Abstract:
A method for determining the signal constellation of a received signal establishes a moment based on each waveform, squares the moment, fourth powers the moment, divides the fourth power by the square to obtain a ratio, and compares the ratio to a threshold. If the ratio is less than threshold, the signal constellation corresponds to a first type, and if greater than the threshold, the signal constellation corresponds to a second type. The method can be generalized to a magnitude mean in place of a second moment.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is generally directed to a method to identify the constellation type of a modulated signal. 
     2. Background 
     Communication systems employ a variety of signal modulation. These include frequency independent types such as pulse amplitude modulated (PAM) signals, quadrature amplitude modulation (QAM) and phase-shift keying (PSK). 
     The number of discrete waveforms may be denoted as M points in the state space constellation. In PAM, the ergodic (i.e., time-dependent) signal waveform s m (t) may be represented by a periodic cosine function that includes a series of discrete amplitudes ranging from m=1, 2, . . . , M. For pulsed signals sent over discrete time intervals, the time t may be replaced by nT where T is the sampling period and n is a positive integer. PAM is similar to vestigial side band (VSB) used in television. The M-PAM signals may be plotted in single dimensioned signal space R (also written as R) at M discrete points along the real axis. The energy for the waveforms may be a proportional to the square of the amplitudes. 
     FIG. 1 shows a 4-PAM signal space diagram  10  with an axis  12  for example M=4. The data points are presented for a binary bit pair having four possible positions at points  16   a  and  16   b  on the left side of the imaginary axis and  16   c  and  16   d  on the right side in this example. Phase modulated signals, such as PSK and QAM, may be multi-dimensional belonging to signal space R N , where N represents the dimension superscript. 
     For N=2, there exist real and imaginary components for representing amplitude and phase. A distance d from the origin of a point on the two-dimensional signal grid in R 2  can be expressed in complex form as d=d i +jd q  where d i  is the in-phase or real component, d q  is the quadrature or imaginary component and j={square root over (−1)}. 
     In PSK, the signal waveforms s m (t) have equal energy and can be plotted as being equal distant from the origin. FIG. 2 shows an 8-PSK signal space diagram  18  for M=8 with data points  20   a  and  20   b  on the real axis  12 ,  20   c  and  20   d  on the imaginary axis  14 , and  20   e ,  20   f ,  20   g , and  20   h  at intermediate positions. 
     QAM may include a series of discrete amplitudes in addition to a phase component to distinguish a set of four points by the quadrant occupied. FIG. 3 shows a 16-QAM signal space diagram  22  for M=16 with the axes  12  and  14  dividing the space into four quadrants  24   a ,  24   b ,  24   c  and  24   d . The first quadrant  24   a  includes four points  26   a ,  26   b ,  26   c  and  26   d . The second quadrant  24   b  includes four points  26   e ,  26   f ,  26   g  and  26   h . The third quadrant  24   c  includes four points  26   i ,  26   j ,  26   k  and  26   l . The fourth quadrant  24   d  includes four points  26   m ,  26   n ,  26   o  and  26   p.    
     For M=4, data values to be represented may range from two-digit binary numbers 00 2 , 01 2 , 10 2 , and 11 2 . For M=8, data values to be represented may range from three-digit binary numbers 000 2 , 001 2 , 010 2 , . . . , 111 2 . For M=16, data values to be represented may range from four-digit binary numbers 0000 2 , 0001 2 , 0010 2 , . . . , 1111 2 . The incoming signal to be interpreted as these data values may be received as voltages or digital numbers, with each discrete data value corresponding to a particular range of voltages. 
     Several communication transmission media are widely in use today, such as satellite, microwave, terrestrial, and cable systems. These transmit data at a variety of data rates. In order to convert the signals from received voltages into data, their amplitude and phase must be resolved. This task may be complicated by electronic noise from a variety of sources. A receiver configured to resolve only a select signal constellation would be unable to resolve an alternate modulation constellation. Smaller integrated chips could allow a wider variety of modulation systems to be received, if these are identified by modulation type. Accordingly, there exists a need for accurate and efficient detection of the modulation constellation type of a signal to enable multi-mode multi-standard operation of communication receivers. 
     SUMMARY OF THE INVENTION 
     A method for determining the signal constellation of a received signal establishes a moment based on each waveform, squares the moment, fourth powers the moment, divides the fourth power by the square to obtain a ratio, and compares the ratio to a threshold. If the ratio is less than threshold, the signal constellation corresponds to a first type, and if greater than the threshold, the signal constellation corresponds to a second type. The method can be generalized to a magnitude mean in place of a second moment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a plot diagram of a 4-PAM state space. 
     FIG. 2 is a plot diagram of an 8-PSK state space. 
     FIG. 3 is a plot diagram of a 16-QAM state space. 
     FIG. 4 is a block diagram of a constellation determiner by the moment ratio according to a specific embodiment of the present invention. 
     FIG. 5 is a block diagram of a normalized constellation determiner according to a specific embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Those of ordinary skill in the art will realize that the following description of the present invention is illustrative only and not in any way limiting. Other embodiments of the invention will readily suggest themselves to such skilled persons having the benefit of this disclosure. 
     In accordance with a presently preferred embodiment of the present invention, the components, process steps, and/or data structures may be implemented using various types of operating systems, computing platforms, computer programs, and/or general purpose machines. In addition, those of ordinary skill in the art will readily recognize that devices of a less general purpose nature, such as hardwired devices, or the like, may also be used without departing from the scope and spirit of the inventive concepts disclosed herein. 
     The present invention relates to a method to determine the constellation type for modulation of a received signal. The method may be used in a receiver of a communications system employing different types of modulations. Examples of such systems include, but are not limited to, multiple data rate systems, adaptive data rate systems and multi-resolution modulation systems. These can be found in satellite, microwave, terrestrial and cable communication systems along with broadcast channels, digital subscriber loops and various size networks. The method may also be used in universal types of receivers designed to operate for multiple applications. Such receivers may be reconfigured according to the modulation system employed. Examples of such universal receiver systems are those used in television set-top boxes that can receive VSB, M-QAM and M-PSK depending on the transmission medium and communication standard used. The method may be used in conjunction with any form of timing and carrier synchronization. It may also be used with equalization used in channel receivers. 
     The inventive method may ascertain the modulation without the need for recovery of carrier identification. The channel intersymbol interference may be treated as additive white Gaussian noise, irrespective of the channel noise level. The symbol timing is assumed to be recovered and the data available at the symbol rate. 
     The waveform series s m (nT) for m=1, 2, . . . , M may be characterized by an average voltage s. The series of these signal waveform may be expressed as an expected value function of its average E(|s|) representing an aggregate absolute voltage of the received signals. The function E may also signify the equivalent low pass filtering operation of the waveforms. 
     The power of the signal may be expressed as a second order moment of the waveform. For the power, the expected value function E(s 2 ) may be taken for the series of the square of the waveform. The variance of signal power may be expressed as a fourth order moment of the waveform. For the signal power variance, the expected value function E(s 4 ) may be taken for the series of the fourth power of the waveform. By dividing the variance function by the power function, a moment ratio R may be expressed by the following relation:        R   =       E        (       s        (   nT   )       4     )         E        (       s        (   nT   )       2     )                                
     Signals arranged in an M-PSK constellation have a constant envelope, i.e., identical distance or moment d of the constellation points from the signal space origin. Since the waveform average s may be replaced the combined or average absolute distance |d|, the resulting expected value function E(|d|) may be treated as proportional to a constant d c . Consequently, M-PSK signals have the same second and fourth order moments irrespective of the number of constellation points M. This allows a PSK moment ratio to be reduced to R=d c   4 /d c   2 =d c   2 . 
     Signals such as QAM, PAM and VSB may exhibit different second and fourth order moment characteristics for increasing numbers of constellation points. As M increases, points may disperse on the signal grid. For example, points for 8-QAM may be located at ±1±j and ±3±j. Due to the differing distances from the origin, the points in these constellations have non-uniform second order moments, and by extension non-uniform fourth order moments. Power and variance functions may vary from one point to another within a constellation. Consequently, as the number of points M within a constellation expands, the E functions monotonically increase for these modulated signals. The moment ratio R may thus be treated as a unique value for each M-QAM and M-PAM constellation, and distinguished from the PSK values of R. 
     A comparison of expected value functions and the moment ratio for selected modulations is shown in Table 1. Each constellation type includes the number of constellation points M and modulation technique. The constellation type is described by point distances from the origin, the expected value function of that distance, the function with respect to the square of the distance, the function with respect to the fourth power of the distance, and the moment ratio. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Const. Type 
                 |d| 
                 E(|d|) 
                 E(d 2 ) 
                 E(d 4 ) 
                 R 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 2-PSK 
                 ∥1 + j∥ = ±{square root over (2)} 
                 {square root over (2)} 
                 2 
                 4 
                 2.0 
               
               
                 4-PSK 
                 ±{square root over (2)} 
                 {square root over (2)} 
                 2 
                 4 
                 2.0 
               
               
                 8-PSK 
                 ±{square root over (2)} 
                 {square root over (2)} 
                 2 
                 4 
                 2.0 
               
               
                 4-PAM 
                 ±1, ±3 
                 4 
                 5 
                 41 
                 8.2 
               
               
                 8-PAM 
                 ±1, ±3, ±5, ±7 
                 8 
                 21 
                 777 
                 37.0 
               
               
                 16-PAM 
                 ±1, ±3, . . . ±15 
                 16 
                 85 
                 12,937 
                 152.2 
               
               
                 16-QAM 
                 ±{square root over (2)}, ±{square root over (10)}, ±3{square root over (2)}, 
                 4 
                 10 
                 132 
                 13.2 
               
               
                   
                 ±{square root over (26)}, ±{square root over (34)}, ±5{square root over (2)} 
               
               
                 64-QAM 
                 ±{square root over (2)}, ±{square root over (10)}, ±3{square root over (2)}, . . .  
                 8 
                 42 
                 2,436 
                 58.0 
               
               
                   
                 ±5{square root over (2)}, . . . ±7{square root over (2)} 
               
               
                 256-QAM 
                 ±{square root over (2)}, . . . ±15{square root over (2)} 
                 16 
                 170 
                 40,324 
                 237.2 
               
               
                   
               
             
          
         
       
     
     Calculation of the moment ratio R may distinguish between modulation by constellation types. The moment ratio may also distinguish M levels within a constellation type (except PSK). An algorithm may include comparing the moment ratio to a threshold for distinguishing between two types of constellations. Alternatively, the thresholding operation may be generalized by comparing the moment ratio to a series of threshold values to identify the constellation type and/or its level among several candidates. 
     FIG. 4 shows a block diagram for the algorithm to determine the constellation type according to a first specific embodiment of the present invention. The algorithm  30  receives an incoming signal  32  into an amplifier  34 . The amplified signal may be digitized in an analog-digital converter (ADC)  36 . The digital signal may be separately input into a second order power (or squaring) function  38  and a fourth order power function  40 . The second and fourth order power functions  38  and  40  may be considered equivalent to a first low pass filter (LPF) to perform the expected value function. The squared value from the function  38  may be input to a ratio-inverter  42  (taken to the −1 power). 
     The smoothed fourth order and inverted squared values may then be input to a multiplier  44  to produce a moment ratio R in a ratio store  46 . A threshold value T may be provided in a threshold store  48 . The moment ratio R and threshold T may be input to a logical comparer  50 . If the moment ratio R is lower than the threshold T, the comparer  50  may indicate a first constellation condition  52 . By contrast, if R is higher than T, the comparer  50  may indicate a second constellation condition  54 . A concatenated series of threshold values may be compared with the moment ratio in order to distinguish between several constellation types. 
     The procedure of determining the constellation type may be further simplified in a second embodiment of the present invention. By employing an automatic gain control, the power level (represented by the expected value function of the square of the point distance or moment) may be normalized to the highest power value among the expected modulation techniques. From the constellation list in Table 1, the highest power level is 170, corresponding to 256-QAM. The point distance d for each constellation type may be multiplied by a coefficient a in order to normalize each power function E(d 2 ) to a value of 170. This normalizing operation may be performed by automatic gain control (AGC). The AGC system for a multi-constellation type receiver may adjust the incoming signal power and ADC input range irrespective of signal modulation type. Thus, the incoming signal power may be uniform regardless of the input constellation. 
     A comparison of expected value functions and the moment ratio for selected modulations is shown in Table 2. Each constellation type includes the number of constellation points M and modulation technique. The constellation type is described by coefficient a, the expected value function of the coefficient and distance product, the function with respect to the square of the product, the unction with respect to the fourth power of the product, and the moment ratio. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Const. Type 
                 a 
                 E(|a · d|) 
                 E([a · d] 2 ) 
                 E([a · d] 4 ) 
                 R 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 2-PSK 
                 9.220 
                 13.0 
                 170.0 
                 28,905.7 
                 170.0 
               
               
                 4-PSK 
                 9.220 
                 18.4 
                 170.0 
                 28,905.7 
                 170.0 
               
               
                 8-PSK 
                 9.220 
                 15.7 
                 170.0 
                 28,905.7 
                 170.0 
               
               
                 4-PAM 
                 5.831 
                 11.7 
                 170.0 
                 47,397.6 
                 278.8 
               
               
                 8-PAM 
                 2.845 
                 11.4 
                 170.0 
                 50,932.4 
                 299.6 
               
               
                 16-PAM 
                 1.414 
                 11.3 
                 170.0 
                 51,746.0 
                 304.4 
               
               
                 16-QAM 
                 4.123 
                 16.5 
                 170.0 
                 38,144.1 
                 224.4 
               
               
                 64-QAM 
                 2.012 
                 16.1 
                 170.0 
                 39,919.9 
                 234.8 
               
               
                 256-QAM 
                 1.000 
                 16.0 
                 170.0 
                 40,324.0 
                 237.2 
               
               
                   
               
             
          
         
       
     
     The multiplication of power normalizing coefficient a by the distance d may produce a factored moment. The incorporation of the factored moment in the expected value function may eliminate the division of the fourth order function by the second order function, since the latter may be normalized as a constant value. A comparison to a threshold may be made either to the fourth order function, or to a moment ratio composed of the fourth order function divided by a constant power value. Consequently, the complexity of the algorithm for determining the constellation type in the second specific embodiment may be reduced from the first specific embodiment. 
     FIG. 5 shows a block diagram for the algorithm to determine the constellation type according to the second specific embodiment of the present invention. The algorithm  60  receives an incoming signal  62  into a normalizing amplifier  64 . The amplified signal may be digitized in an ADC  66 . The digital signal may be input into a fourth order power function  68  (such as an LPF) to produce a value  70  that may be termed a moment ratio. 
     A threshold value T may be provided in a threshold store  72 . The moment ratio R and threshold T may be input to a logical comparer  74 . If the value  70  is lower than the threshold T, the comparer  74  will indicate a first constellation condition  76 . By contrast, if the value  70  is higher than T, the comparer  74  may indicate a second constellation condition  78 . A concatenated series of threshold values  72  may be used to compare with the value  70  in order to distinguish between several constellation types. 
     The normalized moment ratio may be readily segregated by constellation type. The moment ratio for M-PSK in Table 2 is 170. The moment ratio for M-QAM in Table 2 lies between 220 and 240. The moment ratio for M-PAM in Table 2 lies between 270 and 310. The moment ratio may be compared to a threshold to distinguish between two types of constellations. 
     For example, a first threshold value of 200±20 may be employed for deciding between PSK and QAM constellations, with values below the first threshold corresponding to PSK and values above being either QAM or PAM. Alternatively, a second threshold value of 260±10 may be considered to distinguish QAM and PAM constellations, with values above the second threshold corresponding to PAM. 
     The thresholding operation may be generalized by comparing the moment ratio to a series of threshold values to identify the constellation type among several modulation candidates. The M number of points may be determined by further thresholding for narrower differences between threshold values. 
     While embodiments and applications of this invention have been shown and described, it would be apparent to those skilled in the art having the benefit of this application that many more modifications than mentioned above are possible without departing from the inventive concepts herein. The invention, therefore, is not to be restricted except in the spirit of the appended claims.