JP2008070727A - Random number sequence group generator, communication system, random number sequence group generating method, communication method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a random number sequence group generator or the like for generating a random number sequence group consisting of a plurality of random number sequences having a lowest possible correlation with each other. <P>SOLUTION: In the random number sequence group generator 101: a plurality of random number sequence generating sections 102 respectively output, as a random number sequence, the result of applying a prescribed modification function to a pseudo random number generated by using a recurrence formula; an initialization section 103 assigns an initial value for generating random numbers to each of the plurality of random number sequence generating sections 102; and an independent component analysis section 104 performs independent component analysis of the plurality of random number sequences and outputs a plurality of new random number sequences. Preferably, a Chebyshev polynomial can be used as the recurrence formula to be used by the random number sequence generating section 102 so that the orders are made different from each other, and the initial values assigned by the initialization section 103 are made different from each other. When a function satisfying super-efficiency conditions is applied as the modification function, the signal-to-noise ratio when the random number sequence is used as a spread code is particularly enhanced. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a random number sequence group generation apparatus, a random number sequence group generation method suitable for generating a random number sequence group composed of a plurality of random number sequences that have as low correlation as possible, a communication system using an incoming generated random number sequence group, The present invention relates to a communication method and a program for realizing these on a computer.

Conventionally, various methods for generating a random number sequence using a recurrence formula have been proposed. In such a method of generating a random number sequence, a recurrence formula function F (・) is appropriately determined, and an initial value x ₁ is given to the recurrence formula function F (
x _{i + 1} = F (x _i )
Iterative calculation based on
x ₁ , x ₂ , x ₃ , x ₄ ,…
Is what you get. This random number sequence is
x ₁ , F (x ₁ ), F (F (x ₁ )), F (F (F (x ₁ ))), ...
Or
x ₁ , F (x ₁ ), F ² (x ₁ ), F ³ (x ₁ ),…
It can also be written as

The inventors have continued research on the usefulness of chaotic random numbers using Chebyshev polynomials (also referred to as “Chebyshev map”) as a recurrence function, and disclosed the technique in the following documents.
JP 2001-060937 A Ken Umeno, Effectiveness of Chaotic Randomness in Monte Carlo Method, The Institute of Electrical Engineers of Japan, Information Processing Society of Japan, IP-99-7, P.29-36, March 19-20, 1999

  [Patent Document 1] discloses a technique of direct spread spectrum communication using a random number sequence generated by using the Chebyshev map as a spreading code.

  [Non-Patent Document 1] discloses a technique for performing numerical integration by a Monte Carlo method using a random number sequence generated using Chebyshev mapping, and a super-efficiency condition for speeding up convergence of numerical integration Is presented.

  On the other hand, in code division multiplex communication and orthogonal division multiplex communication, a technique of performing spreading using a different spreading code for each subchannel (also referred to as “subcarrier”) has been widely used.

  In the field of such communication technology, when a random number sequence is used as a spreading code, especially when code spreading is performed for each subchannel, a large number of random number sequences are required, but the correlation between the random number sequences is low. Is preferable in terms of improving communication performance.

  Therefore, there is a strong demand for a technique for reducing the correlation between these random number sequences after preparing a plurality of random number sequences, that is, a group of random number sequences.

  The present invention solves the above-described problems, and is suitable for generating a random number sequence group composed of a plurality of random number sequences having a correlation as low as possible, and a random number sequence group generation method It is an object of the present invention to provide a communication system, a communication method, and a program that realizes these on a computer using a random number sequence group that has been generated.

  In order to achieve the above object, the following invention is disclosed in accordance with the principle of the present invention.

  The random number sequence group generation device according to the first aspect of the present invention includes a plurality of random number sequence generation units, an initial setting unit, and an independent component analysis unit, and is configured as follows.

  Here, each of the plurality of random number sequence generation units includes a storage unit, an initialization unit, an output unit, a calculation unit, and an update unit.

  The storage unit temporarily stores the pseudo random number value.

  On the other hand, the initialization unit stores the given initial value in the storage unit as a pseudorandom value and initializes it.

  Further, each time the pseudo random number value is stored in the storage unit, the output unit outputs the random number included in the value random number sequence obtained by applying the correction function to the stored pseudo random number value.

  Then, when the output unit outputs a random number, the calculation unit calculates a result of applying a recurrence function that is associated in advance with the random number sequence generation unit to the pseudo-random number value stored in the storage unit.

  On the other hand, the update unit updates the calculation result of the calculation unit by storing it in the storage unit as a pseudo random number value.

  Further, the initial setting unit gives an initial value to each of the plurality of random number sequence generation units.

  Then, the independent component analysis unit analyzes the plurality of random number sequences output from each of the plurality of random number sequence generation units as an input sequence group, and outputs the resulting output sequence group as a random number sequence group.

  Further, in the random number sequence group generation device of the present invention, the independent component analysis unit is configured to analyze the plurality of random number sequences output from each of the plurality of random number sequence generation units for each predetermined length. be able to.

  Further, in the random number sequence group generation device of the present invention, at least one of the recurrence formula functions associated in advance with each of the plurality of random number sequence generation units can be configured to be a chaotic map.

Further, in the random number sequence group generation device of the present invention, for each of the plurality of random number sequence generation units, the correction function S _i (•) associated with the i (i ≧ 1) th random number sequence generation unit is:
S _i (x) = x
It can be configured to be.

  In addition, the random number sequence group generation device of the present invention can be configured as follows.

That is, for the integer a
T _a (cosθ) = cos (aθ)
A-th order Chebyshev polynomial T _a (·) defined as

On the other hand, for each of the plurality of random number sequence generation units, the i (i ≧ 1) -th random number sequence generation unit has a recurrence function F _i (•) and a correction function S _i (•), which are predetermined. Of an integer sequence a [1], a [2],... And a predetermined integer sequence b [1], b [2],..., An i-th value a [i], b [i] (a [i ] ≧ 2, b [i] ≧ 2), and the recurrence function F _i (·) is
F _i (x) = T _{a [i]} (x)
And the correction function S _i (·) is
S _i (x) = T _{b [i]} (x)-T ₁ (x)
It is.

Further, in the random number sequence group generation device of the present invention, for the number N of a plurality of random number sequence generation units, for integers i, j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N),
a [i] ≠ a [j]
It can be configured to be.

Further, in the random number sequence generation device of the present invention, for the number N of the plurality of random number sequence generation units, for integers i, j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N),
a [i] = a [j]
The initial value setting unit gives different initial values to the plurality of random number generation units. It can be constituted as follows.

Further, in the random number sequence group generation device of the present invention, for each integer i (i ≧ 1), the i-th value q [i] in the predetermined integer sequence q [1], q [2],. q [i] ≧ 2)
b [i] = a [i] ^{q [i]}
It can be configured to be.

  A communication system according to another aspect of the present invention includes a transmission device and a reception device, and is configured as follows.

  That is, each of the random number sequences included in the random number sequence group output by the above random number sequence group generation device is associated with each subchannel of multicarrier communication.

  On the other hand, the transmission apparatus performs code spreading using a random number sequence associated with the subchannel as a spreading code.

  Further, the receiving apparatus performs code despreading using a random number sequence associated with the subchannel as a spreading code.

  In the communication system of the present invention, the multicarrier communication can be configured to be orthogonal frequency division multiplex communication.

  A random number sequence group generation method according to another aspect of the present invention is executed by a random number sequence group generation device including a plurality of random number sequence generation units, an initial setting unit, and an independent component analysis unit, and a random number sequence generation step, An initial setting step and an independent component analysis step are provided and configured as follows.

  That is, each of the plurality of random number sequence generation units includes a storage unit, an initialization unit, an output unit, a calculation unit, and an update unit, and the pseudo random number value is temporarily stored in the storage unit.

  On the other hand, in the random number sequence generation process, an initialization process, an output process, a calculation process, and an update process are executed in each of the plurality of random number sequence generation units.

  Here, in the initialization step, the initialization unit stores the given initial value as a pseudorandom value in the storage unit and initializes it.

  On the other hand, in the output process, every time a pseudorandom value is stored in the storage unit, the stored pseudorandom value or a random number included in a value random number sequence obtained by applying a correction function to the pseudorandom value Output.

  Further, in the calculation step, when the calculation unit outputs a random number in the output step, a result of applying a recurrence function that is associated in advance with the random number sequence generation unit to the pseudo random number value stored in the storage unit is obtained. calculate.

  In the update process, the update unit stores the calculation result in the calculation process in the storage unit as a pseudorandom value and updates it.

  On the other hand, in the initial setting step, the initial setting unit gives an initial value to each of the plurality of random number sequence generation units.

  Further, in the independent component analysis step, the independent component analysis unit performs independent component analysis using a plurality of random number sequences output from each of the plurality of random number sequence generation units as an input sequence group, and the resulting output sequence group is a random number. Output as a group of columns.

  Moreover, in the random number sequence group generation method of the present invention, the independent component analysis step is configured to analyze the plurality of random number sequences output from each of the plurality of random number sequences for each predetermined length. Can do.

  Moreover, in the random number sequence group generation method of the present invention, at least one of the recurrence formula functions associated in advance with each of the plurality of random number sequence generation units can be configured to be a chaotic map.

In the random number sequence group generation method of the present invention, for each of a plurality of random number sequence generation units, the correction function S _i (•) associated with the i (i ≧ 1) -th random number sequence generation unit is:
S _i (x) = x
It can be configured to be.

  The random number sequence group generation method of the present invention can be configured as follows.

That is, for the integer a
T _a (cosθ) = cos (aθ)
A-th order Chebyshev polynomial T _a (·) defined as

On the other hand, for each of the plurality of random number sequence generation units, the i (i ≧ 1) -th random number sequence generation unit has a recurrence function F _i (•) and a correction function S _i (•), which are predetermined. Of an integer sequence a [1], a [2],... And a predetermined integer sequence b [1], b [2],..., An i-th value a [i], b [i] (a [i ] ≧ 2, b [i] ≧ 2)

The recurrence function F _i (
F _i (x) = T _{a [i]} (x)
And the correction function S _i (·) is
S _i (x) = T _{b [i]} (x)-T ₁ (x)
It is.

Further, in the random number sequence generation method of the present invention, for the number N of a plurality of random number sequence generation units, for integers i, j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N),
a [i] ≠ a [j]
It can be configured to be.

Further, in the random number sequence generation method of the present invention, for the number N of a plurality of random number sequence generation units, for integers i, j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N),
a [i] = a [j]
In the initial value setting step, different initial values can be provided to a plurality of random number generators.

In the random number sequence group generation method of the present invention, for each integer i (i ≧ 1), the i-th value q [i] in the predetermined integer sequence q [1], q [2],. q [i] ≧ 2)
b [i] = a [i] ^{q [i]}
It can be configured to be.

  A communication method according to another aspect of the present invention includes a transmission step and a reception step, and is configured as follows.

  That is, each of the random number sequences included in the random number sequence group output by the random number sequence group generation method is associated with each subchannel of multicarrier communication.

  On the other hand, in the transmission step, code spreading is performed using a random number sequence associated with the subchannel as a spreading code.

  Further, in the receiving step, code despreading is performed using a random number sequence associated with the subchannel as a spreading code.

  In the communication method of the present invention, the multicarrier communication can be configured to be orthogonal frequency division multiplex communication.

  A program according to another aspect of the present invention causes a computer to function as the above-described random number sequence group generation device, a transmission device of a communication system, and a reception device of a communication system. The transmitting step in the method and the receiving step in the communication method are executed.

  The program can be recorded on a computer-readable information recording medium (including a compact disk, flexible disk, hard disk, magneto-optical disk, digital video disk, magnetic tape, or semiconductor memory).

  The information recording medium can be distributed and sold independently of the computer, and the program itself can be distributed and sold via a computer communication network such as the Internet.

  According to the present invention, it is possible to provide a cryptographic transmission system, a transmission device, a reception device, a transmission method, a reception method, and a program that realizes these on a computer, which are suitable for encrypting and transmitting information. .

  Embodiments of the present invention will be described below. The embodiments described below are for illustrative purposes and do not limit the scope of the present invention. Accordingly, those skilled in the art can employ embodiments in which each or all of these elements are replaced with equivalent ones, and these embodiments are also included in the scope of the present invention. .

  FIG. 1 is an explanatory diagram showing a schematic configuration of an embodiment of a random number sequence group generation device of the present invention. Hereinafter, a description will be given with reference to FIG.

  The random number sequence group generation apparatus 101 according to the present embodiment includes a plurality (hereinafter referred to as N (N ≧ 2)) of random number sequence generation units 102, an initial setting unit 103, and independent component analysis units 104. The random number sequence group generation apparatus 101 is, for example, a computer having a CPU (Central Processing Unit), a RAM (Random Access Memory), and various input / output devices, a ROM (Read Only Memory), an EEPROM (Electrically Erasable Programmable ROM), a hard disk These units are realized by executing a program recorded on an information recording medium such as a combination of various electronic circuits, for example, an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), It is also possible to configure the random number sequence group generation device 101 according to the present embodiment by a DSP (Digital Signal Processor) or the like.

  First, each of the plurality of random number generators 102 outputs a random number sequence when given an initial value.

  FIG. 2 is a schematic diagram showing a schematic configuration of one random number sequence generation unit 102. Hereinafter, a description will be given with reference to FIG. In order to facilitate understanding, the following description will be made assuming that the random number sequence generation unit 102 is the i (1 ≦ i ≦ N) th of N.

  Each of the random number sequence generation units 102 includes a storage unit 201, an initialization unit 202, an output unit 203, a calculation unit 204, and an update unit 205.

  Here, the storage unit 201 temporarily stores a pseudo random number value. Therefore, it is generally constituted by a RAM, a flash memory, a hard disk or the like, but can also be constituted by a latch circuit or the like.

  On the other hand, the initialization unit 202 initializes the given initial value by causing the storage unit 201 to store it as a pseudo random number value. The random number sequence generation unit 102 is given an initial value from the outside. This value is written in the storage unit. Therefore, the CPU generally functions as the initialization unit 202 in cooperation with the RAM or the like.

Further, every time a pseudo random number value is stored in the storage unit 201, the output unit 203 outputs a random number included in a value random number sequence obtained by applying the correction function S _i (•) to the stored pseudo random number value. The output by the output unit 203 corresponds to a process of acquiring the value every time some overwriting is performed on the storage unit 201. Therefore, the CPU generally functions as the initialization unit 202 in cooperation with the RAM or the like.

The simplest correction function S _i (・) is
S _i (x) = x
This means that the value written in the storage unit 201 is output as it is. Other aspects of the correction function S _i (•) will be described later.

Then, when the output unit 203 outputs a random number, the calculation unit 204 calculates a recurrence function F _i (•) associated with the random number sequence generation unit 102 in advance to the pseudo random number value stored in the storage unit 201. Calculate the applied result.

That is, at a certain time t, when the value stored in the storage unit 201 is x _t ,
x _{t + 1} = F _i (x _t )
And x _{t + 1} obtained as a result of the calculation is written into the storage unit 201 in a later process. Therefore, the CPU generally functions as the calculation unit 204 in cooperation with the RAM or the like.

Since pseudorandom numbers are generated by the recurrence formula, if the same initial value x ₁ is given, the pseudorandom number sequence obtained after that
x ₁ , x ₂ , x ₃ , x ₄ , ...
Will give the same result. Therefore, the initial value x ₁ can be used as a kind of “shared key” by sharing it on both sides in encryption and decryption, for example.

For the recurrence function F _i (•), use various functions that generate pseudo-random numbers, such as the recurrence function by the linear congruential method, the Chebyshev polynomial, the function of the recurrence formula by the Mersenne Twister method, etc. Can do. The recurrence function assigned to each random number sequence generator 102 is generally different, and it is common to use different orders for those with orders such as Chebyshev polynomials. However, it is also possible to use a mixture of functions of completely different families (for example, linear congruential methods and Chebyshev polynomials).

In the following, in order to facilitate understanding, a Chebyshev polynomial will be described as an example. An a-order Chebyshev polynomial for an integer a is
T _a (cosθ) = cos (aθ)
It is a function defined as
T ₀ (x) = 1;
T ₁ (x) = x;
^{_{T 2 (x) = 2x 2}} - 1;
^{_{T 3 (x) = 4x 3}} - 3x; ...
It is a function defined as

  FIG. 3 is an explanatory diagram showing Chebyshev polynomials from the second order to the fifth order in a graph. Hereinafter, a description will be given with reference to FIG.

As shown in this figure, Chebyshev polynomials y = T _a (x) of second order or higher map open interval -1 <x <1 to open interval -1 <y <1, and close interval -1 It is a rational mapping that maps ≦ x ≦ 1 to the closed interval −1 ≦ y ≦ 1. A random number obtained using such a Chebyshev polynomial is called a chaotic random number, and the inventors have studied its characteristics.

An integer a [i] (a [i] ≧ 2) is assigned to the i-th random number sequence generation unit 102 as the order of the Chebyshev polynomial. This order may be different for each random number sequence generator 102, or may be the same for all random number sequence generators 102. That is, for any 1 ≦ i ≦ N, 1 ≦ j ≦ N, i ≠ j,
a [i] ≠ a [j]
It is also good. For any 1 ≦ i ≦ N, 1 ≦ j ≦ N, i ≠ j,
a [i] = a [j]
It is also good.

On the other hand, the update unit 205 updates the calculation result of the calculation unit 204 by causing the storage unit 201 to store the calculation result as a pseudo random number value. That is, when the next x _{t + 1} is calculated from x _t, writes the value in the storage unit 201. Therefore, the CPU generally functions as the update unit 205 in cooperation with the RAM or the like.

  The written value is output from the output unit 203 when the value is written by the initialization unit 202 or the value is written by the update unit 205.

As described above, the output unit 203 uses the correction function S _i (•). However, a Chebyshev polynomial may be used as the correction function S _i (•). At this time, it is assumed that an integer b [i] (b [i] ≧ 2) is assigned to the i-th random number sequence generation unit 102 as the order of the Chebyshev polynomial.
S _i (x) = T _{b [i]} (x)-T ₁ (x)
= T _{b [i]} (x)-x
Can be adopted, especially for any i
b [i] = 4
It can be.

  This is a modification for satisfying the property called “super-efficiency condition”, and other examples that satisfy the super-efficiency condition will be described later.

As described above, N random number generators 102 are prepared, but the initial setting unit 103 sets initial values for the i-th one among the plurality of random number generators 102.
x _{i, 1}
give. That is, the initial value prepared by the initial setting unit 103 is
x _{i, 1} , x _{i, 2} , x _{i, 3} , ..., x _{i, N}
N.

When the recurrence formula functions assigned to the N random number sequence generators 102 are different from each other,
x _{i, 1} = x _{i, 2} = x _{i, 3} =… = x _{i, N}
Although all the initial values may be equal, typically, the initial values are different from each other. That is, for any 1 ≦ i ≦ N, 1 ≦ j ≦ N, i ≠ j,
x _{i, 1} ≠ x _{j, 1}
And

Thus the initial value
x _{i, 1} , x _{i, 2} , x _{i, 3} , ..., x _{i, N}
Is given to each random number sequence generator 102, the first random number sequence generator 102 receives a random number sequence.
x _1,1 , x _1,2 , x _1,3 , x _1,4 ,…
Is output from the second random number sequence generator 102.
x _2,1 , x _2,2 , x _2,3 , x _2,4 ,…
Are output, and the random number sequence from the i-th random number sequence generation unit 102
x _{i, 1} , x _{i, 2} , x _{i, 3} , x _{i, 4} ,…
Are output, and the random number sequence from the Nth random number sequence generation unit 102
x _{N, 1} , x _{N, 2} , x _{N, 3} , x _{N, 4} , ...
And a total of N random number sequences (collectively referred to as “random number sequence group”) are output.

  Then, the independent component analysis unit 104 performs an independent component analysis using the N random number sequences output from each of the N random number sequence generation units 102 as an input sequence group, and outputs the resulting output sequence group as a random number sequence group. Output as.

  Independent component analysis was originally studied in the field of signal separation, and the most typical and ideal application is the audio signal of the entire song played by the orchestra in different locations with N microphones. If you record and analyze the independent components, you can get the sound of the part that played each of the N instruments. Such a technique is called BSS (Blind Source Separation).

  In the present invention, N random number sequences are used as an input sequence group for independent component analysis, and this is analyzed as an independent component analysis to obtain N output sequence groups.

  Here, when a different recurrence function is applied to each random number sequence generator 102, the correlation between the respective random number sequences is relatively low. Therefore, the result of independent component analysis is often obtained by slightly correcting the input series group and reducing the correlation between them.

  Therefore, it can be considered that the output sequence group is also N random number sequences, and moreover, it is “independent of each other” than the input sequence group, and therefore, “lower correlation” can be expected.

  Even if the result of the independent component analysis is further analyzed by the independent component analysis, no further separation occurs, so the number of effective independent component analysis is one.

  In general, it is necessary to determine the length of the input series group for independent component analysis. Therefore, for each length (number of chips) of a spreading code superimposed on one symbol in code division multiplexing or orthogonal frequency division multiplexing, each random number sequence included in the input sequence group is divided and independent for each length. It is common to perform component analysis.

  In addition, when used as a spreading code in a communication device, a random number sequence group having a spreading code length obtained at several intervals (typically the first interval) may be used repeatedly. A random number sequence group having a spreading code length may be used in that order.

  Furthermore, the delimiter length may be a multiple of the spreading code length, or a method of setting an appropriate length unrelated to the spreading code length may be employed.

  It should be noted that such a separation is not necessarily required when using an adaptive independent component analysis method for analyzing an independent component of an infinite length signal sequence.

Random number sequence group that is an input series group
_{x 1,1, x 1,2, x 1,3} , x 1,4, ...,
x _2,1 , x _2,2 , x _2,3 , x _2,4 , ...
......,
x _{i, 1} , x _{i, 2} , x _{i, 3} , x _{i, 4} , ...,
......,
x _{N, 1} , x _{N, 2} , x _{N, 3} , x _{N, 4} , ...
Is a random number sequence group that is the same number and length of output sequence groups.
y _1,1 , y _1,2 , y _1,3 , y _1,4 , ...
y _2,1 , y _2,2 , y _2,3 , y _2,4 , ...,
......,
y _{i, 1} , y _{i, 2} , y _{i, 3} , y _{i, 4} , ...,
......,
y _{N, 1} , y _{N, 2} , y _{N, 3} , y _{N, 4} , ...
Is obtained.

The y _{i, t} is a spreading code that is superimposed on the i-th subchannel (subcarrier) in code division multiplex communication or orthogonal frequency division multiplex communication. It is expected to improve. The result of the numerical simulation will be described later.

  Hereinafter, an embodiment of a communication system that uses the random number sequence group generation apparatus 101 will be described.

  FIG. 4 is a schematic diagram showing a schematic configuration of the communication system according to the present embodiment. Hereinafter, a description will be given with reference to FIG.

  A communication system 401 according to the present embodiment includes a transmission device 411 and a reception device 421.

  In the communication system 401 of the present invention, division multiplexing communication using N subcarriers is performed. Therefore, in the transmission device 411, the transmission signal is decomposed by the transmission side decomposition unit 412, and the spreading unit 413 performs spreading using the random number sequence generated by the random number sequence group generation device 101 for each subcarrier as a spreading code, The transmission side combining unit 414 combines the spread signals, and the transmitting unit 415 transmits the signals.

  On the other hand, in the reception device 421, the signal received by the reception unit 422 is decomposed by the reception side decomposition unit 423, and the despreading unit 424 spreads the random number sequence generated by the random number sequence group generation device 101 for each subcarrier. Despreading is performed as a code, and despread signals are combined by the receiving side combining unit 425 to obtain a transmission signal.

  Here, in the transmitting device 411 and the receiving device 421 that communicate with each other, the initial setting unit 103 of the random number sequence group generation device 101 included in each device outputs the same initial value. As a result, the same spreading code is assigned to the same subcarrier.

  There are various methods such as code division multiplexing, orthogonal frequency division multiplexing, time division multiplexing, etc., but the transmission signal is decomposed into subcarriers on the transmission side, each subcarrier is spread with a corresponding spreading code, The process of combining and transmitting and decomposing the received signal into subcarriers on the receiving side, despreading each subcarrier with the corresponding spreading code, and combining is common.

  FIG. 5 is an explanatory diagram showing a detailed configuration when the communication system is code division multiplex communication. Hereinafter, a description will be given with reference to FIG.

  As shown in the figure, the transmission side decomposition unit 412 includes a serial / parallel conversion unit 511 that performs serial / parallel conversion, and the transmission side combining unit 414 includes an addition unit 512 that adds signals.

  On the other hand, the reception side decomposition unit 423 is configured by a branching unit 521 that branches and duplicates a received signal into a plurality of signals, and the reception side coupling unit 425 is configured by a parallel / serial conversion unit 522 that performs parallel-serial conversion.

  FIG. 6 is an explanatory diagram showing a detailed configuration when the communication system is orthogonal frequency division multiplex communication. Hereinafter, a description will be given with reference to FIG.

  As shown in the figure, the transmission side decomposition unit 412 includes a serial-parallel conversion unit 611 that performs serial-parallel conversion, and an inverse Fourier transform unit 612 that performs inverse Fourier transform on this, after which each subcarrier is spread. Is done. The transmission side coupling unit 414 includes a parallel / serial conversion unit 613 that performs parallel / serial conversion on each signal.

  On the other hand, the reception side decomposition unit 423 is configured by a serial / parallel conversion unit 621 that performs serial / parallel conversion, and the reception side combining unit 425 includes a Fourier transform unit 622 that performs a Fourier transform on each subcarrier after despreading, It is comprised by the parallel-serial conversion part 623 which performs parallel-serial conversion.

  Note that the order of inverse Fourier transform and spreading may be reversed on the transmission side, and the order of despreading and Fourier transform may be reversed on the reception side.

  Hereinafter, the performance when the random number sequence generated by the random number sequence group generation device 101 is used as a spreading code will be described in detail.

  In order to identify a target signal from the mixed signals, it is necessary to suppress inhibition due to interference noise of other signals. For this reason, it is necessary to generate a spreading code that reduces interference noise. The random number sequence group generation apparatus 101 generates a random number sequence suitable for such a purpose as a spreading code.

It can be seen from the signal-to-noise ratio SNR how much interference noise is suppressed with respect to the length of the code and the number of users when a certain code S is used. Here, the statistical average for the code S is expressed as << S >>, the number of codes existing simultaneously is K (corresponding to the number of random number generation units 102 in the random number sequence group generation device 101), and the code length is N. (Corresponding to the length that the independent component analysis unit 104 divides), and if each code is S _{i, j} (0 ≦ i ≦ K−1, 1 ≦ j ≦ N),
SNR = ≪Σ _{j = 1} ^N S _{0, j} ² ≫ / [<< Σ _{i = 1} ^K-1 (Σ _{j = 1} ^N S _{0, j} S _{i, j} ) ² ≫] ^1/2
It becomes.

In general, the signal-to-noise ratio SNR _ICA when the code S is subjected to independent component analysis is analytically
SNR _ICA = [1 + << Avg (S ₀ ) ² >>] / [<< Σ _{i = 1} ^K-1 (Avg (S ₀ ) Avg (S _i )) ² >>] ^1/2 ;
Avg (S _i ) = Σ _{j = 1} ^N S _{i, j} / N
It can be shown as follows.

Now, the code S ^A _{i, j} of the i-th channel at time j is expressed using the Chebychev polynomial as a recurrence function.
S ^A _{i, j + 1} = T _{a [i]} (S ^A _{i, j} );
And for any i ≠ j
a [i] ≠ a [j]
Setting either as, or as giving different initial values to each other, when relaxed restrictions on order, the signal-to-noise ratio SNR ^A of this code S ^A is
SNR ^A = (N / (K-1)) ^1/2
It becomes.

On the other hand, for the average value of this code,
[Avg (S ^A _i )] ² = 1 / N
Is known to hold.

Therefore, the signal-to-noise ratio SNR ^A _ICA when combining Chebyshev polynomials and S ^A is
SNR ^A _ICA = (N + 1) / (K-1) ^1/2
It becomes. This is because in the above embodiment, all the correction functions are
B (x) = x
This corresponds to the case where the function B (•) is set.

In order to further improve the signal-to-noise ratio, the correction function B (
B (x) = T ₄ (x)-T ₁ (x)
Suppose that the obtained code S ^B _{i, j} is used.

At this time, the average of each code before passing through the independent component analysis is
[Avg (S ^B _i )] ² = 1 / N ²
It is known that

Therefore, the signal-to-noise ratio SNR ^B _ICA after independent component analysis is
SNR ^B _ICA = (N ² +1) / (K-1) ^1/2
It becomes.

  FIG. 7 is a graph showing the relationship between the code length and the signal-to-noise ratio when K = 2 for each of the above codes. Hereinafter, a description will be given with reference to FIG.

  As shown in this figure, the performance varies greatly depending on each code, and the performance gradually improves in the order of the methods described above.

  When a normal chaotic signal is used as it is for a spreading code, the signal-to-noise ratio is proportional to the 1/2 of the code length, but by using an appropriate correction function as a filter using independent component analysis, It can be seen that the noise ratio can be made proportional to the square of the code length.

  As for the filter processing by the correction function B (•), if this filter satisfies the super-efficiency condition disclosed in [Non-Patent Document 1], the above-described performance can be improved. become able to.

A specific example is given. When employing a recurrence formula function F _i (·) as T _{a [i]} (·), the coefficients _{a c, a 0, a 1} , a 2, ..., Σ m = 0 for a _{^L L} a _m = 0
As the correction function B (x)
p = a [i]
As
B (x) = a _c + Σ _{m = 0} ^L T (p ^m , x);
T _a (x) = T (a, x)
Can be used to satisfy the super efficiency condition.

In the above example,
L = 2;
p = 2;
a _c = 0;
a ₀ = 0, a ₁ = -1, a ₂ = 1
Using an appropriate integer q [i] of 2 or more,
b [i] = a [i] ^{q [i]}
But
q [i] = 2;
b [i] = 2 ² = 4;
S _i (x) = T _{b [i]} (x)-T ₁ (x) = T ₄ (x)-x
It is.

  By using such a linear sum of Chebyshev polynomials that satisfy the superefficiency condition as a correction function, the signal-to-noise ratio can be further improved.

  As described above, according to the present invention, a random number sequence group generation device, a random number sequence group generation method, and an arrival generation suitable for generating a random number sequence group composed of a plurality of random number sequences having a correlation as low as possible are provided. It is possible to provide a communication system, a communication method using a random number sequence group, and a program for realizing these on a computer.

It is a schematic diagram which shows schematic structure of the random number sequence group generation apparatus which concerns on embodiment of this invention. It is a schematic diagram which shows schematic structure of a random number sequence generation part. It is explanatory drawing which shows the Chebyshev polynomial from 2nd order to 5th order in a graph. It is a mimetic diagram showing the outline composition of the communications system concerning this embodiment. It is explanatory drawing which shows a detailed structure in case a communication system is code division multiplexing communication. It is explanatory drawing which shows a detailed structure in case a communication system is orthogonal frequency division multiplexing communication. It is a graph which shows the relationship between code length and a signal-to-noise ratio.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Random number sequence generation apparatus 102 Random number sequence generation part 103 Initial setting part 104 Independent component analysis part 201 Storage part 202 Initialization part 203 Output part 204 Calculation part 205 Update part 401 Communication system 411 Transmission apparatus 412 Transmission side decomposition part 413 Spreading part 414 Transmission side coupling unit 421 Reception device 422 Reception unit 423 Reception side decomposition unit 424 Despreading unit 425 Reception side coupling unit 511 Series-parallel conversion unit 512 Adder 521 Branch unit 522 Parallel-serial conversion unit 611 Series-parallel conversion unit 612 Inverse Fourier transform 613 Parallel-serial converter 621 Series-parallel converter 622 Fourier-transform 623 Parallel-serial converter

Claims (23)

A plurality of random number sequence generators, each of which
A storage unit for temporarily storing pseudo-random values;
An initialization unit that stores and initializes a given initial value as a pseudo-random value in the storage unit,
An output unit that outputs a value obtained by applying a correction function to the stored pseudo-random number value as a random number included in a random number sequence each time a pseudo-random value is stored in the storage unit,
When a random number is output by the output unit, a calculation unit that calculates a result of applying a recurrence function previously associated with the random number sequence generation unit to the pseudo-random number value stored in the storage unit,
A plurality of random number sequence generation units having an update unit that stores and updates the calculation results by the calculation unit as pseudo-random values in the storage unit;
An initial setting unit that gives an initial value to each of the plurality of random number sequence generation units;
An independent component analysis unit that performs independent component analysis on a plurality of random number sequences output from each of the plurality of random number sequence generation units as an input sequence group, and outputs the resulting output sequence group as a random number sequence group. Random number sequence group generation device characterized. The random number sequence group generation device according to claim 1,
The independent component analysis unit performs independent component analysis on a plurality of random number sequences output from each of the plurality of random number sequence generation units for each predetermined length. The random number sequence group generation device according to claim 1,
At least one of the recurrence function that is associated with each of the plurality of random number sequence generation units in advance is a chaotic map. The random number sequence group generation device according to claim 1,
For each of the plurality of random number sequence generators, the correction function S _i (·) associated with the i (i ≧ 1) th random number sequence generator is:
S _i (x) = x
A random number sequence group generation device characterized in that It is a random number sequence group generator of Claim 1, Comprising: With respect to the integer a
T _a (cosθ) = cos (aθ)
A-th order Chebyshev polynomial T _a (
For each of the plurality of random number sequence generators, the i (i ≧ 1) -th random number sequence generator has a recurrence function F _i (•) and a correction function S _i (•) with a predetermined function. Among the integer sequences a [1], a [2],... And the predetermined integer sequences b [1], b [2],..., The i-th value a [i], b [i] (a [i] ≥2, b [i] ≥2)
The recurrence function F _i (
F _i (x) = T _{a [i]} (x)
And the correction function S _i (·) is
S _i (x) = T _{b [i]} (x)-T ₁ (x)
A random number sequence group generation device characterized in that The random number sequence generation device according to claim 5,
For integers i and j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N) for the number N of the plurality of random number sequence generation units,
a [i] ≠ a [j]
A random number sequence group generation apparatus characterized by The random number sequence generation device according to claim 5,
For integers i and j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N) for the number N of the plurality of random number sequence generation units,
a [i] = a [j]
And
The initial value setting unit provides different initial values to the plurality of random number generation units. The random number sequence group generation device according to any one of claims 5 to 7,
For each of the integers i (i ≧ 1), the i-th value q [i] (q [i] ≧ 2) of the predetermined integer sequence q [1], q [2],.
b [i] = a [i] ^{q [i]}
A random number sequence group generation device characterized in that Each of the random number sequences included in the random number sequence group output by the random number sequence group generation device according to any one of claims 1 to 8 is associated with each subchannel of multicarrier communication,
A transmitter that performs code spreading using a random number sequence associated with the subchannel as a spreading code;
A communication system comprising: a receiving device that performs code despreading using a random number sequence associated with the subchannel as a spreading code. The communication system according to claim 9, wherein
The multicarrier communication is orthogonal frequency division multiplex communication. A random number sequence group generation method executed by a random number sequence group generation device including a plurality of random number sequence generation units, an initial setting unit, and an independent component analysis unit,
Each of the plurality of random number sequence generation units includes a storage unit, an initialization unit, an output unit, a calculation unit, and an update unit, and the pseudo random number value is temporarily stored in the storage unit,
In each of the plurality of random number sequence generators,
An initialization step in which the initialization unit stores and initializes the given initial value as a pseudo-random value in the storage unit;
The output unit outputs a value obtained by applying a correction function to the stored pseudo-random number value as a random number included in a random number sequence each time the pseudo-random value is stored in the storage unit,
When the calculation unit outputs a random number in the output step, a calculation for calculating a result of applying a recurrence function that is associated in advance with the random number sequence generation unit to the pseudo-random number value stored in the storage unit Process,
A random number sequence generating step including an updating step in which the updating unit stores and updates the calculation result in the calculation step as a pseudo-random value stored in the storage unit;
An initial setting step in which the initial setting unit gives an initial value to each of the plurality of random number sequence generation units;
The independent component analysis unit performs independent component analysis using a plurality of random number sequences output from each of the plurality of random number sequence generation units as an input sequence group, and outputs the resulting output sequence group as a random number sequence group. A random number sequence generation method comprising: a component analysis step. The random number sequence group generation method according to claim 11,
In the independent component analysis step, a plurality of random number sequences output from each of the plurality of random number sequences are subjected to independent component analysis for each predetermined length. The random number sequence group generation method according to claim 11,
At least one of the recurrence function associated in advance with each of the plurality of random number sequence generators is a chaotic map. The random number sequence group generation method according to claim 11,
For each of the plurality of random number sequence generators, the correction function S _i (·) associated with the i (i ≧ 1) th random number sequence generator is:
S _i (x) = x
A random number sequence group generation method characterized by It is a random number sequence group generation method of Claim 11, Comprising: With respect to integer a
T _a (cosθ) = cos (aθ)
A-th order Chebyshev polynomial T _a (
For each of the plurality of random number sequence generators, the i (i ≧ 1) -th random number sequence generator has a recurrence function F _i (•) and a correction function S _i (•) with a predetermined function. Among the integer sequences a [1], a [2],... And the predetermined integer sequences b [1], b [2],..., The i-th value a [i], b [i] (a [i] ≥2, b [i] ≥2)
The recurrence function F _i (
F _i (x) = T _{a [i]} (x)
And the correction function S _i (·) is
S _i (x) = T _{b [i]} (x)-T ₁ (x)
A random number sequence group generation method characterized by The random number sequence generation method according to claim 15,
For integers i and j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N) for the number N of the plurality of random number sequence generation units,
a [i] ≠ a [j]
A random number sequence generation method characterized by The random number sequence generation method according to claim 15,
For integers i and j (i ≠ j, 1 ≦ i ≦ N, 1 ≦ j ≦ N) for the number N of the plurality of random number sequence generation units,
a [i] = a [j]
And
In the initial value setting step, different initial values are given to the plurality of random number generation units. The random number sequence generation method according to any one of claims 15 to 17,
For each of the integers i (i ≧ 1), the i-th value q [i] (q [i] ≧ 2) of the predetermined integer sequence q [1], q [2],.
b [i] = a [i] ^{q [i]}
A random number sequence group generation method characterized by Each of the random number sequences included in the random number sequence group output by the random number sequence group generation method according to any one of claims 11 to 18 is associated with each subchannel of multicarrier communication,
A transmission step of performing code spreading using a random number sequence associated with the subchannel as a spreading code;
A communication method comprising: a reception step of performing code despreading using a random number sequence associated with the subchannel as a spreading code. The communication method according to claim 19, wherein
The multicarrier communication is orthogonal frequency division multiplexing communication.   A program that causes a computer to function as each unit of the random number sequence generation device according to claim 1.   A program causing a computer to function as a transmission device of the communication system according to claim 9 or 10.   A program causing a computer to function as a receiving device of the communication system according to claim 9 or 10.

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