KR101269849B1 - Apparatus and method for generating the sequence family to spread the channel of communication system - Google Patents

Abstract

The present invention using, logarithmically on the method of generating the sequence group for channel spreading in a communication system is finite according to the present invention relates to a generating apparatus and a method of sequence group for channel spreading in a communication system q ^d - M-binary (M is a divisor of q-1) sequence of 1 (q is a prime power, d is an integer greater than or equal to 2), arranged in a matrix separated by the q-1 period, and circulated from the arranged matrix Select and store non-equivalent representative strings, and create a sequence by constant multiplying the stored representative strings.

Description

Apparatus and method for generating the sequence family to spread the channel of communication system

The present invention relates to an apparatus and method for generating a sequence group for channel spread in a communication system, and in particular, uses a spread-spectrum technique such as a code-division multiple-access (CDMA) communication system. The present invention relates to an apparatus, a method for generating a sequence family utilized for spreading code in a communication environment, and a recording medium recording the same.

The CDMA communication system utilizes spread spectrum technology to divide each piece of information into a measurement code and a time difference in the entire band, and only the information having the same code and time difference as that used in transmission is transmitted to the receiving side. It is a communication method that selects and restores original signal. Since CDMA can use the same frequency in a plurality of cells in all service areas, the frequency utilization efficiency is much higher than that of other methods. It is very good.

In particular, the spread spectrum (hereinafter referred to as spread spectrum or channel spread term) technology is a technique for transmitting information using a bandwidth much wider than the theoretical bandwidth required for transmitting specific information, and has excellent error efficiency or signal to signal ratio. It has a noise ratio. In addition, even if the strength of the spread signal transmitted is very weak, the communication is possible and strong against the noise signal, so that many senders can send a signal to a specific receiver with a specific code even if the signal is sent at the same time. That is, since a single channel can be used simultaneously by multiple users, the capacity can be increased accordingly. Direct spread (DS) techniques, frequency hopping (FH) techniques, time hopping (TH) techniques, and chip spreading techniques are known in the spread spectrum technique. Hybrid methods are also used.

As the demand for high-speed data communication based on such spread spectrum technology increases, finding a sequence having good correlation characteristics becomes increasingly important. This sequence requires a large linear complexity and a large number of sequences so that a high number of transmitters can simultaneously transmit signals while ensuring high security for use as a multiple access code in a spread spectrum system of wireless communication.

The technical problem to be solved by the present invention is to overcome the limitation that the number of transmission data that can be included in one channel to saturation in accordance with the increasing demand of the communication system using the channel spreading technology, and to prevent illegal wireless communication interception or hacking Concerns can be addressed and, furthermore, to provide a robust security and stability sequence for stream cipher systems and next-generation mobile communication systems.

In order to solve the above technical problem, a method of generating a sequence group for channel spread in the communication system according to the present invention is q ^d -1 (q is a prime power, d is an integer of 2 or more) using a logarithmic function on the finite body Generating an M-binary (M is a divisor of q-1) sequence having a period of; Arranging the M-binary sequences in a matrix by dividing based on a q-1 period; Selecting and storing cyclic non-equivalent representative strings from the arranged matrix; And generating a sequence by multiplying the stored representative sequences, wherein the asymptotic size of the sequence is proportional to the integer power of q.

In addition, the following provides a computer-readable recording medium having recorded thereon a program for causing a computer to execute a method of generating a sequence for spreading channels in a communication system as described above.

In order to solve the above technical problem, the apparatus for generating a sequence group for the channel spread of the communication system according to the present invention is q ^d -1 (q is a prime power, d is an integer of 2 or more) using a logarithmic function on the finite body A sequence generator for generating an M-binary (M is a divisor of q-1) sequence having a period of; An arithmetic unit for arranging the M-binary sequences in a matrix based on a q-1 period and selecting representative sequences that are cyclically non-equivalent from the arranged matrix; A storage unit for storing the arranged matrix and selected representative strings; And a hydrothermal group generating unit generating a hydrothermal group by constant multiplying the stored representative strings, wherein the asymptotic size of the hydrothermal group is proportional to the integer power of q.

In order to solve the above technical problem, in the apparatus, method and recording medium for generating a sequence for the channel spread of the communication system according to the present invention, the M-sin sequence is the M-jin Siedelnikov sequence, the cyclic asymmetry The representative string is preferably the minimum integer of the q-component surplus.

In order to solve the other technical problem, the apparatus for generating a spread signal for channel spread in the communication system according to the present invention includes an input unit for receiving a digitally modulated signal; A spreading code generator for generating a spreading code from a predetermined sequence group; And by spreading the bandwidth by multiplying said generated spreading code with the input signal comprises a spread signal generating for generating a spread signal, and wherein the predetermined sequence group by using a logarithmic function on the finite field ^d -1 q (q is Generate a M-binary (M is a divisor of q-1) with a prime power, d is an integer greater than or equal to 2, and arrange the M-binary sequences in a matrix separated by a period of q-1, It is generated by selecting and storing cyclic non-equivalent representative strings from the arranged matrix, and generating a constant multiple of the stored representative strings, and the asymptotic size of the sequence group is proportional to the integer power of q.

In order to solve the other technical problem, the apparatus for despreading the spread signal for channel spread in the communication system according to the present invention includes a receiving unit for receiving the spread signal; A spreading code generator for generating a spreading code from a predetermined sequence group; And using a logarithmic function on said received by de-spreading the bandwidth by multiplying the generated spread code to the spread signal includes a restoration signal to restore the original signal of the spread signal, and wherein the predetermined sequence group is finite q ^d - Create an M-binary (M is a divisor of q-1) with a period of 1 (q is a prime power, d is an integer greater than or equal to 2), and divide the M-binary sequence by q-1 periods Is generated by selecting and storing cyclic non-representative representative strings from the arranged matrix, and multiplying the stored representative strings, and the asymptotic size of the series is proportional to the integer power of q.

In order to solve the above other technical problem, in the apparatus for generating a spreading signal for channel spreading and the apparatus for despreading the spreading signal in the communication system according to the present invention, the M-number sequence is the M-sincid Delnikoff sequence, It is preferable that the cyclic non-representative string is the minimum integer of the q-component surplus.

The present invention overcomes the limitations of data saturation in the channel by dramatically increasing the number of transmission data that can be included in one channel in response to the explosive increase in the demand for a communication system using a channel spreading technology, and illegal due to the low correlation By providing a sequence having characteristics that are robust against eavesdropping or hacking, it is possible to ensure the strong security and stability required for stream cipher systems and next-generation mobile communication systems.

1 is a flowchart illustrating a method of generating a sequence group for channel spreading in a communication system according to an embodiment of the present invention.
2 is a block diagram illustrating an apparatus for generating a sequence group for channel spread in a communication system according to an embodiment of the present invention.
3 is a diagram for describing a series of communication processes for channel spread in a communication system according to another embodiment of the present invention.
4A and 4B are diagrams illustrating an apparatus for generating a spreading signal for channel spreading and an apparatus for despreading a spreading signal in a communication system according to another embodiment of the present invention, respectively.
5 is a view for explaining and comparing the characteristics of the hydrothermal groups generated by a conventionally known method.

Prior to describing the embodiments of the present invention in detail, an overview of the spread spectrum communication method, which is a representative environment in which embodiments of the present invention can be implemented, will be described.

In general digital communication, data to be transmitted is digitally modulated by PSK (phase shift keying) or FSK (frequency shift keying). When transmitting any information, the theoretical bandwidth required for transmitting the information is calculated, and the bandwidth of the frequency for transmitting the information is determined by the calculation result.

However, spread spectrum communication uses a much wider bandwidth than the theoretically calculated required frequency bandwidth to transmit information. For example, since voice has a frequency band of up to 4KHz, technically, only a bandwidth of 4KHz is required to transmit voice signals. However, in a spread spectrum communication method such as CDMA, a voice signal is transmitted using a frequency bandwidth of 1.25 MHz, which is more than 300 times wider than this.

Specifically, spread spectrum communication multiplies the digitally modulated signal by a fast spreading code to extend the bandwidth of the frequency over a wide bandwidth and then transmits a spreading signal. Subsequently, the receiving side undergoes a despreading process of converting the bandwidth of the frequency into a narrow band by multiplying the same fast spreading code used by the transmitting side and then demodulates it. In general, noise is introduced in the wireless transmission process, and the influence of the introduced noise is reduced by a spreading code multiplied by the receiver.

When this is explained through a simple equation, Equation 1 below.

In Equation 1, S means an original signal, C means a spreading code, and N means noise. In spreading code communication, the spreading signal is transmitted by multiplying the spreading code by the original signal, so the transmitted signal will be S · C. Since noise is introduced during the transmission, the signal arriving at the receiver will be (S · C) + N. Now, since the receiving side multiplies the same spreading code as the spreading code used at the time of transmission to restore the original signal, it can be expressed as {(S · C) + N} · C. Note that the spreading code is characterized by being 1 when the same code is multiplied by each other. Therefore, the calculation result S + N · C as in Equation 1 can be obtained. As can be seen from the result, the original signal S is normally restored on the receiving side, while the noise N is multiplied by the spreading code C, so the influence is reduced.

In a digital cellular CDMA scheme, when a signal having a bandwidth of 10 KHz is spread to have a bandwidth of 1.25 MHz, the spread information signal is spread evenly over a wide frequency band, and the strength of the signal is faint than that of the original signal. As a result, it is difficult to know the existence of the signal because it is necessary to search the entire frequency band to receive such a spread signal. In other words, since the transmission signal is blurred, interference with other signals is reduced and security reliability is increased. In addition, since the spread signal is spread over a wide frequency band, even if interference or noise is included in the propagation process, the influence of the wide frequency band has only a part. Therefore, the quality of the call can be improved since the influence of interference or noise is considerably reduced.

In a CDMA communication system, a low correlation sequence is required for minimizing synchronization and multiple access interference. In particular, in adaptive modulation schemes, a sequence of variable length and alphabet size is desirable to maximize the data rate according to channel characteristics. Furthermore, a large number of distinct sequences are needed to support as many users as possible.

는 q개의 원을 갖는 유한체(finite field)를 의미하고,

는 q^d(d≥2) 개의 원을 갖는 유한체를 의미하고, M은 M≥2인 q-1 의 양의 약수를 의미하고,

이고, α는

의 한 원시원이고, β는

인

의 한 원시원(primitive element)이고, N은 N(x)=

로 주어지는

에서

로의 노름 사상(norm map)이고, Tr은 Tr(x)=

로 주어지는

에서

로의 트레이스 사상(trace map)이며, ψ는 ψ(x)=

로 주어지는 위수(order) M인

의 곱 지표(multiplicative character)를 의미한다. 이제 β를

의 임의의 한 원시원이라 하면,

상의 로그함수(logarithm)는 다음의 수학식 2와 같다.The following proposes a new sequence group that meets this need, and various embodiments of the present invention will be described in detail with reference to the drawings. The following symbols will be used throughout the following embodiments. p means prime number, n means positive integer, q means p ⁿ ,

Means a finite field having q circles,

Is a finite body having q ^d (d≥2) circles, M is a positive divisor of q-1 with M≥2,

And α is

Is a source of, and β is

sign

Is a primitive element of, where N is N (x) =

Given by

in

Norm map of rho, where Tr is Tr (x) =

Given by

in

Is a trace map of λ, where ψ is ψ (x) =

Order M given by

It means the multiplicative character of. Now β

Speaking of any one source of,

The logarithm of the phase is shown in Equation 2 below.

의 어떤 고정된 원시원 β에 대해 주기(period)가 q-1인 M-진(M-ary) 시델니코프(Sidelnikov) 수열(sequence) s(t)는 다음의 수학식 3과 같이 정의된다.now

The M-ary Sidelnikov sequence s (t) with period q-1 for any fixed primitive source of is defined as .

Then, the M-sin Sidnikoff sequence s (t) of period q-1 is briefly described as in Equation 4 below.

or

Weil's estimate of multiplicative character sums is well known to those of ordinary skill in the art.

Next, we will discuss the array structure of M-gene Sidelnikov's sequence whose period is q ^d -1. If M is a divisor of q-1, not a divisor of q ^d -1, under a stronger condition, the M-sin-Sidelnikoff sequence with period q ^d -1 is given by Equation 5 below.

Equation 5 may be expressed as Equation 6 below.

Equation (5) can be derived from the definition of the Sidelnikov process as follows.

라고 가정하면, To prove equation (5)

Let's say

The following equation (9) is derived from the above.

이므로 다음의 수학식 10이 성립함을 알 수 있다.Therefore, when M is a divisor of q-1,

It can be seen that the following equation (10) holds.

의 행렬로 배열한다. 이렇게 배열된 행렬의 l-번째 열 v_l(t) (0≤t≤q-2) 은 다음의 수학식 11과 같이 정의된다.Now the M-sine Sidelnikoff sequence {s (t)} (0≤t≤q ^d -2), where the period of Equation 5 is q ^d -1

Arrange in a matrix of. The l-th column v _l (t) (0 ≦ t ≦ q-2) of the matrix thus arranged is defined as in Equation 11 below.

Then, Equation 11 may be expressed as Equation 12 below.

상의 차수(degree)가 d인 다음의 수학식 13의 다항식(polynomial)이라고 하자.Where f _l (x) for each nonnegative integer l

Assume that the polynomial of the following equation (13) with the degree of phase is d.

Now clearly the following holds true.

)에 대해 다음의 수학식 14가 유도된다.Then, each l (

The following equation (14) is derived.

의

상의 기약 다항식(irreducible polynomial)을 의미하며, d_l은 d의 약수이다.Where p _l (x) is of order d _l

of

Means the irreducible polynomial of d, where d _l is a divisor of d.

를 포함하는 q-원분 잉여류(cyclotomic coset)를

라고 하자. 여기서,

는 q^d-1 로 나눈 나머지이고, d_l은

를 만족하는 최소의 양의 정수이고,

이다. 또한, l은 법 q^d-1에 대한 C_l의 최소의 양의 정수로 선택할 수 있다.Meanwhile,

Q-component surplus (cyclotomic coset) comprising a

Let's say. here,

Is the remainder divided by q ^d -1, and d _l is

Is the smallest positive integer satisfying

to be. Also, l can be selected as a minimum positive integer of C _l to method ^d -1 q.

이고,

인 l에 대하여

은

에서 아무런 근(roots)도 갖지 못한다. 나아가,

인 음이 아닌 정수 l₁, l₂에 대해

및

는 순환 비동치(cyclically inequivalent/distinct)이다. 또한,

이므로,

와

는 각각의

에 대해 순환 동치이다.then,

ego,

Against phosphorus l

silver

Has no roots in. Furthermore,

For nonnegative integers l ₁ and l ₂

And

Is cyclically inequivalent / distinct. Also,

Because of,

Wow

Respectively,

Is a circular equivalent.

에 대한 q-원분 잉여류로부터 각각 하나의 대표원들을 선택한다. 이 경우, 대표원은 각 q-원분 잉여류의 최소 정수인 것이 바람직하다. 여기서, q-원분 잉여류들은 어떤 동치 관계에 대한 동치류이므로 집합

을 분할(partition)한다.Now, the above properties are used to select columns that are cyclically non-equivalent among columns v _l (t) (0 ≦ t ≦ q-2). This is because by selecting the cyclically noncoherent columns, a set of multiple access codes that can be utilized for encoding / decoding of spreading code or stream data can be obtained from the sequence of Equation (5). For this purpose a set of integers

Choose one representative from each of the q-component surpluses for. In this case, the representative member is preferably the minimum integer of each q-component surplus. Where the q-component surpluses are equivalents for some equivalence relationship

Partition

Specifically, the q-component surplus containing set l is expressed by the following equation (15).

을

로 나눈 나머지이고, m_l은

를 만족하는 최소의 양의 정수이다. 또한, l은

에서 최소의 양의 정수로 선택될 수 있으며, m_l은 d_l의 약수이다. 따라서, 만약

이면,

이다. 여기서, σ는

상의

의 Frobenius 자기동형사상(automorphism)으로서,

으로 주어지며, 다음의 수학식 16이 성립한다.here,

of

Remainder divided by m _l is

The smallest positive integer satisfying Also, l is

Can be chosen as the smallest positive integer in which m _l is a divisor of d _l . Thus, if

If so,

to be. Where σ is

top

Of Frobenius automorphism,

Given by Equation 16 below.

으로 구성된 집합에 대해 법

에 대한 q-원분 잉여류의 대표값의 집합에 대응하는 수열의 열 v_l(t)의 상수 곱(constant multiples)으로 구성된 주기 q-1의 M-진 수열의 족(family) Σ을 구성하고자 한다.now,

Act for a set consisting of

To construct a family Σ of M-binary sequences of period q-1 consisting of constant multiples of a sequence of columns v _l (t) corresponding to a set of representative values of the q-component surplus for do.

로 정의하자.

는 q-원분 잉여류의 개수이며, 이는 또한

의 최고차항의 계수가 1인 기약 인자(monic irreducible factor)들의 개수와도 같다. 또한,

를

의 최고차항의 계수가 1인 기약 인자라고 하면,

이고

가 성립한다.A collection of the minimum integers of each q-component surplus

Let's define

Is the number of q-component surpluses, which is also

It is equal to the number of the irreducible factors of which the coefficient of the highest order term is 1. Also,

To

If the coefficient of the highest order term is 1,

ego

Is established.

In the following, assume that d satisfies the condition of Equation 17 below.

In Equation 17, d and q-1 mean each other, and are assumed to impose a restriction on the sequence.

의 원소라고 하고,

를 정수라고 하자. 만약 l₁ = l₂ 이 아니거나 τ = 0 이 아니면,

과

는

상의 서로 다른 기약 다항식(distinct irreducible polynomials)이다. 여기서,

은 다음의 수학식 18과 같이 정리된다.set l ₁ , l ₂

Called the element of,

Let be an integer. If l ₁ = l ₂ Is not or τ = 0,

and

The

Different distinct polynomials (distinct irreducible polynomials). here,

Is summarized as in Equation 18 below.

Then, the sequence group Σ composed of the M-binary sequences of the period q-1 configured above is defined as in Equation 19 below.

The method of generating the hydrothermal group described above is summarized as follows with reference to FIGS. 1 and 2. 1 is a flowchart illustrating a method of generating a sequence group for channel spreading in a communication system according to an embodiment of the present invention, and includes the following steps.

In step 110, a logarithmic function on a finite field is used to generate a M-binary (M is a divisor of q-1) having a period of q ^d −1 (q is a prime power and d is an integer of 2 or more). Here, the M-sin sequence may utilize the M-sin Sidelnikov sequence. Step 110 is performed by the sequence generator 210 of FIG. 2. The sequence generator 210 is a processor capable of processing information and equations in an electronic form and a memory required for such an operation. ) May be implemented, and a controller capable of appropriately controlling data processing between the processor and the storage space may be utilized as necessary. Such a processor, a storage space, and a controller may be appropriately selected by those skilled in the art in consideration of the utilization environment or operating environment of the technical field to which the present invention belongs. Further, in implementing the sequence generator 210, additional software code for controlling the hardware illustrated above may also be utilized.

(d는 1보다 큰 양의 정수)의 형태로 배열한 것이 바람직하다.In step 120, the M-binary sequences generated in step 110 are arranged in a matrix by dividing based on the period q-1. As we discussed earlier, these matrices represent M-binary sequences.

(d is a positive integer greater than 1).

In operation 130, representative strings that are cyclically non-equivalent are selected and stored from the arranged matrix. As discussed above, this cyclic non-representative representative string is preferably the minimum integer of the q-component surplus.

In the above steps 120 and 130, the M-binary sequence is divided into a matrix and arranged in a matrix, and a process of selecting representative sequences that are cyclically non-equivalent from the arranged matrix is performed by the calculator 220 of FIG. 2. The operation unit 220 may also be implemented using a processor capable of processing information and equations in electronic form and a controller capable of controlling these hardware. Meanwhile, the storage 230 of FIG. 2 is required to store the arranged matrix and the selected representative columns. That is, the storage unit 230, which may be implemented in hardware such as a register, is used as a storage space required for arithmetic operations in the matrix array and the representative string selection process. It is also natural that additional software code for controlling the hardware exemplified above can be utilized.

Finally, in step 140, the sequence strings stored in step 130 are constant times to generate a sequence family. This step 140 is performed by the sequence group generator 240 of FIG. 2. The sequence group generator 240 is a processor capable of processing an operation for a constant multiple of representative strings and a storage space for storing the same. It can be implemented in hardware.

(d는 1보다 큰 양의 정수)를 상계(upper bound)로 갖는 것이 바람직하다. 나아가, 생성된 수열 족의 점근적 크기는 q의 정수승(보다 구체적으로는 d-1 승을 의미한다.)에 비례하게 되며, 보다 구체적으로는

(d는 1보다 큰 양의 정수)인 것이 바람직하다. 이러한 수열 족의 최대상관수 및 점근적 크기에 관하여는 이하에서 보다 구체적으로 설명한다.In this case, the maximum correlation magnitude of the generated sequence family is

It is preferred to have (d is a positive integer greater than 1) upper bound. Furthermore, the asymptotic size of the generated sequence is proportional to the integer power of q (more specifically, d-1).

(d is a positive integer greater than 1). The maximum correlation and asymptotic size of these sequence groups will be described in more detail below.

에 대해 다음의 수학식 20이 성립한다.Sequence family of M-gin series with period q-1

Equation 20 below holds for.

Equation 20 may be derived as follows.

또는 τ가

의 범위 내에 있다고 가정하자. 그러면,

와

는 앞서 설명한 수학식 18에 의해

상의 서로 다른 기약 다항식(distinct irreducible polynomials)임을 알 수 있다. 이어서, 수열 족 Σ에서 수열

와

간의 상호-상관 함수(cross-correlation function)

는 다음의 수학식 21과 같이 주어진다.first

Or τ

Suppose you are in the range of. then,

Wow

Is calculated by Equation 18

It can be seen that different distinct polynomials (distinct irreducible polynomials) on the image. Then, the sequence from the sequence family Σ

Wow

Cross-correlation function

Is given by Equation 21 below.

이고,

이다. (d, q-1) = 1 이기 때문에

및

는 모두 M에 의해 약분이 불가능하다. 따라서, ψ₁과 ψ₂는 모두 자명한 곱지표가 아니다.here,

ego,

to be. because (d, q-1) = 1

And

Are not possible to solve by M. Thus, ψ ₁ and ψ ₂ are not self-explanatory indicators.

의 차수가

이고,

의

에서의 서로 다른 근의 개수가

인, 최고차항의 계수가 1인

상의 기약 다항식(monic irreducible polynomials)이라고 하자. 또한,

를

인

의 자명하지 않은 곱 지표(nontrivial multiplicative characters)라고 하자. 그러면,

에 대해 다음의 수학식 22를 추정할 수 있다.Meanwhile,

Degree of

ego,

of

The number of different roots in

, The coefficient of the highest order term is 1

Let's call the monolithic irreducible polynomials. Also,

To

sign

Let's call nontrivial multiplicative characters. then,

Equation 22 can be estimated for.

Now, the absolute values can be summarized as in the following Equation 23 by Equations 21 and 22.

Then, in the case of c ₁ ≠ c ₂ , l ₁ = l _2, and τ = 0, the cross-correlation function is arranged as in Equation 24 below.

는 M에 의해 약분될 수 없으며,

는 자명한 곱지표가 아니다. 따라서, 통상적인 Weil's 정리에 의해 다음의 수학식 25가 성립한다.here,

Cannot be abbreviated by M,

Is not a self-explanatory indicator. Therefore, the following equation (25) holds by the usual Weil's theorem.

Now, let's consider more specifically that the sequences belonging to the sequence Σ are circular asymmetries.

와

가 순환 동치이면,

에 대해

이고, 그 결과 다음의 수학식 26이 성립한다.if

Wow

Is a circular equivalence,

About

As a result, the following equation (26) holds.

이고,

이다. 앞서 수학식 17의 가정에 따르면 이상의 과정은 불가능하다. 따라서,

와

는 같다.here,

ego,

to be. According to the assumption of Equation 17 above, the above process is impossible. therefore,

Wow

Is the same.

의 크기는 다음의 수학식 27과 같이 표현될 수 있다.We will now produce a non-specific but accurate representation of the size of the sequence Σ. A sequence family

The size of may be expressed as Equation 27 below.

의 최고차항의 계수가 1인 기약 인자의 개수

는 다음의 수학식 28과 같이 주어진다.here,

The number of contracting factors with the coefficient of the highest order term of 1

Is given by Equation 28 below.

에 대해 상수항(constant term)이

이고 차수가 f인

상의 최고차항의 계수가 1인 기약 다항식의 개수를

라고 하자. 그러면, 다음의 수학식 29가 성립한다.Now, we will examine what asymptotic magnitude of the sequence Σ is at q → ∞. Any element

The constant term for

And order f

The number of contracted polynomials with a coefficient of

Let's say. Then, the following equation (29) holds.

The following equation (30) is derived from the above equation (29).

를 의미하므로, 수열 족 Σ에서 q→∞ 일 때의 점근적(asymptotic) 크기는 다음의 수학식 31과 같다.this is

Therefore, the asymptotic size of q → ∞ in the sequence Σ is given by Equation 31 below.

Now if d is chosen as, for example, any power P ^a (a≥1) of p, q satisfies the condition of equation (17) for all q with q = p ⁿ (n≥2 (a + 1)), When ∞, the asymptotic size of the sequence Σ is

Here, L = q-1 represents the period of the sequence group Σ.

Examining the size of the sequence group proposed by the embodiment of the present invention described above, it can be seen that the size of the arbitrary power of the period L. The size of these sequences is much higher than the best known L ³ . FIG. 5 is a view for explaining and comparing the characteristics of hydrothermal groups generated by a conventionally known method, and it is possible to easily compare the family sizes of hydrothermal groups.

Thus, according to the embodiments of the present invention described above, in response to the explosive increase in demand of a communication system using a channel spreading technique, the limit of data saturation in a channel is increased by dramatically increasing the number of transmission data that can be included in one channel. In addition, it is possible to provide a hydrothermal family having characteristics that are robust against eavesdropping or hacking illegally due to low correlation properties.

Hereinafter, a method of utilizing in the spread spectrum communication system using the proposed series as described above will be described.

3 is a diagram illustrating a series of communication processes for channel spreading in a communication system according to another embodiment of the present invention. After encoding and transmitting a signal from a transmitter, a process of decoding a signal received at a receiver is performed again. It is shown.

First, the RF oscillator 310 generates a frequency for wireless communication and loads an input signal. Since the present embodiment assumes a spread spectrum communication system, the original signal is spread by multiplying a pseudo random noise code (PN code) generated by the PN code generator 321. Subsequently, the signal amplified by the power amplifier 330 is transmitted through the antenna 341.

Now, the receiving side receives the spread signal through the antenna 342 and then decodes it. In this case, the PN code generator 322 generates the same noise code as the PN code generator 321 of the transmitting side. The PN code generator 322 can restore the original signal by multiplying the generated code. There is a bar.

In the spread spectrum communication system described above, more simultaneous accessors can be accommodated by using the sequence group according to the embodiment of the present invention. That is, according to the embodiment of the present invention, since the size of the sequence group can have a very large value, it is suitable for accommodating a plurality of user signals.

4A and 4B are diagrams illustrating a device for generating a spreading signal and a device for despreading a spreading signal for channel spreading in a communication system according to another embodiment of the present invention. It is to.

First, FIG. 4A illustrates an apparatus for generating a spreading signal for channel spreading of a communication system at a transmitting side, and includes the following configuration.

The input units 410 and 420 receive a voice signal and digitally modulate it. The original signal 41a at this time corresponds to a narrowband signal.

(d는 1보다 큰 양의 정수)의 형태로 배열한 것이 바람직하다.The spreading code generator 435 generates a spreading code from the sequence group 437 presented through the above embodiments. Specifically, the sequence family generates a sequence of M-jines (M is a divisor of q-1) having a period of q ^d -1 (q is a prime power, d is an integer of 2 or more) using a logarithmic function on a finite body. In addition, the M-binary sequence may be generated by dividing the q-based period into a matrix, selecting and storing cyclic non-representative representative columns from the arranged matrix, and multiplying the stored representative columns by constant. The asymptotic size of the sequence is preferably proportional to the integer power of q (more specifically, the d-1 power of q). Furthermore, the M-binary sequence above is the M-bind Sidelnikoff sequence, the cyclically nonrepresentative string is the minimum integer of the q-component surplus, and the matrix is the M-binary sequence.

(d is a positive integer greater than 1).

The spread signal generator 430 multiplies the spread signal generated by the spread code generator 435 with a signal input through the input units 410 and 420 to generate a spread signal by spreading a bandwidth. Accordingly, it can be seen that the spread signal transmitted through the antenna 441 is spread to the wideband signal 41b unlike the original signal 41a, which is a narrowband signal as shown in FIG. 4A.

Next, FIG. 4B illustrates an apparatus for despreading a spreading signal for channel spreading of a communication system at a receiving side, and includes the following configuration.

The receiver 442 receives a spreading signal. At this time, the received signal includes a noise signal 42a in addition to the spread signal 41b.

The spreading code generator 455 now generates a spreading code from the sequence family 457 to recover the received signals (spreading signal and noise signal). It is obvious that the spreading code at this time is the same as the spreading code at the transmitting side and was generated by the same process.

The signal recovery unit 450 restores the original signal 41a of the spread signal by despreading the bandwidth by multiplying the spread signal generated by the spread code generator 455 to the received spread signal. Of course, in the despreading process, the noise signal is also multiplied with the spreading code. As described above in Equation 1, the noise signal is further differentiated from the original signal by the spreading code. Thus, the influence of the noise signal becomes very dilute (smaller). 4B shows how two signals (spread signal and noise signal) are modulated after despreading. That is, it can be seen that the wideband spread signal 41b has been restored to the narrowband original signal 41a by despreading, and the noise signal 42a still exists as the wideband signal 42b.

According to other embodiments of the present invention described above, in response to the explosive increase in demand of a communication system using a channel spreading technique, the number of transmission data that can be included in one channel is dramatically increased to overcome the limitation of data saturation in the channel. In addition, due to the low correlation property, it is possible to construct a spread spectrum communication system having characteristics that are robust against illegal wireless communication interception and hacking.

Meanwhile, the present invention can be embodied as computer readable codes on a computer readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored.

Examples of the computer-readable recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device and the like, and also a carrier wave (for example, transmission via the Internet) . In addition, the computer-readable recording medium may be distributed over network-connected computer systems so that computer readable codes can be stored and executed in a distributed manner. In addition, functional programs, codes, and code segments for implementing the present invention can be easily deduced by programmers skilled in the art to which the present invention belongs.

The present invention has been described above with reference to various embodiments. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the present invention is defined by the appended claims rather than by the foregoing description, and all differences within the scope of equivalents thereof should be construed as being included in the present invention.

210: sequence generator
220: calculator 230: storage
240: hydrothermal foot generator 310: RF oscillator
321, 322: PN code generator
330 power amplifier
341, 342: antenna
410: input unit 420: digital modulator
435, 455: spreading code generation unit 437, 457: sequence family
430 band spreader 450 despreader (signal recovery unit)
441, 442: Antenna
460: digital demodulator 470: output unit

Claims (17)

In the method for generating a sequence family for channel spread of the communication system,
finite body with q circles

Logarithmic function on (q is prime p ⁿ , p is prime, n is positive integer)

(β is any one source of the finite body) using M-ary (M is an order, q- with a period of q ^d −1 (d is an integer greater than or equal to 2)) Generating a divisor sequence of 1);
Dividing the M-number sequence based on the q-1 period and arranging the M-number sequence in a matrix such that the number of rows becomes q-1;
Selecting and storing cyclically inequivalent / distinct representative strings from the arranged matrix; And
Generating a sequence by multiplying the stored representative strings,
Wherein the asymptotic size of the sequence family is proportional to the integer power q ^d-1 (d is a positive integer greater than 1) of q. The method of claim 1,
The cyclic non-representative string is a set

A minimum integer number of q-cyclotomic cosets that partition into: The method of claim 1,
Wherein the M-sin sequence is a M-sin Sidelnikov sequence. The method of claim 1,
The maximum correlation magnitude of the generated sequence family is

(d is a positive integer greater than 1) as upper bound. The method of claim 1,
The asymptotic size is

(d is a positive integer greater than 1). The method of claim 1,
The matrix is the M-binary sequence

(d is a positive integer greater than 1). A non-transitory computer-readable recording medium having recorded thereon a program for executing the method of claim 1. An apparatus for generating a sequence group for channel spread of a communication system,
finite body with q circles

Logarithmic function on (q is prime p ⁿ , p is prime, n is positive integer)

(β is any one source of the finite body) using M-ary (M is an order, q- with a period of q ^d −1 (d is an integer greater than or equal to 2)) 1) a sequence generating unit for generating a sequence;
An arithmetic unit for dividing the M-number sequence based on the q-1 period and arranging them in a matrix such that the number of rows is q-1, and selecting representative sequences that are cyclically non-equivalent from the arranged matrix;
A storage unit for storing the arranged matrix and selected representative strings; And
A hydrothermal group generation unit generating a hydrothermal group by multiplying the stored representative strings by constants,
Wherein the asymptotic size of the series is proportional to the integer power q ^{d-1 of} q, where d is a positive integer greater than one. The method of claim 8,
Wherein the M-gin sequence is M-gin Sidelnikov,
The cyclic non-representative string is a set

And a minimum integer of q-component surplus that partitions. The method of claim 8,
The maximum correlation of the generated sequence group is

(d is a positive integer greater than 1) as upper bound,
The asymptotic size is

(d is a positive integer greater than 1). The method of claim 8,
The matrix is the M-binary sequence

(d is a positive integer greater than 1). An apparatus for generating a spreading signal for channel spreading in a communication system,
An input unit for receiving a digitally modulated signal;
A spreading code generator for generating a spreading code from a predetermined sequence group; And
A spreading signal generator for generating a spreading signal by spreading a bandwidth by multiplying the generated spreading code by the input signal;
The predetermined sequence group is a finite body having q circles

Logarithmic function on (q is prime p ⁿ , p is prime, n is positive integer)

(β is any one source of the finite body) using M-ary (M is an order, q- with a period of q ^d −1 (d is an integer greater than or equal to 2)) Generating a series of numbers, dividing the M-number sequence based on the q-1 period, and arranging them in a matrix such that the number of rows is q-1, and representing cyclically non-representative columns from the arranged matrix. Generated by selecting, storing, and multiplying the stored representative strings,
Wherein the asymptotic size of the series is proportional to the integer power q ^{d-1 of} q, where d is a positive integer greater than one. 13. The method of claim 12,
Wherein the M-gin sequence is M-gin Sidelnikov,
The cyclic non-representative string is a set

And a minimum integer of q-component surplus that partitions. 13. The method of claim 12,
The matrix is the M-binary sequence

(d is a positive integer greater than 1). An apparatus for despreading a spread signal for channel spread in a communication system,
A receiver for receiving a spreading signal;
A spreading code generator for generating a spreading code from a predetermined sequence group; And
A signal reconstruction unit for restoring an original signal of a spread signal by despreading a bandwidth by multiplying the generated spread code by the received spread signal;
The predetermined sequence group is a finite body having q circles

Logarithmic function on (q is prime p ⁿ , p is prime, n is positive integer)

(β is any one source of the finite body) using M-ary (M is an order, q- with a period of q ^d −1 (d is an integer greater than or equal to 2)) Generating a series of numbers, dividing the M-number sequence based on the q-1 period, and arranging them in a matrix such that the number of rows is q-1, and representing cyclically non-representative columns from the arranged matrix. Generated by selecting, storing, and multiplying the stored representative strings,
Wherein the asymptotic size of the series is proportional to the integer power q ^{d-1 of} q, where d is a positive integer greater than one. The method of claim 15,
Wherein the M-gin sequence is M-gin Sidelnikov,
The cyclic non-representative string is a set

And a minimum integer of q-component surplus that partitions. The method of claim 15,
The matrix is the M-binary sequence

(d is a positive integer greater than 1).

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