Adaptive ISO-gain pre-distortion for an RF power amplifier operating in envelope tracking

Abstract

The output of a Radio Frequency (RF) Power Amplifier (PA) is sampled and down-converted, and the amplitude envelope of the baseband feedback signal is extracted. This is compared to the envelope of a transmission signal, and the envelope tracking modulation of the RF PA supply voltage is adaptively pre-distorted to achieve a constant ISO-Gain (and phase) in the RF PA. In particular, a nonlinear function is interpolated from a finite number gain values calculated from the feedback and transmission signals. This nonlinear function is then used to pre-distort the transmission signal envelope, resulting in a constant gain at the RF PA over a wide range of supply voltage values. Since the gains are calculated from a feedback signal, the pre-distortion may be recalculated at event triggers, such as an RF frequency change.

Claims

1. A method, comprising: sensing a first amplitude envelope of a complex baseband transmission signal; generating a radio frequency (RF) signal for transmitting the complex baseband transmission signal; amplifying the RF signal with a power amplifier circuit; sensing a second amplitude envelope of the RF transmitted complex baseband transmission signal; determining instances over a time period where a value of a power supply voltage for the power amplifier circuit is equal to each of a plurality of interpolation node values; for each determined instance, identifying a corresponding value of the second amplitude envelope over that time period; calculating a pre-distortion function from the identified corresponding values; and using the pre-distortion function to subsequently control the power supply voltage for the power amplifier circuit.

2. The method of claim 1, wherein using comprises modulating the power supply voltage in response to the first amplitude envelope and the pre-distortion function.

3. The method of claim 1, wherein the pre-distortion function is a non-linear function, and calculating comprises interpolating to fit the identified corresponding values.

4. The method of claim 3, wherein using comprises multiplying the first amplitude envelope by the non-linear function to generate a power supply modulation control signal for controlling the power supply voltage for the power amplifier circuit.

5. The method of claim 3, wherein the non-linear function comprises a polynomial, and coefficients of the polynomial are determined from the identified corresponding values.

6. The method of claim 5, wherein the polynomial is derived from Newton's algorithm.

7. The method of claim 1, wherein calculating the pre-distortion function comprises determining a plurality of gain values, each gain value representing a ratio of the value of the second amplitude envelope to the corresponding interpolation node value; and wherein using the pre-distortion function comprises using the gain values to apply a predistortion gain to the first amplitude envelope for controlling the power supply voltage of the power amplifier circuit.

8. The method of claim 1, wherein sensing the second amplitude envelope comprises downconverting the RF transmitted complex baseband transmission signal to recover the complex baseband transmission signal and sensing an amplitude envelope of the recovered complex baseband transmission signal.

9. A method, comprising: sensing a first amplitude envelope of a complex baseband transmission signal; generating a radio frequency (RF) signal for transmitting the complex baseband transmission signal; amplifying the RF signal with a power amplifier circuit; sensing a second amplitude envelope of the RF transmitted complex baseband transmission signal; for each instance where a value of a power supply voltage of the power amplifier circuit is equal to one of a plurality of interpolation node values, calculating a gain value equal to a ratio of the second amplitude envelope to the first amplitude envelope; generating a variation in the power supply voltage of the power amplifier circuit as a function of the first amplitude envelope and the calculated gain values.

10. The method of claim 9, wherein the interpolation node values are equally spaced values between a maximum voltage value for the power supply voltage and a minimum voltage value for the power supply voltage.

11. The method of claim 9, wherein generating the variation in the power supply voltage comprises: calculating a pre-distortion function from the gain values; and using the pre-distortion function to control the power supply voltage for the power amplifier circuit.

12. The method of claim 11, wherein using comprises modulating the power supply voltage in response to the first amplitude envelope and the pre-distortion function.

13. The method of claim 12, wherein the pre-distortion function is a non-linear function, and calculating comprises interpolating to fit the gain values.

14. The method of claim 13, wherein using comprises multiplying the first amplitude envelope by the non-linear function to generate a power supply modulation control signal for controlling the variation in the power supply voltage.

15. The method of claim 9, wherein sensing the second amplitude envelope comprises downconverting the RF transmitted complex baseband transmission signal to recover the complex baseband transmission signal and sensing an amplitude envelope of the recovered complex baseband transmission signal.

16. A Radio Frequency (RF) transmitter, comprising: a signal generator configured to generate a complex baseband transmission signal; a reference circuit configured to sense a first amplitude envelope of the complex baseband transmission signal; a mixing circuit configured to up-convert the baseband transmission signal to generate an RF signal; an RF power amplifier configured to amplify the RF transmission signal; a dynamic power supply configured to provide a supply voltage to the RF power amplifier; a feedback circuit configured to sense a second amplitude envelope of the complex baseband transmission signal from the RF transmission signal; a pre-distortion circuit configured to: determine instances over a time period where a value of the supply voltage is equal to each of a plurality of interpolation node values; for each determined instance, identify a corresponding value of the second amplitude envelope over that time period; calculate a pre-distortion function from the identified corresponding values; and using the pre-distortion function to control the dynamic power supply in generating the supply voltage.

17. The transmitter of claim 16, wherein the dynamic power supply is controlled by the pre-distortion circuit to modulate the supply voltage in response to the first amplitude envelope and the pre-distortion function.

18. The transmitter of claim 17, wherein the pre-distortion circuit multiplies the first amplitude envelope by the pre-distortion function to generate a power supply modulation control signal for controlling the dynamic power supply.

19. The transmitter of claim 16, wherein calculation of the pre-distortion function comprises determining a plurality of gain values, each gain value representing a ratio of the value of the second amplitude envelope to the corresponding interpolation node value; and wherein use of the pre-distortion function comprises using the gain values to apply a predistortion gain to the first amplitude envelope for controlling the supply voltage.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. However, this invention should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout.

(2) FIG. 1 is a functional block diagram of a conventional transmitter output, depicting envelope tracking.

(3) FIG. 2A is a graph depicting variations in gain (AM-AM) with supply voltage V.sub.CC variations in a conventional envelope tracking PA.

(4) FIG. 2B is a graph depicting variations in phase AM-PM) with supply voltage V.sub.CC variations in a conventional envelope tracking PA.

(5) FIG. 3A is a graph depicting time-domain variations of the voltage V.sub.CC supplied to a PA by a conventional envelope tracking power supply.

(6) FIG. 3B is a graph depicting the time-domain variations in the gain of a PA receiving a conventional envelope tracking supply voltage.

(7) FIG. 4 is a graph depicting the PA gain as a function of the supply voltage V.sub.CC for a conventional envelope tracking power supply

(8) FIG. 5A is a graph depicting how laboratory measurements (circles) of PA gain vs. supply voltage V.sub.CC can be interpolated using the 2-D polynomial (continuous lines).

(9) FIG. 5B is a graph depicting how laboratory measurements of PA gain (circles) vs. RF PA input signal can be interpolated using the 2-D polynomial (continuous lines).

(10) FIG. 6 depicts the operation of conventional ISO-Gain pre-distortion in the case where V.sub.CC is constant and V.sub.IN varies.

(11) FIG. 7 is a functional block diagram of portions of an RF transmitter employing an envelope tracking power supply with adaptive, feedback-based pre-distortion to achieve ISO-Gain for the PA, according to embodiments of the present invention.

(12) FIG. 8 is a graph depicting a waveform of V.sub.CC(t) as a function of time, with a representative set of interpolation nodes.

(13) FIG. 9 is a table depicting the calculation of coefficients to a nonlinear function.

(14) FIG. 10 is a flow diagram of an adaptive method of pre-distorting an envelope tracking modulation of supply voltage for a RF PA.

(15) FIG. 11A is a graph depicting the evolution of the RF PA supply voltage V.sub.CC(t) over several iterations of the adaptive ISO-Gain method of FIG. 10.

(16) FIG. 11B is a graph depicting the evolution of the RF PA gain over several iterations of the adaptive ISO-Gain method of FIG. 10.

(17) FIG. 12 is a graph depicting RF PA gain vs. supply voltage V.sub.CC(t) over several iterations of the adaptive ISO-Gain method of FIG. 10.

(18) FIG. 13 is a graph depicting RF PA phase vs. supply voltage V.sub.CC(t) over several iterations of the adaptive ISO-Gain method of FIG. 10.

(19) FIG. 14 is a graph depicting the output spectrum of the RF PA over several iterations of the adaptive ISO-Gain method of FIG. 10.

DETAILED DESCRIPTION

(20) It should be understood at the outset that although illustrative implementations of one or more embodiments of the present disclosure are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents.

(21) FIG. 7 depicts a functional block diagram of relevant portions of an RF transmitter 20 employing an envelope tracking power supply 14 with adaptive, feedback-based pre-distortion to achieve ISO-Gain for the PA 16. The basic transmission blocks of the transmitter 20 are as depicted in FIG. 1: a battery 12 provides a slowly-varying DC voltage to a fast switched mode power supply 14, which modulates the supply voltage V.sub.CC provided to a power amplifier (PA) 16 based on the amplitude envelope of an RF transmission signal (the PA 16 input). The PA 16 outputs an amplified RF output signal, through a duplexer 22, to an antenna 18 for transmission. As known in the art, the duplexer 22 isolates the transmitter 20 from a receiver circuit (not shown), and alternately connects the antenna 18 to one of the transmitter 20 and receiver.

(22) The transmitter 20 also includes conventional elements, including a complex signal generator 22, such as a processor or Digital Signal Processor (DSP) generating baseband, time-varying In-band (I) and Quadrature (Q) transmission signal components. These transmission signal components are frequency up-converted to RF in mixers 24, by mixing with high frequency clock signals, phase-separated by 90 in a phase shifter 26. The high frequency clock input to the phase shifter 26 is generated by a source 28, such as a tunable voltage controlled oscillator (VCO), crystal oscillator, phase locked loop, or the like.

(23) According to embodiments of the present invention, the transmitter 20 includes a feedback path 29 and pre-distortion circuit 38 operative to pre-distort an envelope tracking voltage V.sub.CC output by the power supply 14 to the RF PA 16, so as to achieve a constant ISO-Gain G.sub.ISO at the RF PA 16. The feedback path 29 includes an attenuator 30 that taps a fraction of the power of the RF output signal, generating an RF feedback signal. The RF feedback signal is frequency down-converted by mixers 32, generating baseband I.sub.FB and Q.sub.FB components of a feedback signal. An extraction circuit 34 extracts the amplitude envelope of the baseband feedback signal, which is provided to the pre-distortion circuit 38.

(24) The amplitude envelope of the baseband transmission signal is calculated by an envelope circuit 36 from the real and imaginary parts of the complex transmission signal, and is also provided to the pre-distortion circuit 38. The envelope circuit 36 may comprise part of the processor 22. The pre-distortion circuit 38 processes the baseband feedback signal envelope and that of the baseband transmission signal, and outputs control signals to the dynamic power supply 14 that modulate V.sub.CC to achieve ISO-Gain in the PA 16. In one embodiment, the pre-distortion circuit 38 multiplies the baseband transmission signal amplitude envelope by a nonlinear function, where the parameters of the nonlinear function are determined by calculation of the actual gain of the RF PA 16 (e.g., the feedback signal envelope divided by the transmission signal envelope). The pre-distortion circuit 38 may comprise a state machine, processor, DSP, or other computational circuit. The pre-distortion circuit 38 may additionally be implemented as software executed on another processor, such as the signal generator 22.

(25) In this manner, embodiments of the present invention achieve a constant ISO-Gain in the RF PA 16, by using feedback of the RF PA output to adaptively pre-distort the envelope tracking supply voltage V.sub.CC provided by power supply 14. Such adaptive ISO-Gain pre-distortion can compensate distortions of the entire transmitter 20, allowing the linearity constraints on DACs (not shown), mixers 24, and the RF PA 16 to be lowered. Any distortion generated by the feedback loop 29 is not compensated by the pre-distortion algorithm. The adaptive, feedback-based ISO-Gain pre-distortion may additionally compensate non-linearity in the fast switched mode power supply 14. Furthermore, the dynamic control provided by adaptive pre-distortion does not depend on factory calibration results, and hence can account for operational changes, such as changes in RF frequency, output power, temperature, component aging, and the like. Additionally, large LUTs are not required to store voluminous calibration data, as in the case of open-loop pre-distortion methods, and consequently high accuracy is achieved with low latency and low computational complexity.

(26) In one embodiment, the pre-distortion circuit 38 multiplies the reference amplitude envelope of the baseband transmission signal by a nonlinear function to generate control signals for the power supply 14. In one embodiment, the nonlinear function is approximated by a polynomial. The coefficients of the polynomial are calculated (and dynamically updated) using information about the envelope of the baseband feedback signal obtained from the feedback path 29. In this embodiment, the transmitter 20 operates in closed-loop mode only during the calculation or update of the polynomial coefficients, which are stored in small LUTs. During operation, the transmitter 20 operates in open-loop mode, using the calculated/updated polynomial coefficients. At trigger events, such as the expiration of a periodic timer, or operational events such as a transmission frequency change, the transmitter 20 again goes into closed-loop mode to update the polynomial coefficients based on the amplitude envelope of the baseband feedback signal.

(27) In one embodiment, an algorithm for employing a polynomial-based nonlinear function in the pre-distortion circuit 38 includes three steps. First, a measurement, or Learning, Sequence is performed. This is followed by an Interpolation Sequence. Finally, a Computation Sequence is performed. The first two of theseLearning and Interpolationare performed only when an update of the polynomial coefficients is needed.

(28) The Learning Sequence is performed when the transmitter 20 is operational, i.e., transmitting a signal, such as a voice call. The complex RF signal output by the PA 16 is sampled, down-converted to baseband, and converted to I and Q format, in the feedback loop 29. A conversion is then performed in extraction circuit 34 to obtain the amplitude envelope of the baseband feedback signal:
ENV.sub.FB(t)={square root over (I.sub.FB(t).sup.2+Q.sub.FB(t).sup.2)}(9)

(29) Among all measured samples, only N+1 values are selected and stored, for a polynomial of order N. These points are chosen as a function of V.sub.CC, which is an image of the envelope of the baseband feedback signal:
V.sub.CC(t)={square root over (I.sup.2(t)+Q.sup.2(t))}(10)

(30) The samples selection is performed according to the following condition:
If V.sub.CC(t)=V.sub.CC,kstoreENV.sub.FB,k with 0kN(11)
where N is the order of the polynomial used to interpolate the pre-distortion function and V.sub.CC,k are the interpolation points or nodes. FIG. 8 depicts a waveform of V.sub.CC(t) as a function of time, with a representative set of interpolation nodes. The interpolation nodes may be equally spaced, and calculated using a simple equation. Alternatively, the interpolation nodes may be selected by other methods. One example of an interpolation node selection approach that minimizes interpolation error is to select Chebyshev nodes. In this approach,

(31) $\begin{array}{cc}{V}_{\mathrm{CC},k}=\min \left(V_{\mathrm{CC}}\left(t\right)\right)+j.Math.\frac{\max \left(V_{\mathrm{CC}}\left(t\right)\right)-\min \left(V_{\mathrm{CC}}\left(t\right)\right)}{N}\mathrm{with}0jN& \left(12\right)\end{array}$
where min(V.sub.CC(t)) and max(V.sub.CC(t)) are the minimum and maximum values of power supply modulation, respectively. These values must be detected, or may be provided by the digital baseband signal generator 22.

(32) The Learning Sequence thus records the baseband feedback signal envelope ENV.sub.FB and corresponding PA 16 supply voltage V.sub.CC for each of a plurality of interpolation nodes. In one embodiment, the Learning Sequence is preferably performed several times in order to filter the samples through a mean value computation. In one embodiment, the mean values over V.sub.CC,k and ENV.sub.FB,k are calculated, preferably over multiple measurement iterations.

(33) In the Interpolation Sequence, the stored samples are used for interpolating the pre-distortion function. That is, a nonlinear function is generated that is a best fit curve to the sampled (V.sub.CC,k, ENV.sub.FB,k) data points. In one embodiment, the nonlinear function is modeled as a polynomial. In one embodiment, the interpolation is performed using Newton's algorithm. Newton's algorithm is a known mathematical function, which has the advantage that only multiply and sum mathematical operations are required for implementation.

(34) The gain values to be interpolated are determined directly from the stored, sampled (V.sub.CC,k, ENV.sub.FB,k) data points:

(35) $\begin{array}{cc}{G}_{\mathrm{pred},k}=\frac{{\mathrm{ENV}}_{\mathrm{FB},k}}{V_{\mathrm{CC},k}}\mathrm{with}0kN& \left(13\right)\end{array}$

(36) This pre-distortion gain must be normalized in order to neglect any constant gain (or attenuation) that could have been applied to the feedback signal by the feedback loop 29:

(37) $\begin{array}{cc}{G}_{\mathrm{pred},k}=\frac{{\mathrm{ENV}}_{\mathrm{FB},k}}{V_{\mathrm{CC},k}}.Math.\frac{\stackrel{\_}{V_{\mathrm{CC},k}}}{\stackrel{\_}{{\mathrm{ENV}}_{\mathrm{FB},k}}}\mathrm{with}0kN& \left(14\right)\end{array}$
where, in one embodiment, the average values were measured during the Learning Sequence.

(38) After the gain values are calculated, a small table of (N+1)2 is filled with the interpolation inputs:

(39) $\left(\begin{array}{cc}{V}_{\mathrm{CC},0}& G_{\mathrm{pred},0}\\ \mathrm{.Math.}& \mathrm{.Math.}\\ V_{\mathrm{CC},N-1}& G_{\mathrm{pred},N-1}\\ V_{\mathrm{CC},N}& G_{\mathrm{pred},N}\end{array}\right)$

(40) Starting from these values, the gain pre-distortion function is interpolated as a function of V.sub.CC. In one embodiment, the polynomial form of Newton's formula is utilized:

(41) 0$\begin{array}{cc}{G}_{\mathrm{pred}}\left(V_{\mathrm{CC}}\left(t\right)\right)=\frac{}{G_{\mathrm{ISO}}}\left[g_0+g_1.Math.\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},0}\right)+g_2.Math.\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},0}\right).Math.\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},1}\right)+\mathrm{.Math.}+g_N.Math.\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},0}\right).Math.\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},1}\right)\mathrm{.Math.}\left(V_{\mathrm{CC}}\left(t\right)-V_{\mathrm{CC},N-1}\right)\right]& \left(15\right)\end{array}$

(42) One advantage of Newton's formula is that an N.sup.th-degree polynomial, matching the N+1 data points {(x.sub.0, y.sub.0), (x.sub.1, y.sub.1), . . . , (x.sub.N, y.sub.N)} can be recursively obtained as the sum of the (N1).sup.th-degree Newton polynomial matching N data points {(x.sub.0, y.sub.0), (x.sub.1, y.sub.1), . . . , (x.sub.N-1, y.sub.N-1)} and one additional term. See, for example, Won Y. Yang, et al., Applied Numerical Methods Using Matlab, Wiley Interscience, 2005, the disclosure of which is incorporated herein by reference in its entirety. Thus,
p.sub.N(x)=a.sub.0+a.sub.1.Math.(xx.sub.0)+a.sub.2.Math.(xx.sub.0).Math.(xx.sub.1)+ . . . .
p.sub.N(x)=p.sub.N-1+a.sub.N.Math.(xx.sub.0).Math.(xx.sub.1) . . . (xx.sub.N-1) with p.sub.0(x)=a.sub.0=y.sub.0(16)

(43) The polynomial coefficients a.sub.0, a.sub.1, . . . , a.sub.n can be calculated as follows:

(44) $\begin{array}{cc}{a}_0=y_0{a}_1=\frac{y_1-a_0}{x_1-x_0}=\frac{y_1-y_0}{x_1-x_0}{\mathrm{Df}}_0{a}_2=\frac{\frac{y_2-y_1}{x_2-x_1}-\frac{y_1-y_0}{x_1-x_0}}{x_2-x_0}=\frac{{\mathrm{Df}}_1-{\mathrm{Df}}_0}{x_2-x_0}{D}^2{f}_0& \left(17\right)\end{array}$

(45) On the other hand, the general formula for the calculation of the N.sup.th coefficient a.sub.n of a Newton polynomial function is:

(46) $\begin{array}{cc}{a}_N=\frac{D^{N-1}{f}_1-D^{N-1}{f}_0}{x_N-x_0}{D}^N{f}_0& \left(18\right)\end{array}$

(47) This is the divided difference, which can be obtained recursively from the second row of the table depicted in FIG. 9. The coefficients calculation is quite simple and requires only few subtractions and divisions to implement. Furthermore, this calculation is performed only once during the Interpolation Sequence, to generate the nonlinear function from the sampled (V.sub.CC,k, ENV.sub.FB,k) data points.

(48) At the completion of the Interpolation Sequence, (N+1) valuesrepresenting the Newton's polynomial coefficientsreplace the measured samples in the table of values stored during the Learning Sequence.

(49) $\left(\begin{array}{cc}{V}_{\mathrm{CC},0}& G_{\mathrm{pred},0}\\ \mathrm{.Math.}& \mathrm{.Math.}\\ V_{\mathrm{CC},N-1}& G_{\mathrm{pred},N-1}\\ V_{\mathrm{CC},N}& G_{\mathrm{pred},N}\end{array}\right).Math.\left(\begin{array}{cc}{V}_{\mathrm{CC},0}& g_0\\ \mathrm{.Math.}& \mathrm{.Math.}\\ V_{\mathrm{CC},N-1}& g_{N-1}\\ V_{\mathrm{CC},N}& g_N\end{array}\right)$

(50) In the Computation Sequence, the polynomial coefficients g.sub.n are used to dynamically calculate the pre-distortion gain to be applied to V.sub.CC, using equation (15). That is, the pre-distortion circuit 38 multiplies the baseband transmission signal amplitude envelope provided by reference circuit 36 on the fly by equation (15), using the stored values of (V.sub.CC,n, g.sub.n). This calculation, which requires only multiplication and summing functions, is performed in open-loop mode, using the stored (V.sub.CC,n, g.sub.n) values.

(51) At event triggers, such as periodically or at transmitter 20 power or frequency changes, the algorithm is repeated. As depicted in FIG. 10, in a Learning Sequence (block 102), new V.sub.CC and ENV.sub.FB values are measured from the feedback path 29, for N+1 defined interpolation nodes, and these values are stored. In an Interpolation Sequence (block 104), the gain of the RF PA 16 is calculated, and a nonlinear function reflecting the actual gain (ENV.sub.FB/V.sub.CC) is constructed from these feedback data points, such as by using Newton's formula to construct a polynomial. The parameters defining the nonlinear function, such as the coefficients of a Newton's polynomial, are calculated and stored. Subsequently, in an ongoing Computation Sequence (block 106), the amplitude envelope of a baseband transmission signal is multiplied by the nonlinear function to control the power supply 14 to modulate a supply voltage V.sub.CC(t) provided to the RF PA 16. The pre-distorted, envelope-tracking, modulated supply voltage V.sub.CC(t) dynamically matches the power requirements of the RF PA 12 for the RF transmission signal being amplified, while maintaining a constant ISO-Gain. If there is no event trigger, such as expiration of a periodic timer, RF frequency change, or the like (block 108), then the Computation Sequence (block 106) is repeatedthat is, it is an ongoing process. If an event trigger does occur (block 108), then the entire method 100 is repeated, with new parameters for the nonlinear function calculated from the feedback path 29.

(52) The ISO-Gain pre-distortion algorithm described herein was simulated recursively, and the gain linearity improvement tested at each iteration. The simulations used a 5.sup.th-order polynomial, and a LTE 10 MHz full RB. The benefit of ISO-Gain is evaluated taking into account PA 16 instantaneous gain; PA 16 instantaneous phase shifting; E_UTRA Adjacent Channels Power Ratio (ACPR); and UTRA ACPRs.

(53) FIG. 11A depicts the evolution of the RF PA 16 supply voltage V.sub.CC(t), and FIG. 11B depicts the evolution of the RF PA 16 instantaneous gain, after each iteration of the adaptive ISO-Gain algorithm. FIG. 11A clearly depicts that as the number of iterations of the algorithm increase, the RF PA 16 gain becomes increasingly constant versus time. As noted above, it is the decreases in V.sub.CC that cause the greatest dips in PA 16 gain; multiple iterations of the adaptive pre-distortion algorithm of embodiments of the present invention dramatically reduce these downward excursions in the gain. Furthermore, FIG. 11B shows that an additional benefit of the adaptive pre-distortion algorithm disclosed herein is that dynamics of V.sub.CC variations versus time is reduced. This reduction in dynamics improves the accuracy and performance of the power supply 14.

(54) FIGS. 12 and 13 depicts RF PA 16 gain and phases shift variations, respectively, as a function of instantaneous variations in the supply voltage V.sub.CC. After each iteration, both gain and phase shift become more and more constant, even though the supply voltage V.sub.CC varies during the time.

(55) FIG. 14 depicts the output spectrum of the RF PA 16 without, and with one and two iterations of, the feedback-based, pre-distortion envelope tracking power control algorithm disclosed herein. Application of the algorithm reduces spectral emissions outside of the 10 MHz band centred on the carrier frequency (indicated as 0 MHz in FIG. 14 due to the simulator normalizing the spectrum frequency). The improvement is detailed in Table 1 below.

(56) TABLE-US-00001 TABLE 1 Step by Step ACPRs Pre- Output E UTRA UTRA 5 MHz UTRA 5 MHz distortion Power ACPR (dBc) ACPR1 (dBc) ACPR2 (dBc) Iterations (dBm) High Low High Low High Low None 26.6 26.9 26.5 27.7 27.8 31.9 31.6 One 26.4 38.1 37.7 38.9 38.9 43.3 42.9 Two 26.2 43.6 46.2 44.8 44.7 48.4 48.1

(57) Embodiments of the present invention present numerous advantages over prior art envelope tracking pre-distortion methods. By using feedback of the actual amplified signal, the methods disclosed herein can compensate for nonlinearities in the entire transmitter 20 chain, not just the RF PA 16. Although described herein as benefitting the gain of the RF PA 16, the adaptive ISO-Gain envelope tracking additionally improves phase response of the RF PA 16. The method allows modifications to the pre-distortion applied to the supply power V.sub.CC(t) as necessary, such as when the transmitter 20 power or frequency changes, or as components age. The transmitter 20 is thus not reliant on factory calibrations, the elimination of which speeds and simplifies the manufacturing process. The pre-distortion calculations are not computationally intensive, incur little power consumption, and the calculated coefficients are stored in a very small, efficient LUT. Up to 17 dB improvement on ACPRs can be achieved with a 5.sup.th order polynomial.

(58) The present invention may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the invention. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.