Abstract:
The present invention provides a method and apparatus for implementing a continuous phase modulation with an approximate phase constellation. The method reduces complexity by using fewer than all phase points of the nominal phase constellation. The method includes the steps of storing ( 502 ) an approximate phase constellation of phase points ( 100 ) selected from a nominal phase constellation of phase points, identifying ( 504 ) a next phase in the approximate phase constellation of phase points using an N-bit input word, and outputting ( 506 ) the next phase. In reducing the number of phase points used in the modulation, the method may store only unique phase points in said phase constellation, and may further reduce the number of phase points by storing only those phase points differing by at least a phase threshold. In identifying the next phase, the method may shift ( 604 ) an input bit into an N-bit shift register (with an N-bit output) and apply the N-bit output ( 606 ) as an address to a memory that stores the subset of phase points. The memory thereby outputs ( 608 ) the next phase.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to phase constellation modulators. In particular, the present invention relates to reduced complexity phase constellation modulators for continuous phase modulation (CPM) communication systems. 
     A number of modulation schemes are widely used in communication systems. For example, Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Minimum Shift Keying (MSK), Gaussian Minimum Shift Keying (GMSK) and the like are often used to encode raw data into single-bit or multi-bit symbols for digital transmission. In QPSK, for example, two bits are represented by transmitting a waveform with one of four possible phase offsets (e.g., plus/minus 45 degrees and plus/minus 135 degrees) of a carrier, cos(wt+phase), during each symbol time duration. 
     Each of the various types of modulation, of course, has its own advantages and its own drawbacks when used in any particular communication system. For example, both BPSK and QPSK modulations exhibit a power spectral density (PSD) with large side lobes that can cause adjacent channel interference (ACI). The effect of ACI can be mitigated by increasing the frequency separation between channels. However, this solution will result in the reduction of the number of frequency channels that may exist within a given frequency band, and thus reduce the information carrying capacity of the frequency band. The utilization of a filtering process to reduce the side lobes, unfortunately, introduces both intersymbol interference (ISI)—interference between the symbols in the same frequency channel, as well as additional system complexity. 
     Thus, the communication industry has turned to modulation schemes that are by definition bandwidth efficient to begin with. In other words, rather than trying to effect bandwidth efficiency through filtering to remove sidelobes, the communication industry has turned to bandwidth efficient types of modulation. A more bandwidth efficient modulation, such as minimum shift keying (MSK) eliminates step changes in the phase of the transmitted waveform and is therefore denoted as a CPM. Filtered forms of MSK, such as GMSK, will eliminate step changes in the frequency of the transmitted waveform. Thus, for GMSK, a controlled amount of ISI is introduced into the waveform and symbols are transmitted as gradual changes in phase. The result is that the GMSK waveform has a power spectral density (PSD) that falls off extremely quickly, thereby allowing frequency channels to be packed closely together. 
     GMSK and other CPMs enable the information carrying capacity and bandwidth efficiency (and potential revenues) of a communication system to be increased. Additional details on modulation techniques may be found, for example, in Chapters 6 and 13 of  Principles of Analog and Digital Communications,  Second Edition, Jerry D. Gibson, Prentice-Hall (1993). 
     In the past, however, CPMs have been implemented in unduly complex fashion. As an example, past GMSK modulators unnecessarily required hardware to accumulate a running sum of frequency deviation pulses to determine the phase of the modulated waveform. Generally in a digital implementation of a CPM, only a finite number of phase states is possible, but even systems that precompute the phase states have failed to realize several valid simplifying aspects of CPMs that greatly reduce the complexity of the modulator. 
     Each reduction in complexity not only decreases the cost of the communication system, but increases the reliability, manufacturability, and maintainability of the communication system. A need has long existed in the industry for a reduced complexity phase constellation modulator. 
     BRIEF SUMMARY OF THE INVENTION 
     It is one object of the present invention to provide a modulator to generate a CPM. 
     It is a second object of the present invention to provide a GMSK modulator. 
     A third object of the present invention is to provide a GMSK modulator with reduced complexity. 
     A fourth object of the present invention is to provide a GMSK modulator that takes advantage of both the distribution of a nominal phase constellation (NPC), and the NPC itself to reduce the complexity of the modulator. 
     One or more of the foregoing objects are met in whole or in part by the method for modulation described herein. The method reduces complexity by using fewer than all phase points in an NPC. The method includes the steps of storing an approximate phase constellation (APC) generated from the NPC, identifying the next baseband phase point in the APC using an N-bit input word, and outputting the next baseband phase point. 
     The APC may include, for example, phase points comprising in-phase and quadrature-phase values representing a subset of the NPC or phase points derived from the NPC. Note, therefore, that the APC is not limited to including only phase points contained in the NPC. In reducing the number of phase points used in the modulation, the present modulator may identify and group phase points differing by less than a phase threshold. The APC may then store a phase point commensurate with the phase points in each group. The phase threshold may be, for example, 3 degrees. 
     In identifying the next baseband phase point, the method may shift an input bit into an N-bit shift register (with an N-bit output) and apply the N-bit output to a memory that stores the APC. The memory thereby outputs the next baseband phase point. Alternatively, the method may identify the next baseband phase point by applying an input bit to a finite state machine which outputs the next baseband phase point. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates an approximate phase constellation (APC) for GMSK, BT=⅙ truncated to L=6. 
     FIG. 2 is a high level block diagram showing one possible implementation of a baseband CPM waveform generator with digital output. 
     FIG. 3 is a high level block diagram showing one possible implementation of an intermediate frequency CPM waveform generator with analog output. 
     FIG. 4 shows a more detailed block diagram of one possible implementation of a GMSK modulator with absolute phase encoding and BT=⅙ truncated to L=6, whose analog output has been shifted to an intermediate frequency. 
     FIG. 5 presents a high level flow diagram of modulation according to the present invention. 
     FIG. 6 shows a high level flow diagram of modulation according to the present invention using a shift register. 
     FIG. 7 a - 7   d  are graphs illustrating the phase points for an NPC at different sampling rates and offsets. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     At first glance, it would seem an inherent contradiction to describe a CPM with a constellation of discrete phase points. However, this idea turns out to be a useful paradigm. When a CPM is sampled at a multiple of the symbol rate, then there exist only a finite number of values that the phase of the CPM can take. This finite set of phase points will hereafter be referred to as the nominal phase constellation (NPC). The present invention uses the distribution of the possible phase points to simplify the modulator implementation by defining an approximate phase constellation (APC). The APC leads directly to a reduced complexity phase constellation modulator. 
     Turning now to FIG. 1, that figure shows an APC  100  including the set of phase points  102 - 124  used in one implementation of the present GMSK modulator. In particular, the APC  100  is associated with a GMSK modulation scheme with BT=⅙, and the frequency deviation pulse truncated to L=6 symbol intervals. 
     Each of the phase points  102 - 124  is represented in FIG. 1 by an in-phase (I) value and a quadrature-phase (Q) value. For example, the phase point  102  corresponds approximately to an I value of 0.8, and a Q value of approximately 0.4. The I value and Q value scale cosine and sine signal components respectively (See the discussion with respect to FIG. 4, below). However, the phase points need not be decomposed into I and Q components, but may be represented instead in the angle domain, by a single angle offset. 
     The frequency deviation pulse, g(t), (sometimes referred to simply as the frequency pulse), is used to generate the phase transition function, q(t), and in this case is truncated to LT seconds. In one embodiment of the present invention, L=6. A frequency deviation pulse truncated to LT seconds results in at most 2 L  possible phase points in a complete NPC generated by sampling the GMSK waveform at one sample per symbol interval. 
     Although there are, in general, 2 L  possible phase points in a complete NPC, many of the phase points overlap on top of each other. Thus, for L=6, 28 of the 64 phase points are redundant. In other words, the modulation can be exactly performed at a rate of one sample per symbol interval using only 36 phase points. 
     Furthermore, many of the unique phase points in the NPC lie very close to each other, as shown in FIG.  7 . FIG. 7 a  illustrates an NPC for GMSK modulation with BT=⅙, L=6, 1× sampled at the center of each chip. FIG. 7 b  shows an NPC for GMSK modulation with BT=⅙, L=6, 1× sampled at an offset of ½ chip (i.e., sampled between chips). FIGS. 7 c  and  7   d  are similar to FIGS. 7 a  and  7   b,  respectively, but show NPCs associated with 2× sampling (i.e., oversampling). Note that in FIG. 7 a,  the unique phase points may be grouped into 12 sets of 3 phase points (e.g., the phase point group  702 ), where each of the 3 phase points in each group differs by less than 3 degrees from each of the other phase points in the group. 
     Thus, the APC of FIG. 1 may use only 12 phase points at the cost of an extremely small degradation introduced in the modulated waveform. As an example, with L=6 at one sample per symbol interval, the error in the modulated waveform is at −37 dB with respect to the signal constructed using the complete NPC. The phase threshold determines the number of phase points that may be eliminated. Both the phase threshold and the sampling rate determine the amount of degradation. In the discussion above, the phase threshold was approximately 3 degrees. When more or less degradation is allowable (depending on the particular communication system in which the modulator is employed), the phase threshold may be increased or decreased accordingly. 
     In general, the APC includes phase points commensurate with the grouping of phase points observed in the NPC as determined by the phase threshold. As an example, the phase point group  702  is represented in the APC  100  by (at least) the single phase point  104 . The phase point  104  may, for example, be one of the phase points in the phase group  702 , an average of the phase points in the group  702 , or another commensurate phase point chosen in accordance with other criteria. As an example, the phase point  104  may be chosen to represent the phase point group  702  while introducing a minimal amount of (or controlled amount of) signal degradation. 
     In storing the APC, it is further noted that the phase points are symmetrically placed in each quadrant. Thus, in FIG. 1, for example, the phase points  102 - 106 ,  108 - 112 ,  114 - 118 , and  120 - 124  are reflections of each other about the X or Y axis. Thus, rather than storing all 12 phase points  102 - 124  separately, only three values need be stored to represent the APC. 
     In operation the modulator uses an established mapping between the bitstream input and the APC. For a close group of phase points in the NPC that do not differ by more than the phase threshold, the APC stores one phase point of a value commensurate with the group. Then, whenever an ideal modulator would be called upon, mathematically, to use a phase point not actually in the APC, the phase constellation modulator selects (as the next phase point) the closest neighbor that exists in the APC. 
     Turning now to FIG. 2, a high level block diagram of a modulator  200  according to the present invention is shown. The modulator  200  includes an N-bit shift register  202  and a phase ROM  204  (which stores the APC). The modulator  200  accepts an input bit on a data input  206 , configuration bits on a configuration input  208 , and produces the next phase of the transmitted waveform on a next phase output  210 . 
     As each data bit is presented on the data input  206 , the shift register  202  shifts the data bit into the shift register  202  and discards the oldest bit. In general, the shift register  202  produces an N-bit output which forms part of an address (which depends on the last N input bits) for the phase ROM  204 . Another part of the address may optionally be provided by the configuration input  208 , which may for example (and as discussed in more detail below) correspond to an even symbol or odd symbol indicator. The address acts as a next phase selector input to identify a next phase point which is, in turn, output by the phase ROM  204  on the phase output  210 . 
     It is noted that many variations and alternative implementations of the shift register  202  and phase ROM  204  are possible. For example, both may be replaced by a single state machine which transitions between states with each new input bit. The state machine may then output the next phase value using combinatorial logic that decodes the present state. The state machine (or the shift register  202  and phase ROM  204 ) may be implemented in combinatorial logic, for example, or a combination of hardware and software. 
     Turning now to FIG. 3, that figure illustrates an embodiment of an intermediate frequency (IF) CPM waveform generator  300  according to the present invention. The generator  300  includes an N-bit shift register  302  and a waveform ROM  304 . The generator  300  accepts an input bit on a data input  306 , configuration bits on a configuration input  308 , and produces the next digital CPM waveform value on a digital waveform output  310 . The digital waveform value is converted to analog by the D/A converter  312  which produces the actual analog CPM waveform on the waveform output  314 . 
     The generator  300  operates much like the modulator  200  with respect to the input data bits and configuration bits. However, the waveform ROM  304  directly stores samples of the CPM waveform (i.e., cos(wt+phase(t)), where w/2π is the IF used). Note that when w is chosen such that the IF is a multiple of the symbol rate (i.e., w=2πk/T, where T is the symbol interval), then the phase contribution from w is constant, and the APC is preserved. This fact allows the direct output of the CPM signal at an IF, thus eliminating the need for an I-Q modulator. The generator  300  preferably uses a digital to analog (D/A) converter  312  that operates at at least twice the IF rate or four times the chip rate. The modulator of FIG. 3 thus eliminates the dual I-Q D/A converters in an I-Q modulator and therefore the problems that potentially result from mismatched D/A gain and conversion speed. 
     Turning now to FIG. 4, that figure shows a more detailed block diagram of a modulator  400 . The modulator  400  includes a phase ROM  402  outputting in-phase (I) values on the I output  404  and quadrature-phase (Q) values on the Q output  406 . The modulator  400  includes a shift register  408  formed from several 1-bit registers  410 - 420 . An even/odd input  422  is also provided. 
     Each register output is connected to the phase ROM  402  to provide an address that identifies the next phase (e.g., one phase point in the APC) stored in the phase ROM  402 . The even/odd input  422  also forms part of the address and, as described below, links transmitted bits to absolute phase information (as opposed to the inherently differential encoding of bits in typical minimum shift keying). Linking the transmitted bits to absolute phase increases the resultant signal gain by approximately 1.5 dB. 
     The phase ROM  402  responds to the address by outputting the next phase on the I and Q outputs  404 - 406 . Typically, the I output  404  and Q output  406  are routed to digital-to-analog converters  430 - 432 , in-phase and quadrature mixers  434 - 436 , and an adder  438  to produce the resultant modulated waveform at an intermediate frequency for transmission. The inphase and quadrature phase ROM output values may be quantized, for example, to 8-bits for subsequent 8-bit digital-to-analog converters. 
     With respect to the address formed using the shift register  410 - 420  output and the even/odd bit  422 , the linking of transmitted bits to absolute phase is explained with reference to Table 1, below: 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                 even/ 
                   
               
               
                 k 
                 a (k) 
                 b (k) 
                 d (k) 
                 d (k − 1) 
                 odd 
                 phase 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 x 
                 1 
                 −1 
                 x 
                 1 
                 0 
               
               
                 1 
                 −1 
                 1 
                 −1 
                 −1 
                 −1 
                 270 
               
               
                 2 
                 −1 
                 0 
                 1 
                 −1 
                 1 
                 180 
               
               
                 3 
                 −1 
                 0 
                 1 
                 1 
                 −1 
                 90 
               
               
                 4 
                 1 
                 0 
                 1 
                 1 
                 1 
                 180 
               
               
                 5 
                 1 
                 1 
                 −1 
                 1 
                 −1 
                 270 
               
               
                 6 
                 1 
                 1 
                 −1 
                 −1 
                 1 
                 0 
               
               
                 7 
                 −1 
                 1 
                 −1 
                 −1 
                 −1 
                 270 
               
               
                   
               
             
          
         
       
     
     In Table 1, a(k)=(−1) k (d(k)) (d(k−1)) and represents differentially encoded bits, k is the bit number, b(k) represents the binary data to be transmitted, d(k) represents the data to be transmitted in NRZ form, even/odd represents whether k is even or odd, a(k) represents the change in modulator state (e.g., plus or minus 90 degrees) for the current bit, and ‘phase’ represents the final phase value effected (or nearly effected due to the gradual changes in phase) by the given data bit to be transmitted. 
     It may be seen from Table 1 that when b(k)=1, the phase is either 270 or 0, depending on whether ‘k’ is even or odd, and that when b(k)=0, the phase is either 180 or 90, depending on whether ‘k’ is even or odd. Thus, adding the extra even/odd input  422  allows the phase ROM  402  to produce the absolute phase that will result, and link the transmitted data (i.e., the b(k) or set of b(k) values stored in the shift register) to the absolute phase of the carrier. A second example is provided for a different bit sequence below in Table 2. 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                   
                   
                 even/ 
                   
               
               
                 k 
                 a (k) 
                 b (k) 
                 d (k) 
                 d (k − 1) 
                 odd 
                 phase 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 x 
                 1 
                 −1 
                 x 
                 1 
                 0 
               
               
                 1 
                 1 
                 0 
                 1 
                 −1 
                 −1 
                 90 
               
               
                 2 
                 1 
                 0 
                 1 
                 1 
                 1 
                 180 
               
               
                 3 
                 1 
                 1 
                 −1 
                 1 
                 −1 
                 270 
               
               
                 4 
                 −1 
                 0 
                 1 
                 −1 
                 1 
                 180 
               
               
                 5 
                 −1 
                 0 
                 1 
                 1 
                 −1 
                 90 
               
               
                 6 
                 −1 
                 1 
                 −1 
                 1 
                 1 
                 0 
               
               
                 7 
                 1 
                 0 
                 1 
                 −1 
                 −1 
                 90 
               
               
                   
               
             
          
         
       
     
     Table 3 and Table 4, below, provide one possible implementation of the phase ROM  402  responding to seven input (next phase selectors) bits or, stated another way, a seven bit address (e.g., provided by the shift register  308  and the even/odd input  422 ). The decimal value of the address is present in the first column of Tables 3 and 4. As noted above, an even/odd bit forms part of the address, and in Tables 3 and 4 is included as the least significant bit of the decimal value in the first column. 
     Table 3 provides the appropriate output for the in-phase component of the modulated signal. Similarly, Table 4 provides the appropriate output for the quadrature component of the modulated signal. The APC is represented, as shown in the second, third, and fourth columns of Tables 3 and 4, by in-phase and quadrature values 0.44228, 0.70711, and 0.89668. Finally, the symmetry of phase points, noted above, is used to further simplify the phase ROM, by including a negative/positive indicator in column five, rather than duplicating identical phase magnitudes that are simply opposite in sign. As an example, for the input address  42 , the in-phase output will be −0.70711 and the quadrature output will be +0.70711. 
     Note that the phase ROM may be implemented in many ways. For example, the phase ROM may produce a four bit output according to Tables 3 and 4 that, in turn, address a phase value ROM that stores the actual in-phase and quadrature component values. This implementation can be very attractive. Upon closer inspection of the tables, it is clear that column 3-2 is identical to column 4-4, column 3-3 is identical to column 4-3, column 3-4 is identical to column 4-2, and the inverse and reverse ordered version of column 3-5 is identical to column 4-5. This result is intuitively appealing as it only takes four bits of information to specify twelve different phase points. In another embodiment, however, only one phase ROM is used that outputs the component values according to any desired granularity (e.g., 8 bits) in response to the input address. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 In-phase Component 
               
             
          
           
               
                   
                 Column 3-2 
                 Column 3-3 
                 Column 3-4 
                 Column 3-5 
               
               
                 Column 3-1 
                 Out = 
                 Out = 
                 Out = 
                 Out = 
               
               
                 Input 
                 0.44228 
                 0.70711 
                 0.89668 
                 negative 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 1 
                 0 
                 0 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
               
               
                 2 
                 0 
                 1 
                 0 
                 0 
               
               
                 3 
                 0 
                 1 
                 0 
                 0 
               
               
                 4 
                 0 
                 0 
                 1 
                 0 
               
               
                 5 
                 1 
                 0 
                 0 
                 0 
               
               
                 6 
                 0 
                 0 
                 1 
                 0 
               
               
                 7 
                 1 
                 0 
                 0 
                 0 
               
               
                 8 
                 1 
                 0 
                 0 
                 1 
               
               
                 9 
                 0 
                 0 
                 1 
                 0 
               
               
                 10 
                 1 
                 0 
                 0 
                 1 
               
               
                 11 
                 0 
                 0 
                 1 
                 0 
               
               
                 12 
                 0 
                 1 
                 0 
                 1 
               
               
                 13 
                 0 
                 1 
                 0 
                 0 
               
               
                 14 
                 0 
                 1 
                 0 
                 1 
               
               
                 15 
                 0 
                 1 
                 0 
                 0 
               
               
                 16 
                 0 
                 0 
                 1 
                 0 
               
               
                 17 
                 1 
                 0 
                 0 
                 1 
               
               
                 18 
                 0 
                 0 
                 1 
                 0 
               
               
                 19 
                 1 
                 0 
                 0 
                 1 
               
               
                 20 
                 0 
                 1 
                 0 
                 0 
               
               
                 21 
                 0 
                 1 
                 0 
                 1 
               
               
                 22 
                 0 
                 1 
                 0 
                 0 
               
               
                 23 
                 0 
                 1 
                 0 
                 1 
               
               
                 24 
                 0 
                 1 
                 0 
                 1 
               
               
                 25 
                 0 
                 1 
                 0 
                 1 
               
               
                 26 
                 0 
                 1 
                 0 
                 1 
               
               
                 27 
                 0 
                 1 
                 0 
                 1 
               
               
                 28 
                 1 
                 0 
                 0 
                 1 
               
               
                 29 
                 0 
                 0 
                 1 
                 1 
               
               
                 30 
                 1 
                 0 
                 0 
                 1 
               
               
                 31 
                 0 
                 0 
                 1 
                 1 
               
               
                 32 
                 1 
                 0 
                 0 
                 0 
               
               
                 33 
                 0 
                 0 
                 1 
                 0 
               
               
                 34 
                 1 
                 0 
                 0 
                 0 
               
               
                 35 
                 0 
                 0 
                 1 
                 0 
               
               
                 36 
                 0 
                 1 
                 0 
                 0 
               
               
                 37 
                 0 
                 1 
                 0 
                 0 
               
               
                 38 
                 0 
                 1 
                 0 
                 0 
               
               
                 39 
                 0 
                 1 
                 0 
                 0 
               
               
                 40 
                 0 
                 1 
                 0 
                 1 
               
               
                 41 
                 0 
                 1 
                 0 
                 0 
               
               
                 42 
                 0 
                 1 
                 0 
                 1 
               
               
                 43 
                 0 
                 1 
                 0 
                 0 
               
               
                 44 
                 0 
                 0 
                 1 
                 1 
               
               
                 45 
                 1 
                 0 
                 0 
                 0 
               
               
                 46 
                 0 
                 0 
                 1 
                 1 
               
               
                 47 
                 1 
                 0 
                 0 
                 0 
               
               
                 48 
                 0 
                 1 
                 0 
                 0 
               
               
                 49 
                 0 
                 1 
                 0 
                 1 
               
               
                 50 
                 0 
                 1 
                 0 
                 0 
               
               
                 51 
                 0 
                 1 
                 0 
                 1 
               
               
                 52 
                 1 
                 0 
                 0 
                 0 
               
               
                 53 
                 0 
                 0 
                 1 
                 1 
               
               
                 54 
                 1 
                 0 
                 0 
                 0 
               
               
                 55 
                 0 
                 0 
                 1 
                 1 
               
               
                 56 
                 0 
                 0 
                 1 
                 1 
               
               
                 57 
                 1 
                 0 
                 0 
                 1 
               
               
                 58 
                 0 
                 0 
                 1 
                 1 
               
               
                 59 
                 1 
                 0 
                 0 
                 1 
               
               
                 60 
                 0 
                 1 
                 0 
                 1 
               
               
                 61 
                 G 
                 1 
                 0 
                 1 
               
               
                 62 
                 0 
                 1 
                 0 
                 1 
               
               
                 63 
                 0 
                 1 
                 0 
                 1 
               
               
                 64 
                 0 
                 1 
                 0 
                 0 
               
               
                 65 
                 0 
                 1 
                 0 
                 0 
               
               
                 66 
                 0 
                 1 
                 0 
                 0 
               
               
                 67 
                 0 
                 1 
                 0 
                 0 
               
               
                 68 
                 0 
                 0 
                 1 
                 0 
               
               
                 69 
                 1 
                 0 
                 0 
                 0 
               
               
                 70 
                 0 
                 0 
                 1 
                 0 
               
               
                 71 
                 1 
                 0 
                 0 
                 0 
               
               
                 72 
                 1 
                 0 
                 0 
                 1 
               
               
                 73 
                 0 
                 0 
                 1 
                 0 
               
               
                 74 
                 1 
                 0 
                 0 
                 1 
               
               
                 75 
                 0 
                 0 
                 1 
                 0 
               
               
                 76 
                 0 
                 1 
                 0 
                 1 
               
               
                 77 
                 0 
                 1 
                 0 
                 0 
               
               
                 78 
                 0 
                 1 
                 0 
                 1 
               
               
                 79 
                 0 
                 1 
                 0 
                 0 
               
               
                 80 
                 0 
                 0 
                 1 
                 0 
               
               
                 81 
                 1 
                 0 
                 0 
                 1 
               
               
                 82 
                 0 
                 0 
                 1 
                 0 
               
               
                 83 
                 1 
                 0 
                 0 
                 1 
               
               
                 84 
                 0 
                 1 
                 0 
                 0 
               
               
                 85 
                 0 
                 1 
                 0 
                 1 
               
               
                 86 
                 0 
                 1 
                 0 
                 0 
               
               
                 87 
                 0 
                 1 
                 0 
                 1 
               
               
                 88 
                 0 
                 1 
                 0 
                 1 
               
               
                 89 
                 0 
                 1 
                 0 
                 1 
               
               
                 90 
                 0 
                 1 
                 D 
                 1 
               
               
                 91 
                 0 
                 1 
                 0 
                 1 
               
               
                 92 
                 1 
                 0 
                 0 
                 1 
               
               
                 93 
                 0 
                 0 
                 1 
                 1 
               
               
                 94 
                 1 
                 0 
                 0 
                 1 
               
               
                 95 
                 0 
                 0 
                 1 
                 1 
               
               
                 96 
                 1 
                 0 
                 0 
                 0 
               
               
                 97 
                 0 
                 0 
                 1 
                 0 
               
               
                 98 
                 1 
                 0 
                 0 
                 0 
               
               
                 99 
                 0 
                 0 
                 1 
                 0 
               
               
                 100 
                 0 
                 1 
                 0 
                 0 
               
               
                 101 
                 0 
                 1 
                 0 
                 0 
               
               
                 102 
                 0 
                 1 
                 0 
                 0 
               
               
                 103 
                 0 
                 1 
                 0 
                 0 
               
               
                 104 
                 0 
                 1 
                 0 
                 1 
               
               
                 105 
                 0 
                 1 
                 0 
                 0 
               
               
                 106 
                 0 
                 1 
                 0 
                 1 
               
               
                 107 
                 0 
                 1 
                 0 
                 0 
               
               
                 108 
                 0 
                 0 
                 1 
                 1 
               
               
                 109 
                 1 
                 0 
                 0 
                 0 
               
               
                 110 
                 0 
                 0 
                 1 
                 1 
               
               
                 111 
                 1 
                 0 
                 0 
                 0 
               
               
                 112 
                 0 
                 1 
                 0 
                 0 
               
               
                 113 
                 0 
                 1 
                 0 
                 1 
               
               
                 114 
                 0 
                 1 
                 0 
                 0 
               
               
                 115 
                 0 
                 1 
                 0 
                 1 
               
               
                 116 
                 1 
                 0 
                 0 
                 0 
               
               
                 117 
                 0 
                 0 
                 1 
                 1 
               
               
                 118 
                 1 
                 0 
                 0 
                 0 
               
               
                 119 
                 0 
                 0 
                 1 
                 1 
               
               
                 120 
                 0 
                 0 
                 1 
                 1 
               
               
                 121 
                 1 
                 0 
                 0 
                 1 
               
               
                 122 
                 0 
                 0 
                 1 
                 1 
               
               
                 123 
                 1 
                 0 
                 0 
                 1 
               
               
                 124 
                 0 
                 1 
                 0 
                 1 
               
               
                 125 
                 0 
                 1 
                 0 
                 1 
               
               
                 126 
                 0 
                 1 
                 0 
                 1 
               
               
                 127 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Quadrature Component 
               
             
          
           
               
                   
                 Column 4-2 
                 Column 4-3 
                 Column 4-4 
                 Column 4-5 
               
               
                 Column 4-1 
                 Out = 
                 Out = 
                 Out = 
                 Out = 
               
               
                 Input 
                 0.44228 
                 0.70711 
                 0.89668 
                 negative 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 1 
                 0 
                 0 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
               
               
                 2 
                 0 
                 1 
                 0 
                 0 
               
               
                 3 
                 0 
                 1 
                 0 
                 0 
               
               
                 4 
                 1 
                 0 
                 0 
                 0 
               
               
                 5 
                 0 
                 0 
                 1 
                 0 
               
               
                 6 
                 1 
                 0 
                 0 
                 0 
               
               
                 7 
                 0 
                 0 
                 1 
                 0 
               
               
                 8 
                 0 
                 0 
                 1 
                 0 
               
               
                 9 
                 1 
                 0 
                 0 
                 1 
               
               
                 10 
                 0 
                 0 
                 1 
                 0 
               
               
                 11 
                 1 
                 0 
                 0 
                 1 
               
               
                 12 
                 0 
                 1 
                 0 
                 0 
               
               
                 13 
                 0 
                 1 
                 0 
                 1 
               
               
                 14 
                 0 
                 1 
                 0 
                 0 
               
               
                 15 
                 0 
                 1 
                 0 
                 1 
               
               
                 16 
                 1 
                 0 
                 0 
                 1 
               
               
                 17 
                 0 
                 0 
                 1 
                 0 
               
               
                 18 
                 1 
                 0 
                 0 
                 1 
               
               
                 19 
                 0 
                 0 
                 1 
                 0 
               
               
                 20 
                 0 
                 1 
                 0 
                 1 
               
               
                 21 
                 0 
                 1 
                 0 
                 0 
               
               
                 22 
                 0 
                 1 
                 0 
                 1 
               
               
                 23 
                 0 
                 1 
                 0 
                 0 
               
               
                 24 
                 0 
                 1 
                 0 
                 1 
               
               
                 25 
                 0 
                 1 
                 0 
                 1 
               
               
                 26 
                 0 
                 1 
                 0 
                 1 
               
               
                 27 
                 0 
                 1 
                 0 
                 1 
               
               
                 28 
                 0 
                 0 
                 1 
                 1 
               
               
                 29 
                 1 
                 0 
                 0 
                 1 
               
               
                 30 
                 0 
                 0 
                 1 
                 1 
               
               
                 31 
                 1 
                 0 
                 0 
                 1 
               
               
                 32 
                 0 
                 0 
                 1 
                 0 
               
               
                 33 
                 1 
                 0 
                 0 
                 0 
               
               
                 34 
                 0 
                 0 
                 1 
                 0 
               
               
                 35 
                 1 
                 0 
                 0 
                 0 
               
               
                 36 
                 0 
                 1 
                 0 
                 0 
               
               
                 37 
                 0 
                 1 
                 0 
                 0 
               
               
                 38 
                 0 
                 1 
                 0 
                 0 
               
               
                 39 
                 0 
                 1 
                 0 
                 0 
               
               
                 40 
                 0 
                 1 
                 0 
                 0 
               
               
                 41 
                 0 
                 1 
                 0 
                 1 
               
               
                 42 
                 0 
                 1 
                 0 
                 0 
               
               
                 43 
                 0 
                 1 
                 0 
                 1 
               
               
                 44 
                 1 
                 0 
                 0 
                 0 
               
               
                 45 
                 0 
                 0 
                 1 
                 1 
               
               
                 46 
                 1 
                 0 
                 0 
                 0 
               
               
                 47 
                 0 
                 0 
                 1 
                 1 
               
               
                 48 
                 0 
                 1 
                 0 
                 1 
               
               
                 49 
                 0 
                 1 
                 0 
                 0 
               
               
                 50 
                 0 
                 1 
                 0 
                 1 
               
               
                 51 
                 0 
                 1 
                 0 
                 0 
               
               
                 52 
                 0 
                 0 
                 1 
                 1 
               
               
                 53 
                 1 
                 0 
                 0 
                 0 
               
               
                 54 
                 0 
                 0 
                 1 
                 1 
               
               
                 55 
                 1 
                 0 
                 0 
                 0 
               
               
                 56 
                 1 
                 0 
                 0 
                 1 
               
               
                 57 
                 0 
                 0 
                 1 
                 1 
               
               
                 58 
                 1 
                 0 
                 0 
                 1 
               
               
                 59 
                 0 
                 0 
                 1 
                 1 
               
               
                 60 
                 0 
                 1 
                 0 
                 1 
               
               
                 61 
                 0 
                 1 
                 0 
                 1 
               
               
                 62 
                 0 
                 1 
                 0 
                 1 
               
               
                 63 
                 0 
                 1 
                 0 
                 1 
               
               
                 64 
                 0 
                 1 
                 0 
                 0 
               
               
                 65 
                 0 
                 1 
                 0 
                 0 
               
               
                 66 
                 0 
                 1 
                 0 
                 0 
               
               
                 67 
                 0 
                 1 
                 0 
                 0 
               
               
                 68 
                 1 
                 0 
                 0 
                 0 
               
               
                 69 
                 0 
                 0 
                 1 
                 0 
               
               
                 70 
                 1 
                 0 
                 0 
                 0 
               
               
                 71 
                 0 
                 0 
                 1 
                 0 
               
               
                 72 
                 0 
                 0 
                 1 
                 0 
               
               
                 73 
                 1 
                 0 
                 0 
                 1 
               
               
                 74 
                 0 
                 0 
                 1 
                 0 
               
               
                 75 
                 1 
                 0 
                 0 
                 1 
               
               
                 76 
                 0 
                 1 
                 0 
                 0 
               
               
                 77 
                 0 
                 1 
                 0 
                 1 
               
               
                 78 
                 0 
                 1 
                 0 
                 0 
               
               
                 79 
                 0 
                 1 
                 0 
                 1 
               
               
                 80 
                 1 
                 0 
                 0 
                 1 
               
               
                 81 
                 0 
                 0 
                 1 
                 0 
               
               
                 82 
                 1 
                 0 
                 0 
                 1 
               
               
                 83 
                 0 
                 0 
                 1 
                 0 
               
               
                 84 
                 0 
                 1 
                 0 
                 1 
               
               
                 85 
                 0 
                 1 
                 0 
                 0 
               
               
                 86 
                 0 
                 1 
                 0 
                 1 
               
               
                 87 
                 0 
                 1 
                 0 
                 0 
               
               
                 88 
                 0 
                 1 
                 0 
                 1 
               
               
                 89 
                 0 
                 1 
                 0 
                 1 
               
               
                 90 
                 0 
                 1 
                 0 
                 1 
               
               
                 91 
                 0 
                 1 
                 0 
                 1 
               
               
                 92 
                 0 
                 0 
                 1 
                 1 
               
               
                 93 
                 1 
                 0 
                 0 
                 1 
               
               
                 94 
                 0 
                 0 
                 1 
                 1 
               
               
                 95 
                 1 
                 0 
                 0 
                 1 
               
               
                 96 
                 0 
                 0 
                 1 
                 0 
               
               
                 97 
                 1 
                 0 
                 0 
                 0 
               
               
                 98 
                 0 
                 0 
                 1 
                 0 
               
               
                 99 
                 1 
                 0 
                 0 
                 0 
               
               
                 100 
                 0 
                 1 
                 0 
                 0 
               
               
                 101 
                 0 
                 1 
                 0 
                 0 
               
               
                 102 
                 0 
                 1 
                 0 
                 0 
               
               
                 103 
                 0 
                 1 
                 0 
                 0 
               
               
                 104 
                 0 
                 1 
                 0 
                 0 
               
               
                 105 
                 0 
                 1 
                 0 
                 1 
               
               
                 106 
                 0 
                 1 
                 0 
                 0 
               
               
                 107 
                 0 
                 1 
                 0 
                 1 
               
               
                 108 
                 1 
                 0 
                 0 
                 0 
               
               
                 109 
                 0 
                 0 
                 1 
                 1 
               
               
                 110 
                 1 
                 0 
                 0 
                 0 
               
               
                 111 
                 0 
                 0 
                 1 
                 1 
               
               
                 112 
                 0 
                 1 
                 0 
                 1 
               
               
                 113 
                 0 
                 1 
                 0 
                 0 
               
               
                 114 
                 0 
                 1 
                 0 
                 1 
               
               
                 115 
                 0 
                 1 
                 0 
                 0 
               
               
                 116 
                 0 
                 0 
                 1 
                 1 
               
               
                 117 
                 1 
                 0 
                 0 
                 0 
               
               
                 118 
                 0 
                 0 
                 1 
                 1 
               
               
                 119 
                 1 
                 0 
                 0 
                 0 
               
               
                 120 
                 1 
                 0 
                 0 
                 1 
               
               
                 121 
                 0 
                 0 
                 1 
                 1 
               
               
                 122 
                 1 
                 0 
                 0 
                 1 
               
               
                 123 
                 0 
                 0 
                 1 
                 1 
               
               
                 124 
                 0 
                 1 
                 0 
                 1 
               
               
                 125 
                 0 
                 1 
                 0 
                 1 
               
               
                 126 
                 0 
                 1 
                 0 
                 1 
               
               
                 127 
                 0 
                 1 
                 0 
                 1 
               
               
                   
               
             
          
         
       
     
     Turning now to FIG. 5, that figure illustrates a high level block diagram  500  of the modulation method of the present invention. Starting at the storing step  502 , the APC is stored. The phase points may be stored and output as inphase and quadrature phase values, or as angle values. Alternatively, actual CPM waveform samples may be stored, as noted above with respect to FIG.  3 . 
     At the identify step  504 , the method determines which phase point is the next phase. Thus, for example, the address applied to the phase ROM  402  may identify the next phase. Subsequently, the method, at the output step  506 , produces the next phase value for subsequent modulation. Processing then branches back to the identify step  504  in which, typically, the next input bit determines a new next phase. 
     With respect to FIG. 6, that figure illustrates a more detailed block diagram of a modulation method  600  according to the present invention. The modulation method  600  includes a storing step  602 , a shift step  604 , an application step  606 , and an output step  608 . Starting at the storing step  602 , the method saves the APC generated from a complete NPC. As noted above with respect to the storing step  502 , the phase points may be stored as inphase and quadrature phase values or as angle values, and are generally commensurate with groups of phase points that differ by less than a predetermined phase threshold. 
     At step  604 , the next bit to be transmitted (the next input bit) is shifted into a shift register (e.g., shift register  408 ). The oldest bit in the shift register is discarded. At step  606 , the bits stored in the shift register (i.e., the N-bit shift register output) are applied as an address to a memory, for example, the phase ROM  402 . The address (which may further include configuration bits) determines the next phase. The memory outputs the next phase in response to the address. Processing continues at step  604 , at which the next bit to be transmitted is shifted into the shift register. 
     The present invention thereby provides a phase constellation modulator that significantly reduces the complexity of implementing a CPM. Furthermore, the invention achieves these reductions without sacrificing signal quality. More reliable and cost effective communication systems result. 
     While particular elements, embodiments and applications of the present invention have been shown and described, it is understood that the invention is not limited thereto since modifications may be made by those skilled in the art, particularly in light of the foregoing teaching. It is therefore contemplated by the appended claims to cover such modifications and incorporate those features which come within the spirit and scope of the invention.