Abstract:
The present invention is directed to systems and methods for reducing the distortion of power amplifiers. In particular, methods and systems are described that enable a determination of a pre-distortion correction signal to be determined, which when added to the nominal signal, a reduction in the distortion of the power amplifier results. In addition, methods and systems are described that enable calibration of individual power amplifiers to be accomplished for use with the above described approach. More specifically, the methods and systems are described for use in a MIMO application. These approaches may be applied to on-chip power amplifiers, off-chip power amplifiers, or any combination thereof.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. Non-Provisional application Ser. No. 12/139,634, filed Jun. 16, 2008, which claims the benefit of U.S. Provisional Patent Application No. 60/929,150, entitled “Power Amplifier Pre-Distortion”, filed on Jun. 15, 2007, all of which are hereby expressly incorporated by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to power amplifiers, and more specifically to the pre-distortion of power amplifiers. 
     2. Related Art 
     A critical component of any communications system is the power amplifier in the transmitter. The function of the power amplifier is to amplify an input data signal and thereby create a high powered version of that input data signal for subsequent output into a transmission channel. The greater the amplification capability of the power amplifier, the greater the resulting output power level, and therefore the larger the geographic area covered by the communications system. In addition to the increased coverage area, an increased output power level typically results in increased efficiency (as measured by the ratio of resulting output power to input direct current (DC) power to the power amplifier). 
     However, concurrent with these improvements in link coverage and power amplifier efficiency, the distortion in the output data signal unfortunately increases with increasing power level. Such distortion reveals itself in many ways, including as a spillover of transmitted power into frequencies outside the intended frequency band of transmission. It also reveals itself as a degradation of the quality of the in-band signal such that larger constellations and higher throughput rates are inhibited at higher transmission powers. Such distortion, a result of the nonlinearities in the power amplifier, directly diminishes the useful output power range of the power amplifier. It is therefore desirable to minimize the distortion and to thereby capitalize on as much of the available output power from the power amplifier as possible. 
     Traditionally, the final stage of power amplification in a communications transmission system has been performed “off-chip” in order to simultaneously achieve the two goals of having sufficient output power and low distortion. Such off-chip power amplifiers are expensive. Moreover, they do not provide the same integration opportunities afforded by an on-chip amplifier, such as optimization of associated power amplifier (PA) circuitry, integration of the power supplies, consistency of PAs (from one to the next), ease of testing and calibration, and reliable connectivity. It is therefore highly desirable to minimize the distortion of power amplifiers in general, and in particular on-chip power amplifiers, so that benefits of integration can be realized while still providing the required high level of output power. 
     The advent of multiple-input multiple-output (MIMO) communications system architectures has intensified the challenges described above. A MIMO approach exploits the spatial diversity implicit in having multiple transmitters communicating the same data signal to multiple receivers. By spatially propagating more than one version of the same data signal, improvements in communications coverage and link quality readily materialize over that routinely available from the traditional single-input single-output approach. 
     To fully capture these MIMO benefits, a premium is therefore placed on the ability to readily fabricate a multiplicity of low distortion power amplifiers, with uniform performance characteristics, at low cost, and in a form that can be readily integrated with the rest of the transmitter functionality. While many of these benefits can be realized using off-chip power amplifiers, the full potential of benefits comes into fruition through the use of low distortion on-chip power amplifiers. 
     What is needed, therefore, is an approach that solves one or more of these power amplifier challenges in a modern data communications system, namely increased output power, reduced distortion, greater ease of integration with the associated circuitry in the transmitter chain, and lower cost. With respect to a MIMO transmitter application, it is highly desirable that an approach be found that addresses not only the above challenges, but also the uniformity of the performance characteristics of a multiplicity of power amplifiers. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a power amplifier pre-distortion technique that reduces the distortion of a power amplifier by pre-distorting the input signal to that power amplifier. The amount of pre-distortion is determined to be that amount which offsets the distortion that is generated internally by the nonlinearities within the power amplifier. A calibration procedure uses a set of tones over the nonlinear operating range of the power amplifier to determine the level of offset required. Such offsets are stored in a look-up table that can be read in real-time, such that the appropriate level of pre-distortion can be added to the input signal to the power amplifier. 
     In yet another embodiment of this invention, in a MIMO system containing a multiplicity of power amplifiers, each power amplifier is provided with a look-up table for real-time pre-distortion of the input signal to each power amplifier. Different calibration approaches are described that address the varying coupling that may be present between the multiplicity of power amplifiers when they are in an active state. 
     Further embodiments, features, and advantages of the present invention, as well as the structure and operation of the various embodiments of the present invention are described in detail below with reference to accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES 
       The accompanying drawings illustrate the present invention and, together with the description, further serve to explain the principles of the invention and to enable one skilled in the pertinent art to make and use the invention. 
         FIG. 1  is a block diagram that illustrates different components in a transmitter of a conventional analog communications system. 
         FIG. 2  is a block diagram that illustrates the different components in a transmitter of a conventional digital communications system. 
         FIG. 3A  illustrates an exemplary amplitude response of a power amplifier in one of the systems shown in  FIG. 1  or  2 . 
         FIG. 3B  illustrates an exemplary phase response of a power amplifier, such as the amplifier shown in  FIG. 3A . 
         FIG. 4  is a block diagram of a transmitter with power amplifier pre-distortion capability, according to an exemplary embodiment of the present invention. 
         FIG. 5 . is a block diagram that illustrates different components within the power amplifier pre-distortion module shown in  FIG. 4 . 
         FIG. 6  is a block diagram that illustrates the different components along a power amplifier pre-distortion calibration path, according to an exemplary embodiment of the present invention. 
         FIG. 7  illustrates a block diagram of a MIMO-based embodiment of the present invention. 
         FIG. 8  is a flowchart diagram that illustrates a method for pre-distortion for a power amplifier, according to an embodiment of the present invention. 
     
    
    
     The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the reference number. 
     DETAILED DESCRIPTION OF THE INVENTION 
     This specification discloses one or more embodiments that incorporate the features of this invention. The embodiment(s) described, and references in the specification to “one embodiment”, “an embodiment”, “an example embodiment”, etc., indicate that the embodiment(s) described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Furthermore, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. 
       FIG. 1  illustrates typical functionality in a data communications transmitter  100 . A data source  110  outputs data that is subsequently fed into a processing module  120 . Functionality included within the processing module  120  potentially includes modulation, encoding, filtering, frequency up-conversion, and pre-amplification. Output from the processing module  120  is then fed into a conventional power amplifier  130 , which amplifies the input signal to produce an output signal that is coupled to an antenna  140 . The power amplifier  130  can be an on-chip power amplifier, an off-chip power amplifier, or a cascaded combination of on-chip and off-chip power amplifiers. 
       FIG. 2  illustrates a digital implementation  200  of a data communications transmitter, wherein a digital data source  210  is fed into a digital processing module  220 , whose output is fed into a digital-to-analog converter (DAC)  230 . Functionality included within the digital processing module  220  potentially includes digital modulation, digital encoding, digital filtering, digital frequency up-conversion, and digital pre-amplification. The output of the DAC  230  is then fed into a pre-amplifier module  240 , whose output is fed into the power amplifier  130  where the signal is amplified before input to the antenna  140 , as before. Functionality included within the pre-amplifier module  240  potentially includes filtering, frequency up-conversion, and pre-amplification. 
       FIG. 3  illustrates nonlinear effects of the power amplifier  130 ,  FIG. 3A  shows a typical response of a power amplifier  130  as a function of increasing input power. If the power amplifier  130  was ideal, it would provide an output power level that is directly proportional to the input power level, and therefore the plotted response of gain versus input power would be a horizontal line. The power amplifier  130 , however, is not ideal and therefore includes non-linearities. As  FIG. 3A  indicates, nonlinear effects result in the power amplifier  130  going into compression at the higher input power levels. The nonlinear effects are characterized as amplitude modulation (AM) to amplitude modulation (AM) distortion. 
     Similarly,  FIG. 3B  shows a typical response of the power amplifier  130  wherein phase is plotted against increasing input power. Again, if the power amplifier  130  was ideal, there would be a constant phase difference between input and output signals, as the input power varies over its operating range. However, the inherent nonlinearities in the power amplifier  130  result in phase shift variation in response to input power variation. This nonlinear effect is characterized as AM to phase modulation (PM) distortion. 
     The power amplifier  130  exhibits both types of distortion, namely both AM to AM distortion and AM to PM distortion. It is highly desirable that these distortion products be reduced in order to fully exploit the available output power range of the power amplifier  130 . 
     In an embodiment of the present invention, the distortion of a power amplifier  130  can be reduced by suitably pre-distorting the input signal. The amount of pre-distortion added to the input signal is determined by the amplitude and phase distortion characteristics of the particular power amplifier  130 . In essence, harmonics generated by the particular power amplifier  130  will be reduced by introducing customized pre-distortion into the input signal. 
       FIG. 4  illustrates a digital embodiment  400  of the present invention. In the embodiment  400 , the data source  210  outputs a signal that is provided to a pre-processing module  410 . In turn, the pre-processing module  410  outputs an uncorrected signal  420  that is fed into a pre-distortion module  430 . Based on this input, the pre-distortion module  430  determines required amounts of added signal components, in both amplitude and phase, which would offset (i.e., be the inverse of) the internally generated distortion in the power amplifier  130 . 
     These added signal components are then added to the uncorrected signal  420  to form a pre-distorted signal  440 , which is then fed into a post-processing module  460 . It should be noted that the functionality of the digital processing module  220 , shown in  FIG. 2 , is split in  FIG. 4  between the pre-processing module  410  and the post-processing module  460 . As  FIG. 4  shows, a sampled output signal  450  is also input to the pre-distortion module  430 . This input to the pre-distortion module  430  is used for calibration purposes, as described below. Sampled output signal  450  is obtained by passing a portion of the power amplifier output signal through RF block  470 . RF block  470  includes a RF-to-baseband conversion function, sampling, and an optional filtering function. 
       FIG. 5  illustrates an exemplary embodiment  500  of the architecture of a pre-distortion module  430 . While the pre-distortion module  430  is in its regular operating (or “compensating”) state, the uncorrected signal  420  is received at an input to a compensation module  520 . The compensation module  520  parameterizes the uncorrected signal  420 . Based on the relationship between the uncorrected signal  420  and the power level of the power amplifier  130 , the compensation module  520  determines the compensation appropriate to the operating state of the downstream power amplifier  130 . 
     In one simple embodiment of the compensation module  520 , the compensation module  520  generates a single index value that is representative of the instantaneous power level of the operating state of the downstream power amplifier  130 . Based on the index value, the compensation module  520  identifies the appropriate location in a pre-populated look-up table  540  for the correction value. A pre-distortion correction signal  550  is generated based on the correction value in the look-up table  540 . The pre-distortion correction signal  550  is then summed with the uncorrected signal  420  in a summer  560 , to create a pre-distorted signal  440 . Mathematically, this embodiment of the pre-distortion module  430  may be represented as follows:
 
Pre-distorted signal= C *uncorrected signal,
 
     where C=correction factor; 
     C=1+ε; and 
     ε=pre-distortion correction coefficient. 
     As noted in the embodiment  500  described above, the index value (and the pre-distortion correction coefficient ε) is a surrogate for the instantaneous power level of the power amplifier  130 . As such, there is a simple one-to-one relationship between the instantaneous power level and the value of the pre-distortion correction coefficient. As noted above, the look-up table  540  can be used to capture this one-to-one relationship over the power range of interest for the power amplifier  130 . 
     In other embodiments of the current invention, a more complex relationship can exist between the distortion characteristics and the instantaneous output power of the power amplifier  130 . Such is the case for a power amplifier  130  having “memory”, wherein its distortion characteristics are more fully represented by a relationship between not only the current instantaneous power level but also the instantaneous power level at various times immediately preceding the time of interest. In such a case, the relevant functional relationship is a higher order relationship. In some situations, that higher order relationship is an average of the instantaneous power level at various times preceding the time of interest. 
     In the case of a higher order relationship, the compensation module  520  maintains a memory of prior index values associated with the various times immediately preceding the time of interest. The pre-distortion correction value  550  is thus determined based upon a formula that uses the values in the look-up table  540  corresponding to each of the index values in the time series. The formula so used mimics the higher order time-dependent relationship between the distortion characteristics and the operating state of the power amplifier  130 . 
     Similarly, more complete representations of the distortion characteristics of a power amplifier can be obtained by capturing information regarding various non-power properties, e.g. frequency and temperature. In the case of a power amplifier  130  whose distortion characteristics depend on both instantaneous power level and frequency, a multi-dimensional look-up table  540  can be implemented. In this embodiment, the generator determines the frequency of the uncorrected signal  420  in addition to the index value for use in accessing the multi-dimensional look-up table  540 . In a more simplified embodiment, the additional frequency dependence is resolved by recalibration at the other frequencies of interest. 
     Similarly, in the case of the power amplifier  130  whose distortion characteristics depend on both instantaneous power level and temperature, the multi-dimensional look-up table  540  can be implemented. 
     In  FIG. 5 , a temperature sensor  580  is shown, whose output is fed into the compensation module  520 . Should the distortion-temperature relationship be a linear relationship, a suitable pre-distortion correction signal can be generated based on the two parameters that uniquely define the straight-line relationship. These two parameters would typically be stored in the compensation module  520 . 
     In each of the above embodiments, the particular approach relies on a pre-populated look-up table  540 , or its equivalent functional relationship, e.g. linear temperature relationship with the two parameters previously determined. In determining these pre-populated and/or pre-determined values, it should be noted that the relationship between the input power (or other independent variable such as temperature or frequency) and the distortion factor is unique to each power amplifier, similar to the power amplifier  130 . Accordingly, for each power amplifier similar to the power amplifier  130 , a calibration procedure is required in order to populate the pre-distortion module with the pre-distortion correction values unique to that particular power amplifier  130 . 
     In the case where a simple one-to-one relationship exists between the distortion characteristics and output power level, the calibration process results in the generation of a simple look-up table  540 . In such a process, the look-up table is populated in discrete intervals, beginning with the smallest input power level of interest. Continuing with  FIG. 5 ,  FIG. 5  also illustrates the different components involved in such a calibration, according to an exemplary embodiment of the present invention. 
     In  FIG. 5 , a sample signal set  590  may be used for calibration, though the scope of the present invention is not limited in this respect. In calibration mode, the sample signal set provides a series of input signal tones of various power levels, from which the resulting distortion at the output of the power amplifier may be measured, and from which the pre-distortion correction coefficient may be derived and stored in the look-up table  540 . During calibration, the uncorrected signal  420  is disconnected while output from the sample signal set  590  is active. The sample signal set  590  is sent directly to the calibration module  570 , and via a gain block  510  (with adjustable gain B) to the compensation module  520  and summer module  560 . The purpose of the gain block  510  is to set the power level of the sample signal set  590  to the desired level. An attenuation block  530 , with adjustable attenuation B, connects the sampled output signal  450  to the calibration module  570 . The attenuation block  530  serves to reverse the effect of the gain block  510 . 
       FIG. 6  provides a simplified explanation of the calibration module  570  according to an exemplary embodiment of the present invention. The calibration module  570  contains a correlator  610 , a summation unit  620 , and an ε calculator  630 . In one embodiment of the invention, tone samples ‘x i ’ from the sample signal set  590  are fed directly to a correlator  610  and indirectly to the correlator via the cascaded combination of the pre-distortion module  430  and the power amplifier  130 . As noted earlier, the pre-distortion module  430  applies a transformation C, which is equal to C=1+ε. In a similar manner to that described earlier in  FIG. 4 , RF blocks  640  and  650  provide baseband-to-RF and RF-to-baseband conversion functions respectively, sampling and an optional filtering function. 
     Similarly, the power amplifier  130  applies a transformation that will be denoted as A. Accordingly, an output Y of the correlator  610  and the summation unit  620  may be calculated, for example, by the equation, Y=Σ(CA|x| 2 ). At low output signal levels, the power amplifier  130  is linear and, for purposes of this analysis, introduces no significant distortion. At these variables, the correlator output achieves its reference value, denoted by Y 0 . As the output power of the power amplifier  130  increases, distortion is introduced into the output signal, and pre-distortion signals need to be introduced to offset the distortion. Accordingly, ε needs to be chosen by the ε calculator  630  so that a product, CA, at the power level of interest, equals the value of that product at the small signal reference point, C 0 A 0 . While C (and therefore ε) can be determined directly by the formula C 0 Y 0 /Y, such a formula involves complex division. 
     As an alternative, the value of ε (and therefore C) at each output power level of interest can be determined iteratively through the use of the following gradient descent based formula: ε new =(Y 0 Y*−Y 0 Y 0 *)λ+ε old , where Y 0 * is the complex conjugate of Y 0 , and λ is small. Here, the value of λ should be small enough such that convergence is assured. Using this approach, the difficulties of a complex division are avoided and replaced by the time required for the iterative technique to converge. This technique is repeated at each of the discrete power levels of interest over the operating power range of the power amplifier. The increments in power level step size in the look-up table  540  can be programmable. For example, in an exemplary embodiment of the current invention, a scalar register can be used to implement a programmable step increments of the look-up table  540 . 
     In the embodiment of a power amplifier for which a more complex relationship is appropriate to properly characterize the distortion performance of that power amplifier, a multi-dimensional calibration technique would be deployed to capture the relevant characteristics. For example, a power amplifier whose instantaneous distortion performance is best captured by a multi-dimensional relationship with frequency and power level, would be calibrated by introducing a series of test signals over different frequencies and different input power levels in order to provide sufficient characterization coverage of the individual power amplifier. 
     Similarly, for a power amplifier whose distortion performance bears a relationship to operating temperature, that relationship can also be captured. In one embodiment of the current invention, where the relationship between pre-distortion correction value and operating temperature is a linear relationship, a calibration procedure can be developed that captures the two parameter values necessary to describe that linear relationship. 
     Other embodiments may capture solutions to other calibration challenges. For example, calibration can be broken into a plurality of power ranges, wherein the transmission radio frequency (RF) gain is re-set between each of these calibration power ranges. The motivation for the plurality of power ranges is not to overdrive the DAC, which receives the output of the pre-distortion module  430 , after passing through the post-processing module  460 . In another embodiment of the invention, the power amplifier may be recalibrated when the temperature of the system changes. In another embodiment, the power amplifier may be recalibrated initially during startup. In yet another embodiment, the PA may be recalibrated periodically. 
     Various alternatives exist as to the strategy by which the power amplifier  130  may be calibrated. Clearly, the entire look-up table  540  can be computed in a single procedure by stepping throughout the entire operating power range of the power amplifier, and populating an entry into the look-up table  540  for each power level of interest. Computation of each entry requires the use of an iterative algorithm or its equivalent. Such computation can require a substantial amount of time, where this calibration time coming at the expense of actual operations time. For example, a calibration time of 10 milliseconds can represent a considerable opportunity cost in terms of lost communications time in an 802.11 communications system. Moreover, it should be noted that due to changing power amplifier performance characteristics, periodic re-calibrations are often required, rather than a single calibration event that is valid in perpetuity. Such additional calibration cycles further add to the challenge of the appropriate tradeoff between the time devoted to calibration versus the time required for actual operations. 
     In an evaluation of the tradeoff between calibration time and operations time, an alternative to completing the entire calibration (and when necessary re-calibration) in a single transaction includes breaking the calibration effort into a number of smaller calibration transactions that are spread over time, and thereby lessening the impact of the calibration at a particular instant in time. Another alternative reduces the frequency of re-calibrations for portions of the operating power range where the need for such re-calibrations is diminished, e.g, at lower operating power levels where the power amplifier characteristics rarely change over time. In each of these alternatives, a partial calibration procedure would be undertaken whereby the procedure would use a starting power level and an ending power level that represent a sub-range of the overall operating power level of the power amplifier. 
     Another strategy to minimize the time devoted to calibration is to reduce the time required to iteratively determine each entry in the look-up table  540 . The default starting point for the iterative determination of an entry in the look-up table  540  is typically zero. However, any particular convergence time can be accelerated by using a smarter alternative to the starting point. For example, a smarter alternative can be a previously computed look-up table entry for the same power level, i.e. the starting point can be the look-up table entry obtained from a prior calibration for the same power level. Such a choice of starting point makes intuitive sense since power amplifier characteristics often do not change significantly over time. Another smarter starting point alternative is to use a starting point based on the look-up table entry for an adjacent power level to that currently undergoing calibration (or re-calibration). Again, such a starting point makes intuitive sense by virtue of the fact that the AM-AM and the AM-PM characteristics (e.g., see  FIGS. 3A and 3B ) are continuous functions versus power level and therefore nearby points should provide a superior starting point when using an iterative procedure. In summary, it should be noted that all of these alternatives of optimized calibration time may be pursued separately from each other, or may be pursued simultaneously with each other. 
     The advent of MIMO systems has resulted in transmitter system architectures that feature a plurality of power amplifiers, one for each transmission signal.  FIG. 7  illustrates a block diagram for such a MIMO-based embodiment of the current invention  700 . 
     In this embodiment of the present invention for MIMO architectures, a pre-distortion module  430   a  through  430   z  is required for each power amplifier  130   a  through  130   z . Within each pre-distortion module  430   a  through  430   z  is a calibration module for its respective power amplifier  430   a  through  430   z . As above, the pre-distortion modules  430   a  through  430   z  operate in either a calibration mode or in a compensating mode. RF blocks  470   a  through  470   z  each include a RF-to-baseband conversion function, sampling, and an optional filtering function. 
     When the embodiment  700  is operating in a compensating mode, the data source  210  outputs a signal that is provided to a pre-processing module  410 . In turn, the pre-processing module  410  outputs an uncorrected signal  420  that is fed into each of the pre-distortion modules  430   a  through  430   z . Based on this input, each pre-distortion module  430   a  through  430   z  determines the required amounts of added signal components, in both amplitude and phase, which would offset (i.e., be the inverse of) the internally generated distortion in its respective power amplifier  130   a  through  130   z.    
     These added signal components are then added to the uncorrected signal  420  to form a pre-distorted signal  440   a  through  440   z , which is then fed into its respective post-processing module  460   a  through  460   z . As before, the post-processing modules  460   a  through  460   z  are coupled to their respective DACs  230   a  through  230   z , in turn coupled to their respective pre-amplifiers  240   a  through  240   z , to their respective power amplifiers  130   a  through  130   z , and finally to their respective antennas  140   a  through  140   z.    
     When the embodiment  700  is operating in a calibration mode, for each power amplifier  130   a  through  130   z , a sampled output signal  450   a  through  450   z  is input to its respective pre-distortion module  430   a  through  430   z . Each sampled output signal  450   a  through  450   z  is obtained by passing a portion of the respective power amplifier output signal through respective RF block  470   a  through  470   z . This input to each of the pre-distortion modules  430   a  through  430   z  is used for calibration purposes, as described earlier and below. 
     The calibration procedure for such a MIMO architecture can proceed under a number of alternative ways. In an exemplary embodiment, each power amplifier can be activated individually, while all other power amplifiers are shut off. For each active power amplifier, the resulting distortion is captured, and the appropriate correction value is entered into the pre-distortion module. Such an approach works best when the power amplifiers provide significant interference to each other. 
     Where the coupling between power amplifiers is minimal, all of the power amplifiers can be activated at once, and the resulting distortion at each output determined in the presence of all other power amplifiers being active. Based on the distortion so determined, the resulting correction value and relationship is captured. 
     As noted above, there is often a tradeoff between the time needed for calibration of the power amplifier and the time devoted to actual operations. Those same comments apply in the MIMO context, where various alternatives may be exploited to optimize the tradeoff. Such alternatives include breaking the calibration process into smaller calibration processes that focus on a subset of the operating power range of the power amplifier. Other alternatives focus instead on optimization of the iterative process of calibration at each individual power level. As above, these alternatives may be pursued separately from each other, or may be pursued simultaneously with each other. 
     According to an embodiment of the invention, the pre-distortion techniques described herein apply to implementations with on-chip power amplifiers, as well as implementations that also include one or more external power amplifiers in the transmitter. In implementations with more than one cascaded power amplifier, the pre-distortion technique seeks to reduce the total distortion at each operating point. 
       FIG. 8  illustrates a flowchart  800  that further describes the pre-distortion of power amplifiers in a MIMO system. In step  805 , a plurality of power amplifiers are calibrated based on a plurality of calibration tones resulting in an associated look-up table for each power amplifier. In step  810 , for each power amplifier, a pre-distortion correction signal is determined based on an instantaneous input power level of the power amplifier and the associated look-up table. In step  815 , for each power amplifier, a pre-distortion correction signal is coupled, at least indirectly, to an input of each power amplifier. 
     CONCLUSION 
     Example embodiments of the methods, systems, and components of the present invention have been described herein. As noted elsewhere, these example embodiments have been described for illustrative purposes only, and are not limiting. Other embodiments are possible and are covered by the invention. Such other embodiments will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Thus, the breadth and scope of the present invention should not be limited by any of the above described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. 
     The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance. 
     The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.