WO2022051235A2

WO2022051235A2 - Method and apparatus for positioning

Info

Publication number: WO2022051235A2
Application number: PCT/US2021/048293
Authority: WO
Inventors: Jaihyung Cho
Original assignee: Locaila, Inc
Priority date: 2020-09-01
Filing date: 2021-08-30
Publication date: 2022-03-10
Also published as: WO2022051235A3

Abstract

Disclosed is a positioning method performed by a user equipment, the positioning method including receiving a first reference signal from a first transmitter and a second reference signal from a second transmitter, extracting a first sample vector based on received data of the first reference signal measured at a plurality of sample times and a second sample vector based on received data of the second reference signal measured at the plurality of sample times, calculating a first phase vector and a second phase vector by performing an inner product operation of a DFT coefficient vector for DFT operation with respect to each of the first and second sample vectors, and calculating a difference between a travel distance of the first reference signal and a travel distance of the second reference signal based on phase information of components included in a conjugate multiplication of the first and second phase vectors.

Description

IN THE UNITED STATES PATENT AND TRADEMARK OFFICE AS RECEIVING OFFICE FOR THE PATENT COOPERATION TREAT(PCT) TITLE : METHOD AND APPARATUS FOR POSITIONING INVENTOR : JAIHYUNG CHO (DAEGEON, REPUBLIC OF KOREA) CROSS REFERENCE TO RELATED APPLCIATION This application claims the benefit of U.S. Nonprovisional Patent Application. No. 17/008,942, filed September 01, 2020 and U.S. Nonprovisional Patent Application No. No.17/214,962 filed March 29, 2021 and incorporates the disclosure of each application by reference. BACKGROUND 1. FIELD The present disclosure of the following description relates to a method and apparatus for measuring a position of a user equipment (UE) using a wireless signal. 2. Related Art A communication system may include a core network (e.g., a mobility management entity (MME), a serving gateway (SGW), and a packet data network (PDN) gateway (PGW)), a base station (e.g., a macro base station, a small base station, and a relay), a user equipment (UE), and the like. Communication between the base station and the UE may be performed using a variety of radio access technology (RAT), for example, 4-th generation (4G) communication technology, 5-th generation (5G) communication technology, wireless broadband (WiBro) technology, wireless local area network (WLAN) technology, and wireless personal area network (WPAN) technology. In a communication system, a UE may generally transmit and receive data through a base station. For example, if data to be transmitted to a second UE is present, a first UE may generate a message including the data to be transmitted to the second UE and may transmit the generated message to a first base station to which the first UE belongs. The first base station may receive the message from the first UE and may verify that a destination of the received message is the second UE. The first base station may transmit the message to a second base station to which the verified destination, that is, the second UE belongs in a second base station sum time interval. The second base station may receive the message from the first base station and may verify that the destination of the received message is the second UE. The second base station may transmit the message to the verified destination, that is, the second UE. The second UE may receive the message from the second base station and may acquire the data included in the received message. A reference signal may be transmitted and received between a UE and a base station. As another example, a reference signal may be transmitted and received between two different base stations. The reference signal may be used for various purposes. For example, the UE or the base station may perform synchronization or may estimate a position of the UE using the reference signal. As one of positioning methods using RAT, the UE may perform positioning based on a difference in time of arrival (ToA) between positioning reference signals (PRSs) received from a plurality of base stations or a difference in received phase between reference signals. However, it is very difficult to estimate a difference in ToA between reference signals or correlation between a phase difference and a position of a UE. In particular, a different positioning method different from the related art may be required to improve the positioning accuracy. SUMMARY At least one example embodiment provides a positioning method and apparatus that may improve positioning accuracy. According to an aspect, there is provided a positioning method performed by a user equipment, the method including receiving a first reference signal from a first transmitter and receiving a second reference signal from a second transmitter; acquiring phase information depending on carrier frequencies of the first reference signal and the second reference signal based on received data of the first reference signal measured at a plurality of sample times and received data of the second reference signal measured at the plurality of sample times; and outputting information about a difference between a travel distance of the first reference signal and a travel distance of the second reference signal based on the phase information depending on the carrier frequencies. The acquiring of the phase information may include acquiring a first sample vector based on the received data of the first reference signal, acquiring a second sample vector based on the received data of the second reference signal, calculating a first phase vector and a second phase vector by performing an inner product operation of a discrete Fourier transform (DFT) coefficient vector for a DFT operation with respect to each of the first sample vector and the second sample vector, and acquiring the phase information from a conjugate multiplication of the first phase vector and the second phase vector. A waveform of the first reference signal and a waveform of the second reference signal may be configured to continue in a time interval greater than a symbol size corresponding to a frequency interval of orthogonal frequency division multiplex (OFDM). The first reference signal and the second reference signal may be transmitted in different time domains, a first subcarrier group for transmitting the first reference signal and a second subcarrier group for transmitting the second reference signal may be the same. The first reference signal may include a plurality of subcarriers included in a first subcarrier group, and the second reference signal may include a plurality of subcarriers included in a second subcarrier group, and a subcarrier included in the first subcarrier group and a subcarrier included in the second subcarrier group may be orthogonal to each other. The plurality of subcarriers included in the first subcarrier group and the plurality of subcarriers included in the second subcarrier group may be provided at equal intervals in a frequency domain. A correction factor may be calculated based on a conjugate multiplication between a first component of the second phase vector and a second component of the second phase vector having an angular frequency index different from that of the first component, and the phase information may be output based on a result of multiplying the conjugate multiplication of the first phase vector and the second phase vector by the correction factor. A complex signal component of each of the subcarriers included in the first subcarrier group and a complex signal component of each of the subcarriers included in the second subcarrier group may have a conjugate relation. The second subcarrier group may be spaced apart at a desired distance from the first subcarrier group in the frequency domain, and the desired distance may be determined based on a number of subcarriers included in the first subcarrier group and a size of a fast Fourier transform (FFT) window. The acquiring of the phase information may include calculating a parameter depending on a clock error between the first transmitter and the second transmitter and the terminal among parameters constituting the conjugate multiplication by linearly combining phase angles of components included in the conjugate multiplication. The positioning method may further include receiving reference signals from a transmitter group that includes at least three transmitters; calculating first phase information based on reference signals received from a first pair of transmitters among the at least three transmitters included in the transmitter group, and calculating second phase information based on reference signals received from a second pair of transmitters among the at least three transmitters; and determining an integer ambiguity of the second phase information based on the first phase information. An interval between the first pair of transmitters may be less than an interval between the second pair of transmitters. The interval between the first pair of transmitters may be less than the carrier wavelength of the reference signals and the interval between the second pair of transmitters may be greater than the carrier wavelength of the reference signals. According to another aspect, there is provided a positioning reference signal transmission method performed by a plurality of transmitters, the method including transmitting, by a first transmitter, a first reference signal; and transmitting, by a second transmitter, a second reference signal. A waveform of the first reference signal and a waveform of the second reference signal are configured to continue in a time interval greater than a symbol size corresponding to a frequency interval of orthogonal frequency division multiplex (OFDM), and the first reference signal includes a plurality of subcarriers included in a first subcarrier group, and the second reference signal includes a plurality of subcarriers included in a second subcarrier group. The first reference signal and the second reference signal may be transmitted in different time domains and the first subcarrier group and the second subcarrier group may be the same. The first reference signal may include a plurality of subcarriers included in a first subcarrier group, and the second reference signal may include a plurality of subcarriers included in a second subcarrier group, and a subcarrier included in the first subcarrier group and a subcarrier included in the second subcarrier group may be orthogonal to each other, and the plurality of subcarriers included in the first subcarrier group and the plurality of subcarriers included in the second subcarrier group may be provided at equal intervals in a frequency domain. A complex signal component of each of the subcarriers included in the first subcarrier group and a complex signal component of each of the subcarriers included in the second subcarrier group may have a conjugate relation. The method may further include transmitting, by at least one additional transmitter excluding the first transmitter and the second transmitter, a reference signal. In a transmitter group including the first transmitter, the second transmitter, and the at least one additional transmitter, an interval between a first pair of transmitters and an interval between a second pair of transmitters may differ from each other. The interval between the first pair of transmitters may be less than a carrier wavelength of the reference signals and the interval between the second pair of transmitters may be greater than the carrier wavelength of the reference signals. According to at least one example embodiment, a user equipment, for example, a user equipment (UE) 200 of FIG. 1, may receive reference signals transmitted at different positions, may calculate a difference between a travel distance of a first reference signal and a travel distance of a second reference signal from a conjugate multiplication of two phase vectors. Through this, the user equipment may perform positioning in a vertical direction or a horizontal direction at high accuracy. According to at least one example embodiment, the user equipment may analyze reference signals transmitted from at least three transmitters and may solve an integer ambiguity issue of phase information. At least one example embodiment provides a method and apparatus for improving a positioning performance by determining a phase of a wireless signal with high precision and by determining integer ambiguity for a phase difference with high precision. According to an aspect, there is provided a positioning method performed by a user equipment (UE), the positioning method including receiving reference signals from a plurality of base stations; acquiring phase difference information depending on a wavelength of at least one subcarrier among subcarriers included in the reference signals; calculating first estimated coordinates of the UE based on first phase difference information depending on a wavelength of a first subcarrier among the subcarriers; and calculating a first travel distance difference between the reference signals from the first estimated coordinates and estimating integer ambiguity of a second phase difference depending on a wavelength of a second subcarrier from the first travel distance difference. The positioning method may further include calculating k^th estimated coordinates based on k^th phase difference information depending on a wavelength of a k^th subcarrier; and calculating a k^th travel distance difference from the k^th estimated coordinates and estimating integer ambiguity of a (k+1)-th phase difference depending on a wavelength of a (k+1)-th subcarrier from the k^th travel distance difference. The calculating of the k^th estimated coordinates and the estimating of the integer ambiguity of the (k+1)-th phase difference may be repeated until a preset termination condition is met. Here, k denotes a natural number. The wavelength of the (k+1)-th subcarrier may be shorter than the wavelength of the k^th subcarrier. The positioning method may further include acquiring phase difference information depending on a wavelength of a carrier included in the reference signals; estimating integer ambiguity of a phase difference depending on the wavelength of the carrier based on a travel distance difference that is acquired from a phase difference depending on a wavelength of a subcarrier having a longest wavelength among the subcarriers; and calculating a position of the UE based on a phase difference depending on the wavelength of the carrier. The calculating of the k^th estimated coordinates may include calculating initial estimated coordinates of the UE from the k^th phase difference information; and modifying the initial estimated coordinates through an iterative operation and calculating the k^th estimated coordinates. The modifying of the initial estimated coordinates and the calculating of the k^th estimated coordinates may include calculating an n^th travel distance difference between the reference signals from n^th estimated coordinates and calculating (n+1)-th estimated coordinates modified from the n^th estimated coordinates based on an error between the n^th travel distance difference and a travel distance difference corresponding to the k^th phase difference, and the calculating of the n^th travel distance difference and the calculating of the (n+1)-th estimated coordinates may be repeated until a preset termination condition is met. The calculating of the n^th travel distance difference and the calculating of the (n+1)-th estimated coordinates may be repeated until an error between the n^th estimated coordinates and the (n+1)-th estimated coordinates becomes to be less than a preset tolerance. The (n+1)-th estimated coordinates may depend on a product of a partial differential coefficient matrix for a travel distance difference between the reference signals and the error between the n^th travel distance difference and the travel distance difference corresponding to the k^th phase difference. The acquiring of the phase difference information depending on the wavelength of at least one subcarrier among the subcarriers may include acquiring a first sample vector based on received data of a first reference signal and acquiring a second sample vector based on received data of a second reference signal; calculating a first phase vector and a second phase vector by performing an inner product of a discrete Fourier transform (DFT) coefficient vector with respect to each of the first sample vector and the second sample vector; calculating a third phase vector by conjugating a 1-1 partial vector corresponding to a first portion of the first phase vector and a 1-2 partial vector corresponding to a second portion of the first phase vector; calculating a fourth phase vector by conjugating a 2-1 partial vector corresponding to a first portion of the second phase vector and a 2-2 partial vector corresponding to a second portion of the second phase vector; and acquiring phase difference information depending on the wavelength of at least one subcarrier among the subcarriers by conjugating the third phase vector and the fourth phase vector. The acquiring of the phase difference information depending on the wavelength of the carrier included in the reference signals may include acquiring a first sample vector based on received data of a first reference signal and acquiring a second sample vector based on received data of a second reference signal; calculating a first phase vector and a second phase vector by performing an inner product of a DFT coefficient vector with respect to each of the first sample vector and the second sample vector; and acquiring phase difference information depending on the wavelength of the carrier from a conjugate product of the first phase vector and the second phase vector. According to another aspect, there is provided a positioning apparatus including a communicator; and a processor configured to connect to the communicator. The processor is configured to perform a process of receiving reference signals from a plurality of base stations, a process of acquiring phase difference information depending on a wavelength of at least one subcarrier among subcarriers included in the reference signals, a process of calculating first estimated coordinates of a user equipment (UE) based on first phase difference information depending on a wavelength of a first subcarrier among the subcarriers, and a process of calculating a first travel distance difference between the reference signals from the first estimated coordinates and estimating integer ambiguity of a second phase difference depending on a wavelength of a second subcarrier from the first travel distance difference. According to at least one example embodiment, a UE may readily calculate a phase difference depending on a wavelength of a subcarrier or a carrier of reference signals. According to at least one example embodiment, a UE may improve positioning precision by estimating a position of the UE through an iterative operation using a phase difference depending on wavelengths of a plurality of subcarriers or carriers. According to at least one example embodiment, the UE may determine integer ambiguity of a phase difference of a subcarrier or a carrier having a relatively small wavelength based on a phase difference of a subcarrier having a relatively large wavelength. According to at least one example embodiment, the UEmay improve positioning precision by modifying an estimated position using a partial differential coefficient matrix. Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. BRIEF DESCRIPTION OF THE FIGURES Example embodiments will be described in more detail with regard to the figures, wherein like reference numerals refer to like parts throughout the various figures unless otherwise specified, and wherein: FIG. 1 illustrates an example of a communication system according to at least one example embodiment. FIG. 2 is a diagram illustrating an example of a configuration of a communication node included in a communication system according to at least one example embodiment. FIG. 3 is a flowchart illustrating an example of a positioning method according to at least one example embodiment. FIG.4 is a flowchart illustrating an example of performing operation S100 of FIG.3. FIG. 5 illustrates an example of a first subcarrier group and a second subcarrier group according to at least one example embodiment. FIG. 6 illustrates an example of a waveform of a reference signal in the case of configuring the reference signal using a sequence used to generate a general sine wave according to at least one example embodiment. FIG. 7 illustrates an example of a waveform of a reference signal that continues in a plurality of symbol periods according to at least one example embodiment. FIG.8 illustrates an example of a trace of dots having ∆d that is a difference between a distance from a first transmitter and a distance from a second transmitter according to at least one example embodiment. FIG.9 is a graph showing an example in which four transmitters transmit reference signals according to at least one example embodiment. FIG.10 is a graph showing an example in which three transmitters transmit reference signals according to at least one example embodiment. FIG.11 illustrates an example of a communication system according to at least one example embodiment. FIG.12 illustrates an example of a relationship between an amplitude and a phase of a signal wavelength measured by the UE 200 according to an example embodiment. FIG. 13 is a flowchart illustrating an example of a positioning method of the UE 200 according to an example embodiment. FIG. 14 is a flowchart illustrating an example of a process of performing operation S220 of FIG.13. FIG. 15 is a flowchart illustrating an example of a process of performing operation S230 of FIG.13. FIG. 16 is a flowchart illustrating an example of a process of performing operation S250 of FIG.13. DETAILED DESCRIPTION Various modifications and changes may be made to the present disclosure and the disclosure may include various example embodiments. Specific example embodiments are described in detail with reference to the accompanying drawings. The example embodiments, however, may be embodied in various different forms, and should not be construed as being limited to only the specific example embodiments. Rather, the example embodiments should be understood to include all of the modifications, equivalents, and substitutions included in the spirit and technical scope of the disclosure. Although the terms "first," "second," etc., may be used herein to describe various components, the components should not be limited by these terms. These terms are only used to distinguish one component from another component. For example, a first component may also be termed a second component and, likewise, a second component may be termed a first component, without departing from the scope of this disclosure. As used herein, the term "and/or" includes any and all combinations of one or more of the associated items. When a component is referred to as being "connected to" or "coupled to" another component, the component may be directly connected to or coupled to the other component, or one or more other intervening components may be present. In contrast, when a component is referred to as being "directly connected to" or "directly coupled to," there is no intervening component. The terms used herein are used to simply explain specific example embodiments and are not construed to limit the present disclosure. The singular forms "a," "an," and "the," are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises/comprising (incudes/including)," and "has/having" when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups, thereof. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. Terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and/or this disclosure, and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Hereinafter, example embodiments will be described in detail with reference to the accompanying drawings. For simplicity of description and general understanding of the disclosure, like reference numerals refer to like components throughout the present specification although they are illustrated in different drawings. Herein, a reference signal may include, for example, a signal for positioning of a user equipment (UE), a signal for synchronization of the UE or a base station, and the like. However, it is provided as an example only. A method of estimating a reception delay time of a reference signal disclosed herein may apply to estimating a reception delay time of another signal aside from the reference signal. Here, although an example embodiment is described based on an example of estimating the reception delay time of the reference signal for clarity of description, it is provided as an example only. It should be understood that a method of estimating the reception delay time of the other signal aside from the reference signal is included in the example embodiment. FIG. 1 illustrates an example of a communication system according to at least one example embodiment. Referring to FIG. 1, the communication system may include a first transmitter 100A and a second transmitter 100B. Here, each of the first transmitter 100A and the second transmitter 100B may be referred to as, for example, NodeB, next generation NodeB, evolved NodeB, gNodeB, a base transceiver station (BTS), a radio base station, a radio transceiver, an access point, an access node, a road side unit (RSU), a radio remote head (RRH), a transmission point (TP), a transmission and reception point (TRP), a relay node, and the like. A UE 200 may also be referred to as a terminal, an access terminal, a mobile terminal, a station, a subscriber station, a mobile station, a portable subscriber station, a node, a device, and the like. The first transmitter 100A may transmit a first reference signal. The second transmitter 100B may transmit a second reference signal. The UE 200 may receive the first reference signal and the second reference signal. The UE 200 may receive the first reference signal and the second reference signal, may calculate a phase difference between the first reference signal and the second reference signal, and may calculate position information of the UE 200 based on the phase difference. As another information, when the UE 200 transmits information about the phase difference to the first transmitter 100A or the second transmitter 100B, the first transmitter 100A or the second transmitter 100B may also calculate position information of the UE 200. Although FIG. 1 illustrates two transmitters, for example, the first transmitter 100A and the second transmitter 100B, it is provided as an example only. To solve an inter ambiguity issue in calculating a phase difference, the UE 200 may receive reference signals from at least three transmitters, which is further described below. Also, although FIG. 1 illustrates that the first transmitter 100A and the second transmitter 100B are spatially separate from each other, the first transmitter 100A and the second transmitter 100B may belong to the same base station. In this case, modulation of the first reference signal and the second reference signal may be performed through a single base station. FIG. 2 is a diagram illustrating an example of a configuration of a communication node included in a communication system according to at least one example embodiment. Like reference numeral used for the UE 200 of FIG.1 also applies to a reference numeral of the communication node of FIG. 2. A configuration of FIG. 2 may also apply to the first transmitter 100A or the second transmitter 100B. Referring to FIG. 2, a communication node 200 may include at least one processor 210, a memory 220, and a transmission and reception device 230 configured to perform communication through connection to a network. Also, the communication node 200 may further include an input interface device 240, an output interface device 250, and a storage device 260. Here, the components included in the communication node 200 may communicate with each other through connection to a bus 270. The processor 210 may execute a program command stored in at least one of the memory 220 and the storage device 260. The processor 210 may refer to a central processing unit (CPU), a graphics processing unit (GPU), or an exclusive processor that performs methods according to example embodiments. Each of the memory 220 and the storage device 260 may be configured as at least one of a volatile storage medium and a nonvolatile storage medium. For example, the memory 220 may be configured as at least one of read only memory (ROM) and random access memory (RAM). FIG. 3 is a flowchart illustrating an example of a positioning method according to at least one example embodiment. Referring to FIG. 3, in operation S100, the first transmitter 100A may transmit a first reference signal, and the second transmitter 100B may transmit a second reference signal. The first transmitter 100A may transmit the first reference signal in a continuous waveform in a time interval greater than a symbol size. The second transmitter 100B may transmit the second reference signal in a continuous waveform in a time interval greater than the symbol size. If each of the first reference signal and the second reference signal has a continuous waveform in the time interval greater than the symbol size, the UE 200 may easily receive a corresponding reference signal and extract a sample vector. FIG.4 is a flowchart illustrating an example of performing operation S100 of FIG.3. Referring to FIG. 4, in operation S102, the first transmitter 100A and the second transmitter 100B may set a first subcarrier group for transmitting the first reference signal and a second subcarrier group for transmitting the second reference signal. The first transmitter 100A may transmit the first reference signal using the first subcarrier group, and the second transmitter 100B may transmit the second reference signal using the second subcarrier group. Subcarriers of the first subcarrier group may be orthogonal to subcarriers of the second subcarrier group. However, it is provided as an example only. For example, if orthogonality between the first reference signal and the second reference signal is guaranteed in a time domain, the first subcarrier group and the second subcarrier group may not be orthogonal to each other. Subcarriers included in the first subcarrier group may be provided at equal intervals in a frequency domain. FIG. 5 illustrates an example of a first subcarrier group and a second subcarrier group according to at least one example embodiment. Referring to FIG. 5, subcarriers included in the first subcarrier group for transmitting a first reference signal may be provided at equal intervals in a frequency domain. Likewise, subcarriers included the second subcarrier group for transmitting a second reference signal may be provided at equal intervals. Each of the first reference signal and the second reference signal may be transmitted through a plurality of consecutive symbols. Since each of the first reference signal and the second reference signal has a waveform continuous in a boundary between symbols, the UE 200 receiving the first reference signal and the second reference signal may readily acquire sample vectors. FIG.5 illustrates an example in which an interval between the subcarriers of the first subcarrier group is 1 and an example in which an interval between the subcarriers of the second subcarrier group is 1. However, it is provided as an example only. For example, the subcarriers included in the first subcarrier group or the second subcarrier group may be provided at intervals greater than 1. Also, the interval between the subcarriers of the first subcarrier group may differ from the interval between the subcarriers of the second subcarrier group. Referring again to FIG.4, in operation S104, the first transmitter 100A and the second transmitter 100B may determine a sequence of the first reference signal and a sequence of the second reference signal. The first transmitter 100A and the second transmitter 100B may determine the sequence of the first reference signal and the sequence of the second reference signal such that the first reference signal and the second reference signal may be continuous in the boundary between the symbols. In operation S106, the first transmitter 100A may transmit the first reference signal generated using the sequence of the first reference signal. The second transmitter 100B may transmit the second reference signal generated using the sequence of the second reference signal. Hereinafter, a sequence of a reference signal such that the reference signal may be continuous in a boundary between symbols is described. FIG. 6 illustrates an example of a waveform of a reference signal in the case of configuring the reference signal using a sequence used to generate a general sine wave according to at least one example embodiment. Referring to FIG.6, a waveform of a reference signal may be discontinuous in a boundary between symbols due to presence of a cyclic prefix (CP) duration. Therefore, the first transmitter 100A and the second transmitter 100B may phase- shift a sequence of the reference signal by considering the CP duration such that the waveform of the reference signal may be continuous in the boundary between symbols. For example, the first transmitter 100A and the second transmitter 100B may generate a reference signal according to Equation 1. [Equation 1]

In Equation 1,

denotes a frequency domain complex exponentiation representing an initial phase and amplitude of a k-th subcarrier of an ℓ-th symbol, ^^ _^^ denotes a length of a valid period of a symbol, and

denotes a length of a CP duration of an (ℓ-1)-th symbol. Here, ℓ denotes a natural number. In an LTE standard, an index of a symbol may be counted for each slot. If a normal CP is used in the LTE standard, ℓ=1, 2, … 6. If an extended CP is used in the LTE standard, ℓ=1, 2, … 5. In a 5G NR standard, an index of a symbol may continuously increase in a time domain. Accordingly, in the 5G NR standard, ℓ may be a random natural number. Referring to Equation 1, in a sequence of a reference signal, a sequence value corresponding to the ℓ-th symbol may correspond to a value that is phase- shifted by from a sequence value corresponding to the (ℓ-1)-th

symbol. For example, a waveform of a reference signal that continues in a plurality of symbol periods may be represented as FIG.7. Differently representing Equation 1, Equation 1 may be expressed as Equation 2. [Equation 2]

In Equation 2,

denotes a frequency domain complex exponentiation representing an initial phase and amplitude of a k-th subcarrier of an initial symbol (symbol index=0). If the normal CP is applied in the LTE standard, a sequence of a reference signal may be represented as Equation 3. [Equation 3]

In Equation 3, denotes a frequency domain complex exponentiation

representing an initial phase and amplitude of a k-th subcarrier of an initial symbol of an initial slot. Also, ^^ denotes a slot index, ℓ denotes a symbol index, and ^^ _^^,ℓ ^[ ^^^] denotes a frequency domain complex exponentiation representing an initial phase and amplitude of a k-th subcarrier of an ℓ-th symbol of an

slot. If ^^ is an even number,

is 1 at all times. Therefore, an initial phase of a ^^-th subcarrier of a start symbol of a slot may be the same regardless of a slot index. In contrast, if ^^ is an odd number,

is -1 for

number and 1 for ^^=even number. Therefore, the initial phase of the

subcarrier of the start symbol of the slot may vary based on a slot index. If the symbol index ℓ is numbered for each slot, ℓ may be one of 0, 1, 2, … 6. Accordingly,

and

In describing the following equations, the description of notations that repeat the notations of Equation 3 is omitted. If the normal CP is applied in the 5G NR standard, the sequence of the reference signal may be represented as Equation 4. [Equation 4]

= 0,1,2,3.. In Equation 4, mod denotes a modulo function used to acquire a remainder. In the case of the normal CP of the LTE standard, numerology number ^=0 and accordingly, P and ℓ=0, … 6. Also,

is a Dirac delta function that is defined as 1 only if μ=0. An index portion equation of -1 that determines a sign of a subcarrier, i.e., is defined if ^=0, that is, if a subcarrier spacing is 15

kHz. The index portion of -1 is 0 in other subcarrier spacings, that is, if μ>0. Therefore, start symbols of all of the subcarriers have a positive sign. In the 5G NR standard, if the symbol index is numbered based on a subframe unit and, in this instance, if subcarrier spacing=15 kHz, a sequence of a reference signal may be represented as Equation 5. [Equation 5]

With the assumption that the normal CP is applied, if the subcarrier spacing is 15 kHz or higher in the 5G NR standard, a sequence of a reference signal may be represented as Equation 6. [Equation 6]

If the extended CP is applied in the LTE standard and the 5G NR standard, a sequence of a reference signal may be represented as Equation 7. [Equation 7]

In Equation 7, in the LTE standard, ℓ denotes a symbol index number and may be 0 … 5. Also, in the 5G NR standard, ℓ denotes the symbol index number and may be 0...11. If a symbol index is numbered for each subframe and the extended CP is applied, a sequence of a reference signal may be represented as Equation 8. [Equation 8]

In Equation 8, ℓ denotes a symbol index number and may be 0...5. If 60 kHz subcarrier spacing is applied, P = 0 … 23 in a symbol of an extended CP and Tcp/Tu=1/4. A layer of a first resource block for transmitting the first reference signal and a layer of a second resource block for transmitting the second reference signal may be set to differ from each other. Therefore, a subcarrier signal of the first subcarrier group and a subcarrier signal of the second subcarrier group may be modulated to a carrier signal in which a frequency and a phase are synchronized by an independent radio frequency (RF) front end and thereby transmitted through different physical antennas, relays, or external transmission devices. The first transmitter 100A and the second transmitter 100B may be separate from each other in a horizontal direction. In this case, the UE 200 may receive the first reference signal and the second reference signal and may estimate a position of the UE 200 on a horizontal plane. As another example, the first transmitter 100A and the second transmitter 100B may be separate from each other in a vertical direction. In this case, the UE 200 may receive the first reference signal and the second reference signal and may estimate vertical position coordinates of the UE 200. The UE 200 may also estimate a distance between the first transmitter 100A or the second transmitter 100B and the UE 200 in the horizontal direction. As another example, the first transmitter 100A) and the second transmitter 100B may be separate from each other in the horizontal direction and may also be separate from each other in the vertical direction. In this case, the UE 200 may estimate information about a position of the UE 200 both in the vertical direction and the horizontal direction. The first reference signal and the second reference signal may be transmitted through different layers and antenna ports in different timelines on a time axis of a resource grid. Through this, a carrier phase difference, that is, a phase difference using a carrier signal may be easily calculated. The first reference signal and the second reference signal are orthogonal in a time domain. Therefore, although the first subcarrier group and the second subcarrier group include the same or partially overlapping subcarriers, an interference issue may not arise. For example, if the first reference signal is transmitted through an antenna port number 1 using subcarriers to which subcarrier numbers s1, s2, s3 … are allocated on a layer 1 in a time t, the second reference signal may be transmitted through an antenna port number 2 using subcarriers to which the same subcarrier numbers s1, s2, s3 …are allocated on a layer 2 in a time t-u, which differs from the time t. The antenna port refers to a logical configuration and may not be mapped to a physical external antenna or a wireless transmission device. As another example, the first reference signal and the second reference signal may be transmitted in the same timeline and, here, a frequency domain of a subcarrier group of each reference signal may be set to be different. In the case of an OFDM system in which a total number of subcarriers, that is, a size of a fast Fourier transform (FFT) window is N-th, s1-th, s2-th, s3-th … subcarrier signals may have a conjugate relation with (N-s1)-th, (N-s2)-th, (N-s3)-th … subcarrier signals, respectively. In this case, subcarrier signals of two groups may have the same frequency and opposite imaginary part signs. Therefore, if the first subcarrier group includes subcarriers to which subcarrier numbers s1, s2, s3 … are allocated and the second subcarrier group includes subcarriers to which subcarrier numbers N-s1, N-s2, N-s3 … are allocated, the first subcarrier group and the second subcarrier group may be orthogonal to each other. In addition, subcarrier signals of the two groups, that is, the first subcarrier group and the second subcarrier group, have the conjugate relation. Accordingly, a phase difference between reference signals may be easily calculated, which is described below. Hereinafter, the first reference signal transmitted from the first transmitter 100A and the first reference signal received at the UE 200 in operation S100 are described using equations. The following equations are provided to help understanding of example embodiments and thus may be easily modified by those skilled in the art within the scope of the example embodiments. A baseband of the first reference signal transmitted from the first transmitter 100A at a time t may be represented as Equation 9. [Equation 9] I

n Equation 9, denotes a first reference signal transmitted in a baseband at a time t, and Aq denotes an amplitude and an initial phase component of a subcarrier signal having an angular frequency

The first transmitter 100A may modulate the baseband signal of the first reference signal to a passband signal using a carrier signal having an angular frequency

and may transmit the modulated passband signal. Likewise, the second transmitter 100B may also modulate a baseband signal of the second reference signal to a passband signal and may transmit the modulated passband signal. If the first transmitter 100A and the second transmitter 100B belong to the same base station, modulation of the first reference signal and the second reference signal may be performed by a single base station. The first reference signal modulated to the passband signal may be represented as Equation 10. [Equation 10]

In Equation 10,

denotes a first reference signal modulated to a passband signal,

denotes an angular frequency of a carrier, a time t denotes a time in a time interval in which the first reference signal is transmitted. For example, if the reference signal continues during n symbol periods, t may be one of values between 0 and

The first reference signal of passband may arrive at the UE 200 through a linear path if an obstacle between the first transmitter 100A and the UE 200 is absent, and may arrive at the UE 200 through a multipath if the obstacle between the first transmitter 100A and the UE 200 is present. For example, if the first reference signal arrives at the UE 200 through propagation during a time ^a1, the first reference signal received at the UE 200 may be represented as Equation 11. [Equation 11]

The UE 200 may demodulate, to a baseband signal, a first reference signal of a passband received at the UE 200, as represented as Equation 11. The UE 200 may multiply the received passband signal by a factor for removing an angular frequency component ^^ _^^ of a carrier. This process may be represented as Equation 12. [Equation 12]

In Equation 12,

denotes a result of converting a first reference signal received at the UE 200 to a baseband signal, and ^ denotes a local clock error that occurs due to mismatch between a clock of a receiving UE and a clock of a transmitting base station. Referring to Equation 12, in

may disappear, however, a phase shift component may remain due to the delay time ^a1

and the local clock error

Although it is difficult to acquire a detailed value of the phase shift component

a phase shift amount may be proportional to the angular frequency

of the carrier. That is, a result of demodulating the first reference signal received at the UE 200 may include a phase component depending on the angular frequency ω_c of the carrier. Accordingly, phase information used to calculate a difference between a travel distance of the first reference signal and a travel distance of the second reference signal may include a term depending on the angular frequency ω_c of the carrier and a size thereof may be amplified. Accordingly, the positioning performance may be improved. Referring again to FIG.3, in operation S110, the UE 200 may extract a first sample vector. The UE 200 may acquire the first sample vector by converting first reference signals received at a plurality of points in times to baseband signals. For example, the UE 200 may extract the first sample vector by converting first reference signals received at N points in times to baseband signals. In a general OFDM system, a value of N may be determined based on a size of an FFT window. The first sample vector may be represented as Equation 13. [Equation 13]

In Equation 13,

denotes a first sample vector that includes samples of first reference signal received at N sample times. If a waveform of the first reference signal discontinues during a plurality of symbol periods, a time interval in which the following FFT operation is applicable is limited and thus, it may not be easy for the UE 200 to readily change t of Equation 13. In contrast, if the waveform of the first reference signal continues during the plurality of symbol periods, the UE 200 may easily acquire a plurality of sample vectors by changing t of Equation 13, without considering a boundary between symbols. In operation S120 of FIG.3, the UE 200 may calculate a first phase vector from a sample vector of the first reference signal. Hereinafter, a process of calculating, by the UE 200, a phase vector of the first reference signal is described as an example. Complex conjugate numbers of subcarriers corresponding to N sample times may be represented as a vector as shown in Equation 14. [Equation 14]

In Equation 14,

denotes a discrete Fourier transform (DFT) coefficient vector used for an FFT operation of a k-th subcarrier having an angular frequency

and

denotes a local clock error that occurs due to mismatch between a clock of the UE 200 and a clock of the first transmitter 100A. Components of the DFT coefficient vector may rotate on a complex plane according to an increase in

The UE 200 may perform an inner product operation on the sample vector of Equation 13 and the DFT coefficient vector of Equation 14. The UE 200 may extract a phase of each subcarrier component by performing the inner product operation. The UE 200 may calculate a sum of result values acquired by multiplying each of components of the DFT coefficient vector (complex conjugate number values) and each of components of the sample vector through the inner product operation. The aforementioned operation process may be represented as Equation 15. [Equation 15]

In Equation 15,

denotes data acquired by converting a first reference signal received at the UE 200 at a time t to a baseband signal, and N denotes a number of sample vector components. N may correspond to a size of a sum time interval in the inner product operation. In the general OFDM system, N may be determined based on a size of the FFT window. Referring to Equation 15, a result of performing an inner product operation of and

may be represented as a sum of

that is a portion independent from the time t and an error

component

Here,

may act as an interference component by noise and other orthogonal subcarrier components, thereby degrading a positioning accuracy. The UE 200 may converge a value of

to 0 and thereby ignore the same by averaging values calculated by collecting a plurality of samples. To this end, the UE 200 may acquire a plurality of sample vectors by changing a start time t of a time interval of a sample vector. If a waveform of the first reference signal continues during a plurality of symbol periods, the UE 200 may easily acquire a plurality of sample vectors. As described above, ^ denotes the local clock error that occurs due to mismatch between the clock of the UE 200 and the clock of the base station that manages the first transmitter 100A or the first transmitter 100A. In Equation 15, a phase of a component

corresponding to a k-th subcarrier may include a factor that is proportional to a propagation delay time between the first transmitter 100A and the UE 200.

The factor may include a multiplication of That is, in an inner product

operation result of the UE 200, a phase shift amount of an element corresponding to each component of an angular frequency of a subcarrier may depend on an angular frequency of a carrier. In the aforementioned description, only the k-th subcarrier signal having the angular frequency ^^ _^^ is considered. If the first subcarrier group of the first reference signal includes a subcarrier group having angular frequencies

Equation 15 may be normalized as represented as Equation 16. [Equation 16]

In Equation 16, each of

denotes an inner product operation result between a sample vector and a DFT coefficient vector acquired according to Equation 15, and

denotes a vector that includes

For example, may be referred to as a first phase vector. Also, denotes an error vector. Phases of components of the first phase vector

may be proportional to a multiplication of

which is a sum of an angular frequency of a carrier and an angular frequency of a subcarrier, and a propagation delay time

The UE 200 may acquire a plurality of first phase vectors by changing a start point t of a time interval. The UE 200 may extract a phase vector of the second reference signal in a similar manner to a process of extracting a phase vector of the first reference signal, which is described above with reference to Equation 9 to Equation 16. A time interval in which the second reference signal is transmitted may differ from a time interval in which the first reference signal is transmitted. In this case, since orthogonality between the first reference signal and the second reference signal is guaranteed in the time domain, the first subcarrier group and the second subcarrier group may be the same. The following description is made based on an example in which the first reference signal and the second reference signal are transmitted in different time intervals and the first subcarrier group is the same as the second subcarrier group. However, it is provided as an example only. For example, although the first reference signal and the second reference signal are transmitted in different time intervals, the first subcarrier group and the second subcarrier group may be set to differ from each other. Also, the first reference signal and the second reference signal may be transmitted in the same time interval, and the first subcarrier group and the second subcarrier group may be set to differ from each other. For example, a baseband of the second reference signal transmitted from the second transmitter 100B may be represented as Equation 17. [Equation 17]

In Equation 17,

denotes a second reference signal transmitted in a baseband at a time t-u, and B_q denotes an amplitude and an initial phase component of a subcarrier signal having an angular frequency

Compared to Equation 9, in Equation 17, an index of a baseband signal may be changed from a to b and a signal transmission time may be changed from t to t-u. In a similar manner to a method of reaching Equation 16 from Equation 9, an equation that represents a phase vector of the second reference signal may be easily derived from Equation 17. For example, a phase vector of the second reference signal may be represented as Equation 18. [Equation 18]

In Equation 18,

represents an inner product operation result between a sample vector of the second reference signal and a DFT coefficient vector. For example,

may be referred to as a second phase vector. Also, ^^ _^^ denotes an error vector,

denotes a propagation delay time of the second reference signal, and ^^ denotes an clock error between a clock of the UE 200 and a clock of the second transmitter 100B or a base station to which the second transmitter 100B belongs. If the first transmitter 100A and the second transmitter 100B use a clock of the same base station, the clock error represented in Equation 16 and the clock error represented in Equation 18 may be the same. Phases of components of the second phase vector

may be proportional to a multiplication of

which is a sum of an angular frequency of a carrier and an angular frequency of a subcarrier, and a propagation delay time The

UE 200 may acquire a plurality of phase vectors with respect to the second reference signal by changing a start point t-u of a time interval. In operation S130 of FIG.3, the UE 200 may calculate a difference between a travel distance of the first reference signal and a travel distance of the second reference signal based on the first phase vector and the second phase vector. Hereinafter, a process of calculating, by the UE 200, the difference between the travel distance of the first reference signal and the travel distance of the and second reference signal is described as an example. The UE 200 may calculate a conjugate multiplication of the first phase vector and the second phase vector. Through a process of calculating the conjugate multiplication, a factor depending on the local clock error ^ may be removed. The conjugate multiplication of the first phase vector and the second phase vector may be represented as Equation 19. [Equation 19]

In Equation 19,

denotes a difference between a delay time of the first reference signal and a delay time of the second reference signal. The UE 200 may derive the difference between the travel distance of the first reference signal and the travel distance of the second reference signal from Δ ^. The UE 200 may calculate position coordinates of the UE 200 from the difference between the travel distance of the first reference signal and the travel distance of the second reference signal. Referring to Equation 19, the conjugate multiplication of the first phase vector and the second phase vector may not depend on the local clock error ^. Therefore, the UE 200 may derive position information of the UE 200 although information about the local clock error ^ is absent. The conjugate multiplication of the first phase vector and the second phase vector may be represented as a vector, and a phase of each component of the conjugate multiplication may correspond to a multiplication of

which is a sum of an angular frequency of a carrier and an angular frequency of a subcarrier, and

, which is a difference between the delay time of the first reference signal and the delay time of the second reference signal. The UE 200 may calculate a phase angle of each of components of the conjugate multiplication of two phase vectors. For example, the UE 200 may calculate a phase angle of each of components of the conjugate multiplication according to Equation 20. [Equation 20]

In Equation 20, Angle function denotes a function of outputting a phase angle of a complex component. Referring to Equation 20, the UE 200 may calculate phase information Angle

of the first phase vector and the second phase vector using the Angle function. Here, the phase information may include a term that depends on not only but also

Therefore, a value of phase information may increase. In general, since an amplitude of an angular frequency

of a carrier is significantly greater than that of an angular frequency of a subcarrier,

may be easily accurately calculated from positioning phase information by allowing the phase information to depend on the angular frequency

of the carrier, as represented as Equation 20. In Equation 20, since a codomain of the Angle function is -π ~ + π (or 0~ 2 π), an integer ambiguity issue may arise. Considering the integer ambiguity, Equation 20 may be represented again as Equation 21. [Equation 21]

In Equation 21, ℳ denotes an integer ambiguity that occurs during a process of calculating a phase angle. Considering that an angular frequency

of a carrier is generally greater than an angular frequency of a subcarrier,

of Equation 20 may be approximated to

In this case, the difference

between the delay time of the first reference signal and the delay time of the second reference signal from Equation 21 may be represented as Equation 22. [Equation 22]

The UE 200 may calculate an average of phase angles of components of a conjugate multiplication vector. Here, Δ ^ may depend on the average and a factor by the integer ambiguity. By performing an operation process of Equation 21 and Equation 22, the UE 200 may calculate the difference between the delay time of the first reference signal and the delay time of the second reference signal from the conjugate multiplication of the first phase vector and the second phase vector. For example, the UE 200 may calculate a difference between a travel distance of the first reference signal and a travel distance of the second reference signal from the difference

between the delay times according to Equation 23. [Equation 23] In Eq

uation 23, denotes the difference between the travel distance of the first reference signal and the travel distance of the second reference signal, and λc denotes a wavelength of a carrier (also, referred to as a carrier wavelength). For example, if the first transmitter 100A and the second transmitter 100B transmit the first reference signal and the second reference signal through modulation to a carrier frequency of 1 GHz, λc may be 30 cm. Here, c denotes a light velocity. Referring to Equation 23, the UE 200 may calculate ∆ ^^ from the conjugate multiplication, and ∆ ^^ may be proportional to the carrier wavelength λc. In Equation 23, since the integer ambiguity ℳ is still not determined, it may not be easy for the UE 200 to accurately calculate the distance difference ∆ ^^. Among various carrier phase-based positioning methods of a GPS, for example, the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method and the widelane method are known as a method of accurately estimating an integer ambiguity value. A method of estimating an integer ambiguity using signals transmitted from at least three transmitters is further described below. A case in which the first reference signal and the second reference signal are transmitted in different time domains and the first subcarrier group and the second subcarrier group are the same is described. However, if the first reference signal and the second reference signal are transmitted in the same time domain, the first subcarrier group and the second subcarrier group may be set to differ from each other. The following equations are described generally based on a case in which the first reference signal and second reference signal are transmitted in the same time domain and the first subcarrier group and the second subcarrier group are set to differ from each other, however, it is provided as an example only for clarity of description. Although the first reference signal and the second reference signal are transmitted in the same time domain, the first subcarrier group and the second subcarrier group may be set to differ from each other. Hereinafter, a method of calculating, by the UE 200, the difference between the travel distance of the first reference signal and the travel distance of the second reference signal when the first subcarrier group and the second subcarrier group differ from each other is described. For clarity of description, it is assumed that a process of acquiring, by the UE 200, the first phase vector is the same as Equation 9 to Equation 16. However, it is provided as an example only for clarity of description and the example embodiment may be modified by those skilled in the art within the scope of the disclosure. For example, if subcarriers having a conjugate relation with subcarriers of the first subcarrier group are allocated to the second subcarrier group, the first subcarrier group and the second subcarrier group may be orthogonal to each other. For example, if the first subcarrier group includes subcarriers having angular frequencies

the second subcarrier group may include subcarriers having angular frequencies

Here, N denotes a size of an FFT window in the OFDM system. As described above, if the first subcarrier group and the second subcarrier group are set, a frequency magnitude of a subcarrier component of the first reference signal and a frequency magnitude of a subcarrier component of the second reference signal may be the same, however, a sign of an imaginary part of the subcarrier component of the first reference signal may be opposite to a sign of an imaginary part of the subcarrier component of the second reference signal. That is, the subcarrier component of the first reference signal and the subcarrier component of the second reference signal may have a conjugate relation. The conjugate relation may be represented as Equation 24. [Equation 24]

N = size of FFT window For example, if a time at which the second reference signal is set to be the same as a time t at which the first reference signal is transmitted, the second reference signal of the baseband transmitted from the second transmitter 100B may be represented as Equation 25. The development process of the following equations are similar to the aforementioned development process of Equation 9 to Equation 16. Therefore, the description of notations that are not required among notations included in the equations may be omitted. [Equation 25]

The second transmitter 100B may modulate the second reference signal of the baseband to a passband signal having an angular frequency ^^ _^^ and may transmit the modulated second reference signal. The modulated second reference signal may be represented as Equation 26. [Equation 26]

If the second reference signal transmitted from the second transmitter 100B arrives at the UE 200 through propagation during

and, the second reference signal received at the UE 200 may be represented as Equation 27. [Equation 27]

The UE 200 may demodulate the received second reference signal of the passband to a baseband signal. For example, the UE 200 may demodulate the second reference signal to the baseband signal using Equation 28. [Equation 28]

In Equation 28,

denotes a local clock error. The UE 200 may acquire a second sample vector by converting second reference signals received at a plurality of points in times to baseband signals. For example, the UE 200 may acquire the second sample vector according to Equation 29. [Equation 29]

In Equation 29,

denotes a second sample vector that includes samples of second reference signal received at N sample times. The UE 200 may calculate a DFT coefficient vector used for an FFT operation of a subcarrier having an angular frequency

according to Equation 30. [Equation 30]

The UE 200 may perform an inner product operation on the second sample vector of Equation 29 and the DFT coefficient vector of Equation 30, using Equation 31. [Equation 31]

In the aforementioned description, only the subcarrier signal having the angular frequency

is considered. If the second subcarrier group of the second reference signal includes a subcarrier group having angular frequencies Equation 31 may be normalized as represented as Equation 32.

Referring to Equation 32, phases of components of the second phase vector may include a factor that is proportional to a multiplication of

The UE 200 may calculate a conjugate multiplication of the first phase vector represented in Equation 16 and the second phase vector represented in Equation 32. The conjugate multiplication of the first phase vector and the second phase vector may be represented as Equation 33. [Equation 33]

Based on

Equation 33 may be represented as Equation 34. [Equation 34]

If the first subcarrier group and the second subcarrier group are the same, the conjugate multiplication of two phase vectors may depend on the clock error ^ as shown in Equation 19. However, if the first subcarrier group and the second subcarrier group differ from each other, the conjugate multiplication of two phase vectors may depend on the clock error

as shown in Equation 34. The UE 200 may calculate a phase angle of each of components of the conjugate multiplication of two phase vectors. For example, the UE 200 may calculate a phase angle of each of components of the conjugate multiplication according to Equation 35. [Equation 35]

In Equation 35, denotes an output result of Angle function.

Since a codomain of the Angle function includes

, it may be difficult to know the integer ambiguity ℳ. Also, in Equation 35,

depends on the local clock error

Here, it may be difficult for the UE 200 to secure information about the local clock error

. Therefore, the UE 200 may calculate a parameter that does not depend on the local clock error

by combining the respective components of an output vector of the Angle function. For example, the UE 200 may calculate a vector that includes difference values between phase angle components using Equation 36. [Equation 36]

If subcarriers of the first subcarrier group are provided at equal intervals in the frequency domain and subcarriers of the second subcarrier group are provided at equal intervals in the frequency domain, all of components shown in Equation 36 may have the same value. In Equation 36, with the assumption that all of

…are multiples of

However, it is provided as an example only. A value of

may not be equal to

. Here, if subcarriers are provided at equal intervals in the frequency domain, a value of

may be constant regardless of a value of ^^. In this case, all of vector components shown in Equation 36 may have the same value. The UE 200 may calculate

according to Equation 37. [Equation 37]

Referring to Equation 34 and Equation 37, although

depends on

, the UE 200 may calculate

according to Equation 37 without using information about

Using the result of Equation 37, Equation 35 may be represented as Equation 38. [Equation 38]

In Equation 38, m denotes a number of components of conjugate multiplication vector

denotes the integer ambiguity, and

denotes a parameter that represents in a form not depending on the local clock error

Also,

denotes a difference between a last component and a first component of an output vector of the angle function. If

converges to 0, may be ignored. The UE 200 may calculate a difference between a delay time of the first reference signal and a delay time of the second reference signal according to Equation 39. [Equation 39]

Referring to Equation 33 to Equation 39, if the first subcarrier group and the second subcarrier group differ from each other, the conjugate multiplication of two phase vectors may depend on the local clock error ^. However, if subcarriers of the first subcarrier group and subcarriers of the second subcarrier group are provided at equal intervals in the frequency domain, the UE 200 may calculate the difference between the delay time of the first reference signal and the delay time of the second reference signal from the conjugate multiplication of two phase vectors without using information about the local clock error The UE 200 may calculate a difference between a travel distance of the first reference signal and a travel distance of the second reference signal according to Equation 40. [Equation 40]

In the aforementioned description, if the first subcarrier group and the second subcarrier group are the same, the UE 200 may calculate the difference between the travel distance of the first reference signal and the travel distance of the second reference signal according to Equation 23. As another example, if the first subcarrier group and the second subcarrier group differ from each other, the UE 200 may calculate the difference between the travel distance of the first reference signal and the travel distance of the second reference signal according to Equation 40. A case in which subcarrier components of the second subcarrier group and subcarrier components of the first subcarrier group have a conjugate relation is described with reference to Equation 24 to Equation 40. However, it is provided as an example only. For example, the second subcarrier group may be spaced apart at a desired distance d from the first subcarrier group in the frequency domain. The distance d may variously vary based on a scheduling condition. In the condition, the second phase vector shown Equation 32 may reappear in Equation 41. [Equation 41]

In Equation 41, d denotes a difference in angular frequency index between the first subcarrier group and the second subcarrier group in the frequency domain. Referring to Equation 41, the first subcarrier group may include subcarrier components having angular frequencies

and the second subcarrier group may include subcarrier components having angular frequencies

separate at the distance d from the first subcarrier group in the frequency domain. By applying Equation 41, Equation 33 may reappear as shown in Equation 42. [Equation 42]

In Equation 42,

may depend on the local clock error

The UE 200 may multiply the matrix

by a correction factor to calculate a difference in time of arrival (ToA) between the first reference signal and the second reference signal without using information about the local clock error

To multiply the correction factor, the UE 200 may extract, from the second phase vector, a desired number of components having a relatively small angular frequency index and a desired number of components having a relatively high angular frequency index. For example, the UE 200 may extract, from the second phase vector, a low vector having (m-1) components with a relatively low angular frequency index and a high vector having (m-1) components with a relatively high angular frequency index according to Equation 43. [Equation 43]

The UE 200 may calculate a conjugate multiplication of the low vector and the high vector according to Equation 44. [Equation 44]

Referring to Equation 44, it can be known that a phase angle of each component is the same as

in the conjugate multiplication of the low vector and the high vector. Therefore, all

may have a difference from the phase angle

depending on the local clock error by multiples of d in Equation 42. That is, the UE 200 may extract the correction factor based on information about phase angles of components of the conjugate multiplication of the low vector and the high vector. Equation 43 and Equation 44 show, as an example, that an angular frequency index between the components of the low vector and the components of the high vector differs by 1. However, it is provided as an example only. For example, an angular frequency index between the components of the low vector and the components of the high vector may differ by 2 or more. Also, although, in Equation 43, each of the low vector and the high vector includes (m-1) vectors, it is provided as an example only and the example embodiment is not limited thereto. Each of the low vector and the high vector may include a number of components greater than or less than m-1. For example, the UE 200 may extract information about a value of the phase angle

from the second phase vector, using only a conjugate multiplication of a first component (e.g.,

having a relatively small angular frequency index and a second component (e.g.,

having a relatively high angular frequency index. The UE 200 may remove the dependence on the local clock error by multiplying the conjugate multiplication of the first phase vector and the second phase vector by the correction factor. The UE 200 may calculate the difference in ToA between the first reference signal and the second reference signal from the conjugate multiplication multiplied by the correction factor. For example, the UE 200 may calculate the difference in ToA between the first reference signal and the second reference signal according to Equation 45. [Equation 45]

Referring to Equation 45, as the UE 200 multiplies the conjugate multiplication by the correction factor,

may not depend on the local clock error. Therefore, the UE 200 may acquire information about the difference in ToA between the first reference signal and the second reference signal by extracting phase angles of components of

If the integer ambiguity ℳ is not determined in Equation 23 and Equation 40, it may be difficult for the UE 200 to calculate a distance difference. Hereinafter, an integer ambiguity estimation method is described as an example. In Equation 23 and Equation 40, average[Angle

may have a value between -0.5 and 0.5. Therefore, if a value of

is small, the UE 200 may calculate the integer ambiguity ℳ according to Equation 46. [Equation 46]

FIG. 8 illustrates an example of traces of dots having a difference

between a distance from the first transmitter 100A and a distance from the second transmitter 100B according to at least one example embodiment. Referring to FIG. 8, a hyperbola, that is, hyperbolic curves may be formed using traces of dots having the difference

between the distance from the first transmitter 100A and the distance from the second transmitter 100B. In FIG. 8, coordinates of the first transmitter 100A may be (0, +s), coordinates of the second transmitter 100B may be (0, -s), coordinates of the UE 200 may be (x, y), and coordinates of a center point between the first transmitter 100A and the second transmitter 100B may be (0,0). The first transmitter 100A and the second transmitter 100B may be separate from each other at 2s in a y-axial direction. Hyperbolic curves L1 may pass

Two coordinates

at which the hyperbolic curves L1 meet the y axis may correspond to vertices. Referring to the hyperbolic curves L1 of FIG.8, Equation 47 may be satisfied. [Equation 47]

Equation 48 may be derived from Equation 46 and Equation 47. [Equation 48]

Referring to Equation 48, the integer ambiguity ℳ may not be greater than an integer acquired by dividing the distance 2s between the first transmitter 100A and the second transmitter 100B by carrier wavelength λ_c. Therefore, if the first transmitter 100A and the second transmitter 100B are arranged such that the distance 2s between the first transmitter 100A and the second transmitter 100B may be less than the carrier wavelength λc, ℳ=0. That is, in this case, the integer ambiguity issue may be solved. Therefore, the UE 200 may calculate a difference between a travel distance of a first reference signal and a travel distance of a second reference signal according to Equation 23 or Equation 40. As shown in FIG.8, if the distance between the first transmitter 100A and the second transmitter 100B is sufficiently short, the integer ambiguity issue may be solved. In contrast, since coordinates of the UE 200 vary, a difference between a distance d1 and a distance d2, that is, d1-d2 may vary by a small level. Therefore, a level that an error of a calculation result of the UE 200 using Equation 23 or Equation 40 contributes to a positioning error may increase and a positioning resolution may decrease. To outperform the aforementioned issue, the UE 200 may receive reference signals from at least three transmitters. FIG.9 is a graph showing an example in which four transmitters including the first transmitter 100A, the second transmitter 100B, a third transmitter 100C, and a fourth transmitter 100D, transmit reference signals according to at least one example embodiment. Referring to FIG.9, the first transmitter 100A may transmit a first reference signal, the second transmitter 100B may transmit a second reference signal, the third transmitter 100C may transmit a third reference signal, and the fourth transmitter 100D may transmit a fourth reference signal. A distance between the first transmitter 100A and the second transmitter 100B may be less than a distance between the third transmitter 100C and the fourth transmitter 100D. Referring to FIG.9, the distance between the first transmitter 100A and the second transmitter 100B may be less than a carrier wavelength. The distance between the third transmitter 100C and the fourth transmitter 100D may be greater than the carrier wavelength. The UE 200 may calculate phase information, for example, average

of Equation 40, using a sample vector of the reference signal and a sample vector of the fourth reference signal. In this case, since the phase information sensitively varies according to coordinates of the UE 200, a positioning resolution may increase. However, in this case, an integer ambiguity issue may remain unsolved. The UE 200 may calculate phase information based on a sample vector of the first reference signal and a sample vector of the second reference signal. In this case, since the phase information insensitively varies according to coordinates of the UE 200, the positioning resolution may decrease. However, in this case, the integer ambiguity issue may not arise. The UE 200 may estimate the integer ambiguity of second phase information acquired from the third reference signal and the fourth reference signal based on first phase information acquired from the first reference signal and the second reference signal. Referring to FIG.9, a plurality of hyperbolic curves may be formed by focusing on the third transmitter 100C and the fourth transmitter 100D. Each of the hyperbolic curves may correspond to different integer ambiguity. The UE 200 may estimate an appropriate position of the UE 200 based on the first phase information. The UE 200 may estimate the integer ambiguity from approximate position information. Hereinafter, a method of estimating, by the UE 200, the integer ambiguity of the second phase information from the first phase information is described. For example, with the assumption that the distance between the first transmitter 100A and the second transmitter 100B is less than the carrier wavelength λc and the distance between the third transmitter 100C and the fourth transmitter 100D corresponds to M multiples of the carrier wavelength λ_c, the integer ambiguity of the first phase information acquired by the UE 200 may be 0 at all times. Also, referring to Equation 43, the integer ambiguity of the second phase information acquired by the UE 200 may be less than M. Therefore, it may be assumed that M hyperbolic curves corresponding to the second phase information are present in a section in which the first phase information varies ranging from – π to + π or ranging from 0 to 2 π. Therefore, the UE 200 may estimate the integer ambiguity of the second phase information according to Equation 49. [Equation 49]

In Equation 49, ℳ denotes the integer ambiguity of the second phase information and ^^ denotes a ratio between the distance between the third transmitter 100C and the fourth transmitter 100D and the carrier wavelength λc. The UE 200 may determine the integer ambiguity of the second phase information from the first phase information according to Equation 49, and may perform positioning at a high resolution based on the second phase information. FIG. 10 is a graph showing an example in which three transmitters, for example, the first transmitter 100A, the second transmitter 100B, and the third transmitter 100C, transmit reference signals according to at least one example embodiment. Referring to FIG.10, an interval between the first transmitter 100A and the second transmitter 100B may be less than a carrier wavelength. An interval between the first transmitter 100A and the third transmitter 100C or an interval between the second transmitter 100B and the third transmitter 100C may be greater than the carrier wavelength. The UE 200 may acquire first phase information from a first reference signal and a second reference signal. The UE 200 may acquire second phase information from the first reference signal and a third reference signal. As another example, the UE 200 may acquire the second phase information from the second reference signal and the third reference signal. The UE 200 may determine the integer ambiguity of the second phase information based on the first phase information. The positioning method and apparatus according to the example embodiments are described above with reference to FIGS.1 to 10. According to the example embodiments, the UE 200 may receive reference signals transmitted at different positions, and may calculate a difference between a travel distance of the first reference signal and a travel distance of the second reference signal from a conjugate multiplication of two phase vectors. Through this, the UE 200 may perform positioning in a vertical direction or a horizontal direction at high accuracy. Also, the UE 200 may solve an integer ambiguity issue of phase information by analyzing reference signals transmitted from at least three transmitters. FIG.11 illustrates an example of a communication system according to at least one example embodiment. Referring to FIG.11, the communication system may include a first base station 100A, a second base station 100B, and a third base station 100C. Each of the first base station 100A, the second base station 100B, and the third base station 100C may also be referred to as a node base (NodeB), a next generation NodeB, an evolved NodeB, gnodeB, a base transceiver station (BTS), a radio base station, a radio transceiver, an access point, an access node, a road side unit (RSU), a radio remote head (RRH), a transmission point (TP), a transmission and reception point (TRP), a relay node, and the like. The UE 200 may also be referred to as a terminal, an access terminal, a mobile terminal, a station, a subscriber station, a mobile station, a portable subscriber station, a node, a device, and the like. Although FIG. 11 illustrates three base stations as an example, it is provided as an example only. The UE 200 may receive a reference signal from two or three or more base stations during a positioning process. Referring to FIG. 11, the first base station100A may transmit a first reference signal to the UE 200, the second base station 100 may transmit a second reference signal to the UE 200, and the third base station 100C may transmit a third reference signal to the UE 200. Position coordinates of the first base station100A may be (a_x, a_y, a_z), position coordinates of the second base station 100B may be (b_x, b_y, b_z), position coordinates of the third base station 100C may be (c_x, c_y, c_z), and position coordinates of the UE 200 may be (x, y, z). In the case of considering only two-dimensional (2D) coordinates for clarity of description, a travel distance (L_a) of the first reference signal, a travel distance (L_b) of the second reference signal, and a travel distance (L_c) of the third reference signal may be represented as Equation 50. [Equation 50]

Equation 50 is merely provided as an example for clarity of description. For example, a travel distance of a reference signal may be calculated based on three-dimensional (3D) coordinates. Also, if a travel path of the reference signal is not straight, Equation 50 may be modified within the range that is easy to those skilled in the art to modify the travel path to be straight. The UE 200 may calculate a travel distance difference between reference signals by receiving the reference signals and by measuring a phase difference between the reference signals. The UE 200 may calculate a difference between the travel distance (L_a) and the travel distance (L_b) based on a phase difference between the first reference signal and the second reference signal. As another example, the UE 200 may calculate a difference between the travel distance (Lb) and the travel distance (Lc) based on a phase difference between the second reference signal and the third reference signal. The UE 200 may estimate a position of the UE 200 based on a travel distance difference between reference signals. Positioning performance of the UE 200 may depend on phase positioning precision of the UE 200. However, in general, it is not easy for the UE 200 to calculate a phase difference between reference signals. Since a codomain of the phase difference is -π ~ + π (or 0 ~ 2 π), an integer ambiguity issue may occur. FIG.12 illustrates an example of a relationship between an amplitude and a phase of a signal wavelength measured by the UE 200 according to an example embodiment. Referring to FIG.12, if a wavelength of a signal measured by the UE 200 is large, a number of times the wavelength of the signal is repeated between a base station and the UE 200 may decrease. Therefore, estimation of integer ambiguity may become easy. Also, if the wavelength of the signal measured by the UE 200 is large, a phase may change insensitively according to a change in a position of the UE 200. Therefore, positioning resolution may decrease. In contrast, if the wavelength of the signal measured by the UE 200 is small, a number of times the wavelength of the signal is repeated may increase. Therefore, estimation of integer ambiguity may become difficult. Also, if the wavelength of the signal measured by the UE 200 is small, a phase may change sensitively according to a change in a position of the UE 200. Therefore, positioning resolution may increase. Table 1 shows specifications of carriers and subcarriers that constitute a reference signal. [Table 1]

In Table 1, a first column represents a frequency of a carrier or a subcarrier, a second column represents a sampling rate, a third column represents an inverse number of a fast Fourier transform (FFT) size (NFFT), a fourth column represents a wavelength of a carrier or a subcarrier, and a fifth column briefly represents a calculation process for a value of the fourth column. In Table 1, a second row and a third row represent specifications of a carrier signal. In the case of a carrier, a frequency and a wavelength are not associated with a sampling rate and an FFT size and thus a corresponding field is marked blank. Referring to Table 1, it can be verified that the carrier generally has a frequency higher than a frequency of the subcarrier and thus, a wavelength is relatively short. That is, when the UE 200 uses a phase difference depending on the wavelength of the carrier, the phase difference is sensitive to a position of the UE 200, which may lead to increasing a positioning resolution. However, it may be difficult for the UE 200 to determine integer ambiguity of the phase difference depending on the wavelength of the carrier. In general, the wavelength of the subcarrier may be larger than the wavelength of the carrier. The wavelength and the frequency of the subcarrier may variously vary based on the sampling rate and the FFT size. Referring to Table 1, the wavelength of the subcarrier may variously vary from 614 m to 20 m. When the wavelength of the subcarrier is 614 m and an interval between base stations is 1 km, a number of cases of determining the integer ambiguity may be 2 or less. Therefore, the UE 200 may easily determine the integer ambiguity. However, in this case, a positioning resolution of the UE 200 may decrease. When the wavelength of the subcarrier is 20 m, a number of cases of determining the integer ambiguity may increase and it may be difficult for the UE 200 to determine the integer ambiguity. However, in this case, the positioning resolution of the UE 200 may relatively increase. FIG. 13 is a flowchart illustrating an example of a positioning method of the UE 200 according to an example embodiment. Referring to FIG.13, in operation S210, the UE 200 may receive reference signals from base stations, for example, the first base station 100A, the second base station 100B, and the third base station 100C. The UE 200 may acquire received data of the reference signals at a plurality of sample times. In operation S220, the UE 200 may calculate a phase difference depending on wavelengths of subcarriers included in the reference signals. Hereinafter, for clarity of description, description is made based on an example of calculating a phase difference between a first reference signal received at the UE 200 from the first base station100A and a second reference signal received at the UE 200 from the second base station 100B. In a similar manner, the UE 200 may calculate a phase difference between the first reference signal and a third reference signal, a phase difference between the second reference signal and the third reference signal, a phase difference between the third reference signal and a fourth reference signal, and the like. The following equations are merely provided to help the understanding of example embodiments and may be modified within the range easily changed by those skilled in the art. FIG. 14 is a flowchart illustrating an example of a process of performing operation S220 of FIG.13. Referring to FIG. 14, in operation S222, the UE 200 may acquire a first sample vector from the received data of the first reference signal and may acquire a second sample vector from the received data of the second reference signal. For example, the terminal 200 may acquire the first sample vector as shown in Equation 13. In operation S223, the terminal 200 may calculate a first phase vector from the first sample vector. For example, the terminal 200 may acquire the first phase vector as shown in Equation 16. In a similar manner, the UE 200 may calculate the second phase vector. For example, the second reference signal of the baseband transmitted from the second base station 100B may be represented as Equation 51. A process of developing the following equations is similar to a process of developing Equation 9 to Equation 16. Therefore, description related to notations that do not require description among notations described in the equations is omitted. [Equation 51]

The second base station 100B may modulate the second reference signal of the baseband to a passband signal having an angular frequency

and may transmit the modulated second reference signal. The modulated second reference signal may be represented as Equation 52. [Equation 52]

When the second reference signal transmitted from the second base station 100B arrives at the UE 200 through propagation during time ^_b1, the second reference signal received at the UE 200 may be represented as Equation 53. [Equation 53]

The UE 200 may demodulate the received second reference signal of the passband to a baseband signal. For example, the UE 200 may demodulate the second reference signal to the baseband signal using Equation 54. [Equation 54]

In Equation 54,

denotes a local clock error. The UE 200 may acquire a second sample vector by converting second reference signals received at a plurality of times to baseband signals. For example, the UE 200 may acquire the second sample vector using Equation 55. [Equation 55]

In Equation 55,

denotes the second sample vector that includes samples of the second reference signal received at the UE 200 at N sample times. The UE 200 may calculate a second phase vector from the second sample vector using Equation 56. [Equation 56]

In operation S224 of FIG.14, the UE 200 may calculate a third phase vector from the first phase vector. The UE 200 may extract a 1-1 partial vector corresponding to a first portion of the first phase vector and a 1-2 partial vector corresponding to a second portion of the first phase vector. For example, the UE 200 may extract the 1-1 partial vector by extracting a desired number of components having a relatively small angular frequency index from the first phase vector. Also, the UE 200 may extract the 1-2 partial vector by extracting a desired number of components having a relatively high angular frequency index from the first phase vector. For example, the UE 200 may extract, from the first phase vector, the 1-1 partial vector having m-1 components having a relatively low angular frequency index and the 1-2 partial vector having m-1 components having a relatively high angular frequency index. In this case, the 1-1 partial vector and the 1-2 partial vector may be represented as Equation 57. [Equation 57]

In Equation 57,

denotes the 1-1 partial vector and denotes the 1-2 partial vector. In Equation 57, angular frequency

indices of components of the 1-1 partial vector and angular frequency indices of components of the 1-2 partial vector differ by 1. However, it is provided as an example only. For example, angular frequency indices of components of the 1-1 partial vector and angular frequency indices of components of the 1-2 partial vector may differ by 2 or more. Also, although each of the 1-1 partial vector and the 1-2 partial vector includes (m-1) components in Equation 57, it is provided as an example only. For example, each of the 1-1 partial vector and the 1-2 partial vector may include a number of components less than (m-1) components. For example, each of the 1-1 partial vector and the 1-2 partial vector includes only a single component. In this case, each of the 1-1 partial vector and the 1-2 partial vector may include a different component. The UE 200 may calculate the third phase vector by conjugating the 1-1 partial vector and the 1-2 partial vector. Herein, the expression "conjugating A and B" may represent a multiplication of A and a complex conjugate of B. For example, the UE 200 may calculate the third phase vector using Equation 58. [Equation 58]

In Equation 58,

denotes the third phase vector. If subcarriers of the first reference signal are arranged at equal intervals in a frequency domain,

may be satisfied. Here,

denotes a subcarrier spacing in the frequency domain. Therefore, if the subcarriers are provided at equal intervals in the frequency domain, Equation 58 may be represented as Equation 59. [Equation 59]

In operation S225 of FIG.14, the UE 200 may calculate a fourth phase vector from the second phase vector. The UE 200 may extract a 2-1 partial vector and a 2-2 partial vector from the second phase vector. The UE 200 may calculate the fourth phase vector by conjugating the 2-1 partial vector and the 2-2 partial vector. The fourth phase vector may be represented as Equation 60. [Equation 60]

In Equation 60,

denotes the fourth phase vector. In operation S226, the UE 200 may acquire phase difference information depending on a wavelength of a subcarrier based on the third phase vector and the fourth phase vector. The UE 200 may calculate a conjugate product of the third phase vector and the fourth phase vector. The conjugate product of the third phase vector and the fourth phase vector may be represented as Equation 61. [Equation 61]

The UE 200 may calculate phase difference information using Equation 62. [Equation 62]

In Equation

denotes phase difference information between the first reference signal and the second reference signal and ∆ ^^ denotes a difference between a travel time of the first reference signal and a travel time of the second reference signal. Also,

denotes an interval between subcarriers included in the first reference signal and the second reference signal. Also, an angle function represents a function of outputting a phase angle of a complex component. Referring to Equation 62, the UE 200 may calculate a phase difference depending on

and

from the third phase vector and the fourth phase vector. Also, since angular frequencies

of subcarriers may be determined from

, the UE 200 may easily calculate a phase difference depending on an angular frequency of a subcarrier. Also, since a wavelength of a subcarrier is determined based on an angular frequency of the subcarrier, the UE 200 may easily calculate a phase difference depending on a wavelength of each subcarrier. Since a codomain of the angle function is -π ~ + π (or 0 ~ 2 π), an integer ambiguity issue may occur. As described above, as the wavelength of the subcarrier is shorter, it may be more difficult for the UE 200 to determine the integer ambiguity. In the foregoing description, the UE 200 may calculate the phase difference between the first reference signal and the second reference signal. In a similar manner, the UE 200 may calculate a phase difference between the first reference signal and the third reference signal or a phase difference between the second reference signal and the third reference signal. To improve positioning precision, the UE 200 may further calculate phase difference information depending on a wavelength of a carrier having a relatively short wavelength. Referring again to FIG.13, in operation S230, the UE 200 may calculate a phase difference depending on the wavelength of the carrier. Although operation S230 is included in FIG.13, operation S230 may be omitted depending on example embodiments. For example, if the positioning precision is sufficiently secured only with a phase difference depending on wavelengths of subcarriers, the UE 200 may omit operation S230. FIG.15 is a flowchart illustrating an example of a process of performing operation S230 of FIG.13. Referring to FIG.15, in operation S232, the UE 200 may acquire a first sample vector and a second sample vector. Operation S232 of FIG.15 may be similar to operation S222 of FIG.14. Therefore, if the first sample vector and the second sample vector are already acquired by the UE 200 in operation S222, operation S232 may be omitted. In operation S233, the UE 200 may acquire a first phase vector and a second phase vector from the first sample vector and the second sample vector, respectively. Operation S233 of FIG.15 may be similar to operation S223 of FIG.14. Therefore, if the first phase vector and the second phase vector are already acquired by the UE 200 in operation S223, operation S233 may be omitted. In operation S234, the UE 200 may calculate a phase difference depending on a wavelength of a carrier of the first reference signal and the second reference signal based on the first phase vector and the second phase vector. The UE 200 may calculate a conjugate product of the first phase vector and the second phase vector using Equation 63. [Equation 63]

Equation 63 may be represented as Equation 64. [Equation 64]

The UE 200 may calculate a phase difference depending on a wavelength of a carrier by applying an angle function to

Referring again to FIG.13, in operation S240, the UE 200 may select a phase difference between reference signals depending on a wavelength of a k^th subcarrier. When operation S240 is initially performed, the UE 200 may select a phase difference depending on a wavelength of a first subcarrier having a longest wavelength. The phase difference depending on the wavelength of the first subcarrier may be calculated in operation S220. In operation S250, the UE 200 may calculate k^th estimated coordinates based on the phase difference depending on the wavelength of the k^th subcarrier or carrier. A process of calculating, by the UE 200, the k^th estimated coordinates is further described with reference to FIG.16. In operation S260, the UE 200 may determine whether a termination condition is met. For example, the UE 200 may determine whether the k^th subcarrier or carrier is a last component in a preset set. For example, if the k^th subcarrier or carrier is the last component of the preset set, the UE 200 may suspend repetition of operations S240, S250, and S260. As another example, the UE 200 may compare k^th estimated coordinates calculated from the phase difference depending on the wavelength of the k^th subcarrier or carrier and (k-1)- th estimated coordinates calculated from a phase difference depending on a wavelength of a (k-1)-th subcarrier or carrier. For example, when an error between the k^th estimated coordinates and the (k-1)-th estimated coordinates is less than a reference error, the UE 200 may determine that a termination condition is met. Unless the termination condition is met, the UE 200 may calculate integer ambiguity of a phase difference depending on a wavelength of a (k+1)-th subcarrier. The UE 200 may calculate a k^th travel distance difference from the phase difference depending on the wavelength of the k^th subcarrier. Here, the k^th travel distance difference represents a travel distance difference between reference signals calculated from the phase difference depending on the wavelength of the k^th subcarrier. The UE 200 may easily calculate integer ambiguity of a (k+1) phase difference based on a phase difference depending on the wavelength of the k^th subcarrier having a wavelength greater than that of the (k+1)-th subcarrier. The UE 200 may increase an index k and may repeat operations S240 and S250 until the termination condition is met. If the termination condition is met, the UE 200 may discover integer ambiguity of a phase difference depending on a wavelength of a subcarrier or a carrier having a sufficiently small wavelength. Also, the UE 200 may discover a position of the UE 200 using the integer ambiguity and the phase difference of the subcarrier or the carrier having the sufficiently small wavelength. FIG.16 is a flowchart illustrating an example of a process of performing operation S250 of FIG.13. Referring to FIG.16, in operation S252, the UE 200 may calculate initial estimated coordinates of the UE 200 corresponding to the phase difference depending on the wavelength of the k^th subcarrier. For example, the UE 200 may calculate a travel distance difference between reference signals from the phase difference depending on the wavelength of the k^th subcarrier. Also, the UE 200 may determine, as initial estimated coordinates, a single arbitrary point in a set of points (e.g., hyperbolic) that satisfy the travel distance difference. As another, the UE 200 may calculate the initial estimated coordinates from the travel distance difference between the reference signals using a triangulation. The UE 200 may modify the initial estimated coordinates by performing operations S253, S254, and S255. The UE 200 may modify the initial estimated coordinates by repeating operations S253, S254, and S255 until a predetermined termination condition is met. Hereinafter, a method of correcting, by the UE 200, the initial estimated coordinates is described. When coordinates of the UE 200 are represented as (x, y), a distance between the first base station 100A and the UE 200 is represented as r₁, a distance between the second base station 100B and the UE 200 is represented as r₂, and a distance between the third base station 100C and the UE 200 is represented as r3, Equation 65 is satisfied. [Equation 65]

When n^th estimated coordinates of the UE 200 are (xn, yn), Equation 65 may be represented as Equation 66 using Taylor expansion. [Equation 66]

Referring to Equation 66, a travel distance difference between the reference signals may be represented as a partial differential coefficient matrix (or Jacobian matrix) and an error between actual position coordinates (x, y) and the n^th estimated coordinates ^th

may be an n estimated distance difference calculated from the n^th estimated coordinates. In operation S253 of FIG.16, the UE 200 may calculate the n^th estimated distance difference. Equation 66 may be further simplified as Equation 67. [Equation 67]

In Equation 67,

denotes a distance difference vector and corresponds of Equation 66, P denotes actual position coordinates of the UE

200 corresponds to (x, y) of Equation 66, P_n denotes n^th estimated position coordinates of the UE 200 and corresponds to (xn, yn) of Equation 66, F(Pn) denotes an n^th estimated distance difference vector calculated from the n^th estimated position coordinates and corresponds to of Equation 66,

and H denotes a differential coefficient matrix and corresponds to

In Equation 67,

may be determined based on a travel distance difference between reference signals. Also, the travel distance difference between the reference signals may be determined based on a phase difference depending on a wavelength of a k^th subcarrier or carrier of the reference signals. Therefore,

of Equation 67 may be represented as Equation 68. [Equation 68]

In Equation 68,

denotes the wavelength of the k^th subcarrier or carrier, denotes a phase difference vector depending on the wavelength of

the k^th subcarrier or carrier, and denotes an integer ambiguity vector of

the phase difference depending on the wavelength of the k^th subcarrier or carrier. For example,

denotes a phase difference depending on the wavelength of the k^th subcarrier or carrier of the first reference signal and the second reference signal, and

denotes an integer ambiguity of the phase difference depending on the wavelength of the k^th subcarrier or carrier of the first reference signal and the second reference signal. Equation 68 may be further simplified as Equation 69. [Equation 69]

In Equation 69,

denotes a phase difference vector depending on the wavelength of the k^th subcarrier or carrier and corresponds to of

Equation 68. In Equation 69, ^^ denotes an integer ambiguity vector of the phase difference depending on the wavelength of the k^th subcarrier or carrier and corresponds to of Equation 68.

The UE 200 may calculate the (n+1)-th estimated coordinates P_n+1 using Equation 70. [Equation 70]

Referring to Equation 70, may depend on a difference between

and

Therefore, in operation S254, the UE 200 may calculate an error between a travel distance difference ^^ based on a k^th phase difference and a travel distance difference ^th

based on the n estimated coordinates Pn. In operation S255, the UE 200 may calculate using Equation 70.

In operation S260, the UE 200 may verify whether the termination condition is met. For example, when the error between Pn+1 and Pn is less than a tolerance, the UE 200 may determine that the termination condition is met. As another example, if n exceeds a preset reference value, the UE 200 may determine that the termination condition is met. The termination condition may be variously set within the range modifiable by those skilled in the art. If the termination condition is not met, the UE 200 may increase an index n and may further perform operations S253, S254, and S255. If the termination condition is met, the UE 200 may perform operation S260 of FIG.13. The UE 200 may calculate k^th estimated coordinates corresponding to a phase difference of the k^th subcarrier or carrier by sufficiently repeating operations S253, S254, and S255. Here, the phase difference of the k^th subcarrier or carrier may be a phase difference depending on the wavelength of the k^th subcarrier or carrier. Referring again to FIG.13, in operation S270, the UE 200 may calculate integer ambiguity of a (k+1)-th phase difference based on a k^th estimated distance difference that is determined based on the k^th estimated coordinates. The UE 200 may assume that an error between the k^th estimated distance difference and a (k+1)-th estimated distance difference that is determined based on the integer ambiguity of the (k+1)-th phase difference is less than a single wavelength. In this case, the UE 200 may calculate the integer ambiguity of the (k+1)-th phase difference using Equation 71. [Equation 71] In Equation

71, denotes a k^th travel distance difference that is calculated based on a phase difference depending on a phase of the k^th subcarrier or carrier. denotes a phase vector depending on a wavelength of a (k+1)-

th subcarrier or carrier, and

denotes an integer ambiguity vector of a phase difference depending on the wavelength of the (k+1)-th subcarrier or carrier. The UE 200 may calculate a (k+1)-th integer ambiguity vector based on a result acquired by dividing the k^th travel distance difference by the wavelength of the (k+1)-th subcarrier or carrier. When the termination condition is met in operation S260 of FIG.13, the UE 200 may determine the k^th estimated coordinates finally calculated in operation S250 as position coordinates of the UE 200. Although FIG.13 illustrates that all operations S210 to S270 are performed by the UE 200, it is provided as an example only. A portion of operations S220 to S270 may be performed by a base station or another node. For example, the UE 200 may transfer data of the reference signals received in operation S210 to the base station and the base station may perform at least a portion of operations S220 to S270. A positioning method and apparatus according to example embodiments is described with reference to FIGS.11 to 16. According to at least one example embodiment, the UE 200 may easily calculate a phase difference depending on a wavelength of a subcarrier or a carrier of reference signals. According to at least one example embodiment, the UE 200 may improve positioning precision by estimating a position of the UE 200 through an iterative operation using a phase difference depending on wavelengths of a plurality of subcarriers or carriers. According to at least one example embodiment, the UE 200 may determine integer ambiguity of a phase difference of a subcarrier or a carrier having a relatively small wavelength based on a phase difference of a subcarrier having a relatively large wavelength. According to at least one example embodiment, the UE 200 may improve positioning precision by modifying an estimated position using a partial differential coefficient matrix. One of ordinary skill in the art may easily understand that the methods and/or processes and operations described herein may be implemented using hardware components, software components, and/or a combination thereof based on the example embodiments. For example, the hardware components may include a general-purpose computer and/or exclusive computing device or a specific computing device or a special feature or component of the specific computing device. The processes may be implemented using one or more processors having an internal and/or external memory, for example, a microprocessor, a controller such as a microcontroller and an embedded microcontroller, a microcomputer, an arithmetic logic unit (ALU), and a digital signal processor such as a programmable digital signal processor or other programable devices. In addition, or, as an alternative, the processes may be implemented using an application specific integrated circuit (ASIC), a programmable gate array, such as, for example, a field programmable gate array (FPGA), a programmable logic unit (PLU), or a programmable array logic (PAL), and other devices capable of executing and responding to instructions in a defined manner, other devices configured to process electronic devices, and combinations thereof. The processing device may run an operating system (OS) and one or more software applications that run on the OS. Also, the processing device may access, store, manipulate, and create data in response to execution of the software. For purpose of simplicity, the description of a processing device is used as a singular; however, one skilled in the art will appreciate that a processing device may include a plurality of processing elements and/or multiple types of processing elements. For example, the processing device may include a plurality of processor or a single processor and a single controller. In addition, different processing configurations are possible such as parallel processors. The software may include a computer program, a piece of code, an instruction, or some combination thereof, for independently or collectively instructing or configuring the processing device to operate as desired. Software and/or data may be embodied permanently or temporarily in any type of machine, component, physical equipment, virtual equipment, computer storage medium or device, or in a propagated signal wave capable of providing instructions or data to or being interpreted by the processing device. The software also may be distributed over network coupled computer systems so that the software is stored and executed in a distributed fashion. In particular, the software and data may be stored by one or more computer readable storage mediums. The methods according to the example embodiments may be recorded in non-transitory computer-readable recording media including program instructions to implement various operations embodied by a computer. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The media and program instructions may be those specially designed and constructed for the purposes, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of non-transitory computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD ROM, DVD, and blue-rays; magneto-optical media such as floptical disks; and hardware devices that are specially to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, and the like. Examples of program instructions include both machine code, such as produced by a compiler and files containing structural programming languages such as C++ object-oriented programming language and high or low programming languages (assembly languages, hardware technical languages, database programming languages and techniques) to run on one of the aforementioned devices and a processor, a processor architecture, or a heterogeneous combination of combinations of different hardware and software components, or a machine capable of executing program instructions. Accordingly, they may include a machine language code, a byte code, and a high language code executable using an interpreter and the like. Therefore, according to an aspect of at least one example embodiment, the aforementioned methods and combinations thereof may be implemented by one or more computing devices as an executable code that performs the respective operations. According to another aspect, the methods may be implemented by systems that perform the operations and may be distributed over a plurality of devices in various manners or all of the functions may be integrated into a single exclusive, stand-alone device, or different hardware. According to another aspect, devices that perform operations associated with the aforementioned processes may include the aforementioned hardware and/or software. According to another aspect, all of the sequences and combinations associated with the processes are to be included in the scope of the present disclosure. For example, the described hardware devices may be to act as one or more software modules in order to perform the operations of the above-described example embodiments, or vice versa. The hardware devices may include a processor, such as, for example, an MPU, a CPU, a GPU, a TPU, etc., configured to be combined with a memory such as ROM/RAM configured to store program instructions and to execute the instructions stored in the memory, and may include a communicator capable of transmitting and receiving a signal with an external device. In addition, the hardware devices may include a keyboard, a mouse, and an external input device for receiving instructions created by developers. The foregoing description has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular example embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure. Accordingly, the present disclosure is not limited to the aforementioned example embodiments and may belong to the scope of example embodiments disclosed herein and equally or equivalently modified from the claims. For examples, although the methods may be implemented in different sequence and/or components of systems, structures, apparatuses, circuits, etc., may be combined or integrated in different form or may be replaced with other components or equivalents, appropriate results may be achieved. Such equally or equivalently modified example embodiments may include logically equivalent methods capable of achieving the same results according to the example embodiments. Accordingly, the present disclosure and the scope thereof are not limited to the aforementioned example embodiments and should be understood as a widest meaning allowable by law.

Claims

WHAT IS CLAIMED IS: 1. A positioning method performed by a user equipment, the positioning method comprising: receiving a first reference signal from a first transmitter and receiving a second reference signal from a second transmitter; acquiring phase information depending on carrier frequencies of the first reference signal and the second reference signal based on received data of the first reference signal measured at a plurality of sample times and received data of the second reference signal measured at the plurality of sample times; and outputting information about a difference between a travel distance of the first reference signal and a travel distance of the second reference signal based on the phase information depending on the carrier frequencies.

2. The positioning method of claim 1, wherein the acquiring of the phase information comprises: acquiring a first sample vector based on the received data of the first reference signal, acquiring a second sample vector based on the received data of the second reference signal, calculating a first phase vector and a second phase vector by performing an inner product operation of a discrete Fourier transform (DFT) coefficient vector for a DFT operation with respect to each of the first sample vector and the second sample vector, and acquiring the phase information from a conjugate multiplication of the first phase vector and the second phase vector.

3. The positioning method of claim 1, wherein a waveform of the first reference signal and a waveform of the second reference signal are configured to continue in a time interval greater than a symbol size corresponding to a frequency interval of orthogonal frequency division multiplex (OFDM).

4. The positioning method of claim 1, wherein the first reference signal and the second reference signal are transmitted in different time domains, a first subcarrier group for transmitting the first reference signal and a second subcarrier group for transmitting the second reference signal are the same.

5. The positioning method of claim 2, wherein the first reference signal includes a plurality of subcarriers included in a first subcarrier group, and the second reference signal includes a plurality of subcarriers included in a second subcarrier group, and a subcarrier included in the first subcarrier group and a subcarrier included in the second subcarrier group are orthogonal to each other.

6. The positioning method of claim 5, wherein the plurality of subcarriers included in the first subcarrier group and the plurality of subcarriers included in the second subcarrier group are provided at equal intervals in a frequency domain.

7. The positioning method of claim 6, wherein a correction factor is calculated based on a conjugate multiplication between a first component of the second phase vector and a second component of the second phase vector having an angular frequency index different from that of the first component, and the phase information is output based on a result of multiplying the conjugate multiplication of the first phase vector and the second phase vector by the correction factor.

8. The positioning method of claim 6, wherein a complex signal component of each of the subcarriers included in the first subcarrier group and a complex signal component of each of the subcarriers included in the second subcarrier group have a conjugate relation.

9. The positioning method of claim 8, wherein the second subcarrier group is spaced apart at a desired distance from the first subcarrier group in the frequency domain, and the desired distance is determined based on a number of subcarriers included in the first subcarrier group and a size of a fast Fourier transform (FFT) window.

10. The positioning method of claim 7, wherein the acquiring of the phase information comprises calculating a parameter depending on a clock error between the first transmitter and the second transmitter and the terminal among parameters constituting the conjugate multiplication by linearly combining phase angles of components included in the conjugate multiplication.

11. The positioning method of claim 1, further comprising: receiving reference signals from a transmitter group that includes at least three transmitters; calculating first phase information based on reference signals received from a first pair of transmitters among the at least three transmitters included in the transmitter group, and calculating second phase information based on reference signals received from a second pair of transmitters among the at least three transmitters; and determining an integer ambiguity of the second phase information based on the first phase information.

12. The positioning method of claim 11, wherein an interval between the first pair of transmitters is less than an interval between the second pair of transmitters.

13. The positioning method of claim 12, wherein the interval between the first pair of transmitters is less than a carrier wavelength of the reference signals and the interval between the second pair of transmitters is greater than the carrier wavelength of the reference signals.

14. A user equipment comprising: a communicator; and a processor, wherein the processor is configured to perform a process of receiving a first reference signal from a first transmitter, a process of acquiring phase information depending on carrier frequencies of the first reference signal and the second reference signal based on received data of the first reference signal measured at a plurality of sample times and received data of the second reference signal measured at the plurality of sample times, and a process of outputting information about a difference between a travel distance of the first reference signal and a travel distance of the second reference signal based on the phase information depending on the carrier frequencies.

15. A positioning reference signal transmission method performed by a plurality of transmitters, the method comprising: transmitting, by a first transmitter, a first reference signal; and transmitting, by a second transmitter, a second reference signal, wherein a waveform of the first reference signal and a waveform of the second reference signal are configured to continue in a time interval greater than a symbol size corresponding to a frequency interval of orthogonal frequency division multiplex (OFDM), and the first reference signal includes a plurality of subcarriers included in a first subcarrier group, and the second reference signal includes a plurality of subcarriers included in a second subcarrier group.

16. The method of claim 15, wherein the first reference signal and the second reference signal are transmitted in different time domains and the first subcarrier group and the second subcarrier group are the same.

17. The method of claim 15, wherein the first reference signal includes a plurality of subcarriers included in a first subcarrier group, and the second reference signal includes a plurality of subcarriers included in a second subcarrier group, and a subcarrier included in the first subcarrier group and a subcarrier included in the second subcarrier group are orthogonal to each other, and the plurality of subcarriers included in the first subcarrier group and the plurality of subcarriers included in the second subcarrier group are provided at equal intervals in a frequency domain.

18. The method of claim 17, wherein a complex signal component of each of the subcarriers included in the first subcarrier group and a complex signal component of each of the subcarriers included in the second subcarrier group have a conjugate relation.

19. The method of claim 15, further comprising: transmitting, by at least one additional transmitter excluding the first transmitter and the second transmitter, a reference signal, wherein, in a transmitter group including the first transmitter, the second transmitter, and the at least one additional transmitter, an interval between a first pair of transmitters and an interval between a second pair of transmitters differ from each other.

20. The method of claim 19, wherein the interval between the first pair of transmitters is less than a carrier wavelength of the reference signals and the interval between the second pair of transmitters is greater than the carrier wavelength of the reference signals.