Abstract:
Systems and methods are disclosed for providing a linear polar transmitter. The systems and methods may include generating an input amplitude signal and an input phase signal, where the input amplitude signal and the input phase signal are orthogonal components of an input signal, and where the input amplitude signal and the input phase signal are generated on respective first and second signal paths. The systems and methods may also include processing the input amplitude signal along the first signal path using an amplitude error signal to generate a predistorted amplitude signal, and processing the input phase signal along the second signal path using an phase error signal to generate a predistorted phase signal. The systems and methods may also include providing the predistorted amplitude signal along the first signal path and the predistorted phase signal along the second signal path to a power amplifier to generate an output signal, where the amplitude error signal is generated from a comparison of at least an amplitude portion of the output signal with the predistorted amplitude signal and where the phase error signal is generated from a comparison of at least a phase portion of the output signal with the predistorted phase signal.

Description:
RELATED APPLICATION 
     This application claims priority to U.S. Provisional Ser. No. 60/803,871, entitled “Systems, Methods, and Apparatuses for Linear Polar Transmitters,” filed on Jun. 4, 2006, which is incorporated by reference as if fully set forth herein. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to linear polar transmitters, and more particularly to systems, methods, and apparatuses for the performance enhancement of radio frequency (RF) power amplifiers. 
     BACKGROUND OF THE INVENTION 
     In cost-sensitive mobile transmitters, performance trade-offs must be carefully managed to achieve high efficiency and high output power at the required gain and linearity. With an intrinsically nonlinear power amplifier (PA) itself, the only way to achieve a better linear operation is to restrict the dynamic range of signals to a small fraction of the PA&#39;s overall capability. Unfortunately, such a restriction in the dynamic range to achieve a more linear operation is quite inefficient since it requires the construction of an amplifier that is much larger in size and consumes more power. 
     With the demand to increase data transmission rates and communication capacity, Enhanced Data rate for GSM Evolution (EDGE) has been introduced within the existing GSM (Global System for Mobile communications) specifications and infrastructure. GSM is based on a constant envelope modulation scheme of Gaussian Minimum Shift Keying (GMSK), while EDGE is based on an envelope-varying modulation scheme of 3π/8-shifted 8-phase shift keying (8-PSK) principally to improve spectral efficiency. Because of this envelope-varying modulation scheme, EDGE transmitters are more sensitive to PA nonlinearities, which can significantly and negatively affect the performance of an EDGE handset. As a result, EGDE transmitters require accurate amplitude and phase control with additional blocks to compensate for distortion caused by the PA nonlinear characteristics and non-constant envelope variation. 
     To provide for efficiently amplified signal transmissions, many polar transmitter architectures have been proposed in the form of either an open-loop with digital predistortion scheme or a closed-loop with analog feedback scheme. First, in the conventional open-loop with digital predistortion scheme, the PA is characterized by calibration data including power, temperature, and frequency. The calibration data is then stored in look-up tables. The correct coefficients for the operating conditions from the look-up table are selected by digital logic and applied for predistortion. The DSP-based linearization can provide an accurate, stable operation as well as easy modification by the power of software programming. However, this technique requires time-consuming calibration on the production line to compensate for part-to-part variations and cannot easily correct any aging effect in the system. When employing a path for reflecting changes at the PA output to linearization, the circuitry becomes large and costly and consumes a considerable amount of DC power. 
     Second, a polar loop envelope feedback control is generally used for analog linearization. In such a feedback control structure, a precise receiver has to be included within the transmitter and the control loop bandwidth should greatly exceed the signal bandwidth. In addition, the intrinsic gain reduction characteristic in the negative feedback may cause a severe restriction to amplifiers that do not have enough transmission gain. Additionally, conventional polar loop systems feed back both distortion and signal power, thereby reducing the stability of the polar loop systems. Likewise, power amplifiers used in these conventional polar modulation systems are operated at highly nonlinear switching modes for efficiency so the cancellation of high-order distortion components becomes more important. 
     BRIEF SUMMARY OF THE INVENTION 
     Embodiments of the invention may provide for an analog linear polar transmitter using multi-path orthogonal recursive predistortion. This transmitter may operate in a low power mode and achieve greater bandwidth by feeding the low-frequency even-order distortion components (i.e., the deviation from linear gain) back. Moreover, the distortion components may not be added to the input signal as feedback, but rather may be used to predistort the input signal in a multiplicative manner. In particular, the low-frequency even-order distortion components may generate odd-order in-band distortion terms when they are multiplied by the fundamental signal. Thus, such architecture may be inherently more stable than conventional additive polar loop systems. 
     According to an embodiment of the invention, there is a method for providing a linear polar transmitter. The method may include generating an input amplitude signal and an input phase signal, where the input amplitude signal and the input phase signal are orthogonal components of an input signal, and where the input amplitude signal and the input phase signal are generated on respective first and second signal paths, processing the input amplitude signal along the first signal path using an amplitude error signal to generate a predistorted amplitude signal, and processing the input phase signal along the second signal path using an phase error signal to generate a predistorted phase signal. The method may further include providing the predistorted amplitude signal along the first signal path and the predistorted phase signal along the second signal path to a power amplifier to generate an output signal, where the amplitude error signal is generated from a comparison of at least an amplitude portion of the output signal with the predistorted amplitude signal and where the phase error signal is generated from a comparison of at least a phase portion of the output signal with the predistorted phase signal. 
     According to another embodiment of the invention, there is a system for a linear polar transmitter. The system may include an input amplitude signal and an input phase signal, where the input amplitude signal and the input phase signal are orthogonal components of an input signal, and where the input amplitude signal and the input phase signal are provided on respective first and second signal paths. The system may also include a first predistortion module that processes the input amplitude signal along the first signal path using an inverse amplitude error signal to generate a predistorted amplitude signal, and a second predistortion module that processes the input phase signal along the second signal path using an inverse phase error signal to generate a predistorted phase signal. The system may further include a power amplifier that receives the predistorted amplitude signal along the first signal path and the predistorted phase signal along the second signal path and generates an output signal based upon the predistorted amplitude signal and the predistorted phase signal, where the amplitude error signal is generated from a comparison of at least an amplitude portion of the output signal with the predistorted amplitude signal and where the phase error signal is generated from a comparison of at least a phase portion of the output signal with the predistorted phase signal. 
     According to yet another embodiment of the invention, there is a system for a linear polar transmitter. The system may include an input amplitude signal and an input phase signal, where the input amplitude signal and the input phase signal are orthogonal components of an input signal, and where the input amplitude signal and the input phase signal are provided on respective first and second signal paths. The system may also include first means for processing the input amplitude signal along the first signal path using an inverse amplitude error signal to generate a predistorted amplitude signal, and second means for processes the input phase signal along the second signal path using an inverse phase error signal to generate a predistorted phase signal. The system may further include a power amplifier that receives the predistorted amplitude signal along the first signal path and the predistorted phase signal along the second signal path and generates an output signal based upon the predistorted amplitude signal and the predistorted phase signal, where the amplitude error signal is generated from a comparison of at least an amplitude portion of the output signal with the predistorted amplitude signal and where the phase error signal is generated from a comparison of at least a phase portion of the output signal with the predistorted phase signal. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
       Having thus described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein; 
         FIGS. 1A and 1B  illustrate functional block diagrams of an polar transmitter system in accordance with an embodiment of the invention. 
         FIG. 2  illustrates an amplitude error correction loop in accordance with an embodiment of the invention. 
         FIG. 3  illustrates the phase error correction loop in accordance with an embodiment of the invention. 
         FIG. 4  illustrates the amplitude modulation scheme in accordance with an embodiment of the invention. 
         FIG. 5  illustrates the phase modulation scheme in accordance with an embodiment of the invention. 
         FIGS. 6A and 6B  illustrates simulated power amplifier (PA) characteristics without predistortion and with predistortion, respectively, in accordance with an embodiment of the invention. 
         FIGS. 7A and 7B  illustrates the simulated constellation results of an EDGE signal without predistortion (EVMrms: 15.6%, EVMpeak: 24.4%) and with predistortion (EVMrms: 3.4%, EVMpeak: 4.9%), in accordance with an embodiment of the invention. 
         FIG. 8  illustrates the simulated spectrum results of an EDGE signal (Pout_PDoff=21 dBm and Pout_PDon=26 dBm), in accordance with an embodiment of the invention. 
         FIG. 9  illustrates a prototyping platform for an illustrative transmitter architecture verification, in accordance with an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. Indeed, these inventions may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like numbers refer to like elements throughout. 
     Embodiments of the invention may provide linear polar transmitters that are based upon a polar modulation technique using two respective paths for amplitude and phase, and an analog orthogonal recursive predistortion linearization technique. The polar modulation technique may enhance the battery life by dynamically adjusting the bias level of a power amplifier. Additionally, the analog orthogonal recursive predistortion may provide for a substantially instantaneous correction of amplitude and phase errors in a radio frequency (RF) power amplifier (PA), thereby enhancing the linear output power capability and efficiency of the PA. Additionally, embodiments of the invention may utilize even-order distortion components to predistort the input signal in a multiplicative manner, which allows for correction of any distortion that may occur within the correction loop bandwidth, including envelope memory effects. 
       FIG. 1A  illustrates a simplified functional block diagram of an illustrative polar transmitter system  100  in accordance with an embodiment of the invention. As shown in  FIG. 1A , the polar transmitter system  100  may include a baseband modulation &amp; control module  102 , digital-to-analog converters (DACs)  104   a  and  104   b , a phase modulator module  106 , an amplitude predistortion module  108 , an amplifier power control (APC) module  110 , a power amplifier module  112 , an amplitude modulation error detection module  114 , and a phase modulation error detection module  116 . During operation of the polar transmitter system  100 , the baseband modulation &amp; control module  102  may generate two orthogonal input signals—one representing the amplitude and one representing the phase of the input signal, which are respectively provided to the digital-to-analog converters (DACs)  104   a  and  104   b , respectively. The two baseband digital input signals may be synchronized according to an embodiment of the invention. It will be appreciated that while the two orthogonal input signals are associated with amplitude and phase, respectively, other embodiments of the invention may utilize I- and Q-components for a Cartesian system. Furthermore, other orthogonal input signals may be utilized as well without departing from embodiments of the invention. 
     The analog amplitude signal x A (t) at the output of DAC  104   a  may be provided to the amplitude predistortion module  118  as the input amplitude signal. Likewise, the analog phase signal x P (t) at the output of DAC  104   b  is provided to the phase modulation module  106  in order to upconvert the analog phase modulation signal x P (t) from a baseband signal to a RF signal rx P (t). The resulting input amplitude signal rx P (t) may then be provided to the phase predistortion module  120 . 
     The amplitude predistortion module  118  and the phase predistortion module  120  will now be discussed with respect to  FIG. 1B , which provides a more detailed functional block diagram of the polar transmitter system  100  of  FIG. 1A . As illustrated, the amplitude predistortion module  118  may be a multiplier and the predistortion module  118  may be a phase adder. According to an embodiment of the invention, the amplitude multiplier for amplitude predistortion may be a Gilbert cell voltage multiplier, while the phase adder for phase predistortion may be a voltage-controlled variable phase (VVP) shifter. 
     Still referring to  FIG. 1B , the amplitude modulation error detection module  114  may include an attenuator  128  with the attenuation of 1/a 1 , an envelope detector (EDET)  130 , and an amplitude predistortion function  132 . The phase modulation error detection module  116  may include a limiter  134  and a phase predistortion function  136 . The power amplifier module  112  includes a power amplifier  124  having transfer function G{·}. In addition, the power amplifier module  112  may additionally include one or more input matching (IM) circuits  122  and output matching (OM) circuits  126 . The IM circuit  122  may provide for impedance matching at the input of the power amplifier  124  while the OM circuit  126  may provide for impedance matching at the output of the power amplifier  124 . 
     As will be also described in further detail below, the amplitude predistortion module  118  and the phase predistortion module  120  may be operative to predistort the baseband amplitude signal x A (t) and the phase-modulated RF signal rx P (t), respectively. In particular, the amplitude signal input x A (t) may be predistorted by an inverse amplitude error signal e A (t) from the amplitude modulation error detection module  114 , producing an amplitude-predistorted signal z A (t). As a result, the output z A (t) may contain the fundamental term of the input x A (t) as well as the inverse odd-order intermodulation distortion (IMD) terms of the output y A (t), such as third-order IMD, fifth-order IMD, and the like. The inverse amplitude distortion terms may be used in the power amplifier module  112  to compensate for the amplitude distortions of the PA output ry(t). 
     To produce the inverse amplitude error signal e A (t), the amplitude modulation error detection module  114 , and in particular the amplitude predistortion function  132 , generally performs a comparison of the output z A (t) of the predistortion module  118  with the diode-detected output y A (t) of the power amplifier module  112 . For example, the comparison of the output z A (t) of the amplitude predistortion module  118  with the envelope-detected output y A (t) of the PA output ry(t) through a diode envelope detector  130  may be performed by a voltage divider. By dividing the signal z A (t) by the signal y A (t), the odd-order distortion terms, which are located near to the fundamental term, are order-down converted to the lower odd-order distortion terms. The inverse amplitude error signal e A (t) may include the inverse amplitude gain of the power amplifier module  112 . The inverse amplitude error signal e A (t) may also include low-frequency, even-order intermodulation distortion terms, alleviating the required bandwidth of components operating in the amplitude error correction loop. 
     Likewise, the phase-modulated RF signal input rx P (t) may be predistorted by an inverse phase error signal e P (t) from the phase modulation error detection module  116 , producing a phase-predistorted RF signal rz P (t). As a result, the output rz P  (t) may contain the fundamental term of the input rx P (t) as well as the inverse odd-order intermodulation distortion (IMD) terms of the output ry P (t), such as third-order IMD, fifth-order IMD, and the like. The inverse phase distortion terms may be used in the power amplifier module  112  to compensate for the phase distortions of the PA output ry(t). 
     To produce the inverse phase error signal e P (t), the phase modulation error detection module  116 , and in particular, the phase predistortion function  436 , generally performs a comparison of the output rz P (t) of the predistortion module  120  with the amplitude-limited output ry P (t) of the power amplifier module  112 . For example, the comparison of the output rz P (t) of the phase predistortion module  120  with the amplitude-limited output ry P (t) of the PA output ry(t) through a limiter  134  may be performed by a Gilbert-cell voltage multiplier. When relatively small amplitude signals are applied to the input ports of the Gilbert-cell voltage multiple, it may behave as an analog multiplier. If the phase error of the inputs is in the vicinity of 90°, the average value of the output may be linearly proportional to the phase error. The inverse amplitude error signal e P (t) may include the inverse phase deviation of the power amplifier module  112 . The inverse phase error signal e A (t) may also include low-frequency, even-order intermodulation distortion terms, thereby alleviating the required bandwidth of components operating in the phase error correction loop. 
     In  FIG. 1B , the polar transmitter system  100  provides a linearization scheme to look at any changes of the PA output ry(t) and almost instantaneously predistort the input signal x A (t) and rx(t). More specifically, the predistortion mechanism in accordance with an embodiment of the invention may utilize the predistorted signal toward the PA  124  as the reference for recursive predistortion so that the outputs e A (t) and e P (t) of modulation error detection modules  114 ,  116  may be simply the reciprocal of the PA  124  transfer function G {·}. Accordingly, the calculation of the predistortion function (e.g., F A    132 , F P    136 ) may be performed by analog components. 
     If the amplitude modulation (AM) and phase modulation (PM) paths are fully synchronized, then the PA  124  input signal rz(t), which comes from the multiplication of the transmitter input signal rx(t) with the inverse PA distortion signal e(t), may be defined as follows: 
                           rz   ⁡     (   t   )       =       ⁢         z   A     ⁡     (   t   )       ⁢   ∠   ⁢           ⁢       rz   P     ⁡     (   t   )                     =       ⁢       {         x   A     ⁡     (   t   )       ·       e   A     ⁡     (   t   )         }     ⁢   ∠   ⁢     {         rx   P     ⁡     (   t   )       +       e   P     ⁡     (   t   )         }                     =       ⁢       rx   ⁡     (   t   )       ·     e   ⁡     (   t   )           ,                 (   1   )               
where x A (t) and rx P ((t) are the baseband amplitude input and the phase-modulated RF input, respectively. Likewise, e A (t) and e P (t) are the outputs of the predistortion function F A {·} 132  for amplitude and F P {·}  136  for phase, respectively.
 
     As the system  100  of  FIG. 1B  may be based on polar modulation, the amplitude signal e A (t) and phase signal e P (t) of the inverse PA distortion signal e(t) may be calculated separately via the amplitude function F A {·}  132  and phase error predistortion function F P {·}  136 , respectively. When up to third-order terms (K=2) in PA nonlinear components and a complex-form analysis are considered for simplicity, the output y(t) of the PA  124  may be described as follows: 
                           y   ⁡     (   t   )       =       ⁢         rz   ⁡     (   t   )       ·   G     ⁢     {       z   A     ⁡     (   t   )       }                     =       ⁢         [       rx   ⁡     (   t   )       ·     e   ⁡     (   t   )         ]     ·   G     ⁢     {       z   A     ⁡     (   t   )       }         ,                 (   2   )                   G   ⁢     {       z   A     ⁡     (   t   )       }       =       ∑     k   =   1     K     ⁢           ⁢       a       2   ⁢           ⁢   k     -   1       ·       z   A     2   ⁢     (     k   -   1     )         ⁡     (   t   )             ,           (   3   )                   e   ⁡     (   t   )       =       F   ⁢     {       z   A     ⁡     (   t   )       }       =         a   1     ·     G     -   1         ⁢     {       z   A     ⁡     (   t   )       }           ,           (   4   )               
where G{·} is the PA  124  odd-order transfer function, F{·} is the predistortion function comprised of F A    132  and F P    136 , and a k  is the k-th complex coefficient of the PA  124  transfer function. As a result obtained from equations (1) to (4) above, a linearly amplified RE signal a 1 ·rx(t) can simply be produced with this architecture, according to an embodiment of the invention.
 
     Amplitude Error Correction. The amplitude error correction loop, which includes the amplitude modulation error detection module  114 , will be described with reference to  FIG. 2 . The inverse amplitude error signal e A (t) may be obtained by the comparison of the output z A (t) of an amplitude predistortion module  118  (e.g., multiplier) and the output y A (t) of a diode-based envelope detector (EDET)  130 . Once the amplitude error signal e A (t) is obtained, it may be multiplied with the input amplitude signal x A (t) to produce the amplitude-predistorted signal z A (t). This process may be performed recursively. 
     Phase Error Correction.  FIG. 3  illustrates the phase error correction loop, which includes the phase modulation error detection module  116 . As in the amplitude correction loop, the inverse phase error signal e P (t) is obtained from the comparison of the output rz P (t) of a phase predistortion module  120  (e.g., phase adder) and the amplitude-limited output y P (t) of an amplitude limiter  134 . Once the phase error signal e P (t) is obtained, it is added to the phase-modulated RF input signal rx P (t) to produce the phase-predistorted signal rz P (t). Since the output rx P (t) of a phase-locked loop (PLL), which is used as the phase modulation module  106 , is at radio frequency, the phase predistortion module  120  may be implemented by a reflection-type voltage-controlled variable phase shifter (VVP), according to an embodiment of the invention. 
     Amplitude Modulation. In time-division multiple access (TDMA) communication systems such as GSM/EDGE, the power control of a PA output has to meet the time mask specification, while preserving the efficiency of the power supply. This power control may be performed by using a linear regulator, switching regulator, or combined structure. Unlike the GSM system, a polar EDGE system in accordance with an embodiment of the invention may require the tracking of RF envelope signals. Tracking the envelope signal may require a much wider operation bandwidth.  FIG. 4  shows an illustrative example of a combined PA controller  110  scheme that may be employed for power efficiency and wideband operation. As shown in  FIG. 4 , the DC-DC converter  404  may provide the DC and low frequency load current, while the Class-AB linear amplifier  402  may provide the high frequency load current, maintaining the tracking loop closed. The DC-DC converter  404  may be controlled by the output current of the Class-AB amplifier  402 . The hysteric current controller of the DC-DC converter  404  may attempt to minimize the output current of the Class-AB amplifier  402 , to maximize the overall efficiency. The output capacitance  428  of the architecture may be low to maintain the high bandwidth of the Class-AB amplifier  402  loop. Moreover, the ripple current of the DC-DC converter  404  may be principally absorbed by the Class-AD linear amplifier  402  operating in conjunction with a feedback loop. Thus, this linear-assisted architecture may be expected to have a high envelope tracking bandwidth, preserving a good linearity and efficiency. 
     Phase Modulation.  FIG. 5  illustrates a phase modulator module  106  that may be utilized in accordance with an embodiment of the invention. Referring to  FIG. 5 , a phase-modulated intermediate frequency (IF) signal x P (t)  501  is applied to the phase-frequency detector (PFD)  502  for both phase-locking reference and phase modulation. The PFD  502  compares the IF signal  501  to the feedback signal  511  to generate current pulses. In particular, the voltage pulse (e.g., UP/DOWN) directs the charge pump (CP)  504  to supply charge amounts in proportion to the phase error detected. Generally, these pulses are small and substantially the same duration such that the CP  504  produces equal-charge positive and negative pulses when the phase is perfectly matched. The output I CP  Of the CP  504  is provided to a filter  506  (e.g., a loop filter), and the resultant signal Vc is provided to an oscillator  508  to generate a phase-corrected signal rx P (t). 
     In  FIG. 5 , with an IF reference signal  501  carrying the phase information, a large portion of components on the feedback path may be avoided, resulting in low phase noise. Moreover, by using a fractional-N divider  510  for downconversion, the phase modulator module  106  needs only a phase-locked loop (PLL), as provided by PFD  502 , CP  504 , and divider  510 . According to an embodiment of the invention, the phase modulator module  106  may not require one or more of a downconversion mixer, local oscillator (LO), or filter. 
     Simulation Results. The time-domain signal test shown in  FIGS. 6A and 6B  illustrate the improved performance of a PA  124  in accordance with an embodiment of the invention. In particular,  FIG. 6A  illustrates the results obtained without the use of the linearizer, while  FIG. 6B  shows the results with the use of the linearizer implemented using the predistortion provided in accordance with an embodiment of the invention. As shown in  FIG. 6B , the PA  124  output with the linearizer turned on tracks the original input signal well, and the nonlinearity in the amplitude and phase is well linearized, even in the situation with memory effects that display scattered PA  124  characteristics over power. 
     Error vector magnitude (EVM) measurement provides a means of characterizing the magnitude and phase variations introduced by the PA nonlinear behavior over a wide dynamic range. As shown in  FIGS. 7A and 7B , the EVM simulation results exhibits the improvements of 12.2% in root-mean-square (RMS) and 19.5% in peak by use of the predistortion provided by embodiments of the invention.  FIG. 8  shows the spectrum results in which without predistortion, the spectrum  802  violates the regulation mask  804 . On the other hand, in  FIG. 8 , the spectrum  806  from the simulation with the predistortion turned on is well below the mask  804  over the range displayed. 
     Illustrative Implementation.  FIG. 9  shows a system  900  implemented in accordance with an embodiment of the invention. The system  900  may include a phase modulator  906  for the upconversion of a phase modulation signal to an RF signal rx P (t), a predistorter (PD)  908  for the predistortion of the input signal toward a PA  912 , an amplifier power controller (APC)  910  for the power regulation and dynamic power control, an amplitude modulation error detector  914  for the AM/AM distortion extraction, and a phase modulation error detector  916  for the AM/PM distortion extraction. As illustrated, the phase modulator  906  includes an analog phase-locked loop (PLL). In particular, the PLL is formed of a phase frequency detector (PFD)  932 , a charge pump (CP)  934 , a loop filter  936 , a voltage-controlled oscillator (VCO)  938 , and a frequency divider  940  (e.g., divide by N) placed in the feedback loop, as illustrated in  FIG. 9 . The PD  908  includes a multiplier  918  for multiplying the amplitude input signal x A (t) with the amplitude error signal e A (t). In addition, the PD  908  also includes a phase adder  920  for adding a phase error signal e P (t) to the phase-modulated RF input signal rx P (t). The Amplitude Modulation (AM) error detector  914  may include an envelope detector  930  for determining amplitude of the output ry(t) of the PA  912 . In addition, the AM error detector includes a divider  928  for calculating an inverse amplitude error signal e A (t) using the amplitude of the output ry(t) and the predistorted amplitude output of the PD  908 . The phase modulation (PM) error detector  916  includes an amplitude limiter  942 , a multiplier  944 , and a low-pass filter (LPF)  946  for determining an inverse phase error signal e P (t) using the amplitude-limited output ry P (t) of the output ry(t) and the phase-predistorted output rx P (t) of the PD  908 . One of ordinary skill in the art will recognize that the system  900  can be applied to a variety of power amplifiers  912 , including linear PAs and switching PAs. 
     Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.