Abstract:
A communications system ( 10 ) which utilizes an M-ary QAM signal constellation suitable for non-linear applications. The communications system includes a modulator ( 18 ) for utilizing the M-ary constellation to implement the modulation. The M-ary constellation is a circular constellation which provides a simplified amplitude predistortion by utilizing the subject M-ary constellations, enabling more efficient communications can then be achieved through a peak-power-limited non-linear channel ( 16 ). Such non-linear channels ( 16 ) are more power efficient at creating RF energy from DC energy.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to communications systems utilizing M-ary modulation formats and, more particularly, to an apparatus and method for efficiently communicating through a peak-power-limited, non-linear channel. 
     BACKGROUND OF THE INVENTION 
     In high data rate communications systems, such as selected satellite communications systems, data transmission typically employs high power amplifiers such as traveling wave tube amplifiers (TWTAs) or solid state power amplifiers (SSPAs). Such high speed communications systems typically require a relatively high output power so that the signal being transmitted can travel greater distances before being significantly attenuated. However, such power is limited by several considerations, including the limited energy generation and storage in the satellite vehicle. In these types of communications systems, low frequency digital baseband signals comprising the stream of digital data bits are transmitted after being modulated onto a high frequency carrier wave. 
     Various modulation schemes exist and distinguish between the digital bits. Examples of digital modulation schemes include amplitude-shift keying (ASK), binary phase-shift keying (BPSK), quadrature-phase shift keying (QPSK), and quadrature amplitude modulation (QAM). Further, the digital baseband signal may be multi level (M-ary) signals requiring multi level modulation methods. 
     Quadrature modulation schemes provide both amplitude and phase modulation of the carrier because both complex and imaginary representations of the signals are used. In quadrature amplitude modulation schemes, such as QAM, each bit is converted through a bit symbol representing a complex value having an in-phase, real component and a quadrature-phase, imaginary component. Each bit is represented on a graph having an imaginary axis and a real axis to form a constellation pattern representing a group of signals positioned within a circle around the origin of the axes. The distance from the origin represents the amount of power being transmitted. For example, four bits transmitted at a particular time may be represented as 16 symbols. Each symbol of the pattern identifies a complex voltage value having an in-phase component and a quadrature-phase component and represents the complex voltage value for a particular symbol, which is the time during which each symbol is transmitted. The symbols of the constellation pattern are geometrically spread so that they are more equally spaced apart to more readily distinguish the symbols and reduce bit errors. The constellation patterns are processed through the transmitter without being distorted so that the bits are readily distinguishable from each other at the receiver end. 
     High power amplifiers are desirable in high speed communications applications because they provide high gain over wide bandwidths. However, the input signal to a high power amplifier must be controlled because the high power amplifier exhibits non-linear transfer characteristics. At lower input powers, the output-input power relationship of the high power amplifier is approximately linear. At peak power output, the high power amplifier saturates, and further increases the input power beyond the saturation point actually decrease the output power of the amplifier. 
     Non-linear amplifiers are inherently more power efficient at creating radio frequency (RF) energy from direct current (DC) energy but create distortions in the process. Such distortions significantly complicate utilizing traditional signal constellations, such as M-ary QAM. Non-linear channels cause the constellation to rotate and expand non-uniformly. Various methods are available to compensate for this expansion and rotation, but such methods are complex and may be difficult to implement. 
     The non-linearity of the high power amplifier affects the position of the true-invention is particular at predistortion symbols in the constellation pattern by moving them away from the origin. It is known to provide amplifier predistortion techniques in the amplifier when the transmitter is being operated in its non-linear range near peak output power. 
     Thus, it is desirable to provide an efficient communications system utilizing a peak-power-limited, non-linear channel which compensates for distortion. 
     SUMMARY OF THE INVENTION 
     A communications system, comprising a modulator for modulating a digital data stream onto a carrier wave to generate a modulated signal, the modulator converting data in the data stream into symbols for transmission by the communications system, the symbol being encoded into one of M possible symbols of an M-ary constellation, wherein each symbol is defined by one of a plurality of phases and one of a plurality of magnitudes and an amplifier for amplifying the modulated signal prior to transmission to generate an amplified signal, the amplifier having a non-linear characteristic that generates a non-linear distortion in the modulated signal, wherein the M-ary constellation is a 24 point constellation having 16 points defined by a first magnitude and 8 points defined by a second magnitude, wherein the second magnitude is less than the first magnitude. 
     For a more complete understanding of the invention, its objects and advantages, reference should be made to the following specification and to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings, which form an integral part of the specification, are to be read in conjunction therewith, and like reference numerals are employed to designate identical components in the various views: 
         FIG. 1  is a schematic block diagram of a communications system arranged in accordance with the principles of the present invention; 
         FIG. 2  is a constellation diagram for a 24-ary modulation communications system; 
         FIG. 3  is a constellation diagram for a 32-ary modulation communications system; 
         FIG. 4  is a constellation diagram demonstrating a sample predistortion for the constellation diagram of  FIG. 3 ; 
         FIG. 5  is a constellation diagram for a 64-ary, four level modulation communications system; and 
         FIG. 6  is a constellation diagram for a 64-ary, five level modulation communications system. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 1  depicts a block diagram of communications system  10  for exchanging modulated data between a transmitter  12  and a receiver  14  via a communications link  16 . Communications link  16  may be an air link for satellite communications or hard-wired interconnection, such as an electrical connection or fiber optic connection. Transmitter  12  includes a modulator  18 . Modulator  18  receives a data stream at a baseband frequency and modulates the data stream utilizing a quadrature amplitude modulation (QAM) format. In particular, modulator  18  modulates the data utilizing a M-ary QAM modulation format. 
     Typically modulator  18  modulates data bits of the data stream onto an analog carrier wave using mixer  22 . During modulation, modulator  18  identifies for each bit pattern a symbol that includes a in-phase and quadrature-phase component, and maps the symbols into a M-ary constellation pattern, as will be described in greater detail herein. Modulator  18  may be any quadrature amplitude modulator suitable for implementing the M-ary constellations as described herein. 
     Modulator  18  outputs a radio frequency (RF) signal at a baseband frequency. Typically for satellite communications, the RF signal is up-converted to a high frequency for transmission. A mixer  22  up-converts the baseband frequency with a high frequency signal, such as cos(ω 0 t). Mixer  22  up-converts the in-phase and quadrature-phase representation of the complex voltage from modulator  18  to a single high frequency RF signal. The up-converted RF signal is then applied to amplifier  24  to significantly increase the signal gain for transmission. Operation of the mixing step and amplification step for a transmitter of this type is well understood by those skilled in the art. The up-converted, amplified signal from amplifier  24  is applied to RF filter  26  for subsequent RF filtering, such as may be required by Federal Communications Commission (FCC) requirements. The filtered signal is output to an antenna  30  for transmission to receiver  14 . 
     In the configuration of  FIG. 1 , amplifier  24  introduces a distortion into the signal output by modulator  18 . The output for amplifier  24 , which is applied to RF filter  26  has an inherent distortion. As will be described in greater detail herein with respect to  FIGS. 3 and 4 , modulator  18  operates so as to introduce a predistortion into the signal output by modulator  18  and applied to mixer  22 . Amplifier  24  thus adjusts the predistorted signal to output a distortion compensated signal input to RF filter  26 . 
     Antenna  30  receives the filtered signal and outputs over communications link  16  a communications signal which is received by antenna  32  of transmitter  12 . Antenna  32  is connected to an amplifier  34 , which is preferably a low-noise, linear amplifier. Note that although communication system  10  is shown as having a wireless communications link  16 , communications link  16  may be a hard-wired connection, as described above. In such a situation, antennas  30  and  32  are unnecessary. 
     The signal received by antenna  32  at receiver  14  is input to a filter  36 . Filter  36  provides initial filtering of the received signal to filter channel noise and the like. Typically, filter  36  is closely matched to the transmitted signal frequency. The output of filter  36  is applied to a mixer  38  to down-convert the RF signal to an intermediate frequency signal by mixing the RF signal with a high frequency cos(ω 0 t) signal. The down-converted signal from mixer  38  includes baseband in-phase and quadrature-phase components. The down-converted signal is applied to low-pass filter  40  to provide filtering at baseband frequencies. Thus, in receiver  14 , filter  36  acts as a course filter. 
     The filtered baseband signal from low-pass filter  40  is applied to a demodulator  42 . Demodulator  42  demodulates the received signal in accordance with the M-ary QAM format implemented in modulator  18 . Demodulator  42  thus outputs the data initially modulated by modulator  18 . 
     In a particular feature of the subject invention,  FIG. 2  depicts a 24-ary QAM constellation arranged on a Cartesian coordinate system defined by an in-phase axis  46  and quadrature-phase axis  48 . The 24-ary constellation of  FIG. 2  includes an upper amplitude level  50  and a lower amplitude level  52 . Upper amplitude level  50  and lower amplitude level  52  represent differing power levels for driving amplifier  24  of  FIG. 1 . Upper amplitude level  50  represents the peak power of amplifier  24 , and lower amplitude level  52  represents a power level less than the peak power of amplifier  24 . A plurality of upper amplitude symbols  54  are arranged on upper amplitude level  50 . Similarly, a plurality of lower amplitude symbols  56  are arranged on lower amplitude level  52 . 
     In the 24-ary constellation of  FIG. 2 , 16 upper amplitude symbols  54  are arranged along upper amplitude level  50 , and 8 lower amplitude symbols  56  are arranged along lower amplitude level  52 . Amplitude levels  50 ,  52  of the 24-ary constellation of  FIG. 2  define two concentric circles with the upper amplitude level  50  having an amplitude greater than lower amplitude level  52 . Upper amplitude level  52  has a unit radius of 1, and inner amplitude level  52  has a radius of 0.54. Upper amplitude symbols  54  are separated along the upper amplitude level  50  by 22.5° with one upper amplitude symbols  54  located at cartesion coordinates x=1 and y=0, (1,0). Similarly, lower amplitude symbols  56  are arranged along lower amplitude level  52  and are separated by 45°, with one lower amplitude symbol  56  located at Cartesian coordinate x=0.54 and y=0, (0.54, 0). The 24-ary constellation enables modulation of an average 4.58 bit word or symbol. To implement a practical 24-ary system requires mapping of a large number of binary bits(M) to a number (M/4.58) of 24-ary symbols. 
     The arrangement of symbols of upper amplitude level  50  and lower amplitude  56  is particularly selected to maximize the number of points in which amplifier  24  can operate at saturation. In particular, by placing the maximum number of points on upper amplitude level  50 , amplifier  24  operates in saturation mode for transmission of the maximum number of symbols. The symbols placed on lower amplitude level  52  represent operation of amplifier  24  in a backed-off mode. However, due to signal-to-noise-ratio (SNR) considerations, not all points can be placed on upper amplitude level  52 . Arranging and placing symbols on each of upper amplitude level  50  and lower amplitude level  52  preferrably maximizes the number of symbols for which amplifier  24  operates in saturation mode while pursuing good performance in the presence of noise. 
       FIG. 3  depicts a constellation similar to  FIG. 2 , but shows a 32-ary constellation for use by modulator  18  of  FIG. 1 . The 32-ary constellation of  FIG. 3  enables modulation of up to a 5 bit word or symbol. The 32-ary constellation of  FIG. 3  includes three amplitude levels: a first amplitude level  60 , a second amplitude level  62 , and a third amplitude level  64 . First amplitude level  60  has an amplitude greater than second amplitude level  62 , and second amplitude level  62  has a greater amplitude than third amplitude level  64 . Each amplitude level  60 ,  62 ,  64  defines three concentric circles. First amplitude level  60  includes first amplitude symbols  66 , second amplitude level  62  includes second amplitude symbols  68 , and third amplitude level  64  includes third amplitude symbols  70 . First amplitude level  60  has a unit radius of 1, second amplitude level  62  has a radius of 0.662, and third amplitude level  64  has a radius of 0.25. First amplitude level  60  includes 16 first amplitude level symbols  66 , second amplitude level  62  includes 12 second amplitude symbols  68 , and third amplitude level  64  includes four third amplitude symbols  70 . 
     The following chart lists the position of each of the 32 points in polar coordinates and in cartesian coordinates. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Symbol 
                 Radius 
                 Angle 
                 X 
                 Y 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1 
                 11.25 
                 0.980785 
                 0.195 
               
               
                 2 
                 1 
                 33.75 
                 0.83147 
                 0.556 
               
               
                 3 
                 1 
                 56.25 
                 0.55557 
                 0.831 
               
               
                 4 
                 1 
                 78.75 
                 0.19509 
                 0.981 
               
               
                 5 
                 1 
                 101.3 
                 −0.19509 
                 0.981 
               
               
                 6 
                 1 
                 123.8 
                 −0.55557 
                 0.831 
               
               
                 7 
                 1 
                 146.3 
                 −0.83147 
                 0.556 
               
               
                 8 
                 1 
                 168.8 
                 −0.98079 
                 0.195 
               
               
                 9 
                 1 
                 191.3 
                 −0.98079 
                 −0.195 
               
               
                 10 
                 1 
                 213.8 
                 −0.83147 
                 −0.556 
               
               
                 11 
                 1 
                 236.3 
                 −0.55557 
                 −0.831 
               
               
                 12 
                 1 
                 258.8 
                 −0.19509 
                 −0.981 
               
               
                 13 
                 1 
                 281.3 
                 0.19509 
                 −0.981 
               
               
                 14 
                 1 
                 303.8 
                 0.55557 
                 −0.831 
               
               
                 15 
                 1 
                 326.3 
                 0.83147 
                 −0.556 
               
               
                 16 
                 1 
                 348.8 
                 0.980785 
                 −0.195 
               
               
                 17 
                 0.662 
                 22.5 
                 0.611608 
                 0.253 
               
               
                 18 
                 0.662 
                 52.5 
                 0.403 
                 0.525 
               
               
                 19 
                 0.662 
                 82.5 
                 0.086408 
                 0.656 
               
               
                 20 
                 0.662 
                 112.5 
                 −0.25334 
                 0.612 
               
               
                 21 
                 0.662 
                 142.5 
                 −0.5252 
                 0.403 
               
               
                 22 
                 0.662 
                 172.5 
                 −0.65634 
                 0.086 
               
               
                 23 
                 0.662 
                 202.5 
                 −0.61161 
                 −0.253 
               
               
                 24 
                 0.662 
                 232.5 
                 −0.403 
                 −0.525 
               
               
                 25 
                 0.662 
                 262.5 
                 −0.08641 
                 −0.656 
               
               
                 26 
                 0.662 
                 292.5 
                 0.253336 
                 −0.612 
               
               
                 27 
                 0.662 
                 332.5 
                 0.5252 
                 −0.403 
               
               
                 28 
                 0.662 
                 352.5 
                 0.656336 
                 −0.086 
               
               
                 29 
                 0.25 
                 45 
                 0.176777 
                 0.177 
               
               
                 30 
                 0.25 
                 135 
                 −0.17678 
                 0.177 
               
               
                 31 
                 0.25 
                 225 
                 −0.17678 
                 −0.177 
               
               
                 32 
                 0.25 
                 315 
                 0.176777 
                 −0.177 
               
               
                   
               
             
          
         
       
     
     Symbols  1 – 16  define first amplitude symbols  66 , symbols  17 – 28  define second amplitude symbols  68 , and symbols  29 – 32  define third amplitude symbols  70 . As can be seen in the chart, each first amplitude symbol  66  is separated by 22.5°, each second amplitude symbol  68  is separated by 30°, and each third amplitude symbol  70  is separated by 90°. 
     Similarly to  FIG. 2 , amplitude levels  60 ,  62 , and  64  are selected to maximize the number of symbols for which amplifier  24  operates in saturation. Further, second amplitude level  62  and third amplitude level  64  are selected so that amplifier  24  operates as efficiently as possible when amplifying the symbols placed on second amplitude level  62  and third amplitude level  64 . Further yet, the symbols are selected in order to provide suitable signal-to-noise ration for the symbols placed on each restective amplitude level. 
     As discussed above, modulator  18  introduces a predistortion into the signal output by modulator  18  and applied to mixer  22 . Amplifier  24  thus distorts the predistorted signal to output a desired signal for input to RF filter  26 .  FIG. 4  depicts a constellation diagram similar to the constellation diagram of  FIG. 3 . The symbols, however,  FIG. 4  are arranged to show a sample, predistorted constellation output by modulator  18 . It should be noted that similar symbols from  FIG. 3  have been referenced using the same reference number but including a prime (′) to designate the predistorted symbol. The constellation diagram of  FIG. 4  represents the output from modulator  18 . The constellation diagram of  FIG. 3  represents a preferred arrangement for the 32-ary constellation diagram. Amplifier  24  receives symbols arranged in accordance with  FIG. 4  and outputs symbols arranged in accordance with  FIG. 3 . 
       FIG. 5  depicts a 64-ary constellation utilized for QAM by modulator  18 . The 64-ary constellation is depicted as a four level constellation on a Cartesian coordinate system having an in-phase axis  46  and a quadrature-phase axis  48 . The 64-ary constellation includes a first amplitude level  76 , a second amplitude level  78 , a third amplitude level  80 , and fourth amplitude level  82 . As previously described, each respective amplitude level has a plurality of first amplitude symbols  84 , second amplitude symbols  86 , third amplitude symbols  88 , and fourth amplitude symbols  90 . 
     First amplitude level  76  has a radius of 1, second amplitude level  78  has a radius of 0.75, third amplitude level  80  has a radius of 0.54, and fourth amplitude level has a radius of 0.308. First amplitude level  76  includes  24  first amplitude symbols  84 , second amplitude level  78  includes 16 second amplitude symbols  86 , third amplitude level  80  includes 16 third amplitude symbols, and fourth amplitude level includes eight fourth amplitude symbols  90 . First amplitude symbols  84  are separated by 15°, with one first amplitude symbols  84  falling at Cartesian coordinates x=0.980785 and y=0.195 (0.980785, 0.195). Second amplitude symbols  86  are separated by 22.5°, with one second amplitude symbols  86  being located at x=0 and y=0.75, (0, 0.75). Third amplitude symbols  88  are arranged similarly to second amplitude symbols  86 , within one third amplitude symbol  88  located at x=0.54 and y=0, (0.54, 0). Fourth amplitude symbols  90  are separated by 45°, with a fourth amplitude symbol being located at x=0.308 and y=0, (0.308, 0). 
     Alternative four ring implementations to those described with respect to  FIG. 3  may be utilized. For example, a 62-ary constellation may have four rings having 32, 16, 12, and 4 respective symbols. Each ring may have respective amplitude levels of 1.0, 0.75, 0.54, and 0.33. An alternate four-ring implementation may include four rings having 32, 16, 8, and 8 respective symbols. The amplitude level of each respective ring may be 1.0, 0.8, 0.6, and 0.4. 
       FIG. 6  depicts a second implementation of a 64-ary constellation. The 64-ary constellation of  FIG. 6  is implemented as a 5-level constellation. The constellation enables encoding of up to a 6 bit word. The 64-ary constellation of  FIG. 6  includes a first amplitude level  92 , a second amplitude level  94 , a third amplitude level  96 , a fourth amplitude level  98 , and fifth amplitude level  100 . The respective amplitude levels include respective first amplitude symbols  102 , second amplitude symbols  104 , third amplitude symbols  106 , fourth amplitude symbols  108 , and fifth amplitude symbols  110 . First amplitude level  92  has a unit radius of 1; second amplitude level  94  has a radius of 0.75; third amplitude level  96  has a radius of 0.516; fourth amplitude level  98  has a radius of 0.323; and fifth amplitude level  100  has a radius of 0.141. First amplitude level  92  has  24  first amplitude symbols  102 ; second amplitude level  94  has 16 second amplitude symbols  104 ; third amplitude level  96  has 12 third amplitude symbols  106 ; fourth amplitude level  98  has eight fourth amplitude symbols  108 ; and fifth amplitude symbols  100  has four fifth amplitude symbols  110 . 
     First amplitude symbols  102  are separated by 15°, with one first symbol  102  located at coordinates x=1, y=0, (1, 0). Second amplitude symbols  104  are separated by 22.5°, with a second amplitude symbol  104  located at coordinates x=0.738965, y=0 (0.738965, 0). Third amplitude symbols  106  are separated by 30°, with one third amplitude symbol  106  being located at coordinates x=0.511516 and y=0.067342301 (0.5115616, 0.067342301). Fourth amplitude symbols  108  are separated by 45°, with one fourth amplitude symbol  108  located at coordinate x=0.323195, y=0, (0.323195, 0). Fifth amplitude symbols  110  are separated by 90°, with one fifth amplitude symbol  110  located at Cartesian coordinates x=0.130657 and y=0.54120018, (0.130657, 0.54120018). 
     Similarly, as described above, for each 64-ary constellation of  FIGS. 5 and 6 , the number of symbol and position of each symbol placed on the respective amplitude levels is selected so that amplifier  24  operates at peak efficiency for the greatest number of symbols. Thus, the particular number of amplitude levels and the particular number of symbols placed on each amplitude level and the relative position of each symbol is specifically selected to maximize operation of amplifier  24 . 
     The above-described invention utilizes concentric constellations to provide simple compensation amplitude distortion. By utilizing concentric constellations, the expansion of inner constellations is controlled by one setting for a 24-ary constellation, two settings for a 32-ary constellation, and three or four settings, depending upon the number of amplitude levels, for a 64-ary constellation. The spacing between symbols in each M-ary constellation is selected to arrive at a suitable tradeoff between resolution and power and enables available power. 
     Further, fewer amplitude levels may be used when employing the teachings described herein. For example, only three amplitude levels are used rather than five amplitude levels for traditional 32-QAM implementations. Further, when compared to conventional square constellations, the circular constellations defined herein utilize peak-power more efficiently. 
     While the invention has been described in its presently preferred form, it is to be understood that there are numerous applications and implementations for the present invention. Accordingly, the invention is capable of modification and changes without departing from the spirit of the invention as set forth in the appended claims.