Abstract:
A system and method of modulation of digital data to create a low probability of intercept communication system. The method comprises the steps of receiving digital data (or analog data and converting it into digital data), modulating the digital data signal, scrambling the digital data signal using here an eight position shift register with appropriately positioned feedback elements, converting the modulated-scrambled signal into a direct-sequence pseudo noise spread spectrum signal, converting the spread spectrum signal into a gaussian type signal, resulting in a white and gaussian noise-like characteristics. The system and method employ proved and innovative correlative techniques in converting data into a noise-like waveform. This insures a higher degree of immunity to interception, and provides an unmatched level of privacy and security over all types of communication media.

Description:
BACKGROUND 
     Field of the Invention 
     This invention is related to secure data transmission systems. In the prior art, digital data transmission systems were based on independent symbols and minimization of intersymbol interference (ISI). There is a universal use of direct sequence pseudo noise spread spectrum (DS-PN SS) techniques creating white spectral density. This approach is insufficient to create a waveform with the desired white and gaussian characteristics of noise in the natural environment. Such attributes assure the highest possible degree of privacy in communication transmissions. 
     Thus, it is desirable to create a communication system that achieves a higher degree of private transmissions than is presently available today. 
     SUMMARY OF THE INVENTION 
     This invention relates to secure data transmissions. Specifically, it is related to digital data communication systems that communicate digital data in a manner that makes nearly indistinguishable from noise, by giving the transmitted data white noise and gaussian characteristics. Noise-like signal generation is achieved by merging white noise characteristics of DS-PN SS techniques and a unique gaussian distribution technique in the time domain. 
     The basis for achieving the white noise and gaussian characteristics is the application of correlative techniques to the spread spectrum output. In the prior art, correlative techniques have been applied to high speed commercial transmissions and to magnetic disks for memory storage. The unique use of correlative techniques in this application allows for limited amounts of ISI, whereas the prior art teaches to drive the ISI to null. By effectively using correlative techniques, memory is built into the symbols, the symbols are dependent and have patterns that can be interpreted. 
     The system and method for converting digital data into a noise-like waveform utilizes a unique method of modulation that results in a system that makes it very hard or impossible to detect the information contained within the transmitted signal, or even detect the transmitted signal itself. 
     One object of the invention is to utilize spread spectrum technology in order to create output that is essentially white. 
     Another object of the invention is to provide additional security by randomizing the data and carrier. 
     A further object of the invention is to provide an output signal that combines white noise and a gaussian distribution to closely approximate actual noise; such a signal will have continuous spectrum and no discrete features. 
     Yet a further object of the invention is to lower the spectral density of the output signal by up to 3dB. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a system block diagram for conversion of data into a noise-like waveform according to a preferred embodiment of the invention. 
     FIG. 2 is a schematic block diagram of a synchronous digital modulator; 
     FIG. 3 shows an example waveform for the output of the synchronous digital modulator. 
     FIG. 4 is a schematic block diagram of a self-synchronized scrambler and descrambler. 
     FIG. 5 is a schematic block diagram of a direct-sequence pseudo noise spread spectrum converter. 
     FIG. 6 is a schematic block diagram of a gaussian converter. 
     FIG. 7 schematically illustrates an example of a gaussian conversion of a digital signal. 
     FIG. 8 is a state-space diagram for a one dimensional, L=7 noise-like data transmission system. 
     FIG. 9 is a graph depicting a gaussian distribution for the levels in the preferred embodiment of the invention. 
     FIG. 10 is a schematic block diagram of a system for conversion in two dimensions of two independent data sources into a noise like waveform, according to an alternate embodiment of the invention. 
     FIG. 11 schematically illustrates extracting discrete components from a signal using delay and multiply. 
     FIG. 12 graphically illustrates the presence and absence of discrete signal components. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a system block diagram for conversion of data into a noise-like waveform according to a preferred embodiment of the invention. In accordance with the preferred embodiment, a system for conversion of data into a noise-like waveform includes the following components: 
     a digital data source  4  or an analog data source  2  and an analog to digital converter  22 ; 
     a synchronous digital modulator  6 ; 
     a self-synchronized scrambler  8 ; 
     a direct-sequence pseudo noise spread spectrum converter  10 ; 
     a gaussian converter  12 ; and a 
     bandpass filter  14 . The system for conversion of data into a noise-like waveform also can be characterized as having a low speed unit  20  and a high speed unit  16 . These two units will be discussed below. 
     Data may be input to the system from one of two general sources: the first being an analog data source  2 , the second a digital data source  4 . If the data is input from the analog data source  2 , the data is converted into a digital format by an analog-to-digital converter  22 . 
     FIG. 2 is a schematic block diagram of a synchronous digital modulator  6 . Digital data  72 , regardless of its source, is input into a synchronous digital modulator  6 . The synchronous digital modulator  6  includes an EXCLUSIVE-OR (EX-OR) gate  38 A. It will be understood by those skilled in the art that that EX-OR function can be implemented in a number of ways, and that the EX-OR logic function is the same as modulo  2  binary addition without accounting for any carry. A first input of EX-OR gate  38 A receives the digital data  72  and a second input receives a clock signal that functions as a digital carrier  26 . In the preferred embodiment, all the clock signals are generated from a master clock  18  shown in FIG.  1 . The master clock  18  generates a data clock  4 , which is used by the digital data source  4  or the analog-to-digital converter  22 ; a digital carrier  26  for the synchronous digital modulator  6 , and also a spread spectrum faster clock  40 , in FIG. 5 used in direct-sequence pseudo noise spread spectrum converter  10 . 
     FIG. 3 shows an example waveform for the output of the synchronous digital modulator  6 . The output of the synchronous digital modulator  6  is a digitally modulated signal, A t  labeled as  74  in FIG.  2 . In FIG. 3, several clock cycles are numbered. In the first clock cycle, it can be seen that the digital carrier experiences a period of time when the signal level is high, and a period of time when the signal level is low. These periods can be referred to as a logic level  1  and logic level  0 , respectively. For each cycle of the digital carrier  26 , the digital data  72  is at one logic level or the other. For example, in the first digital carrier  26  cycle, the logic level is  1 , in the second it is a logic  0 , and in the third it is a logic  1 . 
     The Digitally Modulated Signal, A t , function is a logic  0  in FIG. 3 when carrier and data are at the same logic level, otherwise is a logic  1 . For example, in the first half of the digital carrier  26  cycle, the logic level is  1 . The data for that time period is also 1, and when the EX-OR function is applied to those two logic levels, the result is a 0, which can be seen on the line entitled “digitally modulated signal”. Then during the second portion of the digital carrier  26  cycle, the logic level of the digital carrier  26  is a 0, while the data is still 1; this creates an exclusive-or output of 1. This process continues indefinitely while data and the digital carrier are present. The waveform shown in FIG. 3 is also known as binary phase shift keying (BPSK). 
     BPSK shifts the phase of the carrier (in this instance a digital carrier  26 ) 180 degrees when there is a change in sign of the data. Note that other modulation schemes may be used, such as: quadrature phase shift keying (QPSK), and others. The only restriction is that the digital form in the preferred embodiment requires that the number of half cycles of the digital carrier  26  per data bit, is an integer. 
     FIG. 4 is a schematic block diagram of a self-synchronized scrambler  8  and descrambler. Referring to FIG. 1, the output of the synchronous digital modulator  6 , is input to the self synchronized scrambler  8 . The self synchronized scrambler  8  works as follows. 
     Shift registers are well known in the art. Data present at the input a certain period of time prior to either a trailing or rising edge (logic  0  or  1 ) of a clock pulse, is latched into the shift register. The shift register has multiple shift register elements ( 34 A-H), each with its own output. On the first clock pulse, the data present at the input will be latched in and become present at the output of the first shift register element  34 H. After the next clock pulse, that data becomes present at the output of the second shift register element  34 G, and so on, until it reaches the last shift register element output  34 A. 
     In the preferred embodiment of the invention, the self-synchronized scrambler  8  uses the second, third and seventh outputs of the shift register  34 . Data present at the input of the first shift register element  34 H before a first clock pulse reaches the output of the seventh shift register element  34 B on the seventh clock pulse. 
     The output B t    74  of the self-synchronized scrambler  8  in FIG. 4 is the output of the eighth shift register element  34 A. B t    74  is one input to the direct sequence pseudo noise spread spectrum converter  10  in FIG. 5. B t    74  is also connected to a first input of a feedback EX-OR gate  36 A in FIG. 4. A second input of the EX-OR gate  36 A is connected to the output of the seventh shift register element  34 B. The EX-OR gate  36 A has a first output, connected to a first input of an EX-OR gate  36 B. The EX-OR gate  36 B has a second input connected to the third shift register element  34  F output of the shift register  34 . 
     The EX-OR gate  36 B has a first output connected to a first input of an EX-OR gate  36 C. The EX-OR gate  36 C has a second input connected to the second shift register element  34 G output of the shift register  34 . The EX-OR gate  36 C has a first output connected to a second input of the EX-OR gate  36 D, and the EX-OR gate  36 D has a first input connected to receive A t    74 , which corresponds to the output of the synchronous digital modulator  6 , FIG.  2 . EX-OR gate  36 D has a first output connected to the input of the first shift register element  34 H of shift register  34 . 
     It can be seen, therefore, that old data is constantly “mixed” with the new data in a process known as “scrambling.” The input data is randomized, yet the original values are not lost. The use of scramblers in this fashion is well known in the art. 
     The self synchronized scrambler  8  randomizes both the data and the BPSK carrier. That is why a digital carrier is used. This randomization is essential to noise-like communication systems. In the preferred embodiment, the self synchronized scrambler  8  has a maximal length of 255 bits. The maximal length is the length, or number of bits that is output from the scrambler before the sequence begins to repeat itself. In other words, the output from the scrambler forms a word that is 255 bits in length. The pattern repeats itself after 255 bits. The maximal length is a function of where the feedback units are placed in the shift register configuration, and is also dependent upon the number N of shift registers. 
     In the example shown in FIG. 4, the maximal length is 255, according to the following relationship: 
     Maximal Length=2 N −1 
     Maximal Length=2 8 −1; which yields 256−1=255 (0 is never used). 
     The positioning of the feedback elements— 36 A-D, is precisely placed. Such positioning is known in the technical literature, as exemplified by F. J. Mac Williams and N. J. Sloane, “Pseudo-Random Sequences and Arrays,” Proceedings of the IEEE, Vol. 64, No.12, December 1976, pp. 1715-1729. The following equations define the relationship between the input to the scrambler A t , and the output, B t .                A   t     =     Input                 to                 scrambler             (   1   )                 B   t     =     Output                 of                 scrambler             (   2   )                 A   t     =       B   t     ⊕       ∑     i   ≤   1              g   i          B     t   -   1          mod                 2                 (   3   )                   B   t     =       A   t     ⊕       ∑     i   ≤   1                      g   i          B     t   -   i                     mod                 2                
            where                   g   i       =     0                 or                 1               (   4   )                                
     Self-synchronization follows FIG.  4  and equations (1) throughout (4) on page 9. Equation (3) represents the function of a scrambler with an input A t  and an output B t . Descrambler, which is identical to scrambler, can be represented by equation (4) provided that A t  is substituted by        (       A   t     ⊕       ∑       i   ≤                           g   i          B     t   -   i          mod                 2         )                          
     as input. If so, then the output of the descrambler is                (       A   t     ⊕       ∑     i   ≤   1                      g   i          B     t   -   i                     mod                 2         )     ⊕       ∑     i   ≤   1                      g   i          B     t   -   i                     mod                 2               (   5   )                                
     as per equation (4). The above equation (5) contains A t  plus two identical terms—all added modulo  2  which is the same logic function as can be performed by an EX-OR gate. Consequently the last two terms are identically zero and the remaining term in (5) is A t  as expected since the circuits in FIG. 4 for scrambler and descrambler are identical. All this is automatically practiced as the incoming waveform from the scrambler slides through the fixed descrambler. Self-synchronization occurs at the synchronization instant and A t  is delivered at the output of descrambler. 
     Increasing the number of register stages increases the maximal length and provides a greater degree of security in transmission of the digital signal. The order of magnitude of the maximal length can be in the thousands. The actual maximal length depends on the specific application of the embodiment of the invention. Therefore the preferred embodiment of the invention does not require a specific maximal length. 
     The following elements in FIG. 1 can be considered part of the low speed unit  20 : digital data source  4  (or analog data source  2  and analog-to-digital converter  22 ), synchronous digital modulator  6  and self-synchronized scrambler  8 . The following components can be considered part of the high speed unit  16 : DS-PN SS converter  10 , gaussian converter  12  and bandpass filter  14 . The difference between the low speed unit  20  and high speed unit  16  is the ratio of clock frequencies. Typically, the ratio of the frequency of the high speed clock to low speed clock can be on the order of 1000:1 or more. The clock that is used in the high speed unit is referred to as F C , with a period of T C  seconds and F C =1/T C  chips per second for DS-PN SS. 
     “Referring to FIGS. 1 and 4, the output of the self-synchronized scrambler  8 , Bt  74  is input to the direct sequence pseudo noise spread spectrum DS-PN SS) converter  10 . FIG. 5 is a schematic block diagram of a direct sequence pseudo noise spread spectrum converter  10 . The DS-PN SS converter  10  comprises an EX-OR gate  383 . A first input of the EX-OR gate  38 B receives the output Bt  74  of the self-synchronized scrambler  8 , and a second input receives a high speed maximal length spread spectrum PN sequence from a high speed maximal length shift register driven by the spread spectrum clock  40 . The output of the DS-PN SS converter  10  is a signal, AK,  78 . This output has white noise characteristics, i.e. has a relatively flat spectral density. The signal is not yet gaussian and it still contains continuous and discrete components. A discrete component is the spread spectrum clock signal.” 
     FIG. 6 is a schematic block diagram of a gaussian converter.  12  in FIG.  1 . The gaussian converter  12  comprises a modulo- 2  adder  28 , a shift register  30  and an algebraic adder  32 . The operation of the gaussian converter  12  is synchronous; that is, all operations are synchronized with either a falling or rising edge of a clock signal. 
     To insert memory into the spread spectrum signal A K    78 , an (L-2) stage shift register  30 , operating at a spread spectrum speed of F c  chips per second. The terminology “chips” is reserved for high speed spread spectrum technology to distinguish it from “bits” used for the “low speed” world, as previously discussed. The subscript “C” in F C  and T C  represents “chips.” As a first step, A K    78  is converted into B K    80 . B K    80  is the encoded version of A K    78 . The purpose of such coding is to facilitate identification of the chips at the receiving end. The inherent memory for each chip is built into each chip; such memory causes error propagation in decoding via A K . Previous chips are not needed to decode the current chip when B K  is used rather than A K . As a result, the probability of error, P e , is reduced, especially in noisy channel transmissions. 
     The output from the DS-PN SS converter  10 , A K    78  is connected to a first input of the modulo  2  adder  28 . A modulo  2  adder has a plurality of inputs, each receiving a chip from some source. The modulo  2  adder has a single output, B K    80 , which represents the modulo  2  sum of all six chips present at the inputs. For each clock period, a new sum is generated. As is well known in the art, if the number of logic level  1  chips present at the input of the modulo  2  adder is odd, the modulo  2  adder sum will be a 1, and if the number of logic level  1  chips is even, the output will be a 0. For example, if the logic levels at the inputs were 101010 (odd number of 1&#39;s) the modulo  2  sum would be 1. Likewise, if the logic levels at the input were 101011 (even number of 1&#39;s), the modulo  2  output would be 0. 
     Referring to FIG. 6, an algebraic sum of C K    82  is produced, which creates L levels (seven in this case) of correlative chip trains. The correlative concept is based on permitting controlled amount of intersymbol interference (ISI) rather than attempting to eliminate it as is done in conventional binary or multilevel digital systems known as Nyquist type (H. Nyquist, “Certain Topics In Telegraph Transmission Theory,” Bell Telephone Laboratories, Inc. Reprint B-331, August 1928) such as BPSK or QPSK. ISI results from preceding and succeeding pulse tails interfering at the sampling instant of a pulse. The net result of allowing some ISI is correlation between successive pulses within the limited group of digits. One of the benefits is white Gaussian characteristic. Another property is substantial increase of symbols per second speed for a fixed bandwidth compared to Nyquist type systems. Further, since correlative pulse trains are not independent, predetermined patterns exist. Violations of such patterns due to interference can be detected. Thus error detection can be accomplished without introducing redundant digits at the transmitter. The patterns are: one successive chip can go one level up or down or stay at the same level relative to previous chip. This is illustrated in FIG. 7 at the row labeled C K   82 . Another property of correlative is absence of discrete components at a clock frequency. This is discussed below and depicted in FIGS. 11 and 12. Example references discussing correlative signal processing are A. Lender, “Correlative (Partial Response) Techniques and Applications,” Chapter 7, pp. 144-183, Digital Communications: Microwave Applications, K.Feher ed. Prentice-Hall, Inc. 1981, which is more general; S Pasupathy, “Correlative Line Coding (Partial Response Signaling) Techniques,” The Froelich/Kent Encyclopedia of Telecommunications, Editor-In-Chief Fritz Froelich, pp. 483-499, Marcel Dekker, Inc. 1992, with easy presentation; and A. Lender, “Correlative Digital Communication Techniques,” IEEE Transactions, pp. 128-135, December 1964, which is mathematically, oriented. 
     FIG. 6 shows several different signals, which are defined below: 
     A K    78 =DS-PN SS binary input to Gaussian converter            A   K        78     =     DS        -        PN                 SS                 binary                 input                 to                 Gaussian                 converter                 B   K        80     =       A   K     ⊕       ∑     n   =   1     5            B     n   -   1          mod                 2                 encoded                 chip                 pulse                 train                     C   K        82     =       ∑     n   =   1     6            B     k   -   n                     algebraic                 seven                 level                   (     L   =   7     )                   output                 of                 Gaussian                 converter                   A   K        78     =         C   K                   mod                 2     =       [       ∑     n   =   1     6            B     k   -   n                     algebraic       ]                   mod                 2                              
     The output, B K    80 , of the modulo  2  adder  28  is connected to an input of the shift register  30 , and to a first input of the algebraic adder  32 . In the preferred embodiment, the shift register  30  has five stages, with output taps  1 - 5  after each shift register stage. The modulo  2  adder  28  has six inputs; a first input connected to receive the DS-PN SS converter  10  output, A K    78 , and five parallel inputs from the shift register  30  output taps  1 - 5 , respectively. The signal B K    80  is serially fed back to shift register  30  as shown in the FIG. 6 example. 
     The shift register  30  output taps  1 - 5  are also connected to the algebraic adder  32 . The algebraic adder  32  sums the number of logic level  1 &#39;s that are present and creates a number representing that sum. For example, if the six inputs to the algebraic adder  32  are 101010, the output of the algebraic adder would be 3 (if the input was 101110, the output of the algebraic adder  32  would be 4, and so on). The output of the algebraic adder  32 , C K    82 , is the output of the gaussian converter  12  in FIG.  1 . It is also useful to describe the output of the modulo  2  adder  28 , B K    80  as will become apparent below. 
     In FIG. 6, B K    80  is formed by adding, in modulo  2  fashion, a single A K    78  chip to the outputs of the shift register  30  which are present at the inputs of the modulo  2  adder  28 . 
     FIG. 7 schematically illustrates an example of a gaussian conversion of a digital signal. The first row of FIG. 7 shows the signal A K    78 , which is the input to the gaussian converter  12  in FIG.  1 . In the column labeled to, A K    78 =0; note that there are columns labeled − 1 , − 2 , − 3 , − 4  and − 5 : these are previous B K &#39;s  80  calculated by the modulo  2  adder  28 . The fifth previous B K    80  with respect to the present A K    78  input of 0, in the column t 0 , is shown at the column labeled − 5 . That is the output at the end of the shift register  30 , or the fifth output tap. This can be represented by the following expression.          B   K     =       A   K     ⊕       ∑   l   5            B     n   -   1          mod                 2                                
     The fourth previous B K    80  is shown at the column labeled − 4 . That is the output of the fourth tap of the shift register  30 . This occurs because of the nature of the shift register. It takes the previously calculated B K    80 , and shifts it in time, keeping it for five clock periods. At the end of each clock period, a new B K    80  is shifted in, the previous B K    80  is shifted along, and earlier previous B K &#39;s  80  are shifted as well. The result is at column t 0  A K    78 =0, and the outputs of the shift register  30  are 11010. The modulo  2  adder  28  adds the chips 011010 and the sum is 1, which is shown in the row labeled B K    80 , column t 0 . These signals and the new B K    80 , are presented to the algebraic adder  32 . The input then to the algebraic adder is 111010. The output of the algebraic adder is 4 (because there are four 1&#39;s). 
     As a result of the unique arrangement of the modulo  2  adder  28 , shift register  30  and algebraic adder  32 , in FIG. 6 each symbol output by the gaussian converter, C K    82 , is independent of the previous and subsequent symbols. The output is called a symbol. Even though the output has the same time duration as a chip, it represents more information than the binary chip (0 or 1) and so is given a separate identity. The independence of the output signal is created because memory is built into each symbol and each can be decoded separately from any others. As a result, if there is an error in any one symbol, i.e. it is received as a different symbol than was transmitted, it will not affect any other symbols. 
     In order to arrive at D K    84 , in FIG. 7,  3  is subtracted from C K    82  by introducing appropriate bias. D K    84  is the output of bandpass filter  14  shown in FIG.  1 . 
     The output waveform distribution of the gaussian converter  12  is, as its name implies, gaussian. The six inputs to the algebraic adder  32  are effectively random binary pulses and each pulse train has a uniform distribution. This means that no one binary pulse is more likely to occur than any other binary pulse. Algebraic additions of such pulse trains approaches gaussian distributions. The more chip trains utilized (i.e. 7, 8, 9 or more inputs to the algebraic adder), the closer the output approaches an ideal gaussian distribution. In this case, as an example only, 7 levels are used, and that is sufficiently accurate. 
     For the gaussian converter  12  shown in FIG. 6, the number of levels generated is seven. An individual level is the symbol number that is generated by the algebraic adder  32 . In this instance, as the table in FIG. 7 shows, there are seven possible outcomes in D K   84  from the algebraic adder: −3, −2, −1, 0, 1, 2 3. These levels, or numbers, are related to the construction of the gaussian converter  12 , by the following: 
     Number of Shift Register Elements=L−2. 
     In this example, it is desired to have seven levels, which, in the preferred embodiment, requires five shift register elements. 
     FIG. 8 is a state-space diagram for a one dimensional, L=7 noise-like data transmission system. As discussed above, there is a relationship between C K , D K  and A K . D K  is formed by subtracting 3 from C K . The bandpass filter  14  in FIG. 1 accomplishes this function. The following relationships are then true: 
     
       
         A K    78 =C K mod 2   
       
     
     A K    78 =D K mod 2 −(Binary inverse of D K mod 2 .) 
     One of the key and unique characteristics of the noise-like signal described here is that only continuous spectral component exists and the discrete component is absent. The reason is spectral density related to Nyquist criteria on rolloffs and inherent properties of correlative techniques. At this point it is appropriate to discuss absence of discrete component in correlative systems. This attribute is of utmost importance for noise-like characteristics of white Gaussian properties. The well-known detector in searching for discrete component is delay and multiply followed by averaging as depicted in FIG.  11 . Mathematics is complex and its net result appears in FIG. 11 It is:                X   _     =       K   1            ∫   ∞   ∞              z        (   f   )       ·     z        (       1     T   c       -   f     )                 f                   (   6   )                                
     where {overscore (X)} is magnitude, K 1  is constant and the two integrands are spectral densities of “multiply” in FIG.  11 . It is clear from above equation that {overscore (X)} is zero when the integrand components do not have common overlapping area. If so, {overscore (X)} then discrete component is absent. FIG. 12 graphically depicts conditions of the equations for {overscore (X)}. It is based on Nyquist criteria in H. Nyquist, “Certain Topics In Telegraph Transmission Theory,” Bell Telephone Laboratories, Inc. Reprint B-331, August 1928. The first waveform in FIG. 12 depicts rectangular spectral density properties with Nyquist baseband bandwidth ½T c  Hz and α=0 and the second with α≠0. Parameter α        α   =           excess                 bandwidth                 over                 Nyquist                 bandwidth       Nyquist                 bandwidth                     and     ≤   α   ≤   1                            
     The top waveform in FIG. 12 illustrates Nyquist bandwidth. It cannot possibly have discrete component—the spectra are disjointed. But anyway Nyquist bandwidth spectrum cannot be physically implemented. Therefore all present systems such as BPSK, QPSK, MSK and others follow Nyquist second criteria with wider bandwidth, such as middle waveform in FIG. 12, with raised cosine shaping and α=1. Any system with α≠0 has common area (shaded) in equation (6) and FIG.  12  and has discrete component. The only exception is correlative. For correlative, Nyquist criteria are not violated as well as equation (6). All have Nyquist bandwidth and α=0. This is shown in FIG.  12 —the last spectrum for L=7 where L is number of levels. The spectral density of correlative in FIG. 12 is:                H        (   f   )       =                  sin        (     L   -   1     )          π                 f                   T   c         sin                 π                 f                   T   c                            for                 f     ≤       1     2                   T   c                       and                 zero                 beyond               (   7   )                                
     In this respect, H(f) in equation (7) is spectral density of correlative 7-level system and has no discrete component. To generalize, all correlative systems are unique in the sense of having Nyquist bandwidth ½T c  and α=0 and absence of discrete spectral component. 
     Going back to FIG. 8, when C K    82  equals 6, this corresponds to the following inputs at the algebraic adder  32  at FIG.  6 : 1111111. If the same logic values constituted input to the modulo  2  adder  28  in FIG. 6, the output would be 0, because there are an even number of 0&#39;s. Thus, it can be shown for every C K    82  there is a corresponding D K    84  and A K    78 . Also, the relationship between A k    78  and D k    84  is invariant to 180° rotation. That is, a D K    84  of 3 has the same A k    78  as a D k    84  of −3. 
     FIG. 9 is a graph depicting a gaussian distribution for the levels in the preferred embodiment of the invention, and the actual distribution. The table below lists the actual and ideal results for an L=7 system for converting digital data into a noise-like waveform. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                   
                   
                 Percent Deviation 
               
               
                   
                 Level 
                 Ideal 
                 Actual 
                 from Ideal 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 3 
                 .0162 
                 .0156 
                 3.7 
               
               
                   
                 2 
                 .0859 
                 .0937 
                 −9.0 
               
               
                   
                 1 
                 .233 
                 .234 
                 −0.4 
               
               
                   
                 0 
                 .326 
                 .313 
                 4.0 
               
               
                   
                 −1 
                 .233 
                 .234 
                 −0.4 
               
               
                   
                 −2 
                 .0859 
                 .0937 
                 −9.0 
               
               
                   
                 −3 
                 .0162 
                 .0156 
                 3.7 
               
               
                   
                   
               
             
          
         
       
     
     The graph in FIG. 9 is characterized by the following relationships:          p        (   x   )       =       e         -     x   2       /   2          σ   2           σ          2                 π                                  
     σ 2 =1.5 
     L=7 
     FIG. 10 is a schematic block diagram of a system for conversion in two dimensions of two independent data sources into a noise like waveform, according to an alternate embodiment of the invention. Two different information sources are transmitted. The entire system is synchronous based on a quadrature master clock  86 . There is a first quadrature data source  42  with an output connected to a first quadrature synchronous digital modulator  46 . The first quadrature synchronous digital modulator  46  has a first output connected to a first quadrature self synchronized scrambler  50 . The first quadrature self synchronized scrambler  50  has a first output connected to a first quadrature DS-PN SS converter  54 . The first quadrature DS-PN SS converter  54  has its output connected to a first quadrature gaussian converter  58  which includes first quadrature modulo  2  adder  62 , first quadrature shift register  66  and quadrature algebraic adder  70  up to the output bandpass filter. 
     The second half of the quadrature system is similar to the first half. There is a second quadrature data source  44  with a first output connected to a second quadrature synchronous digital modulator  48 . The second quadrature synchronous digital modulator  48  has a first output connected to a second quadrature self synchronized scrambler  52 . The second quadrature self synchronized scrambler  52  has a first output connected to a second quadrature DS-PN SS converter  56 . The second quadrature DS-PN SS converter  56  has its output connected to a second quadrature gaussian converter  68 . 
     Within the second quadrature gaussian converter  68  there is a second quadrature modulo  2  adder  64 , and a second quadrature shift register  69  and a quadrature algebraic adder  70 . The first quadrature gaussian converter  58  and the second quadrature gaussian converter  68  share a common element, the quadrature algebraic adder  70  and output bandpass filter. In this alternate embodiment of the invention, it is desirable to use two different Gold codes for the quadrature DS-PN SS. Using different Gold codes is best for low spread spectrum cross correlation. In all other respects, operation of the quadrature system for conversion of data into a noise-like waveform is the same as the embodiment shown in FIG.  1 . 
     Those skilled in the art will appreciate that the embodiments of the present invention can be implemented in hardware, software or a combination of both. As an example, shift registers are available as hardware components and are commonly also implemented within a processor. Accordingly, the above description of the preferred embodiments is not limited to either a hardware or software implementation.