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 . fig1 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 . fig2 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 . fig3 illustrates nonlinear effects of the power amplifier 130 , fig3 a 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 fig3 a 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 , fig3 b 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 . fig4 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 fig2 , is split in fig4 between the pre - processing module 410 and the post - processing module 460 . as fig4 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 . fig5 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 : 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 fig5 , 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 fig5 , fig5 also illustrates the different components involved in such a calibration , according to an exemplary embodiment of the present invention . in fig5 , 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 . fig6 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 fig4 , 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 fig3 a 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 . fig7 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 . fig8 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 . 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 .