Abstract:
An apparatus and method for generating an envelope predistorted radio frequency signal which avoids undesirable spurious emissions. A complex baseband signal, having an in-phase component I and a quadrature component Q, is sampled and filtered in a sampling circuit and filter circuit to obtain samples I k  of the in-phase component and samples Q k , the quadrature component. The magnitude x k  of each sample pair is determined in a first calculation circuit. An amplitude and phase distortion factor D k , based on scaled values of the archyperbolic tangent and the hyperbolic tangent of the baseband sample magnitude is determined in further calculation circuit and a multiplier. Each sample I k  of the in-phase component and Q k  of the quadrature component is multiplied by the corresponding distortion factor D k , and the resulting predistorted components combined and upconverted to provide a predistorted baseband signal which is amplified in a power amplifier having hyperbolic tangent distortion.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application is related to U.S. patent application Ser. No. 09/624,149 filed Jul. 24, 2000. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The present invention pertains to an apparatus for and a method of applying both amplitude predistortion and phase predistortion to a modulated baseband signal. More particularly, the present invention pertains to an apparatus for and a method of generating an amplitude modulated radio frequency signal by amplitude predistorting its baseband signal, using the inverse hyperbolic tangent of a value based on the envelope of the baseband in-phase and quadrature components, and phase predistorting the baseband signal, using the hyperbolic tangent of that value.  
         BACKGROUND OF THE INVENTION  
         [0003]    Environments such as commercial airliners frequently have several radios that operate at different frequencies. Not only must these radios avoid interference with each other, but also they must meet spectrum mask requirements imposed by regulatory agencies, such as the United States Federal Communications Commission. The output from the solid state power amplifier of such a radio often includes distortion that can be characterized by a hyperbolic tangent function. Both amplitude distortion and phase distortion may occur. The transmit spectrum of such a radio signal can spread near the desired signal band if the envelope of the transmitted signal is not constant, particularly if the transmitter power amplifier is being driven into soft saturation. While spurious emissions might be reduced by predistorting of the radio frequency signal envelope just before transmission to the output power amplifier, this requires analog multipliers. Even then, if noise is picked up in the multiplier circuit, that noise will modulate the desired signal and pass through to the output.  
           [0004]    One approach to overcoming power amplifier nonlinearity utilizes the function f(x)=2x/(1+x 2 ) for amplitude predistortion and the function ph(x)=(Bf(x))/6=2Bx/6(1+x 2 ) for phase predistortion, where x is the instantaneous value of the envelope. Another approach to overcoming amplitude distortion is to utilize the “cuber” function f (x)=x+x 3 /3, where again x is the instantaneous value of the envelope. These approaches have been found to provide less than optimum linearity in the power amplifier output.  
         SUMMARY OF THE INVENTION  
         [0005]    The present invention is an apparatus for and a method of amplitude and phase distorting a modulated radio frequency signal such that after passing of the distorted signal through a non-linear power amplifier, undesirable spurious emissions in the resulting spectrum are reduced. In accordance with the present invention, a complex amplitude modulated baseband signal, having an in-phase component I and a quadrature component Q, is sampled to obtain k samples I k  of the in-phase component and k samples Q k  of the quadrature component, and the magnitude of the envelope of the baseband samples is determined. A distortion factor based on the product of the hyperbolic tangent (“tanh”) and the inverse hyperbolic tangent or archyperbolic tangent (“atanh”) of a scaled value of the complex baseband sample magnitude is used to multiply each sample of the in-phase component and of the quadrature component so as to provide predistorted components. These predistorted components are combined and used to provide a distorted radio frequency (“RF”) signal which is applied to the power amplifier. The power amplifier distortion cancels the distortion in the radio frequency signal so that the power amplifier provides a substantially undistorted output signal.  
           [0006]    The scaling factor is obtained by combining a portion of the output signal envelope with the undistorted envelope in a feedback circuit. The feedback circuit preferably computes the mean square error between the undistorted envelope and the output signal envelope. Preferably, to assure that the mean square error is computed correctly, both envelopes are normalized. The mean square error is adjusted by a fixed gain control and integrated, and the result used to scale the undistorted envelope prior to determination of the hyperbolic tangent and archyperbolic tangent functions.  
           [0007]    The envelope of the baseband signal is thus subjected to amplitude and phase predistortion prior to upconversion to the radio frequency signal. This avoids impressing pick-up noise on the transmitted envelope. It is possible to do the predistortion prior to intermediate frequency (IF) and RF bandpass filtering of the radio frequency signal since such filtering has a wide bandwidth, allowing the distorted signal spectrum to pass through the power amplifier.  
           [0008]    Preferably, the predistortion apparatus of the present invention is implemented in a gate array, such as a field programmable gate array. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]    These and other aspects and advantages of the present invention are more apparent from the following detailed description and claims, particularly when considered in conjunction with the accompanying drawings in which like parts bear like reference numerals. In the drawings:  
         [0010]    [0010]FIG. 1 is a block diagram of an apparatus for generating an amplitude and phase predistorted radio frequency signal in accordance with a preferred embodiment of the present invention;  
         [0011]    [0011]FIG. 2 is a block diagram of one preferred embodiment of a circuit suitable for use in the apparatus of FIG. 1;  
         [0012]    [0012]FIG. 3 is a graph of results from a simulation comparing the present invention with the prior art;  
         [0013]    FIGS.  4 A- 4 D plot performance in a simulation of the present invention and the prior art; and  
         [0014]    FIGS.  5 A- 5 D show the output spectra from a simulation of power amplifiers in accordance with the present invention and the prior art. 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0015]    [0015]FIG. 1 depicts an apparatus for generating an amplitude and phase predistorted radio frequency signal in accordance with a preferred embodiment of the present invention. A signal source  10  provides a complex baseband signal xe jφ     k   , where x is the envelope of the signal and, for example, may be an Edge GSM or a D8PSK signal. The signal includes an in-phase component I and a quadrature component Q that are normalized and sampled at, for example, 10.5 kilosamples per second (KSPS). From source  10 , the samples are filtered in filter circuit  12  to produce smooth transitions between phase symbols. The samples I k  of the in-phase component and the samples Q k  of the quadrature component are applied from filter circuit  12  to a calculation circuit  16  which calculates the magnitude of the scaled complex baseband envelope sample, for example by determining the square root of the sum of the squares of the scaled in-phase component sample and the scaled quadrature component sample.  
         [0016]    [0016]FIG. 2 is a block diagram of one preferred embodiment of a calculation circuit for determining an approximation of the magnitude of each complex sample k of the baseband signal. In FIG. 2 the samples I k  of the in-phase component and the samples Q k  of the quadrature component are applied to a first detection circuit  18  which determines the maximum of these samples by determining for each sample pair whether the I k  sample or the Q k  sample is the larger. The I k  and the Q k  samples are also applied to a second detection circuit  20  which determines the minimum of these samples by determining for each sample pair whether the I k  sample or the Q k  sample is the smaller. The detected maximum value (“max k ”) and the detected minimum value (“min k ”) for each sample pair are applied to calculating circuit  22  which computes the value y k =½ (min k /max k ) 2 .  
         [0017]    The y k  output from calculating circuit  22  is applied as an input to each of five multiplier circuits  24 ,  26 ,  28 ,  30  and  32 . The y k  output is also applied to a second input of multiplier  24 . As a consequence, multiplier  24  provides as an output the value y k   2 . This Y k   2  output from multiplier  24  is applied to the second input of multiplier  26  and to a negative input to summation circuit  34 . The output of multiplier  26  is thus the value Y k   3 . This output is applied to the second input of multiplier  28  and to a positive input of summation circuit  34 . Multiplier  28  accordingly provides the output Y k   4  which is used as the second input to multiplier  30  and which is applied to a negative input to summation circuit  34 . Multiplier  30  then provides the output y k   5  to the second input of multiplier  32  and to a positive input to summation circuit  34 . Multiplier  32  provides the output y 6  to a negative input to summation circuit  34 .  
         [0018]    Summation circuit  34  divides the sum of its inputs by 2, thus providing as its output the value ½(−Y k   2 +Y k   3 −Y k   4 +Y k   5 −y k   6 ). This signal is applied as an input to summation circuit  36 , which also receives as inputs the y k  signal from calculation circuit  22  and the constant 1. The output of summation circuit  36  is thus the value { 1+y   k +½(−y k   2 +y k   3 −y k   4 +y k   5 −y k   6 )}. This is equal to the value {(1+y k )/2+{fraction ( 1 / 2 )}(1+y k −y k   2 +y k   3 −y k   4 +y k   5 −y k   6 )}. This signal is applied from summation circuit  36  to one input of multiplier  38 , which receives the max k  signal from detection circuit  18  at its second input. Consequently, the output of multiplier  38  is (max k )×{(1+y k )/2+½(1+Y k −Y k   2 +Y k   3 −Y k   4 +Y k   5 −Y k   6 )} which is an approximation of (I k   2 +Q k   2 ) ½  and thus an approximation of the magnitude x k  of the sample k.  
         [0019]    The output from the apparatus of FIG. 1 is provided by power amplifier  64  to antenna  66 . Radio frequency coupler  70  couples a portion of that output to envelope detector  72 . The detected envelope is applied to analog-to-digital converter  73  which samples at a high sampling rate, shown in FIG. 1 as a sampling rate of 50 megasamples per second (MSPS). The output of analog-to-digital converter  73  is normalized by normalizing circuit  74  so that its maximum valve equals 1. The output of calculation circuit  16  is applied through delay circuit  76  to a positive input of summing circuit  78 , while the output from normalizing circuit  74  is applied to a negative input of the summing circuit. The input to summing circuit  78  from calculation circuit  16  represents the envelope before distortion, while the input to summing circuit  78  from normalizing circuit  74  represents the envelope after distortion. Delay circuit  76  assures that each undistorted sample is summed with the normalized output resulting from that same sample. The resulting signal from summing circuit  78  is applied to one input of multiplier  80  which receives a weighting factor of −8 at its second input. The output from multiplier  80  is applied to one input of multiplying circuit  82  which receives the output from normalizing circuit  74  at its second input. The output from multiplying circuit  82  is applied through low pass filter  84  to sampler  86  which applies samples of that output at periodic intervals of, for example, one minute to integrator  88 . The output of integrator  88  is a scaling factor C and is applied to one input of multiplying circuit  90  which receives the X k  outputs from calculation circuit  16  at its second input. The output of multiplier circuit  90  is thus Cx k .  
         [0020]    The Cx k  output from multiplier circuit  90  is applied as an input to calculation circuit  40  which determines the value of (atanh (Cx k ))/Cx k ). By way of an example, calculation circuit  40  might be a lookup table having values to 16 bits for determining a value X k   2 /3+x k   4 /5+x k   6 /7+ . . . which is an approximation of the value {(atanh (x k ))/x k }−1. The output of the lookup table then is applied to one input of a summation circuit which receives the constant 1 at its second input so as to provide an approximation of (atanh (x k ))/x k . It is preferred that calculation circuit  40 , when in the form of a lookup table, compute the value of the segment {(atanh (x k ))/x k }−1, and that the constant 1 be added by a summation circuit in order to provide the desired accuracy while maintaining the lookup table of a moderate size.  
         [0021]    The x k  output from calculation circuit  16  is also applied as an input to multiplier  92  which receives the value π/6 at its second input. The Cx k  output from multiplier circuit  90  is applied to calculation circuit  94  which calculates the value tanh(Cx k ) and applies that value to an input of multiplier  96 . Calculation circuit  94  might be a lookup table, for example. The second input of multiplier  96  receives the value πx k /6 from multiplier  92 . The output of multiplier  96  is thus (πx k tanh(Cx k ))/6=φ k . This value is applied to lookup table  98  which provides as outputs the values I k N=+cos(φ k ) and Q k N=−sin(φ k ). These values are applied to inputs of multiplier pair  100  which receives the output of lookup table  40  at its second input.  
         [0022]    The output of multiplier circuit  100  is thus the distortion factor {(atanh(Cx k ))/Cx k }e −jφ     k   =D k . This output is applied to one input of multiplier pair  44 . The samples I k  of the in-phase component and the samples Q k  of the quadrature component are also applied to multiplier pair  44 . Each sample of the in-phase component and the quadrature component is thus modified by the respective distortion factor D k , so that the output of multiplier pair  44  is x k e jφ     k   {(atanh (Cx k ))/Cx k }e −jφ     k   =D k x k e −jφ     k   . These samples of the modified signal are resampled in resampling circuit  46  at the same sampling rate as in analog-to-digital converter  73 , shown in FIG. 1 as a resampling rate at 50 MSPS.  
         [0023]    The resampled output from resampling circuit  46  is applied to multiplier pair  48 . Signal generator  50  provides an intermediate frequency signal of a frequency less than half the sampling rate of resampling circuit  46 , shown in FIG. 1 as a frequency of 17 MHz. Sampling circuit  52  samples the sine and cosine outputs from signal generator  50  at the same sampling rate as resampling circuit  46 , shown in FIG. 1 as a sampling rate of 50 MSPS. These sampled sine and cosine signals are applied to multiplier pair  48  so that the multiplier pair provides as outputs the intermediate frequency signals D k ×I k  sin 17 MHz and D k ×I k  cos 17 MHz. These signals are added in summation circuit  54 , and the resulting predistorted, upconverted intermediate frequency signal is applied on line 56 to digital-to-analog converter  58  which samples at the same 50 MSPS rate as resampling circuit  46 .  
         [0024]    The output from digital-to-analog converter  58  is applied to band pass filter  60  which is centered at the 17 MHz frequency of signal source  50  and which has a bandwidth sufficient to avoid distortion of the predistorted envelope, for example a bandwidth of 1 MHz. The output from bandpass filter  60  is upconverted to a radio frequency in upconverter  62  and passed through driver amplifier  68  and power amplifier  64  to antenna  66 . If desired, a radio frequency attenuator could be utilized, rather than upconverter  62  and driver amplifier  68 . Power amplifier  64  has a transfer function C and hyperbolic tangent distortion so that the output of power amplifier  64  is bctanh (xe jφ     k   e −jφ     k   e jφ     k    tanh −1  (cx))/cx=bcxe jφ     k   , where b is the power amplifier gain.  
         [0025]    The feedback circuit of FIG. 1 results in the signal C that is applied from integrator  88  to multiplier  90  converging to the current value of the transfer function C of output amplifier  64 . It is possible to set the gain of the feedback loop so that it converges in just a few iterations. The value of the feedback gain −8 which guarantees stable conversion is upper bounded by the mean square value of the feedback envelope after being normalized by circuit  74 .  
         [0026]    Predistorting the digital envelope of the baseband signal before upconversion to the radio frequency, followed by digital-to-analog conversion, in accordance with the present invention avoids impressing of analog pickup noise directly on the transmitted envelope, as would occur if the envelope correction were performed on the radio frequency analog signal. Implementation of the present invention does not require significant hardware. It can be accomplished in software or firmware. Implementation on a gate array, such as a field programmable gate array, is convenient.  
         [0027]    [0027]FIG. 3 is a plot of power amplifier output as a function of signal input for (1) a computer simulated system in accordance with the present invention with the scaling factor C=0.7, (2) a computer simulated system utilizing the cuber function f(x)=x+x 3 /3, and (3) a computer simulated system utilizing the functions f(x)=2x/(1+x 2 ) and ph (x)=2Bx/6(1+x 2 ), showing the superiority of the present invention.  
         [0028]    FIGS.  4 A- 4 D are quadrature amplitude modulation plots. FIG. 4A plots the computer simulated output of a linear power amplifier. FIG. 4B plots the computer simulated output of a non-linear power amplifier with no predistortion, but with hyperbolic tangent nonlinearity in phase and amplitude. FIG. 4C plots the computer simulated output of such a nonlinear power amplifier with predistortion based on the cuber function f(x)=x+x 3 /3. FIG. 4D plots the computer simulated output of such a nonlinear power amplifier with predistortion in accordance with the present invention. As can be seen, the plot for the present invention in FIG. 4D is substantially the same as the plot for a linear power amplifier in FIG. 4A, while the plots of FIGS. 4B and 4C are not, again showing the superiority of the present invention.  
         [0029]    [0029]FIG. 5A shows the computer simulated output spectrum of a linear power amplifier. FIG. 5B is the computer simulated output spectrum of a nonlinear power amplifier. FIG. 5C is the computer simulated output spectrum of such a nonlinear power amplifier with predistortion based on the cuber function f(x)=x+x 3 /3. FIG. 5D is the computer simulated output spectrum of such a nonlinear power amplifier with predistortion in accordance with the present invention with the scaling factor C=0.7. The simulated output spectrum of the present invention most nearly matches that of a linear power amplifier, once more showing the superiority of the present invention.  
         [0030]    Although the present invention has been described with reference to preferred embodiments, various alterations, rearrangements, and substitutions could be made, and still the result would be within the scope of the invention.