WO2016195094A1 - Communication method and communication device - Google Patents

Communication method and communication device Download PDF

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WO2016195094A1
WO2016195094A1 PCT/JP2016/066654 JP2016066654W WO2016195094A1 WO 2016195094 A1 WO2016195094 A1 WO 2016195094A1 JP 2016066654 W JP2016066654 W JP 2016066654W WO 2016195094 A1 WO2016195094 A1 WO 2016195094A1
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data
complex
code
periodic function
function code
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PCT/JP2016/066654
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French (fr)
Japanese (ja)
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梅野　健
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国立大学法人京都大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/707—Spread spectrum techniques using direct sequence modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/10—Code generation

Definitions

  • the present invention relates to communication using an approximately periodic function code.
  • the approximate periodic function is obtained by generalizing the Fourier series expansion. Specifically, for example, it is configured as a sum of signals having a frequency that is a 1/2 power of the mth prime number p (m). In this case, since the prime power of 1/2 is temporarily independent on the rational number field, these signals cannot be periodic. Although such a signal has never been used in communication, the present inventor proposed non-patent document 1 for the first time to apply to communication.
  • the spreading code length N is increased excessively, the signal processing load increases and the transmission rate decreases, so it is difficult to dramatically increase the number of accessible users.
  • APSS Almost Periodic Spreading Sequence
  • the present invention provides a more specific method for communication using an almost periodic function code.
  • One aspect of the present invention is a communication method including transmitting a signal generated by modulating data with a code, wherein the code is an approximately periodic function code, and the data is real part data. And complex data having imaginary part data, and the modulation includes an operation of multiplying the complex data by the approximate periodic function code.
  • the communication is meant to include broadcasting.
  • Another aspect of the present invention is a communication device.
  • the communication apparatus includes a modulation unit that modulates data with a code, the code is an approximately periodic function code, the data is complex number data having real part data and imaginary part data, and the modulation part is Arithmetic processing for applying an approximate periodic function code to complex data is performed.
  • a communication method includes transmitting a signal generated by modulating data with a code, wherein the code is an approximately periodic function code, and the data includes real part data and imaginary part.
  • Complex data having data, and the modulation includes an operation of multiplying the complex data by the approximate periodic function code.
  • the operation of multiplying the complex data by the approximate periodic function code preferably includes complex multiplication of the complex data by the approximate periodic function code represented by a complex number.
  • N represents the code length of the approximate periodic function code
  • j is an integer of 1 to N
  • a j represents the approximate periodic function code of code length N
  • d represents the complex data
  • the operation of multiplying the complex number data by the approximate periodic function code preferably includes performing a complex multiplication indicated by da j for each j of 1 to N.
  • N the code length of the approximate periodic function code
  • j is an integer of 1 to N
  • a j the approximate periodic function code of code length N
  • d the complex data
  • the operation of multiplying the complex data by the approximate periodic function code preferably includes calculating the sum of N da j .
  • the modulation further includes complex-multiplying the complex data by a complex code different from the approximate periodic function code, and the complex code is a code having a constant power on a complex plane. preferable.
  • the modulation may be spread spectrum modulation using the approximate periodic function code.
  • the communication method may further include receiving and demodulating the signal, and the demodulating may include reproducing the data by multiplying the received signal by a complex conjugate of the approximate periodic function. preferable.
  • the modulation may be quasi-orthogonal multiplex modulation using the approximate periodic function code. By applying an almost periodic function code to the data, a quasi-orthogonal multiple modulation signal is obtained.
  • the pseudo orthogonal multiplexing modulation has a size of K data sequences.
  • the method includes complex multiplication of a K ⁇ N matrix, and the matrix preferably has K number of the substantially periodic function codes having a code length of N.
  • the communication method further includes receiving and demodulating the signal, and the demodulation includes reproducing the data by multiplying the inverse matrix of the matrix used for the quasi-orthogonal multiple modulation. preferable.
  • the communication device includes a modulation unit that modulates data with a code, the code is an approximately periodic function code, and the data is complex data having real part data and imaginary part data.
  • the modulation unit performs arithmetic processing for multiplying the complex data by an approximate periodic function code.
  • An almost periodic function code is a code based on an almost periodic function.
  • the approximate periodic function is obtained by generalizing the Fourier series expansion, and is, for example, the sum of signals whose frequency is the square root of a prime number.
  • the almost periodic function is aperiodic because it is clearly linearly independent on the advantageous number field.
  • the approximate periodic function code a j is given by the following equation (1), for example.
  • the almost periodic function code is a code with constant power on the complex plane, similar to a chaotic spreading code with constant power on the complex plane.
  • the constant power on the complex plane means that the code value is located on a single circumference on the IQ constellation of the code.
  • An almost periodic function code such as the expression (1) is represented by a complex number expression.
  • N and K are preferably 2 powers.
  • ⁇ k is a prime number given to user k or channel k, and takes a different value for each user k or channel k.
  • I is an Image unit.
  • m is the mth root, and is an integer or a real number.
  • ⁇ k is an arbitrary real number and may be zero.
  • the approximate periodic function code can be configured infinitely. Strictly speaking, the almost periodic function code is not an orthogonal code such as a PN code. However, when the code length is infinite, it has the property of being orthogonal. Therefore, if the code length of the almost periodic function code is sufficiently large (for example, N is 100 or more or 1000 or more), it can be treated as being orthogonal (pseudo-orthogonal).
  • the number of users K that can ensure sufficient quality is O (N 2 ), and ultra-high density multiple access communication is possible.
  • N 2 the number of users K that can ensure sufficient quality
  • 1000 to 1000 devices can be connected at the same time, and a plurality of devices can be connected at the same time to the extent that 8K and 16K terrestrial broadcasting is possible.
  • FIG. 1 shows a communication system 10 for spread spectrum communication using an approximately periodic function code.
  • the communication system 10 includes a communication device (transmitter) 20 that performs transmission and a communication device (receiver) 30 that performs reception.
  • Each of the communication devices 20 and 30 has a transmission / reception function.
  • the transmitter 20 includes a modulation unit 21.
  • the modulation unit 21 performs spread spectrum modulation on the transmission data d and outputs a transmission signal s that is a modulated signal.
  • the modulation unit 21 performs spread spectrum modulation by applying the approximate periodic function codes (a 1 , a 2 ,... A N ⁇ 1 , a N ) that are pseudo orthogonal codes to the transmission data d.
  • the receiver 30 includes a demodulator 31.
  • the demodulator 31 despreads the received signal r and demodulates the received signal r to obtain reproduction data of the transmission data d.
  • the demodulator 31 includes complex conjugates (a 1 * , a 2 * ,... A N ⁇ ) of the approximate periodic function codes (a 1 , a 2 ,... A N ⁇ 1 , a N ) used for transmission. 1 * , aN * ) to demodulate. Note that a * represents a complex conjugate of a.
  • the transmission data d is N pieces of data d 1 to d N according to the code length N as shown in FIG.
  • the N data d 1 to d N all have the same value as the data d, and each is complex data. .
  • the N periodic data codes (a 1 , a 2 ,... A N ⁇ 1 , a N ) having a code length N are applied to the N pieces of data d 1 to d N.
  • the approximate periodic function codes (a 1 , a 2 ,... A N ⁇ 1 , a N ) of the same user or the same channel are generated using the same prime number ⁇ k .
  • Different approximate periodic function codes are generated using different prime numbers for each user or channel.
  • the transmission data d is modulated by complex multiplication of the approximate periodic function code with respect to the complex data d using the fact that the transmission data d is complex data and the approximate periodic function code is a complex code.
  • the complex multiplication can be collectively modulate the real part data d R and the imaginary part data d I constituting the complex data. Therefore, according to this embodiment, it is not necessary to modulate the real part data d R and the imaginary part data d I in separate codes. Therefore, according to the present embodiment, the calculation load is reduced. Moreover, according to this embodiment, the number of codes required for modulation can be reduced.
  • the modulation unit 21 multiplies complex data by an approximate periodic function code.
  • the modulation unit 21 may include a plurality (N) of complex multiplication units 21 a and an adder 21 b that adds outputs of the plurality of complex multiplication units 21 a.
  • Each complex multiplier 21a performs complex multiplication of d j that is a complex number and a j that is also a complex number.
  • the adder 21b outputs the sum of d j a j from 1 to N.
  • d j a j When the value of dj is the same value d in 1 to N, d j a j can also be expressed as da j .
  • the sum total of d j a j is output from the modulation unit 21 as a transmission signal (modulation signal).
  • the arithmetic expressions of the complex multiplication d j a j by each complex multiplier 21a are as shown in the following expressions (2-1) to (2-3).
  • the modulation unit 21 not only multiplies complex data d j by an approximate periodic function code a j but also different types of complex data d from the approximate periodic function code a j.
  • the complex code b j may be complex multiplied. In this case, when the complex multiplication by the modulation unit 21 is expressed by an equation, d j a j b j .
  • the complex multiplication d j a j b j performed by the modulation unit 21 may be (d j a j ) and then (d j a j ) multiplied by b j or (d j b j ) may be performed, and then (d j b j ) may be subjected to complex multiplication by a j . In both cases, the result is the same.
  • a complex code b j of a type different from the approximate periodic function code a j is multiplied by d j to the complex number data, so that the preferable property of the code b j is reflected in the modulation signal, and a more suitable modulation signal is obtained. Easy to get.
  • the complex code b j of a type different from the approximate periodic function code a j is, for example, a code with constant power on the complex plane. Be multiplied by a constant power code b j to constant power almost periodic function code a j, it is advantageous because the power does not vary.
  • the code b j with constant power on the complex plane is, for example, a chaotic spreading code or Gold code with constant power on the complex plane. Chaotic spreading codes or Gold codes have good correlation characteristics.
  • the modulation unit 21 can improve the correlation characteristics of the modulation signal d j a j b j by multiplying the data d j by the chaotic spreading code or the Gold code.
  • IQ constellation code transition diagram
  • the square of the radius from the origin to the outer circle corresponds to the power of the code.
  • all codes exist on a single circle (outer circle), and the power is constant.
  • FIG. 6 shows an IQ constellation of a chaotic spreading code with constant power.
  • the black circles in the constellation of FIG. As is clear from FIG. 6, in the chaotic spreading code with constant power, all the codes exist on a single circle and the power is constant.
  • FIG. 7 shows the demodulator 31.
  • the demodulator 31 divides the received signal r into N chips to obtain N chip data r 1 , r 2 ,..., R N, and N chip data r 1 , r 2 ,.
  • a separating portion 31a which separates each r N real part data r R and imaginary part data r I I, the real part data r R and imaginary part data r I each chip data r 1 comprised of I, r 2, .., R N , complex conjugates (a 1 * , a 2 * ,...) Of the approximate periodic function codes (a 1 , a 2 ,... A N ⁇ 1 , a N ) used for transmission.
  • the arithmetic unit 31b performs complex multiplication on the chip data r 1 , r 2 ,..., R N by complex conjugates (a 1 * , a 2 * ,... A N ⁇ 1 * , a N * ). To do.
  • Calculation unit 31 performs calculation according to the following formula (3-1), reproduction data d consisting of d R and d I I.
  • the demodulation unit 31 When the modulation unit 21 is applied with a complex code b j of a type different from the approximate periodic function code a j , the demodulation unit 31 generates codes (b 1 , b 2 ,... B N ⁇ 1 , b N complex conjugate (b 1 * a), b 2 *, ⁇ b N-1 *, the b N *), each chip data r 1, r 2, ⁇ , complex multiplication with respect to r N. In this case, the calculation unit 31 performs a calculation according to the equation (3-2) to obtain reproduction data d.
  • Complex conjugate (b 1 *, b 2 * , ⁇ b N-1 *, b N *) the chip data r 1, r 2, ⁇ ⁇ ⁇ , a complex conjugate with respect to r N (a 1 *, a 2 *, ⁇ a N- 1 *, a N *) is may be complex multiplication after being complex multiplication, complex conjugate with respect to the chip data r 1, r 2, ⁇ , r N Complex multiplication may be performed before (a 1 * , a 2 * ,..., A N ⁇ 1 * , a N * ) are complex multiplied.
  • the transmission data d to which the approximate periodic function code is applied is complex data, so it can take multiple values, and the transmission efficiency is higher than when the transmission data is binary binary data. Is good.
  • the demodulator 31 can obtain complex number data as reproduction data by demodulation processing.
  • FIG. 8 shows a communication device 100 that performs pseudo-orthogonal multiplex communication using an approximately periodic function code.
  • the communication device 20 can transmit and receive pseudo-orthogonal multiplexed signals.
  • the 8 includes a converter 101 and a quasi-orthogonal multiplex modulator 102 for transmission.
  • the converter 101 is, for example, a serial / parallel converter, and converts serial transmission data into a data string (parallel data string) for each channel (user).
  • the number of channels or the number of users is K.
  • the data length (symbol length) of the data string is N.
  • N is the code length of the almost periodic function code.
  • d j k indicating a data symbol indicates the j-th data symbol (transmission code) for the k-th channel (or k-th user). 1 ⁇ k ⁇ K and 1 ⁇ j ⁇ N. Each d j k is complex number data.
  • the data string of the first channel (first user) is (d 1 1 , d 2 1 ,..., D N 1 )
  • the data string of the second channel (second user) is (d 1 2, d 2 2, ⁇ , a d N 2)
  • a data row of the k-th channel (the k-th user) can be a (d 1 k, d 2 k , ⁇ , d N k)
  • the data string of the K-1th channel (K-1th user) is (d 1 K ⁇ 1 , d 2 K ⁇ 1 ,..., D N K ⁇ 1 )
  • the Kth channel (Kth) The data string of (user) is (d 1 K , d 2 K ,..., D N K ).
  • N ⁇ K data symbols d j k are given to the quasi-orthogonal multiplex modulation section 102 and output a quasi-orthogonal multiplex signal y.
  • a quasi-orthogonal multiplexed signal (transmission signal) y generated from N ⁇ K data symbols d j k is a signal for K channels ⁇ K symbols.
  • y i j indicating the transmission symbol of each channel indicates the j-th symbol in the i-th channel. 1 ⁇ i, j ⁇ K.
  • the transmission symbol sequence of the first channel is (y 1 1 , y 1 2 ,..., Y 1 K ⁇ 1 , y 1 K )
  • the transmission symbol sequence of the second channel is , (Y 2 1 , y 2 2 ,..., Y 2 K ⁇ 1 , y 2 K )
  • the transmission symbol string of the k-th channel is (y k 1 , y k 2 ,..., Y k K ⁇ 1 , y k K )
  • the transmission symbol sequence of the K ⁇ 1th channel is (y K ⁇ 1 1 , y K ⁇ 1 2 ,..., y K ⁇ 1 K ⁇ 1 , y K).
  • the transmission symbol string of the Kth channel is (y K 1 , y K 2 ,..., Y K K ⁇ 1 , y K K ).
  • the quasi-orthogonal multiplex modulator 102 performs quasi-orthogonal multiplex modulation processing on the N ⁇ K data symbols d j k according to the following equation (4), and outputs a quasi-orthogonal multiplex signal y.
  • a calculation is performed by multiplying N ⁇ K data symbols d j k by a matrix (modulation matrix) A having a size of K ⁇ N to obtain a quasi-orthogonal multiplex signal y. That is, the quasi-orthogonal multiplex modulator 102 complex-multiplies the matrix A by a matrix composed of K data strings.
  • Complex multiplication for a matrix corresponds to performing N ⁇ K complex multiplications of a j k d j k .
  • the matrix A is obtained by arranging K pieces of approximately periodic function codes (a 1 k , a 2 k ,..., A N ⁇ 1 k , a N k ) having a code length N.
  • 1 ⁇ k ⁇ K The K approximate periodic function codes are generated from K different prime numbers ⁇ k corresponding to the number of channels (number of users) K.
  • the approximate periodic function code a j k generated from the prime number ⁇ k is expressed by the following equation (5). Note that 1 ⁇ j ⁇ N.
  • the transmitted N ⁇ K data symbols d j k can be reproduced by demodulation processing.
  • an inverse matrix A ⁇ 1 of the matrix A is used.
  • a signal y for K symbols (a signal corresponding to the left side in Equation (4) shown in [Expression 4]) is acquired from the received pseudo orthogonal multiplexed signal, and an inverse matrix is obtained for the signal y for K symbols.
  • A- 1 By multiplying by A- 1 , it is possible to obtain N ⁇ K reproduced data symbols d j k .
  • K ⁇ N so that demodulation can be performed.
  • the inverse matrix A ⁇ 1 of the matrix A may be obtained by transposing the matrix A and taking the complex conjugate of each matrix element a j k .
  • the operation of multiplying the inverse matrix A ⁇ 1 for data reproduction is performed by complex multiplication.

Abstract

Provided is a communication method using almost periodic function codes. The communication method includes transmitting signals generated by modulating data using the codes. The codes are almost periodic function codes. The data is complex number data having real part data and imaginary part data. The modulation includes computation of multiplying the complex number data by the almost periodic function codes.

Description

通信方法及び通信機COMMUNICATION METHOD AND COMMUNICATION DEVICE
　本発明は、概周期関数符号を用いた通信に関するものである。 The present invention relates to communication using an approximately periodic function code.
　概周期関数は、フーリエ級数展開を一般化することによって得られる。具体的には、例えば、ｍ番目の素数ｐ（ｍ）の１／２乗を周波数とする信号の和として構成される。この場合、素数の１／２乗は有理数体上一時独立なので、これらの信号は周期的であり得ない。このような信号は、通信で用いられたことはなかったが、本発明者は、非特許文献１によって通信への適用を初めて提案した。 The approximate periodic function is obtained by generalizing the Fourier series expansion. Specifically, for example, it is configured as a sum of signals having a frequency that is a 1/2 power of the mth prime number p (m). In this case, since the prime power of 1/2 is temporarily independent on the rational number field, these signals cannot be periodic. Although such a signal has never been used in communication, the present inventor proposed non-patent document 1 for the first time to apply to communication.
　ここで、スペクトル拡散通信を基本原理とするＣＤＭＡ方式では、ある程度の通信品質を確保しつつ、多重アクセス通信を達成しようとすると、アクセス可能なユーザ数Ｋは、拡散符号長Ｎに比例する（Ｋ＝Ｏ（Ｎ））。しかし、拡散符号長Ｎをむやみに増加させると、信号処理負荷が増加するとともに伝送レートが低下するため、アクセス可能なユーザ数の劇的な増加は困難である。 Here, in the CDMA system based on spread spectrum communication, if multiple access communication is to be achieved while ensuring a certain level of communication quality, the number of accessible users K is proportional to the spread code length N (K = O (N)). However, if the spreading code length N is increased excessively, the signal processing load increases and the transmission rate decreases, so it is difficult to dramatically increase the number of accessible users.
　非特許文献１では、概周期関数に基づく拡散符号（概周期拡散符号：ＡＰＳＳ（Ａｌｍｏｓｔ　Ｐｅｒｉｏｄｉｃ　Ｓｐｒｅａｄｉｎｇ　Ｓｅｑｕｅｎｃｅ）によって、多重アクセス可能なユーザ数Ｋ＝Ｏ（Ｎ２）となり、超高密度多重アクセス通信が可能となることが示されている。 In Non-Patent Document 1, a spread code based on an almost periodic function (almost periodic spreading code: APSS (Almost Periodic Spreading Sequence), the number of users that can be accessed multiple times is K = O (N 2 ), and ultra high density multiple access communication is performed. It has been shown to be possible.
　本発明は、概周期関数符号を用いた通信に関して、より具体的な手法を提供するものである。 The present invention provides a more specific method for communication using an almost periodic function code.
　本発明の一の態様は、通信方法であって、データを符号で変調して生成された信号を送信することを含み、前記符号は、概周期関数符号であり、前記データは、実部データと虚部データを有する複素数データであり、前記変調は、前記複素数データに対して前記概周期関数符号をかける演算を含む。なお、ここでは、通信は、放送を含む意である。本発明の他の態様は、通信機である。通信機は、データを符号で変調する変調部を備え、前記符号は、概周期関数符号であり、前記データは、実部データと虚部データを有する複素数データであり、前記変調部は、前記複素数データに対して概周期関数符号をかける演算処理を行う。 One aspect of the present invention is a communication method including transmitting a signal generated by modulating data with a code, wherein the code is an approximately periodic function code, and the data is real part data. And complex data having imaginary part data, and the modulation includes an operation of multiplying the complex data by the approximate periodic function code. Here, the communication is meant to include broadcasting. Another aspect of the present invention is a communication device. The communication apparatus includes a modulation unit that modulates data with a code, the code is an approximately periodic function code, the data is complex number data having real part data and imaginary part data, and the modulation part is Arithmetic processing for applying an approximate periodic function code to complex data is performed.
スペクトル拡散通信のための送受信系を示すブロック図である。It is a block diagram which shows the transmission / reception system for spread spectrum communications. 送信データと概周期関数符号を示す図である。It is a figure which shows transmission data and an approximate period function code. 変調部のブロック図である。It is a block diagram of a modulation part. 変調部のブロック図である。It is a block diagram of a modulation part. 概周期関数符号のコンスタレーションである。This is a constellation of an approximately periodic function code. パワー一定のカオス拡散符号のコンスタレーションである。This is a constellation of chaotic spreading code with constant power. 復調部のブロック図である。It is a block diagram of a demodulation part. 擬似直交多重通通信機のブロック図である。It is a block diagram of a quasi-orthogonal multiple communication device.
　以下、本発明の好ましい実施形態について添付図面を参照しながら説明する。 Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings.
［１．実施形態の概要］ [1. Outline of Embodiment]
（１）実施形態に係る通信方法は、データを符号で変調して生成された信号を送信することを含み、前記符号は、概周期関数符号であり、前記データは、実部データと虚部データを有する複素数データであり、前記変調は、前記複素数データに対して前記概周期関数符号をかける演算を含む。 (1) A communication method according to an embodiment includes transmitting a signal generated by modulating data with a code, wherein the code is an approximately periodic function code, and the data includes real part data and imaginary part. Complex data having data, and the modulation includes an operation of multiplying the complex data by the approximate periodic function code.
（２）前記複素数データに対して前記概周期関数符号をかける演算は、前記複素数データに対して複素数で表される前記概周期関数符号を複素乗算することを含むのが好ましい。 (2) The operation of multiplying the complex data by the approximate periodic function code preferably includes complex multiplication of the complex data by the approximate periodic function code represented by a complex number.
（３）Ｎが前記概周期関数符号の符号長を表し、ｊが１以上Ｎ以下の整数であり、ａｊが符号長Ｎの前記概周期関数符号を表し、ｄが前記複素数データを表すときに、前記複素数データに対して前記概周期関数符号をかける演算は、１～Ｎまでのそれぞれのｊについて、ｄａｊで示される複素乗算をすることを含むのが好ましい。 (3) When N represents the code length of the approximate periodic function code, j is an integer of 1 to N, a j represents the approximate periodic function code of code length N, and d represents the complex data In addition, the operation of multiplying the complex number data by the approximate periodic function code preferably includes performing a complex multiplication indicated by da j for each j of 1 to N.
（４）Ｎが前記概周期関数符号の符号長を表し、ｊが１以上Ｎ以下の整数であり、ａｊが符号長Ｎの前記概周期関数符号を表し、ｄが前記複素数データを表すときに、前記複素数データに対して前記概周期関数符号をかける演算は、Ｎ個のｄａｊの総和を算出することを含むのが好ましい。 (4) When N represents the code length of the approximate periodic function code, j is an integer of 1 to N, a j represents the approximate periodic function code of code length N, and d represents the complex data In addition, the operation of multiplying the complex data by the approximate periodic function code preferably includes calculating the sum of N da j .
（５）前記変調は、前記複素数データに対して、前記概周期関数符号とは異なる複素符号を複素乗算することを更に含み、前記複素符号は、複素平面上でパワー一定の符号であるのが好ましい。 (5) The modulation further includes complex-multiplying the complex data by a complex code different from the approximate periodic function code, and the complex code is a code having a constant power on a complex plane. preferable.
（６）前記変調は、前記概周期関数符号を用いたスペクトル拡散変調とすることができる。 (6) The modulation may be spread spectrum modulation using the approximate periodic function code.
（７）通信方法は、前記信号を受信して復調することを更に含み、前記復調は、受信した前記信号に前記概周期関数の複素共役をかけて、前記データを再生することを含むのが好ましい。 (7) The communication method may further include receiving and demodulating the signal, and the demodulating may include reproducing the data by multiplying the received signal by a complex conjugate of the approximate periodic function. preferable.
（８）前記変調は、前記概周期関数符号を用いた擬似直交多重変調とすることができる。データに対して概周期関数符号をかけることで、擬似直交多数変調信号が得られる。 (8) The modulation may be quasi-orthogonal multiplex modulation using the approximate periodic function code. By applying an almost periodic function code to the data, a quasi-orthogonal multiple modulation signal is obtained.
（９）Ｋが、チャネル数又はユーザ数を表し、Ｎが、データ列を構成する複素数データの数を表すときに、前記疑似直交多重変調は、Ｋ個のデータ列に対して、大きさがＫ×Ｎの行列を複素乗算することを含み、前記行列は、符号長Ｎの前記概周期関数符号をＫ個有するのが好ましい。 (9) When K represents the number of channels or the number of users, and N represents the number of complex data constituting the data sequence, the pseudo orthogonal multiplexing modulation has a size of K data sequences. Preferably, the method includes complex multiplication of a K × N matrix, and the matrix preferably has K number of the substantially periodic function codes having a code length of N.
（１０）通信方法は、前記信号を受信して復調することを更に含み、前記復調は、擬似直交多重変調に用いられた行列の逆行列をかけて、前記データを再生することを含むのが好ましい。 (10) The communication method further includes receiving and demodulating the signal, and the demodulation includes reproducing the data by multiplying the inverse matrix of the matrix used for the quasi-orthogonal multiple modulation. preferable.
（１１）実施形態に係る通信機は、データを符号で変調する変調部を備え、前記符号は、概周期関数符号であり、前記データは、実部データと虚部データを有する複素数データであり、前記変調部は、前記複素数データに対して概周期関数符号をかける演算処理を行う。 (11) The communication device according to the embodiment includes a modulation unit that modulates data with a code, the code is an approximately periodic function code, and the data is complex data having real part data and imaginary part data. The modulation unit performs arithmetic processing for multiplying the complex data by an approximate periodic function code.
［２．実施形態の詳細］
［２．１　概周期関数符号］
　概周期関数符号とは、概周期関数に基づく符号である。概周期関数は、フーリエ級数展開を一般化することによって得られるものであり、例えば、素数の平方根を周波数とする信号の和である。概周期関数は、有利数体上で明らかに一次独立であるため、非周期的である。 [2. Details of Embodiment]
[2.1 Almost periodic function code]
An almost periodic function code is a code based on an almost periodic function. The approximate periodic function is obtained by generalizing the Fourier series expansion, and is, for example, the sum of signals whose frequency is the square root of a prime number. The almost periodic function is aperiodic because it is clearly linearly independent on the advantageous number field.
　概周期関数符号ａｊは、例えば、以下の式（１）で与えられる。概周期関数符号は、複素平面上でパワー一定のカオス拡散符号と同様に、複素平面上でパワー一定の符号である。複素平面上でパワー一定とは、符号のＩＱコンスタレーション上において、符号の値が単一の円周上に位置することである。式（１）のような概周期関数符号は、複素数表現で示される。ただし、概周期関数符号の形式は、式（１）に限られない。
Figure JPOXMLDOC01-appb-M000001
 ここで、
Ｎ，Ｋは、２の冪であるのが好ましい。
ρｋは、ユーザｋ又はチャネルｋに与えられた素数であり、ユーザｋ又はチャネルｋ毎に異なる値をとる。
Ｉは、Ｉｍａｇｉｎａｒｙ単位である。
ｍは、ｍ乗根であり、整数又は実数である。
θｋは、任意の実数でありゼロであってもよい。 The approximate periodic function code a j is given by the following equation (1), for example. The almost periodic function code is a code with constant power on the complex plane, similar to a chaotic spreading code with constant power on the complex plane. The constant power on the complex plane means that the code value is located on a single circumference on the IQ constellation of the code. An almost periodic function code such as the expression (1) is represented by a complex number expression. However, the format of the almost periodic function code is not limited to the equation (1).
Figure JPOXMLDOC01-appb-M000001
 here,
N and K are preferably 2 powers.
ρ k is a prime number given to user k or channel k, and takes a different value for each user k or channel k.
I is an Image unit.
m is the mth root, and is an integer or a real number.
θk is an arbitrary real number and may be zero.
　素数は、無限に存在するため、概周期関数符号は無限に構成することができる。概周期関数符号は、厳密には、ＰＮ符号などのように直交する符号ではない。ただし、符号長無限では直交するという性質を有する。したがって、概周期関数符号の符号長を十分に大きく（例えば、Ｎが１００以上又は１０００以上）すれば、直交しているものとして扱うことができる（擬似直交）。 Since primes exist infinitely, the approximate periodic function code can be configured infinitely. Strictly speaking, the almost periodic function code is not an orthogonal code such as a PN code. However, when the code length is infinite, it has the property of being orthogonal. Therefore, if the code length of the almost periodic function code is sufficiently large (for example, N is 100 or more or 1000 or more), it can be treated as being orthogonal (pseudo-orthogonal).
　スペクトル拡散通信において、概周期関数符号を用いると、十分な品質を担保できるユーザ数ＫはＯ（Ｎ２）となり、超高密度多重アクセス通信が可能となる。例えば、１０００－１０００のデバイスが同時に接続可能となり、また、８Ｋ、１６Ｋの地上波による放送が可能となる程度に同時に複数接続可能となる。 In the spread spectrum communication, when an almost periodic function code is used, the number of users K that can ensure sufficient quality is O (N 2 ), and ultra-high density multiple access communication is possible. For example, 1000 to 1000 devices can be connected at the same time, and a plurality of devices can be connected at the same time to the extent that 8K and 16K terrestrial broadcasting is possible.
［２．２　概周期関数符号を用いたスペクトル拡散通信］
　図１は、概周期関数符号を用いたスペクトル拡散通信のための通信システム１０を示している。この通信システム１０は、送信を行う通信機（送信機）２０と、受信を行う通信機（受信機）３０と、を含んでいる。なお、各通信機２０，３０は、送受信機能を有するものである。 [2.2 Spread Spectrum Communication Using Almost Periodic Function Code]
FIG. 1 shows a communication system 10 for spread spectrum communication using an approximately periodic function code. The communication system 10 includes a communication device (transmitter) 20 that performs transmission and a communication device (receiver) 30 that performs reception. Each of the communication devices 20 and 30 has a transmission / reception function.
　送信機２０は、変調部２１を備えている。変調部２１は、送信データｄに対してスペクトル拡散変調を行い、変調信号である送信信号ｓを出力する。変調部２１は、送信データｄに対して、擬似直交符号である概周期関数符号（ａ１，ａ２，・・・ａＮ－１，ａＮ）をかけることで、スペクトル拡散変調を行う。 The transmitter 20 includes a modulation unit 21. The modulation unit 21 performs spread spectrum modulation on the transmission data d and outputs a transmission signal s that is a modulated signal. The modulation unit 21 performs spread spectrum modulation by applying the approximate periodic function codes (a 1 , a 2 ,... A N−1 , a N ) that are pseudo orthogonal codes to the transmission data d.
　受信機３０は、復調部３１を備えている。復調部３１は、受信信号ｒに対して、逆拡散を行い、受信信号ｒを復調して、送信データｄの再生データを得る。復調部３１は、送信に用いられた概周期関数符号（ａ１，ａ２，・・・ａＮ－１，ａＮ）の複素共役（ａ１ ＊，ａ２ ＊，・・・ａＮ－１ ＊，ａＮ ＊）をかけることで、復調する。なお、ａ＊は、ａの複素共役を示す。 The receiver 30 includes a demodulator 31. The demodulator 31 despreads the received signal r and demodulates the received signal r to obtain reproduction data of the transmission data d. The demodulator 31 includes complex conjugates (a 1 * , a 2 * ,... A N− ) of the approximate periodic function codes (a 1 , a 2 ,... A N−1 , a N ) used for transmission. 1 * , aN * ) to demodulate. Note that a * represents a complex conjugate of a.
　図２及び図３は、変調部２１による変調の仕方を示している。本実施形態において、送信データｄは、実部データｄＲと虚部データｄＩを有する複素数データである。すなわち、送信データｄ＝ｄＲ＋ｄＩＩである。送信データｄは、図２に示すように、符号長ＮにあわせてＮ個のデータｄ１～ｄＮとされる。ここで、ｄ＝ｄ１＝ｄ２＝・・・＝ｄＮ－１＝ｄＮであり、Ｎ個のデータｄ１～ｄＮは全てデータｄと同じ値をもち、それぞれが複素数データである。 2 and 3 show a method of modulation by the modulation unit 21. FIG. In the present embodiment, the transmission data d is a complex number data having a real part data d R and the imaginary part data d I. That is, transmission data d = d R + d I I. The transmission data d is N pieces of data d 1 to d N according to the code length N as shown in FIG. Here, d = d 1 = d 2 =... = D N−1 = d N , and the N data d 1 to d N all have the same value as the data d, and each is complex data. .
　Ｎ個のデータｄ１～ｄＮに対して、符号長Ｎの概周期関数符号（ａ１，ａ２，・・・ａＮ－１，ａＮ）がかけられる。なお、同一ユーザ又は同一チャネルの概周期関数符号（ａ１，ａ２，・・・ａＮ－１，ａＮ）は、同一の素数ρｋを用いて生成される。また、ユーザ又はチャネル毎に異なる素数を用いて異なる概周期関数符号が生成される。 The N periodic data codes (a 1 , a 2 ,... A N−1 , a N ) having a code length N are applied to the N pieces of data d 1 to d N. In addition, the approximate periodic function codes (a 1 , a 2 ,... A N−1 , a N ) of the same user or the same channel are generated using the same prime number ρ k . Different approximate periodic function codes are generated using different prime numbers for each user or channel.
　本実施形態では、送信データｄが複素数データであるとともに、概周期関数符号が複素符号であることを利用して、複素数データｄに対する概周期関数符号を複素乗算することで、送信データｄを変調する。複素乗算を行うことで、複素数データを構成する実部データｄＲと虚部データｄＩとを一括して変調できる。したがって、本実施形態によれば、実部データｄＲと虚部データｄＩとを別々の符号で変調する必要がない。したがって、本実施形態によれば、演算負荷が低下する。また、本実施形態によれば、変調に必要な符号の数を少なくできる。 In this embodiment, the transmission data d is modulated by complex multiplication of the approximate periodic function code with respect to the complex data d using the fact that the transmission data d is complex data and the approximate periodic function code is a complex code. To do. By performing the complex multiplication can be collectively modulate the real part data d R and the imaginary part data d I constituting the complex data. Therefore, according to this embodiment, it is not necessary to modulate the real part data d R and the imaginary part data d I in separate codes. Therefore, according to the present embodiment, the calculation load is reduced. Moreover, according to this embodiment, the number of codes required for modulation can be reduced.
　変調部２１は、複素数データに対して概周期関数符号を複素乗算する。変調部２１により生成される送信信号（変調信号）ｓは、ｓ＝ｄ１ａ１＋ｄ２ａ２＋ｄ３ａ３＋・・・＋ｄＮ－１ａＮ－１＋ｄＮａＮである。図３に示すように、変調部２１は、複数（Ｎ個）の複素乗算部２１ａと、複数の複素乗算部２１ａの出力を加算する加算器２１ｂと、を含んで構成することができる。各複素乗算部２１ａは、複素数であるｄｊと、同じく複素数であるａｊと、の複素乗算を行う。加算器２１ｂは、１からＮまでのｄｊａｊの総和を出力する。１～Ｎにおいてｄｊの値が同じ値ｄである場合、ｄｊａｊを、ｄａｊと表すこともできる。ｄｊａｊの総和が、変調部２１から送信信号（変調信号）として出力される。各複素乗算部２１ａによる複素乗算ｄｊａｊの演算式は、以下の式（２－１）～（２－３）のとおりである。
Figure JPOXMLDOC01-appb-M000002
 The modulation unit 21 multiplies complex data by an approximate periodic function code. The transmission signal (modulation signal) s generated by the modulation unit 21 is s = d 1 a 1 + d 2 a 2 + d 3 a 3 +... + D N−1 a N−1 + d N a N. As illustrated in FIG. 3, the modulation unit 21 may include a plurality (N) of complex multiplication units 21 a and an adder 21 b that adds outputs of the plurality of complex multiplication units 21 a. Each complex multiplier 21a performs complex multiplication of d j that is a complex number and a j that is also a complex number. The adder 21b outputs the sum of d j a j from 1 to N. When the value of dj is the same value d in 1 to N, d j a j can also be expressed as da j . The sum total of d j a j is output from the modulation unit 21 as a transmission signal (modulation signal). The arithmetic expressions of the complex multiplication d j a j by each complex multiplier 21a are as shown in the following expressions (2-1) to (2-3).
Figure JPOXMLDOC01-appb-M000002
　図４に示すように、変調部２１は、複素数データｄｊに対して概周期関数符号ａｊを複素乗算するだけでなく、複素データｄに対して、概周期関数符号ａｊとは異なる種類の複素符号ｂｊを複素乗算してもよい。この場合、変調部２１による複素乗算を式で表すと、ｄｊａｊｂｊとなる。変調部２１による複素乗算ｄｊａｊｂｊは、（ｄｊａｊ）を行ってから、（ｄｊａｊ）に対してｂｊを複素乗算することであってもよいし、（ｄｊｂｊ）を行ってから、（ｄｊｂｊ）に対してａｊを複素乗算することであってもよい。いずれも結果は同じである。 As shown in FIG. 4, the modulation unit 21 not only multiplies complex data d j by an approximate periodic function code a j but also different types of complex data d from the approximate periodic function code a j. The complex code b j may be complex multiplied. In this case, when the complex multiplication by the modulation unit 21 is expressed by an equation, d j a j b j . The complex multiplication d j a j b j performed by the modulation unit 21 may be (d j a j ) and then (d j a j ) multiplied by b j or (d j b j ) may be performed, and then (d j b j ) may be subjected to complex multiplication by a j . In both cases, the result is the same.
　概周期関数符号ａｊとは異なる種類の複素符号ｂｊが複素数データにｄｊに乗じられていることで、符号ｂｊが有する好ましい性質を変調信号に反映させて、より好適な変調信号を得るのが容易となる。概周期関数符号ａｊとは異なる種類の複素符号ｂｊは、例えば、複素平面上でパワー一定の符号であるのが好ましい。パワー一定の概周期関数符号ａｊにパワー一定の符号ｂｊを乗じても、パワーが変動しないので有利である。複素平面上でパワー一定の符号ｂｊは、例えば、複素平面上でパワー一定のカオス拡散符号又はＧｏｌｄ符号である。カオス拡散符号又はＧｏｌｄ符号は、良好な相関特性を有する。変調部２１が、カオス拡散符号又はＧｏｌｄ符号をデータｄｊに乗じることで、変調信号ｄｊａｊｂｊの相関特性を向上させることができる。 A complex code b j of a type different from the approximate periodic function code a j is multiplied by d j to the complex number data, so that the preferable property of the code b j is reflected in the modulation signal, and a more suitable modulation signal is obtained. Easy to get. It is preferable that the complex code b j of a type different from the approximate periodic function code a j is, for example, a code with constant power on the complex plane. Be multiplied by a constant power code b j to constant power almost periodic function code a j, it is advantageous because the power does not vary. The code b j with constant power on the complex plane is, for example, a chaotic spreading code or Gold code with constant power on the complex plane. Chaotic spreading codes or Gold codes have good correlation characteristics. The modulation unit 21 can improve the correlation characteristics of the modulation signal d j a j b j by multiplying the data d j by the chaotic spreading code or the Gold code.
　図５は、符号長Ｎ＝１００，ρｋ＝３，θρｋ＝０としたときの周期関数符号のＩＱコンスタレーション（符号遷移図）を示している。図５に示すＩＱコンスタレーションでは、外円と内円とに囲まれた領域が形成され、原点を含む内円内の領域は、空白となる。コンスタレーションが原点を通らないことは通信にとって有利である。なお、図５において、原点から外円までの半径の二乗が符号のパワーに相当する。図５から明らかなように、概周期関数符号においては、符号が全て単一の円（外円）上に存在し、パワー一定である。 FIG. 5 shows an IQ constellation (code transition diagram) of the periodic function code when the code length N = 100, ρ k = 3, θρ k = 0. In the IQ constellation shown in FIG. 5, a region surrounded by an outer circle and an inner circle is formed, and a region in the inner circle including the origin is blank. It is advantageous for communication that the constellation does not pass through the origin. In FIG. 5, the square of the radius from the origin to the outer circle corresponds to the power of the code. As is apparent from FIG. 5, in the almost periodic function code, all codes exist on a single circle (outer circle), and the power is constant.
　図６は、パワー一定のカオス拡散符号のＩＱコンスタレーションを示している。図６から明らかなように、図６のコンスタレーション中の黒丸が符号を示している。図６から明らかなように、パワー一定のカオス拡散符号においては、符号が全て単一の円上に存在し、パワー一定である。 FIG. 6 shows an IQ constellation of a chaotic spreading code with constant power. As is clear from FIG. 6, the black circles in the constellation of FIG. As is clear from FIG. 6, in the chaotic spreading code with constant power, all the codes exist on a single circle and the power is constant.
　図７は、復調部３１を示している。復調部３１は、受信信号ｒを、Ｎチップに分割して、Ｎ個のチップデータｒ１，ｒ２，・・・，ｒＮとし、Ｎ個のチップデータｒ１，ｒ２，・・・，ｒＮそれぞれを実部データｒＲと虚部データｒＩＩに分離する分離部３１ａと、実部データｒＲと虚部データｒＩＩで構成される各チップデータｒ１，ｒ２，・・・，ｒＮに対して、送信に用いられた概周期関数符号（ａ１，ａ２，・・・ａＮ－１，ａＮ）の複素共役（ａ１ ＊，ａ２ ＊，・・・ａＮ－１ ＊，ａＮ ＊）をかける演算部３１ｂと、を備えている。演算部３１ｂは、チップデータｒ１，ｒ２，・・・，ｒＮに対して、複素共役（ａ１ ＊，ａ２ ＊，・・・ａＮ－１ ＊，ａＮ ＊）を複素乗算する。演算部３１は、以下の式（３－１）に従った演算を行い、ｄＲとｄＩＩからなる再生データｄを得る。
Figure JPOXMLDOC01-appb-M000003
 FIG. 7 shows the demodulator 31. The demodulator 31 divides the received signal r into N chips to obtain N chip data r 1 , r 2 ,..., R N, and N chip data r 1 , r 2 ,. a separating portion 31a which separates each r N real part data r R and imaginary part data r I I, the real part data r R and imaginary part data r I each chip data r 1 comprised of I, r 2, .., R N , complex conjugates (a 1 * , a 2 * ,...) Of the approximate periodic function codes (a 1 , a 2 ,... A N−1 , a N ) used for transmission. A calculation unit 31b for multiplying a N-1 * , a N * ). The arithmetic unit 31b performs complex multiplication on the chip data r 1 , r 2 ,..., R N by complex conjugates (a 1 * , a 2 * ,... A N−1 * , a N * ). To do. Calculation unit 31 performs calculation according to the following formula (3-1), reproduction data d consisting of d R and d I I.
Figure JPOXMLDOC01-appb-M000003
　変調部２１にて概周期関数符号ａｊとは異なる種類の複素符号ｂｊがかけられている場合、復調部３１は、符号（ｂ１，ｂ２，・・・ｂＮ－１，ｂＮ）の複素共役（ｂ１ ＊，ｂ２ ＊，・・・ｂＮ－１ ＊，ｂＮ ＊）を、各チップデータｒ１，ｒ２，・・・，ｒＮに対して複素乗算する。この場合、演算部３１は、式（３－２）に従った演算を行い、再生データｄを得る。複素共役（ｂ１ ＊，ｂ２ ＊，・・・ｂＮ－１ ＊，ｂＮ ＊）は、チップデータｒ１，ｒ２，・・・，ｒＮに対して複素共役（ａ１ ＊，ａ２ ＊，・・・ａＮ－１ ＊，ａＮ ＊）が複素乗算された後に複素乗算してもよいし、チップデータｒ１，ｒ２，・・・，ｒＮに対して複素共役（ａ１ ＊，ａ２ ＊，・・・ａＮ－１ ＊，ａＮ ＊）が複素乗算される前に複素乗算してもよい。 When the modulation unit 21 is applied with a complex code b j of a type different from the approximate periodic function code a j , the demodulation unit 31 generates codes (b 1 , b 2 ,... B N−1 , b N complex conjugate (b 1 * a), b 2 *, ··· b N-1 *, the b N *), each chip data r 1, r 2, ···, complex multiplication with respect to r N. In this case, the calculation unit 31 performs a calculation according to the equation (3-2) to obtain reproduction data d. Complex conjugate (b 1 *, b 2 * , ··· b N-1 *, b N *) , the chip data r 1, r 2, · · ·, a complex conjugate with respect to r N (a 1 *, a 2 *, ··· a N- 1 *, a N *) is may be complex multiplication after being complex multiplication, complex conjugate with respect to the chip data r 1, r 2, ···, r N Complex multiplication may be performed before (a 1 * , a 2 * ,..., A N−1 * , a N * ) are complex multiplied.
　本実施形態では、概周期関数符号がかけられる送信データｄは、複素数データであるので、多値をとることが可能であり、送信データが２値のバイナリデータである場合に比べて、送信効率が良い。また、復調器３１では、復調処理によって、再生データとして複素数データを得ることができる。なお、複素数データｄにおいて、ｄＲ＝ｄＩでもよいし、ｄＩまたｄＲの一方はゼロでもよい。 In the present embodiment, the transmission data d to which the approximate periodic function code is applied is complex data, so it can take multiple values, and the transmission efficiency is higher than when the transmission data is binary binary data. Is good. Further, the demodulator 31 can obtain complex number data as reproduction data by demodulation processing. In the complex data d, d R = d I may be used, and one of d I or d R may be zero.
［２．３　概周期関数符号を用いた擬似直交多重通信］
　図８は、概周期関数符号を用いた擬似直交多重通信を行う通信機１００を示している。この通信機２０は、擬似直交多重信号の送受信が可能である。 [2.3 Pseudo-orthogonal multiplex communication using approximate periodic function code]
FIG. 8 shows a communication device 100 that performs pseudo-orthogonal multiplex communication using an approximately periodic function code. The communication device 20 can transmit and receive pseudo-orthogonal multiplexed signals.
　図８の通信機は、送信のため、変換器１０１と、擬似直交多重変調器１０２と、を備えている。変換器１０１は、例えば、シリアルパラレル変換器であり、シリアルの送信データを、チャネル（ユーザ）毎のデータ列（パラレルデータ列）に変換する。ここでは、チャネル数又はユーザ数をＫとする。データ列のデータ長（シンボル長）はＮである。Ｎは、概周期関数符号の符号長である。 8 includes a converter 101 and a quasi-orthogonal multiplex modulator 102 for transmission. The converter 101 is, for example, a serial / parallel converter, and converts serial transmission data into a data string (parallel data string) for each channel (user). Here, the number of channels or the number of users is K. The data length (symbol length) of the data string is N. N is the code length of the almost periodic function code.
　図８及び以下の説明において、データシンボルを示すｄｊ ｋは、ｋ番目のチャネル（又はｋ番目のユーザ）のための、ｊ番目のデータシンボル（送信符号）を示す。１≦ｋ≦Ｋであり、１≦ｊ≦Ｎである。なお、各ｄｊ ｋは、複素数データである。 In FIG. 8 and the following description, d j k indicating a data symbol indicates the j-th data symbol (transmission code) for the k-th channel (or k-th user). 1 ≦ k ≦ K and 1 ≦ j ≦ N. Each d j k is complex number data.
　つまり、第１チャネル（第１ユーザ）のデータ列は、（ｄ１ １，ｄ２ １，・・・，ｄＮ １）であり、第２チャネル（第２ユーザ）のデータ列は、（ｄ１ ２，ｄ２ ２，・・・，ｄＮ ２）であり、第ｋチャネル（第ｋユーザ）のデータ列は、（ｄ１ ｋ，ｄ２ ｋ，・・・，ｄＮ ｋ）であり、第Ｋ－１チャネル（第Ｋ－１ユーザ）のデータ列は、（ｄ１ Ｋ－１，ｄ２ Ｋ－１，・・・，ｄＮ Ｋ－１）であり、第Ｋチャネル（第Ｋユーザ）のデータ列は、（ｄ１ Ｋ，ｄ２ Ｋ，・・・，ｄＮ Ｋ）である。 That is, the data string of the first channel (first user) is (d 1 1 , d 2 1 ,..., D N 1 ), and the data string of the second channel (second user) is (d 1 2, d 2 2, ··· , a d N 2), a data row of the k-th channel (the k-th user) can be a (d 1 k, d 2 k , ···, d N k) , The data string of the K-1th channel (K-1th user) is (d 1 K−1 , d 2 K−1 ,..., D N K−1 ), and the Kth channel (Kth) The data string of (user) is (d 1 K , d 2 K ,..., D N K ).
　これらのＮ×Ｋ個のデータシンボルｄｊ ｋは、擬似直交多重変調部１０２に与えられ、擬似直交多重信号ｙを出力する。Ｎ×Ｋ個のデータシンボルｄｊ ｋから生成される擬似直交多重信号（送信信号）ｙは、Ｋチャネル×Ｋシンボル分の信号である。 These N × K data symbols d j k are given to the quasi-orthogonal multiplex modulation section 102 and output a quasi-orthogonal multiplex signal y. A quasi-orthogonal multiplexed signal (transmission signal) y generated from N × K data symbols d j k is a signal for K channels × K symbols.
　図８及び以下の説明において、各チャネルの送信シンボルを示すｙｉ ｊは、ｉ番目のチャネルにおける、ｊ番目のシンボルを示す。１≦ｉ，ｊ≦Ｋである。 In FIG. 8 and the following description, y i j indicating the transmission symbol of each channel indicates the j-th symbol in the i-th channel. 1 ≦ i, j ≦ K.
　つまり、送信信号ｙにおいて、第１チャネルの送信シンボル列は、（ｙ１ １、ｙ１ ２，・・・，ｙ１ Ｋ－１，ｙ１ Ｋ）であり、第２チャネルの送信シンボル列は、（ｙ２ １、ｙ２ ２，・・・，ｙ２ Ｋ－１，ｙ２ Ｋ）であり、第ｋチャネルの送信シンボル列は、（ｙｋ １、ｙｋ ２，・・・，ｙｋ Ｋ－１，ｙｋ Ｋ）であり、第Ｋ－１チャネルの送信シンボル列は、（ｙＫ－１ １、ｙＫ－１ ２，・・・，ｙＫ－１ Ｋ－１，ｙＫ－１ Ｋ）であり、第Ｋチャネルの送信シンボル列は、（ｙＫ １、ｙＫ ２，・・・，ｙＫ Ｋ－１，ｙＫ Ｋ）である。 That is, in the transmission signal y, the transmission symbol sequence of the first channel is (y 1 1 , y 1 2 ,..., Y 1 K−1 , y 1 K ), and the transmission symbol sequence of the second channel is , (Y 2 1 , y 2 2 ,..., Y 2 K−1 , y 2 K ), and the transmission symbol string of the k-th channel is (y k 1 , y k 2 ,..., Y k K−1 , y k K ), and the transmission symbol sequence of the K−1th channel is (y K−1 1 , y K−1 2 ,..., y K−1 K−1 , y K). −1 K ), and the transmission symbol string of the Kth channel is (y K 1 , y K 2 ,..., Y K K−1 , y K K ).
　擬似直交多重変調器１０２は、以下の式（４）に従って、Ｎ×Ｋ個のデータシンボルｄｊ ｋに対して、擬似直交多重変調処理を行い、擬似直交多重信号ｙを出力する。
Figure JPOXMLDOC01-appb-M000004
 The quasi-orthogonal multiplex modulator 102 performs quasi-orthogonal multiplex modulation processing on the N × K data symbols d j k according to the following equation (4), and outputs a quasi-orthogonal multiplex signal y.
Figure JPOXMLDOC01-appb-M000004
　擬似直交多重変調処理は、Ｎ×Ｋ個のデータシンボルｄｊ ｋに対して、大きさがＫ×Ｎである行列（変調行列）Ａをかける演算を行い、擬似直交多重信号ｙを得る。すなわち、擬似直交多重変調器１０２は、Ｋ個のデータ列からなる行列に対して、行列Ａを複素乗算する。行列のための複素乗算は、ａｊ ｋｄｊ ｋの複素乗算をＮ×Ｋ回行うことに相当する。行列Ａは、符号長Ｎの概周期関数符号（ａ１ ｋ，ａ２ ｋ，・・・，ａＮ－１ ｋ，ａＮ ｋ）をＫ個並べたものである。ここで、１≦ｋ≦Ｋである。Ｋ個の概周期関数符号は、チャネル数（ユーザ数）Ｋに対応して、Ｋ種類の異なる素数ρｋから生成される。 In the quasi-orthogonal multiplex modulation process, a calculation is performed by multiplying N × K data symbols d j k by a matrix (modulation matrix) A having a size of K × N to obtain a quasi-orthogonal multiplex signal y. That is, the quasi-orthogonal multiplex modulator 102 complex-multiplies the matrix A by a matrix composed of K data strings. Complex multiplication for a matrix corresponds to performing N × K complex multiplications of a j k d j k . The matrix A is obtained by arranging K pieces of approximately periodic function codes (a 1 k , a 2 k ,..., A N−1 k , a N k ) having a code length N. Here, 1 ≦ k ≦ K. The K approximate periodic function codes are generated from K different prime numbers ρ k corresponding to the number of channels (number of users) K.
　素数ρｋから生成される概周期関数符号ａｊ ｋは、次の式（５）で表される。なお、１≦ｊ≦Ｎである。
Figure JPOXMLDOC01-appb-M000005
 The approximate periodic function code a j k generated from the prime number ρ k is expressed by the following equation (5). Note that 1 ≦ j ≦ N.
Figure JPOXMLDOC01-appb-M000005
　擬似直交多重信号ｙの受信側では、復調処理によって、送信されたＮ×Ｋ個のデータシンボルｄｊ ｋを再生することができる。復調処理には、行列Ａの逆行列Ａ－１が用いられる。復調処理では、受信した擬似直交多重信号からＫシンボル分の信号ｙ（［数４］で示す式（４）における左辺に相当する信号）を取得し、Ｋシンボル分の信号ｙに対して逆行列Ａ－１をかけることで、再生されたＮ×Ｋ個のデータシンボルｄｊ ｋを得ることができる。ここでは、復調が行えるようにＫ≧Ｎとする。行列Ａの逆行列Ａ－１は、行列Ａを転置し、各行列要素ａｊ ｋの複素共役をとればよい。データ再生のために逆行列Ａ－１をかける演算は、複素乗算によって行われる。 On the receiving side of the quasi-orthogonal multiplexed signal y, the transmitted N × K data symbols d j k can be reproduced by demodulation processing. In the demodulation process, an inverse matrix A −1 of the matrix A is used. In the demodulation processing, a signal y for K symbols (a signal corresponding to the left side in Equation (4) shown in [Expression 4]) is acquired from the received pseudo orthogonal multiplexed signal, and an inverse matrix is obtained for the signal y for K symbols. By multiplying by A- 1 , it is possible to obtain N × K reproduced data symbols d j k . Here, K ≧ N so that demodulation can be performed. The inverse matrix A −1 of the matrix A may be obtained by transposing the matrix A and taking the complex conjugate of each matrix element a j k . The operation of multiplying the inverse matrix A −1 for data reproduction is performed by complex multiplication.
１０　通信機
２０　送信機
２１　変調部
３０　受信機
３１　復調部
１００　通信機
１０１　変換部
１０２　擬似直交多重変調部 DESCRIPTION OF SYMBOLS 10 Communication apparatus 20 Transmitter 21 Modulation part 30 Receiver 31 Demodulation part 100 Communication apparatus 101 Conversion part 102 Pseudo orthogonal multiplexing modulation part

Claims (11)

  1. 　通信方法であって、
    　データを符号で変調して生成された信号を送信することを含み、
    　前記符号は、概周期関数符号であり、
    　前記データは、実部データと虚部データを有する複素数データであり、
    　前記変調は、前記複素数データに対して前記概周期関数符号をかける演算を含む
    　通信方法。     A communication method,
    Transmitting a signal generated by modulating data with a code;
    The code is an approximately periodic function code;
    The data is complex data having real data and imaginary data,
    The communication method includes a calculation of multiplying the complex data by the approximate periodic function code.
  2. 　前記複素数データに対して前記概周期関数符号をかける演算は、前記複素数データに対して複素数で表される前記概周期関数符号を複素乗算することを含む
    　請求項１に記載の通信方法。     The communication method according to claim 1, wherein the operation of multiplying the complex data by the approximate periodic function code includes complex multiplication of the complex data by the approximate periodic function code represented by a complex number.
  3. 　Ｎが前記概周期関数符号の符号長を表し、ｊが１以上Ｎ以下の整数であり、ａｊが符号長Ｎの前記概周期関数符号を表し、ｄが前記複素数データを表すときに、
    　前記複素数データに対して前記概周期関数符号をかける演算は、１～Ｎまでのそれぞれのｊについて、ｄａｊで示される複素乗算をすることを含む
    　請求項１又は２に記載の通信方法。     N represents the code length of the approximate periodic function code, j is an integer of 1 to N, a j represents the approximate periodic function code of code length N, and d represents the complex data,
    The communication method according to claim 1, wherein the operation of multiplying the complex number data by the approximate periodic function code includes performing a complex multiplication represented by da j for each j of 1 to N.
  4. 　Ｎが前記概周期関数符号の符号長を表し、ｊが１以上Ｎ以下の整数であり、ａｊが符号長Ｎの前記概周期関数符号を表し、ｄが前記複素数データを表すときに、
    　前記複素数データに対して前記概周期関数符号をかける演算は、Ｎ個のｄａｊの総和を算出することを含む
    　請求項１～３のいずれか１項に記載の通信方法。     N represents the code length of the approximate periodic function code, j is an integer of 1 to N, a j represents the approximate periodic function code of code length N, and d represents the complex data,
    The communication method according to any one of claims 1 to 3, wherein the operation of multiplying the complex data by the approximate periodic function code includes calculating a sum of N da j .
  5. 　前記変調は、前記複素数データに対して、前記概周期関数符号とは異なる複素符号を複素乗算することを更に含み、
    　前記複素符号は、複素平面上でパワー一定の符号である
    　請求項２～４のいずれか１項に記載の通信方法。     The modulation further includes complex-multiplying the complex data with a complex code different from the approximate periodic function code;
    The communication method according to any one of claims 2 to 4, wherein the complex code is a code having constant power on a complex plane.
  6. 　前記変調は、前記概周期関数符号を用いたスペクトル拡散変調である
    　請求項１～５のいずれか１項に記載の通信方法。     The communication method according to any one of claims 1 to 5, wherein the modulation is spread spectrum modulation using the approximate periodic function code.
  7. 　前記信号を受信して復調することを更に含み、
    　前記復調は、受信した前記信号に前記概周期関数の複素共役をかけて、前記データを再生することを含む
    　請求項６記載の通信方法。     Further comprising receiving and demodulating the signal;
    The communication method according to claim 6, wherein the demodulation includes reproducing the data by multiplying the received signal by a complex conjugate of the approximate periodic function.
  8. 　前記変調は、前記概周期関数符号を用いた擬似直交多重変調である
    　請求項１記載の通信方法。     The communication method according to claim 1, wherein the modulation is quasi-orthogonal multiple modulation using the approximate periodic function code.
  9. 　Ｋが、チャネル数又はユーザ数を表し、Ｎが、データ列を構成する複素数データの数を表すときに、
    　前記疑似直交多重変調は、Ｋ個のデータ列に対して、大きさがＫ×Ｎの行列を複素乗算することを含み、
    　前記行列は、符号長Ｎの前記概周期関数符号をＫ個有する
    　請求項８記載の通信方法。     When K represents the number of channels or the number of users, and N represents the number of complex data constituting the data sequence,
    The quasi-orthogonal multiplex modulation includes complex multiplication of a matrix having a size of K × N with respect to K data strings,
    The communication method according to claim 8, wherein the matrix has K approximately periodic function codes having a code length of N.
  10. 　前記信号を受信して復調することを更に含み、
    　前記復調は、擬似直交多重変調に用いられた行列の逆行列をかけて、前記データを再生することを含む
    　請求項８又は９記載の通信方法。     Further comprising receiving and demodulating the signal;
    The communication method according to claim 8 or 9, wherein the demodulation includes reproducing the data by applying an inverse matrix of a matrix used for quasi-orthogonal multiplex modulation.
  11. 　通信機であって、
    　データを符号で変調する変調部を備え、
    　前記符号は、概周期関数符号であり、
    　前記データは、実部データと虚部データを有する複素数データであり、
    　前記変調部は、前記複素数データに対して概周期関数符号をかける演算処理を行う
    　通信機。     A communication device,
    A modulation unit for modulating data with a code;
    The code is an approximately periodic function code;
    The data is complex data having real data and imaginary data,
    The modulation unit is a communication device that performs arithmetic processing for multiplying the complex data by an approximate periodic function code.
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