Abstract:
Multilevel code mates A and B expanded in accordance with the expression  , b K  and B=a K , b are compressed to a lobeless basic mate pair by repeatedly compressing corresponding code mate pairs in successive stages to provide diminishing codes of half the code length by amplifying the code mates by a predetermined amplification factor and then adding and subtracting the code mates in accordance with the expressions A i-1  =A i  +B i   K .sbsp.i and B i-1  =A i   K .sbsp.i -B i  where i is the i th  compression stage and K i  is the amplification factor applied to the codes A i  and B i .

Description:
The invention described herein may be manufactured, used and licensed by or for the Government for governmental purposes without the payment of any royalties thereon or therefor. 
     CROSS REFERENCE TO RELATED APPLICATIONS 
     This invention is related to the following co-pending applications filed in the name of the present inventor: 
     U.S. Ser. No. 502,416, now abandoned, entitled, &#34;Code Compressor For Interleaved Multiplexed Noise Codes&#34;, filed in the name of the present inventor on June 8, 1983; 
     U.S. Ser. No. 456,157, now U.S. Pat. No. 4,471,342 entitled, &#34;Pulse Compressor For Multiplexed Noise Codes&#34;, filed in the name of the present inventor on Jan. 6, 1983; 
     U.S. Ser. No. 533,183 entitled, &#34;Multilevel Noise Code Mate Pair Generation And Utilization Of Such Codes&#34;, filed in the name of the present inventor on Sept. 19, 1983; and 
     U.S. Ser. No. 536,064 entitled, &#34;Expanded Multilevel Noise Code Generator Employing Butting&#34;, filed in the name of the present inventor on Sept. 26, 1983. 
     FIELD OF THE INVENTION 
     This invention relates generally to the compression of noise codes having autocorrelation functions which upon detection with a matched filter provides an impulse and more particularly to the compression of such codes comprised of expanded multilevel multiplexed noise code mate pairs generated by the process of butting. 
     BACKGROUND OF THE INVENTION 
     Radio communication systems utilizing multiplexed noise codes are generally known. A typical example is shown and described in U.S. Pat. No. 4,293,953, entitled, &#34;Bi-Orthogonal PCM Communication System Employing Multiplexed Noise Codes&#34;, which issued to Frank S. Gutleber, the present inventor, on Oct. 6, 1981. 
     The concept of code expansion and compression for the general class of multiplexed noise codes comprised of noise code mate pairs having autocorrelation functions which upon detection in a matched filter provide an impulse is also generally known. Such concepts are disclosed, for example, in U.S. Pat. No. 3,461,451, entitled, &#34;Code Generator To Produce Permutations Of Code Mates&#34;, which issued to the present inventor on Aug. 12, 1969; U.S. Pat. No. 3,519,746, entitled, &#34;Means And Method To Obtain An Impulse Autocorrelation Function&#34;, which issued to the present inventor on July 7, 1970; and U.S. Pat. No. 3,634,765, entitled, &#34;System To Provide An Impulse Autocorrelation Function . . . &#34;, which issued to the present inventor on Jan. 11, 1972. 
     In the above mentioned related abandoned application, U.S. Ser. No. 502,416, entitled, &#34;Code Compressor For Interleaved Multiplexed Noise Codes&#34;, there is disclosed the concept of repetitively compressing corresponding code mate pairs in successive stages to provide ever diminishing codes of half the bit quantity and twice the amplitude until a single pulse results at the location of the final code bit whose amplitude is increased by a factor of twice the number of bits in each of the original interleaved codes. The apparatus employed comprises a series of cascaded code separators separated by delay lines providing ever increasing delays which are multiples of the pulsewidth of each code bit and wherein the delay is doubled at each stage until the last stage is reached and a delay of one half the original code length of the interleaved codes is provided, whereupon a combining of the codes results in an impulse autocorrelation function. 
     In the aforementioned related application, U.S. Ser. No. 536,064, entitled, &#34;Expanded Multilevel Noise Code Generator Employing Butting&#34;, there is disclosed the concept of the generation of code mate pairs comprising a pair of expanded noise code mates having code portions of more than one amplitude level and which are generated by butting noise code mates of different amplitude levels such that mutually transposed butted code mates in the expanded code mate pairs have respective code bits which are amplified by a predetermined gain factor and wherein one of the butted code mates comprises the complement or negative of the original code mates. 
     One known method for compressing a code mate pair is by employing a matched filter comprised of a separate tapped delay line for each code with the output of the taps matched to the input code bits in reverse order to the input sequence. The linear summation of the matched outputs in each delay line then provides the compressed code for each code of the pair. Each output, moreover, is equal to the autocorrelation function of the respective code being matched and the simple linear sum of the two outputs results in a single lobeless output signal. This approach, however, becomes relatively expensive and difficult to implement for extremely long codes since a separate tap and amplifier with or without an inverter is required for each of the input code bits. 
     Accordingly, it is an object of the present invention to provide an improvement in the compression of noise codes. 
     Another object of the present invention is to provide an improvement in the compression of multiplexed code mate pairs having more than one amplitude level. 
     Still another object of the invention is to provide an improvement in the compression of multilevel, multiplexed code mate pairs generated by the process of butting code mates. 
     SUMMARY 
     These and other objects are achieved by compressing multilevel multiplexed code mate pairs that result from the expansion of code mates using a code butting process which utilizes the repeated application of an expansion rule forming expanded codes A and B in accordance with the following expressions: A=a, b K  and B=a K , b, where the exponent K represents the amplification factor of the code bits of codes a and b, b represents the complement or the negative of code b, and the comma signifies that code b is butted to code a. Furthermore in the expansion process, any of the four subelements making up the expanded code may be inverted or made negative and the amplified segments can, when desired, be transposed. The code mates thus expanded are compressed in this invention to a lobeless basic mate pair by repeatedly compressing corresponding code mate pairs in successive stages to provide diminishing codes of half the code length by amplifying the code mates by a predetermined amplification factor and then adding and subtracting the code mates in accordance with the following general rule: A i-1  =A i  +B i .sup. K.sbsp.i and B i-1  =A i   K .sbsp.i -B i  where i is the i th  compression stage and the exponent K i  is the amplification factor for the i th  stage. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a functional block diagram illustrative of transmitter apparatus for a noise modulated communication system utilizing a pair of expanded multilevel code mates generated by the process of butting; 
     FIG. 2 is a functional block diagram illustrative of receiver apparatus of a noise modulated communications system for receiving and compressing the expanded multilevel codes in accordance with the principle of this invention; and 
     FIG. 3 is a diagram illustrative of an embodiment of the code compressor shown in FIG. 2. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention is directed to digital codes referred to as noise codes, meaning that the information is coded with a code that is &#34;noise like&#34; and that it will compress to an impulse when detected with a matched filter. In particular, one class of noise codes are known wherein pairs of coded signals termed &#34;code mates&#34; have autocorrelation functions which provide a peak output at a given time and a zero output or outputs having the same magnitude but opposite polarity, at all other times. When code mate signals, for example, are multiplexed, matched filter detected and linearly added, there is provided a lobeless impulse output of relatively high amplitude at one given time (τ=0) and a zero output at all other times (τ≠0). Mathematically, for a pair of code mates a and b, 
     
         φ.sub.a (τ)=-φ.sub.b (τ)                   (1) 
    
     for all τ≠0, where φ a  (τ) is the autocorrelation function of code a, φ b  (τ) is the autocorrelation function of code b and wherein τ=0 is the location of the main lobe. 
     In the above referenced related application Ser. No. 536,064, entitled, &#34;Expanded Multilevel Noise Code Generator Employing Butting&#34;, there is disclosed a code length expansion process which results in multilevel code mate pairs which meet the requirement of equation (1) while being generated by the repeated application of the following general rule: 
     
         A=a, b.sup.K                                               (2) 
    
     
         B=a.sup.K, b                                               (3) 
    
     where the exponent signifies an amplitude gain factor of the code bits a 1  . . . a n  in code a and b 1  . . . b n  in code b, b represents the complement or negative of code b nd wherein the comma signifies that the second code portion of each expanded code mate A and B follows the ends of the first code portion a by having a time delay (τ) which is equal to the code length of code a. Further, in the expansion process signified by equations (2) and (3), either code a or b may be negative, i.e., a or b and the amplified segments a K  and b K  may be transposed. U.S. Ser. No. 536,064 may be resorted to for a further understanding of this expansion process. 
     Returning attention now to the present invention, consider for purposes of illustration a multilevel code mate pair where A=A 3  and B=B 3  and having been generated in accordance with the expansion rule expressed in equations (2) and (3). The expansion process, furthermore, can be illustrated in the following example. Letting a and b represent the basic code mate pair, using the aforementioned expansion rule results in A 1  and B 1  being developed as: 
     
         A.sub.1 =a, b.sup.K.sbsp.1                                 (4) 
    
     
         B.sub.1 =a.sup.K.sbsp.1, b                                 (5) 
    
     Expanding codes A 1  and B 1  yields codes A 2  and B 2  which can be expressed as: 
     
         A.sub.2 =a, b.sup.K.sbsp.1, a.sup.K.sbsp.1.sup.K.sbsp.2, b.sup.K.sbsp.2 (6) 
    
     
         B.sub.2 =a.sup.K.sbsp.2, b.sup.K.sbsp.1.sup.K.sbsp.2, a.sup.K.sbsp.1, b (7) 
    
     Utilizing a third expansion stage and expanding codes A 2  and B 2  results in codes A 3  and B 3  being developed and which can be expressed as: 
     
         A.sub.3 =a, b.sup.K.sbsp.1, a.sup.K.sbsp.1.sup.K.sbsp.2, b.sup.K.sbsp.2, a.sup.K.sbsp.2.sup.K.sbsp.3, b.sup.K.sbsp.1.sup.K.sbsp.2.sup.K.sbsp.3, a.sup.K.sbsp.1.sup.K.sbsp.3, b.sup.K.sbsp.3               (8) 
    
     
         B.sub.3 =a.sup.K.sbsp.3, b.sup.K.sbsp.1.sup.K.sbsp.3, a.sup.K.sbsp.1.sup.K.sbsp.2.sup.K.sbsp.3, b.sup.K.sbsp.2.sup.K.sbsp.3, a.sup.K.sbsp.2, b.sup.K.sbsp.1.sup.K.sbsp.2, a.sup.K.sbsp.1, b(9) 
    
     The expanded code mates A 3  and B 3  form multilevel code mate pairs which satisfy equation (1) in that φ A .sbsb.3 (τ)=-φ B .sbsb.3 (τ) for all τ≠0 and which compresses to a lobeless impulse when the individual mate code pairs are detected in their respective matched filters and linearly added. 
     Rather than compressing the two expanded codes A=A 3  and B=B 3  in a conventional matched filter, the present invention compresses the codes collectively rather than individually. An inspection of the two codes A 3  and B 3  reveals that compression of these codes results when the following mathematical operations are performed, resulting in amplified versions of A 2  and B 2  being generated as code mates in the following manner: 
     
         A.sub.2 &#39;=A.sub.3 +B.sub.3.sup.K.sbsp.3                    (10) 
    
     
         B.sub.2 &#39;=A.sub.3.sup.K.sbsp.3 -B.sub.3                    (11) 
    
     Utilizing the above relationships results in codes which can be expressed as: 
     
         A.sub.2 &#39;=a.sup.(K.sbsp.3.spsp.2.sup.+1), b.sup.K.sbsp.1.sup.(K.sbsp.3.spsp.2.sup.+1), a.sup.K.sbsp.1.sup.K.sbsp.2.sup.(K.sbsp.3.spsp.2.sup.+1), b.sup.K.sbsp.2.sup.(K.sbsp.3.spsp.2.sup.+1)               (12) 
    
     
         B.sub.2 &#39;=a.sup.K.sbsp.2.sup.(K.sbsp.3.spsp.2.sup.+1), b.sup.K.sbsp.1.sup.K.sbsp.2.sup.(K.sbsp.3.spsp.2.sup.+1), a.sup.K.sbsp.1.sup.(K.sbsp.3.spsp.2.sup.+1) b.sup.(K.sbsp.3.spsp.2.sup.+1) (13) 
    
     Noting that A 2  &#39; and B 2  &#39; are equal to A 2  and B 2  multiplied by (K 3   2  +1), an inspection of these two compressed codes reveals that the same general operation can provide an amplified version of further compressed code mates A 1  and B 1  resulting in codes A 1  &#39; and B 1  &#39; being generated when utilizing multiplying factor K 2  and which can be expressed as: 
     
         A.sub.1 &#39;=A.sub.2 +B.sub.2.sup.K.sbsp.2                    (14) 
    
     
         B.sub.1 &#39;=A.sub.2.sup.K.sbsp.2 -B.sub.2                    (15) 
    
     Performing these operations results in: 
     
         A.sub.1 &#39;=a.sup.(K.sbsp.3.spsp.2.sup.+1)(K.sbsp.3.spsp.2.sup.+1), b.sup.K.sbsp.1.sup.(K.sbsp.2.spsp.2.sup.+1)(K.sbsp.3.spsp.2.sup.+1) (16) 
    
     
         B.sub.1 &#39;=a.sup.K.sbsp.1.sup.(K.sbsp.2.spsp.2.sup.+1)(K.sbsp.3.spsp.2.sup.+1), b.sup.(K.sbsp.2.spsp.2.sup.+1)(K.sbsp.3.spsp.2.sup.+1)    (17) 
    
     The codes A 1  &#39; and B 1  &#39; are equal to compressed codes A 1  and B 1  multiplied by the factor (K 2   2  +1)(K 3   2  +1). Applying the expansion process a third time results in amplified versions of the basic code mates. Utilizing the multiplying factor K 1 , there results: 
     
         A.sub.o &#39;=A.sub.1 +B.sub.1.sup.K.sbsp.1                    (18) 
    
     
         B.sub.o &#39;=A.sub.1.sup.K.sbsp.1 -B.sub.1                    (19) 
    
     Applying these compression equations yields: 
     
         A.sub.o &#39;=a.sup.(K.sbsp.1.spsp.2.sup.+1)(K.sbsp.2.spsp.3.sup.+1)(K.sbsp.3.spsp.2.sup.+1)                                                     (20) 
    
     
         B.sub.o &#39;=b.sup.(K.sbsp.1.spsp.2.sup.+1)(K.sbsp.2.spsp.2.sup.+1)(K.sbsp.3.spsp.2.sup.+1)                                                     (21) 
    
     It can be seen from equations (20) and (21) that the multilevel mate pairs A 3  and B 3  have been compressed lobelessly down to the basic mate pair a and b amplified by the factor (K 1   2  +1)(K 2   2  +1)(K 3   2  +1) which corresponds to the coherent summation of the individual bits and is equal to that which would result from a matched filter detector, i.e. φ a  (τ) and φ b  (τ), in accordance with the known prior art. 
     Thus what has been shown and described is a compression process wherein codes generated from the general expansion rule set forth in equations (10) and (11) are coherently compressed to a lobeless basic mate pair by repeatedly applying the following general operation: 
     
         A.sub.i-1 =A.sub.i +B.sub.i.sup.K.sbsp.i                   (22) 
    
     
         B.sub.i-1 =A.sub.i.sup.K.sbsp.i -B.sub.i                   (23) 
    
     While a functional block diagram of a code compressor which is operable to perform the operations identified above is shown in FIG. 3, noise modulated digital communications system employing such codes is typically disclosed in FIGS. 1 and 2. 
     Referring first to FIG. 1, reference numeral 10 denotes a basic code mate generator for generating code mates a and b and which are utilized to generate multilevel expanded codes A and B in accordance with the foregoing description. The codes a and b are fed out in a time related multi-bit binary digital sequence to code expander apparatus designated by reference numeral 12 and which are generated, for example, in accordance with the expansion process disclosed in the aforementioned related application, U.S. Ser. No. 536,064 entitled, &#34;Expanded Multilevel Noise Code Generator Employing Butting&#34;. The expanded multilevel codes A and B are applied to respective modulator circuits 14 and 16 which additionally have applied thereto a carrier frequency generated by a carrier frequency generator 18. The output of the modulators 14 and 16 comprise, for example, separate biphase modulated codes which are fed to a multiplexer 20 which operate to either time or frequency multiplex the carrier modulated signals A and B. The output of the multiplexer 20 is fed to an RF amplifier 22 where an RF carrier containing the multiplexed codes A and B are radiated from an antenna 24. 
     With respect to FIG. 2, there is disclosed receiver apparatus which is responsive to the RF signal radiated from the antenna 24 and containing the codes A and B. Accordingly, the radio receiver apparatus 26 is shown coupled to a receiving antenna 28 which is operable to translate the multiplexed codes A and B at the RF frequency to an IF frequency whereupon they are fed to a demultiplexer 30. The demultiplexer is operable to orthogonally separate and output the expanded multilevel codes A and B where they are applied to a code compressor 32, the details of which are shown in FIG. 3 and which is operable to compress the codes to an amplified version of codes a and b which corresponds to the respective autocorrelation function outputs φ a  (τ) and φ b  (τ). The autocorrelation function outputs of the compressor 32 are applied to the linear adder 34 which is operable to develop a substantially lobeless single impulse output signal φ T  (τ). 
     Referring now to FIG. 3, there is disclosed a functional block diagram of the compressor 32 shown in FIG. 2 where A=A 3  and B=B 3 . The compressor as shown in FIG. 3 is comprised of three compressor stages 36 1 , 36 2  and 36 3 , each of which separately implements the compression process defined by the general equations (22) and (23). The first expansion stage 36 1  implements mathematical operations set forth in equations (10) and (11) whereupon the input multilevel code mates A 3  and B 3  are compressed to half their length into the compressed codes A 2  &#39; and B 2  &#39;. As shown, input code B=B 3  is fed to an amplification stage comprised of a pulse amplifier 38 1  where it is amplified by the gain factor K 3 . The output of the amplifier 38 1  is fed to a first linear adder 40 1  which also is coupled to the other input code A=A 3 . The output of the adder 40 1  comprises a compressed code A 2  &#39; in accordance with equation (10). The code mate of A 2  &#39; is obtained by feeding the code B 3  to a signal inverter 42 1  which is operable to change the polarity of a positive pulse to a negative pulse and vice versa, and thus outputs the complement or negative of code B 3 , i.e. B 3 . The code output from the inverter 42 1  is fed to a second linear adder 44 1  along with the code A 3  which has been multiplied by the gain factor K 3  in the amplifier 46 1 . Since an algebraic subtraction can be obtained by changing the sign of the subtrahend and thereafter performing an addition, the adder 44 1  provides an output of code B 2  &#39; as defined in equation (11). It can be shown that the compressed code B 2  &#39; is actually delayed in time relative to the code A 2  &#39; by half the input code width which corresponds to 4nτ where n is equal to the number of code bits in the codes A 3  and B 3  and τ is equal to the pulsewidth of each code bit. It becomes necessary therefore to time delay the compressed code A 2  &#39; by 4nτ to line it up with the delayed code B 2  &#39; prior to compressing the codes in the next or succeeding compression stage 36 2 . This is provided by the time delay device 48 1  which typically comprises a delay line, a well known piece of apparatus. 
     Referring now to the second compression stage 36 2 , the code B 2  &#39; is amplified by the gain factor K 2  in the amplifier 38 2  and added to the delayed code A 2  &#39;d in the linear adder 40 2  providing the compressed output code A 1  &#39;. The code mate to A 1  &#39; is obtained by inverting the code B 2  &#39; in the inverter 42 2  and adding it to the delayed code A 2  &#39;d after amplifying it by a factor K 2  in the amplifier 46 2 . Thus equations (14) and (15) are implemented. 
     The base codes a and b are obtained utilizing a third compression stage 36 3  which is identical to the preceding stages with the exception of the time delay provided by the time delays 48 1  and 48 2 . As shown, the A 1  &#39; code mate provided by the second compression stage 36 2  is delayed by a time delay of 2nτ in the delay device 48 2  in order to line up the codes A 1  &#39; and B 1  &#39;, both of which have had their code lengths again reduced by one half. As before, the code B 1  &#39; is amplified by a gain factor K 1  in the amplifier 38 3  where it is added to the delayed code A 1  &#39;d in the adder 40 3  to yield the code A o  &#39; in accordance with equation (20). Code B o  &#39; is achieved by inverting the code B 1  &#39; by the inverter 42 3  and adding it to the delayed code A 1  &#39;d after it is amplified by a factor K 1  in the amplifier 46 3 . Codes A o  &#39; and B o  &#39; correspond to the original code mate pairs a and b but now amplified by the gain factor (K 1   2  +1) (K 2   2  +1) (K 3   2  +1). In order that a single impulse output can be provided by the adder 34 shown in FIG. 2, a third delay device 48 3  providing a time delay of nτ is provided in order that the two codes line up. 
     Although the pulse compressor shown in FIG. 3 has been described for apparatus compressing a code length of 8n where n corresponds to the number of code bits in each basic code mate a and b, the repeated application of the process described at each compression stage can compress a code structure of any length down to the basic code mate. The compressed codes, moreover, are lobeless and are obtained with much less hardware than that required for other known approaches. For a code length comprising N blocks of n bits, only p compression stages are needed to compress the code down to n bits where 2 p  =N. For example, with n=1 only p=10 compression stages with each stage including one delay device, two amplifiers, two adders and an inverter would be required to compress a 1024 bit code down to a lobeless impulse. 
     Thus what has been shown and described is the concept of compressing multilevel code mate pairs that have been generated by butting two code mates having autocorrelation functions of codes that are equal in magnitude but of opposite sense for all values of time delay τ except at τ=0. These codes, moreover, can when appropriately utilize improve the entire field of communications since they are capable of optimizing all transmission systems including not only communications systems, but also multiple access systems, radar systems, altimeters, fuses, missile guidance, navigation, traffic control, etc. by reducing self-interference, providing anti-jam (A/J) protection, low probability of intercept (LPI), as well as providing increased range and velocity resolution and their accuracy of measurement. 
     Having thus shown and described what is at present considered to be the preferred method and means for implementing the subject invention, it is noted that the same has been made by way of illustration and not limitation. Accordingly, all modifications, alterations and substitutions may be made without departing from the spirit and scope of the invention as set forth in the appended claims.