Abstract:
A method for determining the initial state of shift registers constituting a modular type or simple construction type maximum length linearly occurring code sequence generator used in a spread spectrum communication system is disclosed, by which it is determined by the following equation; ##EQU1## where yj(0) is the j-th element of Y (0), and 
     X=P X (0).

Description:
FIELD OF THE INVENTION 
     This invention relates to a spread spectrum communication (hereinbelow abbreviated to SSC) system, by which demodulation of necessary information is effected by using correlation output between signals whose spectrum is spread by means of a maximum length linearly occurring code sequence (hereinbelow abbreviated to m sequence) generated on the sender side and that generated on the receiver side and in particular to a method for determining the initial state of the m sequence generator. 
     BACKGROUND OF THE INVENTION 
     In a direct SSC using a correlator such as a surface acoustic wave (hereinbelow abbreviated to SAW) convolver, as dividing means for a communication channel in the case where an m sequence serves as spreading codes, it is conceivable to utilize not only the sort of the m sequence but also the initial phase of the m sequence both on the sender and the receiver sides. The algorithm for determining the data demodulation timing and the information concerning the initial phase and so forth have been already disclosed by the same applicant of this invention in JP-A-59-2733. 
     However the result obtained by the algorithm for determining the information concerning the initial phase of the m sequence (hereinbelow called simply initial phase information) can be applied only to the case where a simple construction type m sequence generator is used and no algorithm for determining the initial phase information, which can be applied in a general manner both to the simple construction type and the modular type m sequence generators, were known. 
     OBJECT OF THE INVENTION 
     The object of this invention is to provide a method for determining the initial phase information of the m sequence suitable to the SSC method, which can be applied in a general manner both to the simple construction type and the modular type m sequence generators. 
     SUMMARY OF THE INVENTION 
     In order to achieve this object a method for determining the initial state of the m sequence generator in an SSC system according to this invention, as described at the beginning of this specification, is characterized in that the initial state of shift registers constituting the m sequence generator is determined by the following equation; ##EQU2## where j=1, . . . , n, 
     yj(0) is the j-th element of Y(0) and 
     X=PX(O). 
     The shift registers described above may be either simple construction type or modular type. 
     An algorithm for determining the initial phase information, which can be applied in a general manner both to the simple construction type and the modular type m sequence generators is proposed so that a communication channel can be divided by determining previously the initial phase on the sender and the receiver sides. 
     These and other objects and advantages of the present invention will become apparent by reference to the following description and drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 and 2 are block diagrams illustrating the construction of a modular type m sequence generator; 
     FIGS. 3 and 4 are block diagrams illustrating the construction of a simple construction type m sequence generator; 
     FIG. 5 is a scheme showing the phase relation between the sent and received m sequences; and 
     FIG. 6 is a flow chart showing the procedure according to this invention for determining the initial phase information. 
    
    
     DETAILED DESCRIPTION 
     All the following calculations are effected according to the Boolean algebra. 
     (a) Equation of state representing the initial state of shift registers constituting the m seuqence generator 
     Models representing m sequence generators on the sender and the receiver sides, respectively, are indicated in FIGS. 1 to 4 for those of modular type (FIGS. 1 and 2) and for those of simple construction type (FIGS. 3 and 4). FIGS. 1 and 3 show the construction on the sender side and FIGS. 2 and 4 the construction on the receiver side. In the figures, SR 1  ˜SR n  represent flip-flops; EOR 1  ˜EOR n-1  exclusive OR gates; and TAP 1  ˜TAP n  terminals to which signals described below for setting the initial state of the m sequence generator are applied, which signals are given by a computer not shown in the figures. It is supposed that communication is performed between two devices having a same construction. 
     At this time the equation of state of the shift registers can be written with respect to the dispersion time k, as follows; 
     &lt;On the sender side&gt;for κ k   
     
         X(k+1)=AX(k),X(k)≠0                                  (1) 
    
     &lt;On the receiver side&gt;for κ k   
     
         Y(k+1)=BX(k),Y(k)≠0                                  (2) 
    
     where X(k) and Y(k) are given by the following equations; ##EQU3## and A and B are 
     in the case of the modular type ##EQU4## 
     in the case of the simple construction type ##EQU5## 
     In Eqs. (1) and (2), n represents the number of stages of the shift registers (hereinbelow abbreviated to SR); X(k) and Y(k) the state vector of the SR (n×1); A and B the state transition matrix of the SR (n×n); and I n-1  is a unit matrix (n-1)×(n-1). Further, h j , l j  (j=1, . . . , n-1) indicate the state of the feedback line and feedbak &#34;ON&#34;→h j , l j  =1, feedback &#34;OFF&#34;→h j , l j  =0. 
     Furthermore A and B have the following properties; 
     (i) 
     A N  =B N  =I n   
     N=2 n  -1 (length of code sequence) 
     (ii) A -1  =B, B -1  =A 
     (b) Expression of the m sequence (1 period long) outputted by TAP 1   
     Supposing that X(O) and Y(O) represent the initial state of the SR on the sender and the receiver sides, the sent and the received code patterns U and W, respectively, outputted by TAP 1  (i=1˜n) at k=0˜N-1 can be represented as follows; 
     &lt;On the sender side&gt; ##EQU6## 
     &lt;On the receiver side&gt; ##EQU7## 
     (c) Deduction of Y(O) 
     The method according to this invention is applied to the dividing method I in the application described previously. The phase relation between the m code sequences on the sender and the receiver sides for realizing the dividing method I is shown in FIG. 5. That is, using U=W, 
     
         PX(O)=QY(O)                                                (5) 
    
     where ##EQU8## are valid and Y(O) can be obtained analytically, as indicated by Eq. (6) by using Cramer&#39;s formular. ##STR1## where yj(0) is the j-th element of Y(O) and 
     X=PX(O). 
     As explained above, the procedure for obtaining Y(O) can be summarized as indicated in FIG. 6. 
     Furthermore the calculations of the exponential of the matrix A in FIG. 6 can be performed simply by using Eqs. (24) and (28) in the application stated previously in the case of the simple construction type m sequence generator and by using the following Eqs. (7) and (8) in the case of the modular type m sequence generator. 
     Calculation algorithm of A d  &lt;I&gt;  used in the case of d≦N/2 
     (i) For the 2nd˜n-th rows of A d  the 1st˜(n-1)-th rows are shifted as they are. 
     (ii) The 1st row of A d-1  can be obtained by the following calculation. ##EQU9## Calculation algorithm of A 2  &lt;II&gt; used in the case of d&gt;N/2 
     (i) For the 1st˜(n-1)-th rows of B r  (=A d ) the 2nd˜n-th rows are shifted as they are. 
     (ii) The n-th row of B r  (=A d ) can be obtained by the following calculation. ##EQU10## 
     As explained above, according to this invention, since the communication channel can be divided by determining previously the initial phase of the m code sequencies both on the sender and the receiver sides by the procedures from (a) to (c) as described above, it is possible to divide the communication channel even by using a same m code sequence at the sender and at the receiver. Therefore the number of communication channels can be remarkably increased so that multi-users can be sufficiently satisfied. The method according to this invention can be applied to the simple construction type m sequence generator as well as to the modular type m sequence generator. 
     While particular embodiments of the invention have been shown and described, it will be obvious to those skilled in the art that various changes and modifications may be made without departing from the present invention in its broader aspect.