permutation of rows of the modular sonar array. When a is “0”, that corresponds to all cyclic shifts in a time side of a sequence pattern one to one in a two-dimension pattern of a time/frequency. 
     Third, when the original generated M×N modular sonar sequence is f(i), 1≦i≦N (or 0≦i≦N−1), f(i) is sheared in the unit of s for modulo m. The above function is represented as equation 3 below. 
         f   shear(s) ( i )= f ( i )+ si  (mod  m )   (3)
 
     Equation 3 indicates that columns of the modular sonar array are sheared in the unit of s. 
     In short, the function f corresponds to the M×N modular sonar sequence. If u is the unit of the modular m, g may be defined as equation 4 below, and g also corresponds to the M×N modular sonar sequence. 
         g ( i )= uf ( i )+ si+a  (mod  m ) (4) 
     The present invention forms a pattern of a Positioning Reference Signal (PRS) by using the modular sonar sequence. 
     A method of forming the pattern of the PRS by using the modular sonar sequence according to an aspect (first aspect) of an embodiment of the present invention is described below. 
     a. Modular sonar sequence sizes M and N are determined from combinations capable of using as many available rows and columns as possible from Ms and Ns combinable in table 1 and in consideration of numbers of rows and columns available for positioning reference signals in a two dimensional single subframe structure having a frequency axis (a symbol axis in an OFDM structure) and a time (a subcarrier axis in an OFDM structure) axis for each subframe (e.g. an MBSFN subframe, a normal subframe with a normal CP, and a normal subframe with an extended CP). 
     b. Based on the selected M and N, the M×N modular sonar sequence is generated by the construction method illustrated in table 1. 
     c. According to the generated modular sonar sequence, positioning reference signals in a two dimensional single subframe structure having a frequency axis (a symbol axis in an OFDM structure) and a time (a subcarrier axis in an OFDM structure) axis for each subframe are mapped to rows and columns available for the positioning reference signals. 
     For example, when the generated M×N modular sonar sequence is {a, b, c, . . . , j, . . . }, {(x,y)|(x — 1,y — 1)=(1,a), (x — 2,y — 2)=(2,b), (x — 3,y — 3)=(3,c), . . . , (x_i,y_i)=(i,j), . . . }, and an ith sequence value of the PRS is mapped to a position where an xth (or yth) available column (symbol axis) and a yth (or xth) available row (subcarrier axis) intersect. In other words, when the ith sequence value of the generated M×N modular sonar sequence is f(i)=j, the ith sequence value of the PRS for the subframe is mapped to a position where an ith available column (symbol axis) and a f(i)th available row (subcarrier axis) intersect, or a position where a f(i)th available column (symbol axis) and an ith available row (subcarrier axis) intersect. 
     d. Different PRS sequence patterns required for each base station (or cell), each relay node, or each UE (or MS) are generated through the following methods. 
     When the M×N modular sonar sequence generated through one method in table 1 corresponds to f(i), 1≦i≦N (or 0≦i≦N−1), f(i) may be changed to the following three functions. 
     Addition by a modulo m, f +a (i)=f(i)+a (mod m) 
     Multiplication by a unit u modulo m, f ×i (i)=uf(i) (mod m) 
     Shearing by s modulo m, f shear(s) (i)=f(i)+si (mod m) 
     By adding the three changed functions together, a new M×N modular sonar sequence corresponding to a function g(i), which is g(i)=uf(i)+si+a (mod m), 1≦i≦N (or 0≦i≦N−1), may be generated. Through the new M×N modular sonar sequence, sequence patterns of different PRSs may be generated. 
     At this time, a, u, and s may be determined by a function according to a base station (or cell), a relay node, a UE (or MS), or other specific information (a subframe number, a CP (Cyclic Prefix) size, etc.). Particularly, it can be seen that different patterns for each base station (or cell) (cell-specific patterns) may be generated from the fact that u, s, and a may be determined according to base station (or cell) information. 
     The above steps may be implemented by the apparatus illustrated in  FIG. 1 . The apparatus for forming the pattern of the PRS by using the modular sonar sequence largely includes an M×N modular sonar sequence generator  110  and a PRS mapper  120 . The M×N modular sonar sequence generator  110  generates the modular sonar sequence and sizes M and N of the generated modular sonar sequence are determined through a modular sonar sequence size (M, N) determinator  112 . Each modular sonar sequence generated through the M×N modular sonar sequence generator  110  is specifically determined for each base station (or cell) according to different parameter values determined by a system-specific information (cell-specific information) mapper  114 . 
     A detailed operation for each apparatus is described below. The modular sonar sequence size (M, N) determinator  112  performs a function corresponding to step a in the method of generating the pattern of the PRS by using the modular sonar sequence according to the aspect of the embodiment of the present invention. That is, numbers of rows and columns available for position reference signals in a two dimensional single subframe structure having a frequency axis and a time axis for each subframe are calculated, and M and N are determined from combinations capable of using as many available rows and columns as possible from Ms and Ns combinable in table 1. The M×N modular sonar sequence generator  110  first generates M×N modular sonar sequence f(i), 1≦i≦N (or 0≦i≦N−1) according to the construction method illustrated in table 1 based on the sizes of M and N determined through the modular sonar sequence size (M, N) determinator  112 . Subsequently, the system-specific information mapper  114  receives different parameter values of a, u, and s determined as a function according to a base station (or cell), a relay node, a UE (or MS) or other specific information (a subframe number, a CP (Cyclic Prefix) size, etc.), and then generates the M×N modular sonar sequence represented as different specific patterns for each system (particularly, for each base station (or cell)) (cell-specific pattern), which corresponds to g(i) that is g(i)=uf(i)+si+a (mod m), 1≦i≦N (or 0≦i≦N−1). A PRS mapper  120  maps a PRS to a row and a column available for the PRS in one subframe structure constructing a two-dimensional structure including a time axis (symbol in an OFDM structure) and a frequency axis (subcarrier in an OFDM structure) according the M×N modular sonar sequence g(i), 1≦i≦N (or 0≦i≦N−1) generated through the M×N modular sonar sequence generator  110 . That is, if an ith sequence value of the generated M×N modular sonar sequence is g(i)=j, the ith sequence value of the PRS for the subframe is mapped to a position where an ith available column (symbol axis) and a g(i)th available row (subcarrier axis) intersect and a position where a g(i)th available column (symbol axis) and an ith available row (subcarrier axis) intersect. 
     The method of generating the pattern of the PRS according to the present invention can generate a flexible pattern size. That is, since the method can variously select M and N in generating the M×N sequence, the method can flexibly apply pattern sizes. 
     The modular sonar sequence may be applied to various cases due to various cases of parameters of M and N. 
     For example, an MBSFN (Multicast Broadcast Single Frequency Network) subframe has a no-transmission region of 12 subcarriers×10 symbols excluding a control region. Applicable values of M and N, an available frequency (subcarrier) and a time (symbol) size may be generated in consideration of a size of the two-dimensional no-transmission region for the subframe for the positioning and a case where parameters of M and N are available as illustrated in table 1. For example, in the MBSFN subframe, a size M×N is determined as 11 (subcarriers)×10 (symbols) through “Exponential Welch” method and 10 (symbols)×11 (subcarriers), and the modular sonar sequence may be generated through the sizes. 
     When 11 (subcarriers)×10 (symbols) is selected as the size M×N through “Exponential Welch” method of table 1, modulo M has a value of “11” and a length N has a value of “10”. That is, M=11 is used for 11 available frequency horizontal axes among a total of 12 frequencies (subcarriers) of the horizontal axis in an MBSFN subframe of a two-dimensional time/frequency pattern. N=10 is used for 10 available time (symbol) vertical axes among a total of 10 times (symbols) of the vertical axis in the MBSFN subframe. 
     The M×N modular sonar sequence may be extended to very various two-dimensional sequence patterns discriminated by g(i)=uf(i)+si+a (mod m). 
     At this time, the determined M×N modular sonar sequence may be extended to the M×M×Ω c (M) number of distinct PRS patterns through g(i)=uf(i)+si+a (mod m). 
     Here, Ω c (M) is defined as equation 5 below. 
       Ω c ( M )= n ( u={i| 1 ≦i&lt;M,  gcd( i,M )=1})   (5)
 
     In equation 5, gcd is the greatest common divisor. 
     Each of patterns included in the determined g(i), 1≦i≦N (or 0≦i≦N−1) has “minimum ambiguity”. That is, although the original PRS pattern is cyclic-shifted (or is time or/and frequency delayed in an aspect of the system) in a time axis or/and a frequency axis, the maximum number of overlapped PRS symbols (or PRS sequence symbols, PRS sequence elements, or resource elements from an aspect of an OFDM-based resource allocation structure) is “1” (“0” or “1”), and a larger number of PRS patterns or a PRS pattern having a higher reuse factor may be additionally generated. 
     The method of forming the PRS pattern by using the modular sonar sequence according to another aspect (second aspect) of the embodiment of the present invention will now be described. 
     a. In consideration of a larger value between the number of available rows and the number of columns for positioning reference signals in a two dimensional single subframe structure having a frequency axis (a symbol axis in an OFDM structure) and a time (a subcarrier axis in an OFDM structure) axis for each subframe (e.g. an MBSFN subframe, a normal subframe with a normal CP, and a normal subframe with an extended CP), the value is determined as M. 
     b-1. Based on the selected M, the M×N modular sonar sequence is generated by the construction method illustrated in table 1. At this time, when M=N from the M×N sequence, that is, a modular sonar sequence of N×N corresponds to an N×N modular sonar sequence and an N×N modular (or perfect) costas array. 
     b-2. When it is determined that a larger value is M and a smaller value is (N−N′) betweem the number of available rows and the number of available columns for the PRS in the subframe structure, an M×(N−N′) modular sonar sequence is generated by truncating an end of the M×N modular sonar sequence by N′ where N is a length generated through b-1. 
     c/d. It is the same as step c/d according to the previous aspect of the embodiment of the present invention. However, in the previous aspect, the M×N modular sonar sequence is used, but in this aspect, the M×(N−N′) modular sonar sequence is used. At this time, there are two methods of generating a specific modular sonar sequence (particularly, a base station (cell)-specific modular sonar sequence) for each system from the M×N modular sonar sequence. In a first method, the M×N modular sonar sequence is generated, the generated M×N modular sonar sequence is converted according to system-specific information, and then N′ is truncated from the converted M×N modular sonar sequence, so that the M×(N−N′) modular sonar sequence is generated. In a second method, the M×N modular sonar sequence is generated, and N′ is truncated from the generated M×N modular sonar sequence, so that the M×(N−N′) modular sonar sequence is generated. Then, the generated M×(N−N′) modular sonar sequence is converted to a system-specific M×M×(N−N′) modular sonar sequence according to system-specific information. 
     The method according to another aspect (second aspect) of the embodiment of the present invention may be implemented by an apparatus of  FIG. 9 . According to the present invention, another apparatus for generating the pattern of the PRS by using the modular sonar sequence largely includes an M×N modular sonar sequence generator  610 , an M×(N−N′) modular sonar sequence generator  620 , and a PRS mapper  630 . The M×N modular sonar sequence generator  610  generates the modular sonar sequence and sizes M and N of the generated modular sonar sequence are determined through a modular sonar sequence size (M, N) determinator  612 . The M×(N−N′) modular sonar sequence generator  620  generates the M×(N−N′) modular sonar sequence by truncating an end of the generated M×N modular sonar sequence by N′. At this time, the M×N modular sonar sequence is specifically determined for each base station (cell) (cell-specific) according to different parameter values determined according to a system-specific information (cell-specific information) mapper  622 , and then an end of the converted M×N modular sonar sequence is truncated by N′, so that the M×(N−N′) modular sonar sequence may be generated, or the end of the converted M×N modular sonar sequence is first truncated by N′ and then the M×(N−N′) modular sonar sequence is specifically determined for each base station (cell) (cell-specific) according to different parameter values. 
     A detailed operation for each apparatus is described below. The modular sonar sequence size (M, N) determinator  612  calculates a larger value of the number of available rows and the number of available columns for the PRS in one subframe structure, and then determines the larger value as M. Based on selected value of M, the M×N modular sonar sequence generator  610  generates the M×N modular sonar sequence through the construction method in table 1. When it is determined that a larger value is M and a smaller value is (N−N′) among the number of available rows and the number of available columns for the PRS in the subframe structure, the M×(N−N′) modular sonar sequence generator  620  generates the M×(N−N′) modular sonar sequence by truncating an end of the M×N modular sonar sequence generated by the M×N modular sonar sequence generator  610  by N′ where N is a length of the modular sonar sequence. At this time, as described above, the M×N modular sonar sequence is specifically determined for each base station (cell) (cell-specific) according to different parameter values determined according to the system-specific information (cell-specific information) mapper  622 , and then an end of the M×N modular sonar sequence is truncated by N′, so that the M×(N−N′) modular sonar sequence may be generated, or the end of the converted M×N modular sonar sequence is first truncated by N′ and then the M×(N−N′) modular sonar sequence is specifically determined for each base station (cell) (cell-specific) according to different parameter values. At this time, the system-specific information mapper  622  receives different parameter values of a, u, and s determined as a function according to a base station (or cell), a relay node, a UE (or MS) or other specific information (a subframe number, a CP (Cyclic Prefix) size, etc.), and then generates the modular sonar sequence represented as different specific patterns for each system, particularly, for each base station (cell-specific patterns), which corresponds to g(i) that is g(i)=uf(i)+si+a (mod m), 1≦i≦N (or 0≦i≦N−1). The PRS mapper  620  maps a PRS to a row and a column available for the PRS in one subframe structure constructing a two-dimensional structure including a time axis (symbol in an OFDM structure) and a frequency axis (subcarrier in an 
     OFDM structure) according the M×(N−N′) modular sonar sequence g(i), 1≦i≦N−N′ (or 0≦i≦(N−N′)−1) generated through the M×(N−N′) modular sonar sequence generator  620 . That is, if an ith sequence value of the generated M×(N−N′) modular sonar sequence is g(i)=j, the ith sequence value of the PRS for the subframe is mapped to a position where an ith available column (symbol axis) and a g(i)th available row (subcarrier axis) intersect and a position where a g(i)th available column (symbol axis) and an ith available row (subcarrier axis) intersect. 
     In the method (or apparatus) for forming the pattern of the PRS by using the M×N modular sonar sequence according to the aspect (first aspect) of the embodiment of the present invention, the M×N modular sonar sequence may be extended to the M×M×Ω c (M) number of different RPS patterns by g(i)=uf(i)+si+a (mod m). At this time, a, u, and s are determined according to system information, particularly, base station (or cell) information, so that different patterns specific for each base station (cell) (cell-specific patterns) may be generated. At this time, when all of PRS patterns do not have to be used since the number of M×M×Ω c (M) PRS patterns according to an aspect of the present invention is much more than the number of specific-information pieces, which should be discriminated, the method (or apparatus) according to the aspect of the present invention may be changed to the following method (or apparatus). 
     A first method (or apparatus) determines a value of “freq_shift_value, and a value of “time_shift_value” to be cyclic-shifted in a frequency axis and a time axis according to system-specific information, particularly, base station (or cell) information, and then cyclic-shifts the generated M×N modular sonar sequence f(i), 1≦i≦N (or 0≦i≦N−1) by the values in a frequency axis and a time axis. At this time, the number of values, which can be cyclic-shifted in a frequency axis and a time axis, is M and N, respectively, so that the M×N number of different system-specific (particularly, base station (cell)-specific) PRS patterns may be generated. That is, for example, when the Cell_ID_Group number of base station (cell)-specific information pieces is to be discriminated, a quotient and a remainder generated by dividing Cell_ID_Group by M (or N) are obtained, and the quotient and the remainder are determined as the value of “freq_shift_value, and the value of “time_shift_value” to be cyclic-shifted in a frequency axis and a time axis, respectively. For example, when 12×12 modular sonar sequence is used, the maximum number of distinct base station (cell)-specific information pieces is 144. At this time, when Cell_ID_Group=T≦144 and 0≦t≦T−1, it is determined that a quotient is “freq_shift_value(=(t−(t mod 12))/12= └t/12┘ )” and a remainder is “‘time_shift_value(=t mod 12)” by dividing T by 12. In contrast, when it is determined that a quotient is “‘time_shift_value(=t mod 12)” and a remainder is “freq_shift_value(=(t−(t mod 12))/12= └t/12┘ )”, a cyclic-shift is performed in a frequency axis by “freq_shift_value” and in a time axis by “‘time_shift_value”. That is represented as an equation below. When f 0 (i), 0≦i&lt;N(f(0)=f(N)) corresponds to the M×N modular sonar sequence generated in advance and an ith (0≦t&lt;T) M×N modular sonar sequence to be converted through a frequency/time axis cyclic-shift is f t (i), 0≦i&lt;N, f t (i), 0≦i&lt;N may be represented as equation 6 below. 
         f   t ( i )=( f   0 ((i+└ t/M ┘) mod  N )+( t  mod M)) mod  M,  0 ≦i&lt;N    (6)
 
     A second method (or apparatus) constructs PRS patterns only with patterns, which are not overlapped at all, among the M×M×Ω c (M) number of patterns by the M×N modular sonar sequence, and generates specific PRS patterns for each system, particularly for each base station (cell) through a 1:1 correspondence table between the patterns and system-specific (particularly base station (cell)-specific) information. For example, when the M×M×Ω c (M) number of PRS patterns is generated, some of the patterns are not overlapped at all (0 overlapped patterns) and one pattern of the remaining patterns is overlapped (1 overlapped pattern). When the number of not overlapped patterns is “X”, a 1:1 correspondence table between the maximum “X” number of patterns and the “X” number of base station numbers (cell_ID) is generated and the maximum “X” number of base station (cell)-specific PRS patterns may be generated through the 1:1 correspondence table. 
     Two changes of the step of generating different system-specific (particularly base station (cell)-specific) PRS patterns in the method (or apparatus) for forming the pattern of the PRS by using the M×N modular sonar sequence according to the aspect of the embodiment of the present invention may be identically applied to the method (or apparatus) for forming the PRS pattern by using the M×(N−N′) modular sonar sequence in the same manner according to another aspect of the present invention. 
     The method of forming the pattern of the PRS by using the modular sonar sequence according to still another aspect (third aspect) of the embodiment of the present invention first calculates the number of available time (symbol) axes (the number is determined as M or N), and a maximum size of M×N modular sonar sequence, which may be combined from table 1, may be generated based on the number of available time (symbol) axes. For example, in a MBSFN subframe, the number of available time (symbol) axes is 10 and thus it is possible to generate the 11×10 modular sonar sequence. 
     Accordingly, the maximum number of available frequency (subcarrier) axes may be obtained. In the MBSFN subframe, the number is 11. The number of 11 is considered as the total number of frequency (subcarrier) axes and mapped as a period. That is, when the PRS pattern is repeated every 12 subcarriers on a frequency axis in the aspect and another aspect of embodiments of the present invention (specifically, when 11 subcarriers are used on a 12-subcarrier period), the PRS pattern is repeated every 11 subcarriers in still another aspect (third aspect) of the present invention. That is, 11 subcarriers are used on a 11-subcarrier period. 
     Hereinafter, exemplary embodiments of forming the PRS pattern by using the M×N modular sonar sequence according to an aspect of an embodiment of the present invention are described in detail with reference to  FIGS. 2 to 8 . 
       FIGS. 2 to 4  illustrate embodiments in an MBSFN subframe structure of an LTE system. 
     Referring to  FIG. 2 , when available columns correspond to 10 symbols among 10 symbol axes as a time (or a symbol or column axis) and available rows correspond to 11 subcarriers among 12 subcarrier axes as a frequency (or a subcarrier or row axis), the 11×10 modular sonar sequence is generated through “Exponential Welch” method of table 1. 
     The sequence generated through “Exponential Welch” method corresponds to {2, 4, 8, 5, 10, 9, 7, 3, 6, 1 }, and is mapped in the manner of  FIG. 2 . (In  FIG. 2 , a first PRS pattern is formed in a position where an available first row (symbol axis) and a second subcarrier axis from the bottom corresponding to a second subcarrier axis intersect, on an assumption that the bottom subcarrier axis is a first subcarrier axis in a subframe structure as shown in  FIG. 2 . However, when it is assumed that the bottom subcarrier axis is a zeroth subcarrier axis, the first PRS pattern is formed in a position where the available first row (symbol axis) and a third subcarrier axis from the bottom corresponding to the second subcarrier axis intersect. In this case, total RPS patterns are mapped such that the PRS patterns are upward cyclic-shifted by 1 in a subcarrier (frequency) axis from the signal patterns shown in  FIG. 2 .) In  FIG. 2 ,  11  subcarrier axes excluding a twelfth subcarrier axis are used as available axes and certain 11 rows among 12 rows may be selected as available rows. 
     Different PRS sequence patterns are generated by g(i)=uf(i)+si+a, and then inherent PRS patterns for each system-specific information (particularly base station (cell)-specific information) may be generated. Further, the PRS patterns may be generated through a simple cyclic shift in a time/frequency axis. 
     That is, when the sequence {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} corresponds to f(i), 1≦i≦10 as a example, the sequence {1, 3, 7, 4, 9, 8, 6, 2, 5, 11} corresponds to a case where u=1, s=0, a=10(=−1 mod 11) from g(i)=uf(i)+si+a and may be mapped in a manner of  FIG. 3 . 
     As another example, the sequence {1, 2, 4, 8, 5, 10, 9, 7, 3, 6} corresponds to a case where the sequence {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} is cyclic-shifted by 1 in a time axis, and may be mapped in a manner of  FIG. 4 . 
     In the 11×10 modular sonar sequence, the generation of the 11×11×10=1210 number of inherent patterns may be expected. At this time, when 1210 patterns are not required since the number 1210 is too much, 11×10=110 different PRS patterns may be generated only through a cyclic-shift of the generated patterns in a frequency axis and a time axis according to system-specific information. Further, by selecting only patterns, which are not overlapped at all, among the patterns, a 1:1 correspondence table between the patterns and system-specific (particularly base station (cell)-specific) information is generated and specific-PRS patterns for each system (particularly for each base station (cell)) may be generated through the 1: 1 correspondence table. 
       FIG. 5  illustrates embodiments in a normal subframe structure having a normal CP (Cyclic Prefix) of an LTE system. 
     Referring to  FIG. 5 , in the normal subframe having the normal CP, a no-transmission region except a control region corresponds to 12 (subcarriers)×12 (symbols). When an additional 3 time vertical (or column) axes for CRS are considered as non-available vertical (or column) axes, 10 (subcarriers)×9 (symbols) by the “Lempel” method or the “Colomb” method of table 1 may be an embodiment of the present invention. The subframe structure of  FIG. 5  is an example of a 10 (subcarriers)×9 (symbols) structure by the “Lempel” method. A 10×9 modular sonar sequence {5, 3, 2, 7, 1, 8, 4, 6, 9} by the “Lempel” method may be mapped as shown in  FIG. 5 . At this time, distinct patterns having 400 “minimum ambiguity” which is obtained by 10×10×4 may be generated. Available columns correspond to 9 symbols among 12 symbol axes as a time (or a symbol or column axis) and available rows correspond to 10 subcarriers among 12 subcarrier axes as a frequency (or a subcarrier or row axis), and the 10×9 modular sonar sequence is generated. 
     At this time, the pattern is generated by selecting only certain 10 subcarrier axes among total 12 subcarrier axes. In embodiments of  FIG. 5 , 2 frequency horizontal axes from the top among 4 frequency horizontal axes including CRS are selected as non-available frequency horizontal (or row) axes. 
       FIG. 6  illustrates embodiments in a normal subframe structure having an extended CP of an LTE system. 
     Referring to  FIG. 6 , in the normal subframe structure having an extended CP, a no-transmission region except a control region corresponds to 12 (subcarriers)×10 (symbols). When an additional 3 time vertical (or column) axes for CRS are considered as non-available vertical (or column) axes, 8 (subcarriers)×7 (symbols) by the “Lempel” method or the “Colomb” method or 7 (subcarriers)×8 (symbols) by the “Quadratic” method of table 1 may be embodiments of the present invention. The subframe structure of  FIG. 6  is an example of an 8 (subcarriers)×7 (symbols) structure by the “Lempel” method. An 8×7 modular sonar sequence {2, 1, 6, 4, 7, 3, 5} by the “Lempel” method may be mapped as shown in  FIG. 6 . At this time, distinct patterns having 256 “minimum ambiguity” which is obtained by 8×8×4 may be generated. Available columns correspond to 7 symbol axes among 10 symbol axes as a time (or a symbol or column axis) and available rows correspond to 8 subcarrier axes among 12 subcarrier axes as a frequency (or a subcarrier or row axis), and the 8×7 (or 7×8) modular sonar sequence is generated. 
     At this time, the pattern is generated by selecting only a certain 8 subcarrier axes among total 12 subcarrier axes. In embodiments of  FIG. 6 , 4 frequency horizontal axes including CRS are selected as non-available frequency horizontal (or row) axes. 
       FIGS. 7 and 8  illustrate another embodiment in the normal subframe structure having the extended CP of an LTE system. 
     Referring to  FIG. 7 , available columns correspond to 7 symbol axes among 10 symbol axes as a time (or a symbol or column axis) and available rows correspond to 6×2=12 subcarrier axes among 12 subcarrier axes as a frequency (or a subcarrier or row axis), and they may be constructed by two 7×6 modular sonar sequences. 
     Through the two 7×6 modular sonar sequences, 12 subcarrier axes are divided into two groups each having 6 subcarriers, and each sequence is mapped to each group. As shown in the example of the structure of  FIG. 7 , the first 6 subcarrier axes may be a first group and the rest 6 subcarrier axes may be a second group or even number (or odd number) subcarrier axes may be a first group and the rest of odd number (or even number) subcarrier axes may be a second group. 
     Referring to  FIG. 8 , the pattern of the PRS in the normal subframe structure having the extended CP of an LTE system includes two 7 (symbols)×6 (subcarriers) modular sonar sequences. At this time, a 7×6 sequence {3, 6, 1, 5, 4, 2} by the “Lempel” method and a 7×6 sequence {6, 4, 2, 5, 7, 3} by the “Colomb” method are mapped as the PRS pattern of an embodiment of the  FIG. 8 . 
     At this time, a method of mapping the 7 (symbols)×6 (subcarriers) modular sonar sequence in  FIG. 8  is different from a general method of mapping M (subcarriers)×N (symbols). In a M (subcarriers)×N (symbols) modular sonar sequence g(i), 1≦i≦N (or 0≦i≦N−1), when an ith sequence value of the M (subcarriers)×N (symbols) modular sonar sequence is g(i)=j, the ith sequence value of the PRS for the subframe is mapped to a position where an ith available column (symbol axis) and a g(i)th available row (subcarrier axis) intersect. However, in a M (symbols)×N (subcarriers) modular sonar sequence g(i), 1≦i≦N (or 0≦i≦N−1) like 7 (symbols)×8 (subcarriers) in  FIG. 8 , the ith sequence value of the PRS for the subframe is mapped to a position a position where a g(i)th available column (symbol axis) and an ith available row (subcarrier axis) intersect. 
     Hereinafter, exemplary embodiments for forming the pattern of the PRS by using the M×(N−N′) modular sonar sequence according to another aspect of an embodiment of the present invention are described in detail with reference to  FIGS. 7 and 8 . 
     As described above, when the M×N modular sonar sequence is generated, M is considered as one largest value among available frequency axes and time axes, and the PRS pattern may be generated. Here, referring to that considered available frequency axes correspond to 12 subcarriers and available time axes correspond to 10, 9, or 7 symbols in one subframe structure, M is determined as 12 and a 12×N modular sonar may be generated through a value of M. At this time, available values of N from table 1 are 12 by the “Logarithmic Welch” method, 11 by the “Lempel” method or “Golomb” method, and 13 by the “Shift sequence” method. That is, an end of the sequence having a length of 12 (or 11, 13) may be truncated by N′ from a 12×12 (or 12×11, 12×13) modular sonar sequence having the generated modular value of 12 and the length of 12 (or 11, 13). Finally, the M×(N−N′) modular sonar sequence is generated. For example, in an MBSFN subframe which can have a maximum of 12 available frequency (subcarrier) axes and 10 available time (symbol) axes, an end of the sequence having a length of 12 (or 11, 13) is truncated by 2 (or 1, 3). Finally, a 12 (frequency axes)×10 (time axes) modular sonar sequence is generated. In a normal subframe having the normal CP, an end of the sequence having a length of 12 (or 11, 13) is truncated by 3 (or 2, 4) by using the same method. Finally, a 12 (frequency axes)×9 (time axes) modular sonar sequence is generated. In a normal subframe having the extended CP, a 12 (frequency axes)×7 (time axes) modular sonar sequence is generated. Although an end of a sequence length is truncated, the performance is nearly the same since the discernible “distinct modular differences property” is almost maintained. However, there is an advantage in that a maximum number of available frequency axes (12 frequency axes in the above example) may be fully used. 
     For example, when the 12×12 modular sonar sequence is generated by using the “Logarithmic Welch” method, a sequence {12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} is generated. (In  FIG. 10 , a first PRS pattern is formed in a position where an available first row (symbol axis) and a twelfth subcarrier axis from the bottom corresponding to a twelfth(=0th) subcarrier axis intersect, on an assumption that the bottom subcarrier axis is a first subcarrier axis in a subframe structure as shown in  FIG. 10 . However, when it is assumed that the bottom subcarrier axis is 0th subcarrier axis, the first PRS pattern is formed in a position where the available first row (symbol axis) and a 0th subcarrier axis from the bottom corresponding to the twelfth(=0 th ) subcarrier axis intersect. In this case, total RPS patterns are mapped such that the PRS patterns are upward cyclic-shifted by 1 in a subcarrier (frequency) axis from the signal patterns shown in  FIG. 2 .) 
       FIG. 10  illustrates embodiments in an MBSFN (Multicast Broadcast Single Frequency Network) subframe structure of an LTE system. 
     Referring to  FIG. 10 , by truncating the last 2 sequences, a 12×10 modular sonar sequence {12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10} may be generated and mapped. 
       FIG. 11  illustrates embodiments in a normal subframe structure having the normal CP of an LTE system. 
     Referring to  FIG. 11 , by truncating the last 3 sequences, a 12×9 modular sonar sequence {12(=0), 1, 4, 2, 9, 5, 11, 3, 8} may be generated and mapped. 
       FIG. 12  illustrates embodiments in a normal subframe structure having the extended CP of a LTE system. 
     Referring to  FIG. 12 , by truncating the last 5 sequences, a 12×7 modular sonar sequence {12(=0), 1, 4, 2, 9, 5, 11} may be generated and mapped. 
     As another example, when a 12×11 modular sonar sequence is generated by “Lempel” method, a sequence {6, 10, 5, 7, 3, 1, 4, 9, 8, 2, 11} is generated. 
       FIG. 13  illustrates embodiments in an MBSFN subframe structure of an LTE system. 
     Referring to  FIG. 13 , by truncating the last 1 sequence, a 12×10 modular sonar sequence {6, 10, 5, 7, 3, 1, 4, 9, 8, 2} is generated and mapped. 
       FIG. 14  illustrates embodiment in a normal subframe having the normal CP of an LTE system. 
     Referring to  FIG. 14 , by truncating the last 2 sequences, a 12×9 modular sonar sequence {6, 10, 5, 7, 3, 1, 4, 9, 8} is generated and mapped. 
       FIG. 15  illustrates embodiments in a normal subframe structure having the extended CP of an LTE system. 
     Referring to  FIG. 15 , by truncating the last 4 sequences, a 12×7 modular sonar sequence {6, 10, 5, 7, 3, 1, 4} is generated and mapped. 
     At this time, methods of generating different pattern of the sequences generated in the embodiments may use g(i)=uf(i)+si+a (mod m) as described above, use only cyclic-shifted patterns in a time/frequency axis from the generated patterns, or select only patterns corresponding to the 0 overlapped pattern among patterns generated through the two methods and then use the selected patterns. 
     Further, when the cyclic-shifted patterns in a time/frequency axis are used for the modular sonar sequence generated in the above embodiments, the patterns are cyclic-shifted in both time and frequency axes, or the patterns are fully cyclic-shifted in one axis of the time axis and the frequency axis but the patterns are partially cyclic-shifted in the other axis. In the latter case, as an example, the patterns are fully cyclic-shifted in the frequency axis but the patterns are cyclic-shifted only in one or two time axes, and then the PRS patterns may be generated. 
     First, when the 12×12 modular sonar sequence is generated by using the “Logarithmic Welch” method, the generated original M×N modular sonar sequence where M=12 and N=12 corresponds to f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6}. At this time, a method of generating 144 PRS sequences is as follows. 
     a. A M×N modular sonar sequence f 0 (i), 0≦i&lt;(f(0)=f(N)) is generated by the construction method in table 1. In the above example where M=12, df 0 (0), f 0 (1), f 1 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 1, 1, 3, 8, 10, 7, 6} is generated. 
     b. A tth (0≦t&lt;T=M×N) M×N modular sonar sequence f t (i) (0≦i&lt;N) is generated by equation 6. In the above example, T=144 and the 144 number of distinct 12×12 modular sonar sequences is generated. Equation 6 is defined as follows. 
         f   t ( i )=( f   0 (( i+└t/M ┘) mod  N )+( t  mod M)) mod  M,  0 ≦&lt;N    (6)
 
     In equation 6, └t/M┘ is a quotient of t/M and used for a cyclic-shift in a time axis. (t mod M) is a remainder of t/M and used for a cyclic-shift in a frequency axis. 
     c. As illustrated in equation 7 below, a truncated M×(N−N′) modular sonar sequence f t (i)=f t (i) (0≦i&lt;N−N′) is generated. Of course, there may be a case where the truncation is not required, that is, N′ has a value of “0”. 
         f   t ′( i )= f   t ( i ) for 0≦ N−N′   (7)
 
     d. The PRS pattern is generated. In the PRS pattern in a two-dimensional structure including M×(N−N′) frequency (subcarrier)/time (symbol) , a PRS pattern for an OTDOA positioning subframe is formed in a position where an ith available symbol axis and a f t (i)th available subcarrier axis intersect for 0≦i&lt;N−N′ (0=N−N′ mod (N−N′)). 
     e. The PRS sequence is mapped to the PRS pattern of the generated OTDOA positioning subframe. 
     As described above, the patterns may be cyclic-shifted in both the time axis and the frequency axis, or the patterns are fully cyclic-shifted in one axis of the time axis and the frequency axis but the patterns are partially cyclic-shifted in the other axis. As an example where the patterns are generated by cyclic-shifting the patterns in all frequency axes and in two time axes, a case where the 12×12 modular sonar sequence is used without any change or used by truncating the sequence is described. At this time, a cyclic-shift is possible in 12 frequency axes and 2 time axes so that 24 patterns may be generated. 
     A method of generating 24 PRS sequences from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12 is as follows. 
     A modular sonar sequence f 0 (i), 0≦i&lt;N (f(0)=f(N)) is constructed by the construction method in table 1. In the above case where M=12, f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} is generated. 
     b. A tth (0≦t&lt;T=2M) M×N modular sonar sequence f t (i)(0≦i&lt;N) is generated by equation 8 below. When M=12, T=24 and distinct 12×12 modular sonar sequences are generated. In equation 8 below, k has values from 1 to 11. For example, when k=1, 2 time axes used for a cyclic shift correspond to cyclic shifting the M×N modular sonar sequence in a time axis zero time and one time. When k=6, the 2 time axes used for the cyclic shift correspond to cyclic shifting the M×N modular sonar sequence in a time axis zero time and six times. 
         f   t ( i )=( f   0 (( i+k·└t/M ┘) mod  N )+( t  mod  M )) mod  M,  0 ≦i &lt;N′   (8)
 
     In equation 8, └t/M┘ is a quotient of t/M and used for a cyclic-shift in a time axis. (t mod M) is a remainder of t/M and used for a cyclic-shift in a frequency axis. 
     c. A truncated M×(N−N′) modular sonar sequence f t (i)=f t (i) (0≦N−N′) is generated by equation 7. Of course, there may be a case where the truncation is not required, that is, N′ has a value of “0”. 
     d. The PRS pattern is generated. In the PRS pattern in a two-dimensional structure including M×(N−N′) frequency (subcarrier)/time (symbol) , a PRS pattern for an OTDOA positioning subframe is formed in a position where an ith available symbol axis and a f t (i)th available subcarrier axis intersect for 0≦i≦N−N′ (0=N−N′ mod (N−N)). 
     e. The PRS sequence is mapped to the PRS pattern of the generated OTDOA positioning subframe. 
     A case where the PRS pattern is generated by cyclic-shifting the PRS pattern in all frequency axes and 1 time axis, or only all frequency axes is described as an example in which 12×12 modular sonar sequence is used without any change or is used after the truncation. At this time, the PRS pattern is generated by cyclic-shifting the PRS pattern in all frequency axes so that 12 patterns may be generated. 
     A method of generating 12 PRS sequences from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12 is as follows. 
     a. A modular sonar sequence f 0 (t), 0≦t&lt;N (f(0)=f(N)) is constructed by the construction method in table 1. In the above case where M=12, f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} is generated. 
     b. A tth (0≦t&lt;T=M) M×N modular sonar sequence f t (i)(0≦N) is generated by equation 9 below. When M=12, T=12 and the 12 total number of distinct 12×12 modular sonar sequences are generated. 
         f   t ( i )=( f   0 ( i )+ t ) mod  M,  0 ≦i&lt;   (9)
 
     The rest c/d/e steps are identical to c/d/e steps of the method of generating the 144 PRS patterns or the 24 PRS patterns. 
     Further, as described above, both the time axis and the frequency axis may be fully cyclic-shifted, one axis of the time axis and the frequency axis may be fully cyclic-shifted, or a part of the time axis and/or a part of the frequency axis may be cyclic-shifted. 
     For example, 6 PRS sequences may be generated by cyclic-shifting only a half (M/2) of the frequency axis from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={12(=0), 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12. A method is identical to the method of generating the 12 PRS sequences, but there is only a difference in a range of t where 0≦t&lt;T=M/2. Further, in step d, the PRS pattern for the OTDOA positioning subframe is formed in all positions where an ith available symbol axis and a ((f t (i)+└M/2┘) mod M)th available subcarrier axis intersect as well as all positions where an ith available symbol axis and a f t (i)th available subcarrier axis intersect. 
     In the above examples, T is 144, 24, 12, and 6, respectively, and corresponds to the total number of system-specific information which should be discriminated. If system-specific information corresponds to a base station (cell) ID, that is, a PCI (Physical Cell Identify), T may be a value generated by multiplying all base station (cell) IDs by groups corresponding to T. That is represented as equation 10 below, and T corresponds to 144, 24, 12, and 6 in equation 10 like the above examples. 
       0 ≦t=N   ID   cell  mod  T&lt;T    (10)
 
     For example, when T=144, that is, when the total number of patterns is 144, equation 10 may be represented as 0≦t=N ID   cell  mod 144&lt;T. Here, N ID   cell  has a value of 0≦N ID   cell &lt;504 and corresponds to a PCI (Physical Cell Identity). 
     In the above description, it has been discussed that the PRS pattern is generated by cyclic-shifting the modular sonar sequence in both the time axis and the frequency axis, fully in one axis of the time axis and the frequency axis, or partially in the time axis and/or the frequency axis. At this time, in general, an apparatus for generating the PRS pattern by using the modular sonar sequence has the same basic construction as that of the apparatus illustrated in  FIG. 1  or  9 , but only a part of functions of forming the PRS pattern through the aforementioned steps is different. Accordingly, a description for apparatuses for implementing the functions is replaced with the detailed description for the apparatus illustrated in  FIG. 1  or  9 . 
     In the embodiments, it has been described that the M×N modular sonar sequence is used for generating the PRS pattern, but the M×N modular sonar sequence according to the present invention may be used for other reference signals other than the PRS, for example, a particular signal inserted into a frequency domain grid for a frequency domain channel estimation at regular or irregular intervals, a reference signal which is a symbol, a reference symbol, or a pilot symbol. For example, reference signals in an uplink transmission include a DM-RS (DeModulation RS) and an SRS (Sounding RS). In a downlink transmission, the M×N modular sonar sequence may be used in a permissible range for generating patterns of a CRS (Cell-specific RS), an MBSFN RS, and a UE-specific RS as the reference signal, and a CSI-RS (CQI-RS) as the reference signal transmitted from a base station in order to enable a user device (terminal) to obtain Channel Spatial Information (CSI) of a central cell or neighbor cells. Of course, the M×N modular sonar sequence may be used for all reference signals currently defined or to be defined in the future, or all reference signals having a changed definition. 
     Further, the M×N modular sonar sequence may be used for forming patterns of all signals which a terminal or a base station determines to transmit and receive in a specific time and frequency band for a channel estimation, a position estimation, and a transmission/reception of information for control information or a scheduling required for a process of wireless communication between the terminal and the base station. At this time, when a particular signal or symbol is inserted into a two-dimensional domain grid of a time and a frequency at regular or irregular intervals, the signal pattern corresponds to a form in which the particular signal is inserted in a two-dimensional region of a time and a frequency. 
     In the embodiments, it has been described that the M×N modular sonar sequence may be used for forming the pattern of the reference signals including the PRS, but one or more sequences having the same characteristic as that of the aforementioned M×N modular sonar sequence may be used for generating the pattern of the reference signal including the PRS in the present invention. For example, as described in the example, the M×N modular sonar sequence where M=N has the same characteristic as that of the N X N modular (or perfect) costas array. In this case, the modular sonar sequence includes the modular castas array. 
     Meanwhile, In the embodiments, methods of generating 144, 24, 12, and 6 PRS patterns in one subframe has been described, but the methods are only illustrative. Further, various numbers of PRS patterns are generated according one subframe form and then the PRS patterns may be used for the positioning of the OTDOA manner. 
     In the embodiments, the method of generating the PRS patterns with different patterns, which are specific for each cell, by using the modular sonar sequence based on one subframe has been described. However, in one or more subframes of a radio frame including subframes, the particular signal specific for each cell, for example, PRS patterns may be generated by using the aforementioned modular sonar sequence. 
     Further, the particular signal specific for each cell, for example, PRS patterns may be generated by using the aforementioned modular sonar sequence in the particular number of subframes in every frame on a particular frame period in an aspect of the frame. 
     Hereinafter, frame periods, on which the particular signals specific for each cell, for example, PRS patterns are generated by using the aforementioned modular sonar sequence in the particular number of subframes and resource blocks of a corresponding frame, will be described. 
       FIG. 16  illustrates structures of the frame in which the PRS pattern is formed in one or more subframes and the subframe according to still another embodiment of the present invention. 
     Referring to  FIG. 16 , a basic subframe structure may include one or more PRS subframes on a particular period, for example, a period of 16, 32, 64, or 128 for the OTDOA positioning. Only 0.1% to 1% of subframes among all subframes may be used for the OTDOA positioning in consideration of an overhead. For example, when a 32 radio frame period is selected, subframes for PRS are included on a 320 subframe (1 radio frame=10 subframes) period and first 1 or 2 subframes may be used. When a 64 radio frame period is selected, subframes for the PRS are included on a 640 subframe period and first 4 or 6 subframes may be used. 
     At this time, the subframe may include an MBSFN (Multicast Broadcast Single Frequency Network) subframe, a normal subframe having a normal CP (Cyclic Prefix), or a normal subframe having an extended CP of a communication system, for example, an LTE system. 
     At this time, one constructed PRS subframe may use all BandWidths (BWs) in a frequency axis, but embodiments of the present invention are not limited thereto and may use a part of all BW. 
     That is, when the BW corresponds to 10 Mhz, there exist 50 resource blocks in the BW. The constructed PRS pattern corresponds to one RB in a frequency axis so that the one constructed PRS subframe may be used to generate PRS subframes in a frequency axis. In this case, the generated one PRS subframe pattern may be copied and then 50 PRS RBs having the same patterns may be constructed in a frequency axis, or PRS RBs having different patterns may be generated. 
     As described above, in a time axis, first 1, 2, 4, or 6 PRS subframes may be used among 10 subframes included in a single radio frame on a radio frame period of 16, 32, 64, or 128. At this time, the remaining subframes other than the PRS subframe may be constructed with existing subframes. 
     At this time, a maximum of 6 PRS subframes in a time axis may have the same pattern as that of the generated one subframe (time non-varying which means there is no change in a time axis), or may have a different pattern from that of the generated one subframe (time-varying which means there is a change in a time axis). That is, PRS subframes may be changed for each subframe number or may not be changed. 
     Further, a time of arrival for signal power may be measured in an OTDOA method by simultaneously considering repetitive patterns synthetically in order to obtain a time accumulation effect, and each time of arrival for signal power may be measured for each PRS subframe in order to discriminate more system-specific information. 
     For example, when 2 subframes are periodically used for the PRS subframe, if a time of arrival for signal power is measured in an OTDOA method by simultaneously considering all signals (in all particular time and frequency bands where REs corresponding to the pattern are located) corresponding to 2 subframe time/frequency patterns synthetically, a time accumulation effect is obtained so that errors generated in detecting a UE location may be reduced (performance may be improved). If a time of arrival for signal power in each PRS subframe is separately measured, square times of information may be distinct in comparison with a case where a single subframe is used. 
     In a time non-varying case, the existing PRS subframe pattern generated for each case may be constructed without any change in the N subframe  number of subframes to be periodically used in a time axis in the same pattern. That is represented as table 2 below according to each case. At this time, a time of arrival for signal power is measured by simultaneously considering the repetitive N subframe  number of subframe patterns synthetically so that a time accumulation effect for the N subframe  number of subframes may be obtained. 
     1. Time Non-Varying Case 
     : the N subframe  number of accumulations (N subframe =1, 2, 4, 6) 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 a) Case 1: 144 Cell Groups, N subframe  number accumulations 
               
            
           
           
               
               
               
               
            
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                 Case1 
                 Case1 
                 Case1 
               
            
           
           
               
            
               
                 b) Case 2: 24 Cell Groups, N subframe  number accumulations 
               
            
           
           
               
               
               
               
            
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                 Case2 
                 Case2 
                 Case2 
               
            
           
           
               
            
               
                 c) Case 3: 12 Cell Groups, N subframe  number accumulations 
               
            
           
           
               
               
               
               
            
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                 Case3 
                 Case3 
                 Case3 
               
            
           
           
               
            
               
                 d) Case 4: 6 Cell Groups, N subframe  number accumulations 
               
            
           
           
               
               
               
               
            
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                 Case4 
                 Case4 
                 Case4 
               
               
                   
                   
               
            
           
         
       
     
     In a time varying case, the existing PRS subframe pattern generated for each case may be constructed in the N subframe  number of subframes to be periodically used in a time axis in different patterns for each subframe. In case 2 where 24 patterns exist, 24 patterns are cyclic-shifted in a frequency axis by 12 and are not cyclic-shifted or are cyclic-shifted by 1 in a time axis. 
     That is, in a first PRS subframe of case 2, 24 patterns are generated by a 12 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 0 and 12 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 1 (or 6). Accordingly, 10 cyclic-shifts in a time axis corresponding to cases where cyclic-shifts are 2-11 (or 1-5 and 7-11) are not used for forming the PRS patterns but may be used for the rest subframes. 
     For example, 24 patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 0 and 1 in a first PRS subframe, and 24 different patterns from the PRS patterns used in the first subframe may be generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 2 and 3 in a second PRS subframe. In a third PRS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 4 and 5, and then the generated PRS patterns are used. In a fourth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 6 and 7, and then the generated PRS patterns are used. In a fifth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 8 and 9, and then the generated PRS patterns are used. In a sixth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 10 and 11, and then the generated PRS patterns are used. 
     Through another method, 24 patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 0 and 6 in a first PRS subframe in a first PRS subframe, and 24 different patterns from the PRS patterns used in the first subframe may be generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 1 and 7 in a second PRS subframe. In a third PRS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 2 and 8, and then the generated PRS patterns are used. In a fourth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 3 and 9, and then the generated PRS patterns are used. In a fifth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 4 and 10, and then the generated PRS patterns are used. In a sixth RPS subframe, PRS patterns are generated when cyclic-shifts in a time axis are 5 and 11, and then the generated PRS patterns are used. 
     The above function is represented as an equation below. 
     2-1. Time-Varying Case 2 
     N subframe  accumulations and (0≦t=N ID   cell  mod 2M&lt;2M and t=N ID   cell  mod 24, where M=12) 
     A method of constructing different patterns for each subframe in the N subframe  number (N subframe =1, 2, 4, 6) of subframes to periodically use 24 generated PRS subframe patterns in a time axis from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={11, 0, 3, 2, 9, 4, 10, 2, 7, 9, 6, 5} or 10, 1, 4, 3, 10, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12 is as follows. 
     1) Case 2 (T=2M, N subframe =1, 2, 4, 6) 
     a) The original M×N modular sonar sequence f 0 (i), 0≦i&lt;N (f(0)=f(N)) is constructed by the construction method in table 1. In the example where M=12, f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={0, 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6} is generated. 
     b) In a n subframe th (0≦n subframe =└n s /2┘&lt;N subframe ) subframe, a tth (0≦t&lt;T=2M) M×N modular sonar sequence f n     subframe     ,t (i), 0≦i&lt;N is generated. 
     When M=12, T=24 and 24 distinct 12×12 modular sonar sequences are generated. When N subframe =6, in a first PRS subframe, 24 patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 0 and 12 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 6. In a second PRS subframe, 24 different patterns from the PRS patterns used in the first subframe may be formed, and the different patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts are 1 and 7 in a time axis. In a third RPS subframe, 24 different PRS patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 2 and 8. In a fourth RPS subframe, 24 different PRS patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 3 and 9. In a fifth RPS subframe, 24 different PRS patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 4 and 10. In a sixth RPS subframe, 24 different PRS patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 5 and 11. 
         f   n     subframe     ,t ( i )=( f   0 (( i+n   subframe +6 ·└t/M ┘) mod  N )+( t  mod  M )), mod  M,  0 ≦i&lt;N    (11)
 
     In equation 6, └t/M┘ is a quotient of t/M and used for a cyclic-shift in a time axis. (t mod M) is a remainder of t/M and used for a cyclic-shift in a frequency axis. 
     c) A truncated M×(N−N′) modular sonar sequence f n     subframe     ,t ′(i), 0≦i&lt;N−N′ is generated by equation 12 below. Of course, there may be a case where the truncation is not required, that is, N′ has a value of “0”. 
         f   n     subframe     ,t ′( i )= f   n     subframe     ,t ( i ) for 0 ≦i&lt;N−N′   (12)
 
     d) The PRS pattern is generated. In the PRS pattern in a two-dimensional structure including M×(N−N′) frequency (subcarrier)/time (symbol), a PRS pattern for an OTDOA positioning subframe is formed in all positions where an ith available symbol axis and a f n     subframe     ,t ′(i)th available subcarrier axis intersect for 0≦i&lt;N−N′ (0=N−N+ mod (N−N′)). 
     e) The PRS sequence is mapped to the PRS pattern of the generated OTDOA positioning subframe. 
     In a first PRS subframe of case 3, 12 patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shirt in a time axis is 0. Accordingly, the remaining 11 cyclic-shifts in a time axis corresponding to cases where cyclic-shifts are 1-11 in a time axis are not used for forming the PRS signals but may be used for the remaining subframes. 
     The above function is represented as equation below. 
     2-2. Time-Varying Case 3 
     : N subframe  accumulations (0≦t=N ID   cell  mod M&lt;M and t=N ID   cell  mod 12, where M=12) 
     A method of constructing different patterns for each subframe in the N subframe  number (N subframe= 1, 2, 4, 6) of subframes to periodically use 12 PRS subframe patterns in a time axis from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={11, 0, 3, 2, 9, 4, 10, 2, 7, 9, 6, 5} or {0, 1, 4, 3, 10, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12 is as follows. 
     1) Case 3 (T=2M, N subframe =1, 2, 4, 6) 
     a) The original M×N modular sonar sequence f 0 (i), 0≦i&lt;N (f(0)=f(N) is constructed by the construction method in table 1. In the example where M=12, f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={0, 1, 4, 3, 10, 5, 11, 3, 8, 10, 7, 6} is generated. 
     b) In an n subframe th (0≦n subframe =└n s /2┘&lt;N subframe ) subframe, a tth (0≦t&lt;T=M) M×N modular sonar sequence f n     subframe     ,t (i)0≦i&lt;N is generated by equation 13. 
     When M=12, T=24 and 12 distinct 12×12 modular sonar sequences are generated. When N subframe =6, in a first PRS subframe, 12 patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 0. In a second PRS subframe, 12 different patterns from the PRS patterns used in the first subframe may be formed, and the different patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shift is 2 in a time axis. In third, fourth, fifth, and sixth RPS subframes, 12 different PRS patterns are generated by 12 cyclic-shifts in a frequency axis when cyclic-shifts in a time axis are 4, 6, 8, and 10, respectively. 
         f   n     subframe     ,t ( i )=( f   0 (( i+ 2 ·n   subframe ) mod  N )+( t  mod  M )) mod  M,  0 ≦i&lt;N    (13)
 
     In equation 13, (t mod M) is a remainder of t/M and used for a cyclic-shift in a frequency axis. 
     c) A truncated M×(N−N) modular sonar sequence f n     subframe     ,t ′(i), 0≦i&lt;N−N′ is generated by equation 14 below. Of course, there may be a case where the truncation is not required, that is, N′ has a value of “0”. 
         f   n     subframe     ,t ′( i )= f   n     subframe     ,t ( i ) for 0 ≦i&lt;N−N′   (14)
 
     d) The PRS pattern is generated. In the PRS pattern in a two-dimensional structure including M×(N−N′) frequency (subcarrier)/time (symbol), a PRS pattern for an OTDOA positioning subframe is formed in all positions where an ith available symbol axis and a f n     subframe     ,t ′(i)th available subcarrier axis intersect for 0≦i&lt;N−N′ (0=N−N′ mod (N−N′)). 
     e) The PRS sequence is mapped to the PRS pattern of the generated OTDOA positioning subframe. 
     Similarly, in a first PRS subframe of case 4, 6 patterns are generated by 6 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 0. Accordingly, the remaining 11 cyclic-shifts in a time axis corresponding to cases where cyclic-shifts are 1-11 in a time axis are not used for forming the PRS signals but may be used for the remaining subframes. For example, in a second PRS subframe, 12 different patterns from the PRS patterns used in the first subframe may be formed, and the different patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shift is 2 in a time axis. 
     In a third PRS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 4, and then the generated PRS patterns are used. In a fourth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 6, and then the generated PRS patterns are used. In a fifth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 8, and then the generated PRS patterns are used. In a sixth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 10, and then the generated PRS patterns are used. 
     The above function is represented as an equation below. 
     2-3. Time-Varying Case 4 
     : N subframe  accumulations (0≦t=N ID   cell  mod M &lt;M and t=N ID   cell  mod 12, where M=12) 
     A method of constructing different patterns for each subframe in the N subframe  number (N subframe= 1, 2, 4, 6) of subframes to periodically use 12 PRS subframe patterns in a time axis from the original M×N modular sonar sequence f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={11, 0, 3, 2, 9, 4, 10, 2, 7, 9, 6, 5} or {0, 1, 4, 3, 10, 5, 11, 3, 8, 10, 7, 6} where M=12 and N=12 is as follows. 
     1) Case 4 (T=└M/2┘, N subframe =1, 2, 4, 6) 
     a) The original M×N modular sonar sequence f 0(i),  0≦t&lt;N (f(0)=f(N)) is constructed by the construction method in table 1. In the example where M=12, f 0 ={f 0 (0), f 0 (1), f 0 (2), f 0 (3), f 0 (4), f 0 (5), f 0 (6), f 0 (7), f 0 (8), f 0 (9), f 0 (10), f 0 (11)}={0, 1, 4, 3, 10, 5, 11, 3, 8, 10, 7, 6} is generated. 
     b) In a n subframe th (0≦n subframe =└n s /2┘&lt;N subframe ) subframe, a tth (0≦t&lt;T=M) M×N modular sonar sequence f n     subframe,t   (i), 0≦i&lt;N is generated by equation 15. 
     When M=12, T=24 and 12 distinct 12×12 modular sonar sequences are generated. When N subframe =6, in a first PRS subframe, 6 patterns are generated by 6 cyclic-shifts in a frequency axis when a cyclic-shift in a time axis is 0. In a second PRS subframe, 12 different patterns from the PRS patterns used in the first subframe may be formed, and the different patterns are generated by 12 cyclic-shifts in a frequency axis when a cyclic-shift is 2 in a time axis. 
     In a third PRS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 4, and then the generated PRS patterns are used. In a fourth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 6, and then the generated PRS patterns are used. In a fifth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 8, and then the generated PRS patterns are used. In a sixth RPS subframe, different PRS patterns are generated when a cyclic-shift in a time axis is 10, and then the generated PRS patterns are used. 
         f   n     subframe     ,t ′( i )=( f   0 (( i+ 2 ·n   subframe ) mod  N )+( t  mod M)) mod  M,  0 ≦i&lt;N    (15)
 
     In equation 15, (t mod M) is a remainder of t/M and used for a cyclic-shift in a frequency axis. 
     c) A truncated M×(N−N) modular sonar sequence f n     subframe     ,t ′(i), 0≦i&lt;N−N′ is generated by equation 16 below. Of course, there may be a case where the truncation is not required, that is, N′ has a value of “0”. 
         f   n     subframe     ,t ′( i )= f   n     subframe     ,t ( i ) for 0 ≦i&lt;N−N′   (16)
 
     d) The PRS pattern is generated. In the PRS pattern in a two-dimensional lo structure including M×(N−N′) frequency (subcarrier)/time (symbol), a PRS pattern for an OTDOA positioning subframe is formed in a position where an ith available symbol axis and a f n     subframe     ,t (i)th available subcarrier axis intersect and a point where an ith available symbol axis and a (f n     subframe     ,t (i)+└M/2┘) mod Mth available subcarrier axis intersect for 0≦i&lt;N−N′ (0=N−N′ mod (N−N′)). 
     e) The PRS sequence is mapped to the PRS pattern of the generated OTDOA positioning subframe. 
     At this time, a time of arrival for signal power is measured by simultaneously considering the repetitive N number of subframe patterns synthetically so that a time accumulation effect for the N number of subframes may be obtained. 
     The above function is represented as a table below. 
     2. Time Varying Case 
     : N subframe  accumulations (N subframe =1, 2, 4, 6) 
     a) Case 1: 144 Cell Groups, No Accumulation 
     b) Case 2: 24 Cell Groups, N subframe  Accumulations 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                   
               
             
            
               
                   
                 Case2 (0)   
                 Case2 (n     —     subframe)   
                 Case2 (N−1)   
               
               
                   
                   
               
            
           
         
       
     
     In table 3, f 0 (i) of case 2 (n     —     subframe)  corresponds to cyclic-shifting f 0 (i) of Case 2 (0)  in a time axis by 2*(n_subframe) or n_subframe, and t =N   ID   cell  mod 24. 
     c) Case 3: 12 Cell Groups, N subframe  Accumulations 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                   
               
             
            
               
                   
                 Case3 (0)   
                 Case3 (n     —     subframe)   
                 Case3 (N−1)   
               
               
                   
                   
               
            
           
         
       
     
     In table 4, f 0 (i) of case 3 (n     —     subframe ) corresponds to cyclic-shifting f 0   (i)  of Case 3 (0)  in a time axis by 2*(n_subframe), and t=N ID   cell  mod 12. 
     d) Case 4: 6 Cell Groups, N subframe  Accumulations 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 . . . 
                 Subframe N − 1 
               
               
                   
                   
               
             
            
               
                   
                 Case4 (0)   
                 Case4 (n     —     subframe)   
                 Case4 (N−1)   
               
               
                   
                   
               
            
           
         
       
     
     In table 5, f 0   (i)  of case 4 (n     —     subframe)  corresponds to cyclic-shifting f 0   (i)  Case 4 (0)  in a time axis by 2*(n_subframe), and t=N ID   cell  mod 6. 
     As described in the above method, the time of arrival for signal power is measured in an OTDOA method by simultaneously considering repetitive patterns synthetically in order to obtain a time accumulation effect. That is, when two or more subframes are periodically used for the PRS subframe, if a time of arrival for signal power is measured in an OTDOA method by simultaneously considering all signals (in all particular time and frequency bands where REs corresponding to the pattern are located) corresponding to two or more subframe time/frequency patterns synthetically, a time accumulation effect is obtained so that errors generated in detecting a UE location may be reduced (performance may be improved). 
     Unlike the above case, the time of arrival for signal power in each PRS subframe is measured in order to discriminate more system-specific information. That is, if a time of arrival for signal power in each PRS subframe is separately measured, more pattern types may be generated in comparison with a case where a single subframe is used and thus more system-specific information may be discriminated. 
     For example, when 2 subframes are used, a total of 24 patterns are generated in a first subframe through case 2 and accordingly a maximum of 24 system-specific information pieces (cell-IDs) may be discriminated. Similarly, 24 patterns may be generated in a second subframe. When each time of arrival for signal power in each PRS subframe is separately measured, a total of 24*24=576 patterns may be obtained through 24 patterns included in each of 2 subframes. Accordingly, when 2 subframes are constructed, 576 system-specific information pieces (cell-IDs) may be discriminated. 
     When 4 subframes are used, 24*24*24*24 system-specific information pieces may be discriminated in the same manner. When the system-specific information is a cell-ID, since current LTE Rel-8 PCIs (Physical Cell Identities) having the total number of 504 may be discriminated by the number of cases of 576 patterns. When 4 subframes are divided into 2 groups each having 2 subframes and the above method is applied to each group, 24*24=576 system-specific information pieces may be discriminated and simultaneously a time accumulation effect as much as 2 may be obtained. 
     When 6 subframes are used, 24*24=576 system-specific information pieces may be discriminated and simultaneously a time accumulation effect as much as 3 may be obtained by applying the same method to each group, the 6 subframes being divided into 3 groups and the 3 groups each having 2 subframes. 
     That is represented as a table below. 
     3. Time Varying Case 
     : N subframe /2 accumulations (N subframe =2, 4, 6) 
     1) Case 2-1: 24*24=576 cell groups (504 PCIs may be all discriminated), 1 accumulation 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 Subframe 1 
               
               
                   
                   
               
             
            
               
                   
                 Case2 (0)   
                 Case2 (1)   
               
               
                   
                   
               
            
           
         
       
     
     In table 6, ) f 0   (i)  of case 2 (1)  corresponds to cyclic-shifting f 0   (i)  of case 2 (0)  in a time axis by 2 (or 1), and t of case 2 (0)  is still defined by t=N ID   cell  mod 24, but t of case 2 (1)  is defined by t=└N ID   cell /24┘. 
     That is, when times of arrival for signal power are separately measured in each of the first PRS subframe and the second PRS subframe having generated 24 different patterns, a total of 24*24=576 patterns may be obtained through 24 patterns included in each of 2 subframes. Accordingly, 576 system-specific information pieces (cell-IDs) may be discriminated. 
     Case 2-2: 24*24=576 cell groups (504 PCIs may be all discriminated), 2 accumulations 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 Subframe 1 
                 Subframe 2 
                 Subframe 3 
               
               
                   
                   
               
             
            
               
                   
                 Case2 (0)   
                 Case2 (1)   
                 Case2 (2)   
                 Case2 (3)   
               
               
                   
                   
               
            
           
         
       
     
     In table 7, f 0 (i) of case 2 (1)  corresponds to cyclic-shifting f 0 (i) of case 2 (0)  in a time axis by 2 (or 1), f 0 (i) of case 2 (2)  corresponds to cyclic-shifting f 0 (i) of case 2 (0)  in a time axis by 4 (or 2), f 0 (i) of case 2 (3)  corresponds to cyclic-shifting f 0 (i) of case 2 (0)  in a time axis by 6 (or 3), and t of case 2 (0)  and case 2 (2)  is still defined by t=N ID   cell  mod 24, but t of case 2 (1)  and case 2 (3)  are defined by t=└N ID   cell /24┘. 
     When 4 subframes are used, 24*24=576 system-specific information pieces may be discriminated and simultaneously a time accumulation effect as much as 2 may be obtained by applying the same method to each group, the 4 subframes divided into 2 groups and the 2 groups each having 2 subframes. 
     3) Case 2-2: 24*24=576 cell groups (504 PCIs may be all discriminated), 3 accumulations 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 Subframe 0 
                 . . . 
                 Subframe 5 
               
               
                   
                   
               
             
            
               
                   
                 Case2 (n     —     subframe=0)   
                 Case2 (n     —     subframe)   
                 Case2 n     —     subframe=5)   
               
               
                   
                   
               
            
           
         
       
     
     In table 8, f 0 (i) of case 2 (n     —     subframe)  corresponds to cyclic-shifting f 0 (i) of case 2 (0)  in a time axis by 2*(n_subframe) or n_subframe, and t of case 2 (n     —     subframe=even number (0, 2, 4))  is still defined by t=N ID   cell  mode 24, but t of case 2 (n     —     subframe=odd number (1, 3, 5)  defined by t=└N ID   cell /24┘. 
     When 6 subframes are used, 24*24=576 system-specific information pieces may be discriminated and simultaneously a time accumulation effect as much as 3 may be obtained by applying the same method to each group, the 6 subframes being divided into 3 groups and the 3 groups each having 2 subframes. 
     Hereinafter, an example of a downlink physical channel in a wireless communication system to which a method and an apparatus for allocating PRS patterns by using the M×N modular sonar sequence according to an embodiment of the present invention is described. 
       FIG. 17  illustrates a structure of the downlink physical channel in a wireless communication system to which embodiments of the present invention are applied. 
     Referring to  FIG. 17 , the wireless communication system  900  to which embodiments of the present invention are applied includes a scrambler  910 , a modulation mapper  912 , a layer mapper  914 , a precoder  916 , a resource element mapper  918 , and an OFDM signal generator  920 . Further, the wireless communication system  900  includes a PRS mapper  922 . At this time, the PRS mapper may be the same as the aforementioned PRS mapper  120  or  630  illustrated in  FIG. 1  or  9 . The PRS mapper  922  is associated with the resource element mapper  918  and performs a mapping process in a resource element corresponding to a PRS resource in a signal resource mapping process in all resource elements of the resource mapper  918 . That is, the PRS mapper corresponds to a device for performing a special function of the resource element mapper  918  associated with the PRS in the mapping of the resource element. When both components are the same, the wireless communication system  900  may include other components other than the PRS mappers  120  and  630  of  FIGS. 1 and 9 . 
     Meanwhile, the wireless communication system  900  may be a communication system of a base station or a transmission device of a base station including an apparatus illustrated in  FIG. 1  or  FIG. 9  for transmitting the PRS, respectively. 
     Bits input in a form of codewords via a downlink channel coding are scrambled by the scrambler  910  and then input to the modulation mapper  912 . The modulation mapper  912  modulates the scrambled bits to complex modulation symbols, and the layer mapper  914  maps the complex modulation symbols to one transmission layer or a plurality of transmission layers. Then, the precoder  916  precodes complex modulation symbols on each transmission channel of an antenna port. Next, the resource element mapper  918  maps the complex modulation symbol for each antenna port to a corresponding resource element. Meanwhile, the PRS mapper  922  forms a PRS pattern from a second M×N modular sonar sequence generated through the M×N modular sonar sequence generator  110  described above with reference to  FIG. 1  and maps the PRS, or forms a PRS pattern from a second N×(N−N′) modular sonar sequence generated through the N×(N−N′) modular sonar sequence generator  110  described above with reference to  FIG. 1  and maps the PRS. 
     The PRS mapper  922  is generated by a particular RPS sequence in the wireless communication system  900 , allocates PRSs generated via at least one of apparatuses  910 ,  912 ,  914 , and  916  to resource elements corresponding to resources, in which a particular OFDM symbol (time axis) and a subcarrier (frequency axis) are located, according to PRS patterns formed from the modular sonar sequence, and multiplex with a base station transmission frame according to a predetermined frame timing. 
     At this time, the existing RS and control signals and data input from the precoder  916  are allocated to resource elements corresponding to resources, in which a particular OFDM symbol (time axis) and a subcarrier (frequency axis) are located, by the resource element mapper  918 . Here, the PRS mapper corresponds to an apparatus responsible for performing a special function (of forming a PRS pattern to map the PRS) added to the resource element mapper  918  in order to allocate the PRS to a corresponding each resource element. 
     Then, the OFDM signal generator  920  generates a complex time domain OFDM signal for each antenna. The complex time domain OFDM signal is transmitted through an antenna port. 
     The structure of generating the downlink physical channel signal in the wireless communication system to which embodiments of the present invention are applied has been described with reference to  FIG. 17 , but the present invention is not limited thereto. That is, in the structure of generating the downlink physical channel signal in the wireless communication system to which embodiments of the present invention is applied, other components may be omitted, replaced with or changed to other components, or other components may be added. 
       FIG. 18  illustrates a structure of a receiver in a wireless communication system. 
     Referring to  FIG. 18 , a receiver  1000  of a terminal in a wireless communication system includes a reception processor  1010 , a decoder  1912 , and a controller  1014 . At this time, the receiver  1000  may be a base station receiving information on the received PRS again from a terminal (UE) including the apparatus of  FIG. 1  or  FIG. 9  for receiving and decoding the PRS. 
     The signal received through each antenna port is converted to a complex time domain signal by the reception processor  1010 . Further, the reception processor  1010  extracts PRSs of particular resource elements from received signals. The decoder  1012  decodes the extracted PRSs. The controller  1014  measures a distance from a base station by using a relative arrival time from the base station through information on the decoded PRSs. 
     At this time, the controller  1014  can calculate the distance from the base station by using the relative arrival time from the base station, or the controller  1014  transmits the relative arrival time to the base station and then the base station can calculate the distance. At this time, since distances from three or more base stations are measured, a terminal location may be calculated. 
     At this time, when PRS patterns specific for each cell are generated and transmitted by using the modular sonar sequence in two or more subframes, the receiver accumulates information received from PRS patterns of subframes for a predetermined time and then can measure a relative arrival time from each cell. 
     As described above, the time of arrival for signal power may be measured in an OTDOA method by simultaneously considering repetitive patterns synthetically in order to obtain the time accumulation effect. That is, when two or more subframes are periodically used for the PRS subframe, if a time of arrival for signal power is measured in an OTDOA method by simultaneously considering all signals (in all particular time and frequency bands where REs corresponding to the pattern are located) corresponding to two or more subframe time/frequency patterns synthetically, a time accumulation effect is obtained so that errors generated in detecting a UE location may be reduced (performance may be improved). 
     Unlike the above case, each time of arrival for signal power in each PRS subframe may be measured in order to discriminate more system-specific information. That is, if a time of arrival for signal power in each PRS subframe is separately measured, more pattern types may be generated in comparison with a case where a single subframe is used and thus more system-specific information may be discriminated. 
     The receiver  1000  is a device, which makes a pair with the wireless communication system or transmitter  900  described with reference to  FIG. 17  and receives a signal transmitted from the transmitter  900 . The receiver  1000  includes components for processing a signal of a reverse process of the transmitter  900 . Accordingly, a detailed description for the receiver  1000  may be replaced with a detailed description for the components for processing the signal of the reverse process of the transmitter  900  in a one-to-one correspondence manner. 
     So far, embodiments of the present invention have been described with reference to the figures, but the present invention is not limited thereto. 
     Meanwhile, the methods of generating 144, 24, 12, and 6 PRS patterns in one subframe are described in the embodiments of the present invention, but they are only illustrative. Further, various numbers of PRS patterns may be generated according to one subframe type and the PRS patterns may be used for the positioning of the OTDOA method. 
     In the embodiments, the method of generating the PRS patterns with different patterns, which are specific for each cell, by using the modular sonar sequence based on one subframe has been described. However, in one or more subframes of a radio frame including subframes, the PRS patterns specific for each cell may be generated by using the aforementioned modular sonar sequence. For example, in one radio frame including 10 subframes, PRS patterns specific for each cell may be generated in 1, 2, 3, 4, or 6 subframes by using the modular sonar sequence. 
     Further, the PRS patterns specific for each cell may generated by using the modular sonar sequence in the particular number of subframes in every radio frame on a frame period of 16, 32, 64, or 128 in an aspect of each radio frame. For example, when the 10 number of 1 ms subframes consist of one radio frame (a total of 10 ms), cell-specific PRS patterns may be generated in 1, 2, 3, 4, or 6 subframes of one radio frame by using the modular sonar sequence on a 32 radio frame period (320 ms). 
     At this time, when cell-specific PRS patterns are generated and transmitted by using the modular sonar sequence in two or more subframes, the receiver accumulates information received from PRS patterns of subframes for a predetermined time and then can measure a relative arrival time from each cell. 
     In the embodiments, it has been described that the M×N modular sonar sequence is used for generating the PRS patterns, but the M×N modular sonar sequence according to the present invention may be used for other reference signals other than the PRS, for example, a particular signal inserted into a frequency domain grid for a frequency domain channel estimation at regular or irregular intervals, a reference signal which is a symbol, a reference symbol, or a pilot symbol. For example, reference signals in an uplink transmission include a DM-RS (DeModulation RS) and an SRS (Sounding RS). In a downlink transmission, the M×N modular sonar sequence may be used in a permissible range for generating patterns of a CRS (Cell-specific RS), an MBSFN RS, and a UE-specific RS as the reference signal, and a CSI-RS (CQI-RS) as the reference signal transmitted from a base station in order to enable a user device (terminal) to obtain Channel Spatial Information (CSI) of a central cell or neighbor cells. Of course, the M×N modular sonar sequence may be used for all reference signals currently defined or to be defined in the future, or all reference signals having a changed definition. 
     In the embodiments, it has been described that the M×N modular sonar sequence may be used for forming the pattern of the reference signals including the PRS, but one or more sequences having the same characteristic as that of the aforementioned M×N modular sonar sequence may be used for generating the pattern of the reference signal including the PRS in the present invention. For example, as described in the example, the M×N modular sonar sequence where M=N has the same characteristic as that of the N×N modular (or perfect) costas array. In this case, the modular sonar sequence includes the modular costas array. 
     A method of generating the PRS according to still another embodiment of the present invention is described below. 
     1. A basic PRS pattern is formed in a ½ resource block including 2 slots and 6 subcarriers by a particular sequence. At this time, an example of a used particular sequence is {0, 1, 2, 3, 4, 5, 6}. Further, the 2 slots correspond to 2 time slots included in subframes for the positioning. Here, the method of forming the PRS patterns by the particular sequence is described below. 
     1-a) When the particular sequence corresponds to f(i)={f(0),f(1),f(2),f(3),f(4),f(5)}={0, 1, 2, 3, 4, 5, 6}, the PRS pattern is formed in a position of a subcarrier on a frequency domain corresponding to a first value of sequences in the last symbol in each of the two slots as shown in  FIG. 19 . That is, in the last symbol, the PRS pattern is formed in a 0 th  subcarrier position since a first value of sequences is 0. Next, in a second symbol from the last, the PRS pattern is formed in a subcarrier position on a frequency domain corresponding to a second value of sequences. That is, in the second symbol from the last, the PRS pattern is formed in 1st subcarrier position since the second value of sequences is 1. In the same way, PRS patterns are formed in corresponding subcarrier positions on a frequency domain corresponding to values of sequences from the last symbol to a 6 th  symbol from the last in each of the two slots. 
     1-b) As shown in  FIG. 20 , PRS patterns formed in positions corresponding to symbol axes including control regions such as a PDCCH (Physical Downlink control CHannel), a PHICH (Physical Hybrid-ARQ Indicator CHannel), and a PCFICH (Physical Control Format Indicator CHannel) and a CRS (Cell-specific Reference Signal), and REs (Reference Elements) including a PSS (Primary Synchronization Signal), an SSS (Secondary Synchronization Signal), and a BCH (Broadcast Channel) are excluded from the generated basic PRS patterns. 
     1-equation) A process of forming the basic PRS patterns through 1-a) and 1-b) is represented by an equation below. 
     When it is determined that v indicates a value for defining locations of different PRSs in a frequency domain, N symb   DL  indicates the number of all OFDM symbols in each slot in a downlink, the basic PRS pattern for a corresponding I th  OFDM symbol at each slot is formed based on equation 17 below. 
     
       
         
           
             
               
                 
                   
                     v 
                     = 
                     
                       5 
                       - 
                       l 
                       + 
                       
                         N 
                         CP 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       l 
                       = 
                       
                         
                           
                             N 
                             symb 
                             DL 
                           
                           - 
                           
                             i 
                              
                             
                                 
                             
                              
                             for 
                              
                             
                                 
                             
                              
                             i 
                           
                         
                         = 
                         1 
                       
                     
                     , 
                     2 
                     , 
                     4 
                     , 
                     L 
                     , 
                     
                       4 
                       + 
                       
                         ( 
                         
                           
                             n 
                             s 
                           
                            
                           mod 
                            
                           
                               
                           
                            
                           2 
                         
                         ) 
                       
                       + 
                       
                         N 
                         CP 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       N 
                       CP 
                     
                     = 
                     
                       { 
                       
                         
                           
                             1 
                           
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               normal 
                                
                               
                                   
                               
                                
                               C 
                                
                               
                                   
                               
                                
                               P 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               extended 
                                
                               
                                   
                               
                                
                               C 
                                
                               
                                   
                               
                                
                               P 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     A value of N symb   DL  is 7 when a normal CP is used, a value of N symb   DL  is 6 when an extended CP is used. A value of (n s  mod 2) is 0 in even slots, and a value of (n s  mod 2) is 1 in odd slots. Accordingly, in equation 17 may be defined as follows. 
     
       
         
           
             l 
             = 
             
               { 
               
                 
                   
                     
                       2 
                       , 
                       3 
                       , 
                       5 
                       , 
                       6 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           0 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         1 
                       
                     
                   
                 
                 
                   
                     
                       1 
                       , 
                       2 
                       , 
                       3 
                       , 
                       5 
                       , 
                       6 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           1 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         1 
                       
                     
                   
                 
                 
                   
                     
                       2 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           0 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         0 
                       
                     
                   
                 
                 
                   
                     
                       1 
                       , 
                       2 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           1 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         0 
                       
                     
                   
                 
               
             
           
         
       
     
     2. The basic PRS patterns formed in 2 slots consisting of one subframe and ½ resource block including 6 subcarriers are allocated to the N subframe  number of subframes up to a system bandwidth in a frequency axis and every particular period in a time axis. 
     For example, when a system bandwidth corresponds to 10 Mhz in a frequency axis, a total of 50 RBs exist, so that the basic PRS pattern formed in the ½ RB is repeated 100 times in a frequency axis without any change. When the number of total RBs corresponding to the downlink system bandwidth is N RB   DL , the total number of 2·N RB   DL  is repeated. 
     The basic PRS patterns are allocated in the N subframe  number of subframes in every particular period, and are differently distributed for each Subframe Number (SFN), each cell-specific information piece such as a PCI (Physical Cell Identity), and each time axis, unlike in a frequency axis. That is implemented by identically cyclic-shifting subcarrier locations, in which the PRS in each symbol is formed, as much as v shift , by adding v shift  indicating values to be shifted in a frequency axis to indicating values for defining locations of different positioning reference signals in a frequency domain according to a subframe number and cell-specific information. 
     Process 2 for a k th  subcarrier in an entire system bandwidth including N RB   DL N sc   RB  number of subcarriers is represented as equation 12. N RB   DL  refers to the number of total RBs corresponding to the downlink system bandwidth, N sc   RB  refers to the number of subcarriers in one RB, and a normal subframe including the positioning subframe may use equation 18 below. 
         k= 6 m +( v+v   shift ) mod 6  m= 0,1, . . . , 2· N   RB   DL −  (18)
 
     In equation 18, v indicates values for defining locations of different PRSs described in process 1 in a frequency domain, and v shift  indicates values for identically and additionally cyclic-shifting subcarrier locations, in which the PRS in each symbol is formed, according to a subframe number and cell-specific information. At this time, v shift  may include remainders generated by dividing a value generated by the subframe number and a cell-specific information function by 6, which is a maximum available frequency shift value. Particularly, is obtained by deriving one or more pseudo-random sequence values from a pseudo-random sequence, which is generated with cell-specific information as an initial value such as a PCI, by a function of positioning subframe numbers, multiplying the derived pseudo-random sequence values by a predetermined constant, calculating a sum of the multiplied values, and then obtaining a remainder remaining after dividing the sum by 6, which corresponds to a maximum available frequency shift value. The above function is represented as equation 19 below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           v 
                           shift 
                         
                         = 
                           
                          
                         
                           
                             f 
                              
                             
                               ( 
                               
                                 
                                   n 
                                   subframe 
                                 
                                 , 
                                 
                                   N 
                                   cell 
                                   ID 
                                 
                               
                               ) 
                             
                           
                           -&gt; 
                           
                             v 
                             shift 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 i 
                               
                                
                               
                                 
                                   a 
                                   i 
                                 
                                 · 
                                 
                                   c 
                                    
                                   
                                     ( 
                                     
                                       f 
                                        
                                       
                                         ( 
                                         
                                           
                                             n 
                                             subframe 
                                           
                                           , 
                                           i 
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                            
                           mod 
                            
                           
                               
                           
                            
                           6 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     In equation 19, 0≦N Cell   ID &lt;504 denotes a PCI, a denotes a constant, c(i) denotes a pseudo-random sequence, and c init =N Cell   ID  is given to an initial value of c and initialized in every subframe for each positioning. 
     Processes 1 and 2 together are represented as an equation below. 
     That is, a PRS r l,n     s   (m) mapped to a k,l   (p) , which is a complex-valued modulation symbol used as a positioning reference symbol for an antenna port p in a n s  th slot is represented as equation 20. 
     
       
         
           
             
               
                 
                   
                     
                       a 
                       
                         k 
                         , 
                         l 
                       
                       
                         ( 
                         p 
                         ) 
                       
                     
                     = 
                     
                       
                         r 
                         
                           l 
                           , 
                           
                             n 
                             s 
                           
                         
                       
                        
                       
                         ( 
                         
                           m 
                           ′ 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     k 
                     = 
                     
                       
                         6 
                          
                         m 
                       
                       + 
                       
                         
                           ( 
                           
                             v 
                             + 
                             
                               v 
                               shift 
                             
                           
                           ) 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         6 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       l 
                       = 
                       
                         
                           
                             N 
                             symb 
                             DL 
                           
                           - 
                           
                             i 
                              
                             
                                 
                             
                              
                             for 
                              
                             
                                 
                             
                              
                             i 
                           
                         
                         = 
                         1 
                       
                     
                     , 
                     2 
                     , 
                     4 
                     , 
                     L 
                     , 
                     
                       4 
                       + 
                       
                         ( 
                         
                           
                             n 
                             s 
                           
                            
                           mod 
                            
                           
                               
                           
                            
                           2 
                         
                         ) 
                       
                       + 
                       
                         N 
                         CP 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       m 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         2 
                         · 
                         
                           N 
                           RB 
                           DL 
                         
                       
                       - 
                       1 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       m 
                       ′ 
                     
                     = 
                     
                       m 
                       + 
                       
                         N 
                         RB 
                         
                           max 
                           , 
                           DL 
                         
                       
                       - 
                       
                         N 
                         RB 
                         DL 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       N 
                       CP 
                     
                     = 
                     
                       { 
                       
                         
                           
                             1 
                           
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               normal 
                                
                               
                                   
                               
                                
                               C 
                                
                               
                                   
                               
                                
                               P 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               extended 
                                
                               
                                   
                               
                                
                               C 
                                
                               
                                   
                               
                                
                               P 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     In equation 20, l is represented as follows. 
     
       
         
           
             l 
             = 
             
               { 
               
                 
                   
                     
                       2 
                       , 
                       3 
                       , 
                       5 
                       , 
                       6 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           0 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         1 
                       
                     
                   
                 
                 
                   
                     
                       1 
                       , 
                       2 
                       , 
                       3 
                       , 
                       5 
                       , 
                       6 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           1 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         1 
                       
                     
                   
                 
                 
                   
                     
                       2 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           0 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         0 
                       
                     
                   
                 
                 
                   
                     
                       1 
                       , 
                       2 
                       , 
                       4 
                       , 
                       5 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         
                           n 
                           s 
                         
                          
                         mod 
                          
                         
                             
                         
                          
                         2 
                       
                       = 
                       
                         
                           1 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             N 
                             CP 
                           
                         
                         = 
                         0 
                       
                     
                   
                 
               
             
           
         
       
     
     At this time, v indicating values for defining locations of different positioning reference signals in a frequency domain and v shift  are represented as equation 21 below. Particularly, v shift  is a cell-specific and positioning subframe number-specific value. 
     
       
         
           
             
               
                 
                   
                     v 
                     = 
                     
                       5 
                       - 
                       l 
                       + 
                       
                         N 
                         CP 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           
                             v 
                             shift 
                           
                           = 
                             
                            
                           
                             
                               f 
                                
                               
                                 ( 
                                 
                                   
                                     n 
                                     subframe 
                                   
                                   , 
                                   
                                     N 
                                     cell 
                                     ID 
                                   
                                 
                                 ) 
                               
                             
                             -&gt; 
                             
                               v 
                               shift 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               ( 
                               
                                 
                                   ∑ 
                                   i 
                                 
                                  
                                 
                                   
                                     a 
                                     i 
                                   
                                   · 
                                   
                                     c 
                                      
                                     
                                       ( 
                                       
                                         f 
                                          
                                         
                                           ( 
                                           
                                             
                                               n 
                                               subframe 
                                             
                                             , 
                                             i 
                                           
                                           ) 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                              
                             mod 
                              
                             
                                 
                             
                              
                             6 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     In equation 21, n subframe  corresponds to a positioning subframe number, and c init −N Cell   ID  is given as an initial value of c in pseudo-random sequence c(i) and is initialized in every subframe for each positioning. 
     Methods of generated PRS patterns by using the modular sonar sequence proposed herein may be applied to all OFDM-based wireless mobile communication systems. Examples of OFDM-based wireless mobile communication systems include an E-UTRAN (LTE), an E-EUTRAN (LTE-Advanced), WIBRO, and Mobile Wi-MAX, and may be also applied to all wireless mobile communication systems in which all OFDM-based mobile communication terminals require the positioning. 
     While the exemplary embodiments have been shown and described, it will be understood by those skilled in the art that various changes in form and details may be made thereto without departing from the spirit and scope of this disclosure as defined by the appended claims and their equivalents. Thus, as long as modifications fall within the scope of the appended claims and their equivalents, they should not be misconstrued as a departure from the scope of the invention itself. 
     This application is further related to the U.S. Patent Application having attorney docket number (your docket number), which claims priority from and the benefit of Korean Patent Application Nos. 10-2009-0031548, 10-2009-0038564, 10-2009-0056705, 10-2009-0056708, and 10-2009-0059978, filed on Apr. 10, 2009, Apr. 30, 2009, Jun. 24, 2009, Jun. 24, 2009, and Jul. 1, 2009, respectively. These applications, assigned to the assignee of the current application, are hereby incorporated by reference for all purposes as if fully set forth herein.