Abstract:
An apparatus for and a method of generating an envelope predistorted radio frequency signal. A complex baseband signal, having an in-phase component I and a quadrature component Q, is sampled and filtered. The magnitude u k  of each complex baseband sample pair is determined by the square root of the sum of the squares of the in-phase component sample and the quadrature component sample. A distortion factor D k , is determined based on a scaled value of the inverse hyperbolic tangent or archyperbolic tangent (“atanh”) of the baseband sample magnitude divided by that scaled sample magnitude. Each sample of the in-phase component I k  and of the quadrature component Q k  is multiplied by the corresponding distortion factor D k  so as to provide predistorted components. The predistorted components are then combined to provide a predistorted baseband signal.

Description:
FIELD OF THE INVENTION 
     The present invention pertains to an apparatus for and a method of predistorting a complex baseband signal. More particularly, the present invention pertains to an apparatus for and a method of generating an amplitude modulated radio frequency signal by predistorting its baseband signal using the inverse hyperbolic tangent of a value based on the envelope of the baseband in-phase and quadrature signals. 
     BACKGROUND OF THE INVENTION 
     The outputs from many solid state power amplifiers include distortion that can be characterized by a hyperbolic tangent function. Various radio applications, such as VHF data radio utilized by commercial airliners, must meet spectrum mask requirements imposed by regulatory agencies, such as the United States Federal Communications Commission. 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. 
     SUMMARY OF THE INVENTION 
     The present invention is an apparatus for and a method of generating an amplitude modulation of a desired radio frequency signal such that after passing through the 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 samples I k  of the in-phase component and samples Q k  of quadrature component, and the magnitude of the envelope of the baseband sample is determined by finding the square roots of the sums of the squares of the in-phase component samples and the quadrature component samples. A distortion factor equal to the inverse hyperbolic tangent or archyperbolic tangent (“atanh”) of a scaled value of the complex baseband sample magnitude divided by that scaled 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 then upsampled, upconverted, and combined to provide a predistorted intermediate frequency (“IF”) carrier signal which is further upconverted to an analog radio frequency (“RF”) signal and filtered, leaving the desired upconverted signal. 
     If desired, the scaling factor can be 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 archyperbolic tangent function. 
     The envelope of the baseband signal is thus subjected to digital envelope predistortion prior to upconversion. This avoids impressing pick-up noise on the transmitted envelope. It is possible to do the predistortion prior to 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. 
     In the prior art to predistortion has been achieved by subjecting the signal to an inverse nonlinearity, for example, by passing the linear signal y(t) through an inverse nonlinear predistorter to generate f(y(t))=atanh(Cy(t)). In contrast, the present invention multiplies y(t) by {atanh(Cy(t))}/Cy(t), which can be considered an expander function. 
     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 
     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: 
     FIG. 1 is a block diagram of an apparatus for generating an envelope predistorted radio frequency signal in accordance with a first preferred embodiment of the present invention; 
     FIG. 2 is a block diagram of one preferred embodiment of a circuit suitable for use in the apparatus of FIG. 1; and 
     FIG. 3 is a block diagram of an apparatus for generating an envelope predistorted radio frequency signal in accordance with a second preferred embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 depicts an apparatus for generating an envelope predistorted radio frequency signal in accordance with a first preferred embodiment of the present invention. A signal source  10  provides a complex baseband signal, including 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 applied to filter circuit  12 , which might include a pair of raised cosine filters for shaping differential eight-phase shift keying (D8PSK) modulation, one filter for the in-phase component and one for the quadrature component. Filter circuit  12  resamples the provided signals at a multiple of the sampling rate of source  10 , shown in FIG. 1 as a resampling rate of 52.5 KSPS. The samples of the in-phase component I k  and the quadrature component Q k  are applied from filters  12  to a gain control amplifier pair  14  that receives a gain control or scaling signal, which might be a constant value, from an appropriate source such as system software. A multiplier pair could be used in place of the gain control amplifier pair. The output of gain control amplifier pair  14  is applied to a calculation circuit  16  which calculates the magnitude of the scaled complex baseband envelope sample by determining the square root of the sum of the squares of the scaled in-phase component sample and the scaled quadrature component sample. 
     FIG. 2 is a block diagram of one preferred embodiment of an apparatus for determining an approximation of the magnitude of each complex sample k of the baseband signal. In FIG. 2 an in-phase component I k  and a quadrature component Q k  of a normalized baseband signal, which have been sampled at an appropriate sampling rate such as 52.5 KSPS, are applied to a first detection circuit  18  which determines the maximum of these components by determining for each sample pair whether the I k  component or the Q k  component is the larger. The I k  component and the Q k  component samples are also applied to a second detection circuit  20  which determines the minimum of these components by determining for each sample pair whether the I k  component or the Q k  component 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 . 
     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 . 
     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+½(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 ) 1/2 =u k , and thus an approximation of the magnitude of the sample k. 
     Returning to FIG. 1, the input to calculation circuit  16  is C×I k  and C×Q k , and so the output from the calculation circuit is C×(I k   2 +Q k   2 ) 1/2 =C×u k =x k . This x k  output is applied as an input to calculation circuit  40  which determines 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. Calculation circuit  40  might be a look-up table for this purpose, having values to 16 bits. The output of calculation circuit  40  is applied to one input of summation circuit  42  which receives the constant 1 at its second input. It is preferred that calculation circuit  40 , when in the form of a look-up table, compute the value of the segment {(atanh(x k ))/x k }−1, and that the constant 1 be added at summation circuit  42  in order to provide the desired accuracy while maintaining the look-up table of a moderate size. 
     The output of summation circuit  42  is thus the distortion factor (atanh(x k ))/x k =(atanh(Cu k ))/Cu k =D k . This distortion factor is applied to one input of multiplier pair  44 , which also receive the u k  samples of the in-phase component I k  and the quadrature component Q k  from filter circuit  12 . Each sample of the in-phase component I k  and the quadrature component Q k  is thus modified by the distortion factor D k , so that the output of multiplier pair  44  is e jθ     k    (atanh(Cu k ))/C. These samples of the modified signal are then resampled at a high rate, such as 50 megasamples per second (MSPS) in resampling circuit  46 , and the resulting samples are applied to multiplier pair  48 . A signal generator  50  applies sine and cosine outputs to sampling circuit  52 . Signal generator  50  operates at a frequency less than half the sampling rate of resampling circuit  46 , depicted in FIG. 1 as a frequency of 21.4 MHz. Sampling circuit  52  samples the sine and cosine outputs from signal generator  50  at the same sampling rate as used by sampling circuit  46 , depicted in FIG. 1 as 50 MSPS. The sampled sine and cosine signals from sampling circuit  52  are applied to multiplier pair  48  so that the multiplier pair provide as outputs the intermediate frequency signal D k ×I k  sin 21.4 MHz and D k ×Q k  cos 21.4 MHz. These signals are applied to summation circuit  54  which adds them to provide the predistorted upconverted intermediate frequency signal on its output line  56 . 
     This predistorted intermediate frequency signal is applied to digital-to-analog converter  58 , which samples at the same rate as sampling circuit  46 , shown in FIG. 1 as 50 MSPS. The output of digital-to-analog converter  58  is applied to band pass filter  60 . Band pass filter  60  is centered at the frequency of signal generator  50 , depicted in FIG. 1 as 21.4 MHz, and, has a bandwidth sufficient to avoid distortion of the predistorted envelope, for example a bandwidth in the order of 30 kHz. From band pass filter  60  the signal is applied to radio frequency attenuator  62  which receives an input, such as a constant value from system software, to set its power level. The output of attenuator  62  is V(t)=e jθ(t)  (atanh(Cu k ))/C. This signal is then applied to power amplifier  64  which has a transfer function of b×tanh(C×V(t)), where b is a constant. The output from power amplifier  64  is b×Cu(t)e jθ(t) . Preferably, the gain control or scaling signal applied to gain control amplifier pair  14  is equal to C. 
     FIG. 3 depicts an apparatus for generating an envelope predistorted radio frequency signal in accordance with a second preferred embodiment of the present invention in which the scaling factor is determined by an adaptive feedback loop based on the root mean square error of the signal from the output power amplifier. Signal source  10  provides a complex baseband signal that is normalized and sampled and applied to filter circuit  12 . The samples of the in-phase component and the quadrature component are applied to calculation circuit  16 , which can be the circuit of FIG.  2 . The output of calculation circuit  16  is thus (I k   2 +Q k   2 ) 1/2 =U k . The output from the apparatus of FIG. 3 is provided by power amplifier  64 , and radio frequency coupler  70  couples a portion of that output to linear envelope detector  72 . The detected envelope is applied to analog-to-digital converter  74  which samples at the same rate as digital-to-analog converter  58 , depicted in FIG. 3 as 50 MSPS. 
     The sampled output from analog-to-digital converter  74  is normalized to the maximum amount by normalizing circuit  76 . The output of calculation circuit  16  is applied to a positive input of summing circuit  78 , while the output from normalizing circuit  76  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  76  represents the envelope after distortion. The resulting signal is applied by circuit  78  to one input of multiplier  80  which receives a weighting factor of −λ 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  76  at its second input. The output from multiplying circuit  82  is applied through low pass filter  84  to sampler  86  which applies a sample of that output at periodic intervals of, for example, one minute to integrator  88 . The output of integrator  88  is a scaling factor W and is applied to one input of multiplying circuit  90  which receives the u k  outputs from calculation circuit  16  at its second input. The output of multiplier circuit  90  is thus W×u k =x k . This output is applied to calculation circuit  40  which calculates the value {(atanh(x k ))/x k }−1, as in the embodiment of FIG.  1 . 
     As in the embodiment of FIG. 1, the output of calculation circuit  40  is applied to summing circuit  42  in which the constant 1 is added, so that summing circuit  42  applies to multiplier pair  44  the distortion factor (atanh(x k ))/x k =(atanh(Wu k ))/Wu k =D k . The u k  samples of the in-phase component I k  and the quadrature component Q k  are also applied to multiplier pair  44 . Each sample of the in-phase component I k  and the quadrature component Q k  is thus modified by the respective distortion factor D k , so that the output of multiplier pair  44  is e jθ     k    (atanh(Wu k ))/W. These samples of the modified signal are resampled in resampling circuit  46  at a high sampling rate, shown in FIG. 3 as a resampling rate at 50 MSPS. 
     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. 3 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. 3 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 . 
     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 MHz. The output from bandpass filter  60 ′ is upconverted to a radio frequency in upconverter  61  and passed through driver amplifier  63  and power amplifier  64  to antenna  66 . If desired, a radio frequency attenuator could be utilized, rather than upconverter  61  and drive amplifier  63 , as in the embodiment of FIG.  1 . Likewise, an upconverter and a driver amplifier could be used in the FIG. 1 embodiment, if desired. 
     The feedback circuit of FIG. 3 results in the signal W that is applied from integrator  88  to multiplier  90  converging to the current value of C, the transfer function 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 λ which guarantees stable conversion is upper bounded by the mean square value of the feedback envelope after being normalized by circuit  76 . 
     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. 
     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.