Patent Publication Number: US-2005141637-A1

Title: Powers amplifiers

Description:
The present invention relates to improvements in or relating to power amplifiers. In particular, the invention relates to improving the efficiency of power amplifiers in the base station apparatus of radio telecommunications systems.  
      In radio telecommunications systems, high power base stations are used to establish connections to a plurality of mobile units (handsets). The new 2.5G and 3 rd  generation (3G) telecommunications systems, such as GPRS and UMTS, demand certain features in the base stations. Notably 2.5G and 3G systems require the base stations to use high power amplifiers.  
      Power amplifiers (PA) are used in both base stations and mobile handsets to amplify input signals. In much of the following discussions the examples of input signals are simple two-tone signals having tones at two distinct frequencies, f 1  and f 2 . Input signals amplified by PAs are more generally multicarrier signals.  
      The PAs used in base stations must be robust at high power levels. Substantially linear transfer characteristics are considered important to the provision of robust high power amplifiers (HPA).  
      An ideal linear amplifier would give an amplified version of an input signal, which at every point in its operating range has been amplified by a constant factor.  
      One result of the use of non-ideal power amplifiers can be the appearance of intolerable levels of side band distortion.  
      Distortion in PAs may be both amplitude distortion and phase distortion. An amplifier may cause an amplitude modulation to phase modulation (AM/PM) transfer characteristic, whereby phase variations in the output amplified signal are dependent upon amplitude variations in the input signal. Distortion may also be purely or partly AM/AM in nature.  
      Distortion is a consequence of physical factors, including changes in the operational characteristics of the PA, temperature variations, power supply fluctuations and load mis-matches.  
      In the absence of PAs with perfect linear transfer characteristics, some non-linear distortion effects are to be expected. Distortion effects can appear as specious signals having frequencies which are generally in simple arithmetic selection as input frequencies; for example harmonic distortion and intermodulation distortions (IMD).  
      Intermodulation and harmonic distortions are important classes of effects generally termed “mixing products”.  
      For the purposes of the following discussion, intermodulation distortion (IMD) products can be characterised in terms of their origins. The “order” of a mixing product, f, is given by the sum: 
 
 O ( f )=| m|+|n|+ . . . +|z| 
 
      where f=mf 1 +nf 2 + . . . +zf i    
      Thus the third harmonic of f 1 , 3f 1 , is of order three; so too is the IMD product (2f 1 −f 2 ). A short hand for 3 rd  order intermodulation distortion product, IM3, will be adopted hereafter.  
      In the high power amplified generally used in broadband radio frequency (RF) communications systems, the present of IMD is highly unwelcome. Amplification of the multicarrier signals of 2.5G and 3G systems leads to a plethora of IMD products as each channel can potentially mix with every other channel.  
      In response to non-linear transfer characteristics in PAs, it is known to seek to compensate for non-linearities. The apparatus for compensating for non-linear transfer characteristics is variously termed ‘predistorter’, ‘linearizer’ and ‘equaliser’. The difference between terms is one of emphasis: a predistorter being an apparatus for applying a predistortion that seeks to complement any distortion introduced by the component of a PA. ‘linearizer’ emphasis the need to bring the combine linearizer and PA arrangement as close as possible to an ideal linear PA.  
      All compensating apparatus share the feature that they seek to apply a compensating function to counter the distorting effects of PAs. The compensating function may be viewed as an approximation to the inverse or complimentary function to the non-linear transfer function associated with the PA.  
      The inverse function can be modelled in a variety of ways. In one example an arrangement of diodes is provided, the arrangement approximating the inverse of the distortion effects in the PA. In further examples software is used to emulate the effect of hardware predistortion devices in real time.  
      Both the non-linear transfer function and the complementary predistortion function may be approximated by polynomial expansions. Polynomial predistortion is known.  
      It is further remarked that compensating apparatus is generally implemented within either a feed-forward or a feed-back circuit arrangement.  
      Adaptive predistortion has been shown to be an essential technique for reducing the peak error power, and hence improving the efficiency of feed-forward amplifiers. Known polynomial predistorters, such as the predistorter disclosed in UK patent application number GB 0123494.7 (attorney docket number 2001P09343), are unfortunately not effective for frequency dependent non-linear distortion where memory is required.  
      In the following discussion, the term memory refers to the dispersion of a signal through components which results in the delay of the signal.  
      When a PA displays memory effects, at least a component of the non-linear transfer characteristics will depend significantly upon previous signals passing through the PA. Consequently, the predistorter used to compensate for the memory effects must have memory too.  
      Furthermore, from recent research it has been realised that the dependency of IM3 products on both carrier frequency and envelope frequency can be significant. The dependency of the IM3 products upon envelope frequency is generally stronger.  
      In the case of envelope frequency dependency, the strength of the response can be damped. A compensating apparatus must therefore be provided with means to compensate for envelope frequency dependence and potentially memory effects too.  
      It is therefore an object of the invention to obviate or at least mitigate the aforementioned problems.  
      In accordance with one aspect of the present invention, there is provided a compensating apparatus for compensating for intermodulation products, the apparatus comprising: a phase splitting unit, which splits an input RF signal into an in-phase component and a quadrature component; first multiplying units, which square the value of the in-phase component and the quadrature component respectively and sum the squared values to generate an X 2  signal; combining units, which combine the X 2  signal, the in-phase and quadrature components, and an external signal with respective predistorting coefficients; and an adder, which generates a predistorted RF signal from the output of the combining units.  
      The compensating apparatus may be provided upon an application specific integrated circuit.  
      An output carrying the X 2  signal may be coupled to a delay unit (T 1 ) and the output of the delay unit is fed back into the apparatus as the external signal, so that the external signal is a delayed signal derived from the X 2  signal.  
      Alternatively the apparatus may further comprise a further multiplier, which squares the X 2  signal again to give a X 4  signal, wherein the external signal is the X 4  signal.  
      By cascading more than one instance of the compensating apparatus, both carrier frequency and envelope frequency dependent effects due to IM3 products may be compensated for substantially simultaneously.  
      In a further aspect of the present invention there is provided a hybrid compensating apparatus for substantially simultaneously compensating for both carrier frequency and envelope frequency dependent effects due to IM3 products, the hybrid apparatus comprising: a first compensating apparatus coupled to a delay unit and arranged to compensate for envelope frequency effects; a second compensating apparatus, arranged to compensate for carrier frequency effects; a carrier delay unit, which imposes a predetermined delay upon the RF input signal supplied to the second compensating apparatus; and a further adder which sums the outputs of the first and second compensating apparatuses.  
      In accordance with another aspect of the present invention there is provided a feed forward amplifier arrangement comprising: a compensating apparatus as above; an amplifier having non-linear transfer characteristics that distort signals amplified thereby, the amplifier being coupled to the output of the compensating apparatus; a controller which generates coefficients for feeding into the compensating apparatus; and a sampling means which samples an output signal from the amplifier and which feeds the sample back to the controller.  
      In accordance with a further aspect of the present invention, there is provided a method of compensating for intermodulation products, the method comprising: splitting an input RF signal into an in-phase component and a quadrature component; squaring the in-phase component and the quadrature component respectively and summing their squares to generate an X 2  signal; combining the X 2  signal, the in-phase and quadrature components, and an external signal with respective predistorting coefficients; and generating a predistorted RF signal.  
      The compensating apparatus may also be referred to hereafter as an adaptive polynomial equaliser (APE). As will be understood, the APE is a modified polynomial predistorter and is able to compensate for envelope and carrier frequency dependent effects even when the transfer characteristics of the PA include memory effects.  
      The following discussion also delineates an architecture for a radio frequency application specific integrated circuit (RF-ASIC) predistorter. The proposed APE implements a predistortion technique that is re-configurable for narrowband and broadband applications. As such, the proposed APE improves efficiency and bandwidth of feed forward amplifiers.  
      A further benefit of the APE is to reduce substantially the error amplifier size thereby significantly reducing costly output filter delays. 
    
    
      For a better understanding of the present invention, reference will now be made, by way of example only, to the accompanying drawings in which:— 
       FIG. 1  shows IM3 products as measured on a first PA device, Device A;  
       FIG. 2  shows IM3 products as measured on a second PA device, Device B;  
       FIG. 3  shows a model for PA linear transfer function;  
       FIG. 4  shows a model for carrier frequency dependent non-linearity in PA;  
       FIG. 5  shows a model for envelope frequency dependent non-linearity in PA;  
       FIG. 6  shows an overall transfer function of the PA;  
       FIG. 7  shows a simulation set-up;  
       FIG. 8  shows a block diagram of a predistorter configured for Device A;  
       FIG. 9  shows Error Power improvement for Device A;  
       FIG. 10  shows spectral improvement for Device A;  
       FIG. 11  shows a block diagram of an equaliser configured for Device B;  
       FIG. 12  shows Error Power reduction for Device B;  
       FIG. 13  shows spectral improvements for Device B;  
       FIG. 14  shows an APE RF-ASIC device configured as a 5 th  order predistorter;  
       FIG. 15  shows an APE RF-ASIC device configured for envelope frequency (3 rd  order) compensation;  
       FIG. 16  shows an arrangement of APE RF-ASIC devices suitable for performing envelope and carrier frequency equalisation; and  
       FIG. 17  shows a block diagram of an implementation of an APE in a feed forward loop. 
    
    
      To illustrate the types of memory effects which prior art predistorters find problematic, the results of non-linear memory measurements are disclosed and a simulation model is derived (see FIGS.  1  to  7 ). Block diagrams and architectural drawings of configurations and applications of the predistorter of the present invention are shown in FIGS.  8  to  17 .  
      The non-linear memory is manifested by variation of IM3 side band levels and side band symmetry over the frequency range. The levels are dependent on the envelope frequency, and the carrier frequency. The significance of memory effects is well known.  
      There are many examples of linear amplifier devices which may be adopted in base stations. For the purposes of the following discussion two known devices are considered: Device A and Device B. Both devices have been tested for two-tone inter-modulation over carrier and envelope frequency. The test results are shown in FIGS.  1  (Device A) and  2  (Device B).  
      In Device A, the IM3 products are shown to have a slight dependence on carrier frequency. The envelope dependency is stronger; there is a resonance at dF=10 MHz.  
      In the case of Device B, the IM3 products are not dependent on carrier frequency. The envelope dependency is very small between 2110 MHz to 2160 MHz, but there is a strong resonance at the band edge (dF=25-30 MHz).  
      It is important to note that in both devices, the 5 th  order distortion is 8-10 dB below the 3rd order products. This indicates that the higher order terms could be neglected at the drive levels at which the measurements of  FIG. 1  and  FIG. 2  were taken.  
      In the case of practical power amplifiers (PA), the carrier frequency dependent 3rd order non-linearity and the envelope frequency dependent 3rd order non-linearity dominates the transfer function. This is confirmed by measurements such as the studies of Devices A and B described above, which indicate that the 5th and higher order terms are generally 8-10 dB below the 3rd order products for a PA that operates at 20-30% efficiency.  
      In order to understand the behaviour of practical PAs it has been considered useful to develop a general model of these devices. Power amplifiers with memory can be modelled using Volterra series. Volterra series are considered particularly appropriate when non-linear effects are weak but not insignificant.  
      M. Schetzen describes the Volterra series and its application for non-linear systems in detail in “Volterra and Wiener Theories of Non-linear System”, Schetzen, M. (1980) John Wiley &amp; Sons, [ISBN 0-471-04455-5].  
      The general expression for a 2p-1 order model is given by the equation 1:  
           y   n     =       ∑       i   1     =   0       M   -   1       ⁢           ⁢       h     i   1       (   1   )       ⁢     x     n   -   i             ,       +       ∑       i   1     =   0       M   -   1       ⁢           ⁢       ∑       i   2     =   0       M   -   1       ⁢           ⁢       ∑       i   3     =   0       M   -   1       ⁢           ⁢     h       i   1     ,     i   2     ,       i   3     ⁢     x     n   -     i   1         ⁢     x     n   -     i   2         ⁢     x     n   -     i   3       *           (   3   )               +       ∑       i   1     =   0       M   -   1       ⁢           ⁢     …   ⁢       ∑       i       2   ⁢   p     -   1       =   0       M   -   1       ⁢           ⁢       h       i   1     ,     …   ⁢           ⁢     i       2   ⁢   p     -   1             (       2   ⁢   p     -   1     )       ⁢     x     n   -     i   1         ⁢   …   ⁢           ⁢     x     n   -     i   p         ⁢     x     n   -     i     p   +   1         *     ⁢     x     n   -     i       2   ⁢   p     -   1         *                   
 
      To represent the carrier frequency effects, the indices i 1 , i 2  and i 3  in equation 1 are set as follows:  
             i   1           i   2           i   3             0       0       0           0       1       1           ⋮       ⋮       ⋮             M   -   1         0       0           
 
      For the envelope frequency dependent term, the indices are set as follows:  
             i   1           i   2           i   3             0       0       0           0       1       1           ⋮       ⋮       ⋮           0         M   -   1           M   -   1             
 
      Using the reduced set of indices, equation 1 can be truncated to deal with three dominant effects: 1) Linear transfer function, 2) 3rd order carrier frequency dependent transfer function and 3) 3rd order envelope frequency dependent transfer function. The truncation gives a simplified model as set out in equation 2:  
         y   n     =         ∑       i   1     =   0       M   -   1       ⁢           ⁢       h     i   1       (   1   )       ⁢     x     n   -     i   1             +              x   n          2     ⁢       ∑       i   2     =   0       M   -   1       ⁢           ⁢       h     i   2       (     3   ⁢   cw     )       ⁢     x     n   -     i   2               +       x   n     ⁢       ∑       i   3     =   0       M   -   1       ⁢           ⁢       h     i   3       (     3   ⁢   env     )       ⁢            x     n   -     i   3              2                 
 
      A simplified model of PA behaviour based on equation 2 has been implemented. The block diagrams for each term of the equation are shown in  FIGS. 3, 4  and  5  respectively.  FIG. 6  shows the block diagram generated to simulate the overall transfer function of the power amplifier.  
      For simplicity, the impulse response for each term is implemented by single delay element that forms a two-tap FIR (finite impulse response) structure. Such a simple structure can produce a slope or a single curvature in an output signal which is adequate to represent the measured response of devices such as Device A or Device B ( FIGS. 1 and 2 ).  
      It should be noted that all coefficients in the above discussion of equations 1 and 2 are complex coefficients. This means that both AM/AM and AM/PM effects can be modelled (AM being amplitude modulation, PM being phase modulation). However, measurements made on spectral density only (using a spectrum analyser), do not allow the AM and the PM sidebands to be distinguished.  
      The block diagrams in FIGS.  3  to  6  seek to model the behaviour of known PA devices. The coefficients in  FIGS. 3, 4  and  5  were set to produce a ripple similar in magnitude to that of measured values the device to be modelled: for Device A and Device B, the ripple produced is similar to that in  FIG. 1  and  FIG. 2  respectively.  
      For example, the model of Device A has a linear ripple of +/−0.25 dB (not shown on  FIG. 1 ), the CW (carrier wave) dependent sidebands varied between −34 dBc to −36 dBc and the envelope dependent sidebands varied between −32 dBc to −36 dBc. Throughout, the notation dBc denotes the dB measured relative to the carrier signal amplitude.  
      Where no carrier frequency dependency is evident in a device for modelling, e.g. Device B, the linear ripple and the carrier frequency dependent variation are set to zero. The model of Device B does however allow the envelope dependent IM3 sidebands to vary between −25 dBc to −35 dBc.  
      It should further be noted that the high level of −25 dBc envelope dependent sidebands only occurs at the band edges. In practice, this resonance can be moved out of band and thereby avoided. However, in order to confirm the feasibility of an adaptive polynomial equaliser, the simulation allowed for variations of the order measured for Device B.  
      The purpose of the simulation was: firstly, to confirm that the simplified Volterra model, which was derived from the two-tone measurements, is also valid for the general multi-carrier case; but also to estimate the achievable Peak Error power Ratio (PER) for Device A and for Device B respectively. The estimation of achievable PER being made both using a polynomial predistorter, without memory, and using an adaptive polynomial equaliser, which gives predistortion with memory.  
      The simulation set-up is shown in  FIG. 7 . The PA distortion block  702  is based on the simplified Volterra model as illustrated in FIGS.  3  to  6 .  
      Under the simulation, the signal source comprises four equal CW tones; the frequencies are set to excite a variety of IM3 products. The simulated test case represents a typical multi-carrier scenario.  
      The Error block  704  calculates the difference between the reference  712  and the output signal  714 . This calculation bears some similarity to a signal cancellation loop in a feed forward circuit. The error signal  716  is plotted relative to the Peak Envelope Power of the reference signal.  
      The model operates in continuous and gated modes for observing the spectra and the time domain waveforms respectively.  
      The properties of the PA models are summarised in Table 1 below. The model of Device A (shown in  FIG. 8 ) simulates a weak memory case. On the other hand the model of Device B (shown in  FIG. 11 ) requires stronger memory simulation.  
                       TABLE 1                       Model Name   Device A   Device B                                                    Linear response ripple   +/−0.25   dB   0   dB       Carrier Dependent IM3   Min. −36   dBc   −35   dBc       levels   Max. −34   dBc   +/−0   dB       Envelope Dependent   Min −36   dBc   Min −35   dBc       IM3 levels   Max −32   dBc   Max −25   dBc                  
 
      The predistorter block  710  in  FIG. 7  is reconfigured to compensate for each respective PA distorter block  702 . Thus the predistorter in  FIG. 8  corresponds to the model of Device A and similarly the predistorter in  FIG. 11  corresponds to the model of Device B.  
      It will be noted that the Device A predistorter in  FIG. 8  does not have any delay elements and cannot therefore compensate for memory. However, as has been noted earlier, Device A does have a relatively small sideband ripple.  
      The error signal  716  from the system with Device A is shown in  FIG. 9 . The Peak Error Ratio improves by 7 dB (i.e. from −28 dBc to −35 dBc). The spectrum of the output signal  714  is shown in  FIG. 10 . Here too improvement can be observed.  
      In terms of the expected performance in a Feed Forward Loop, at 80W PEP, the Peak Error Power is only 25 mW. The Error amplifier needs to deliver only 250 mW peak when used with a 10 dB output coupler.  
      It is interesting point out that the 5th order coefficients of  FIG. 8  are set to zero. In further research, it has been found that these terms could not reduce the peak error any further, so these terms are not essential in the RF-ASIC implementation.  
      The polynomial predistorter model ( FIG. 8 ) performed very poorly when applied to the Device B model. Only 1 dB PER improvement was achieved. Given the strong memory component included in the Device B model, this poor performance was expected. In order to achieve better cancellation, an adaptive polynomial equaliser which includes delay (memory) is required.  
      The required equaliser comprises essentially the same building blocks as the predistorter of  FIG. 8 . However, as may be seen from the block diagram in  FIG. 11 , a delay element (T 1 ) is now added and the multipliers are re-configured to produce two sets of IM3 products (instead of a single 3 rd  order term and a  5   th  order term).  
      As remarked above a simple arrangement with two taps is able to generate a slope or a curvature. Here the two-tap FIR structure is used to equalise the envelope dependent transfer function of the power amplifier. The achievable improvement using the predistorter of  FIG. 11  with the Device B model is shown by  FIGS. 12 and 13 .  
      The equaliser reduced the Peak Error Power to −37 dBc. For the purposes of the simulation, this was achieved by manually adjusting the coefficients for minimum Peak Error Power. In the real system, the same task can be performed adaptively using a minimum PEP search algorithm.  
      In terms of the simulated performance in a Feed Forward Loop, at 86W PEP, the Peak Error Power is now only 20 mW. The Error amplifier needs to deliver only 200 mW peak when used with a 10 dB output coupler.  
      It should be noted, that the improvement of 14 dB illustrated in  FIG. 12  can not be guaranteed in anything other than special cases: the simple PA model produced a smooth curve instead of the sharp ripple as shown on  FIG. 2 . For accurate realisation of the distortion (and for its inverse) a larger number of taps will be required, corresponding to a longer delay (memory).  
      Accurate realisation of the distortion may be achieved with digital predistortion. On the other hand, there is no benefit from more than 10 dB improvement because the 5th and higher order terms are present at 8-10 dB below anyway.  
      In one embodiment of the present invention, an apparatus for compensating for the IMD products generated in PAs is provided. The compensating apparatus is configurable in accordance with the transfer characteristics of the PA for which it compensates. Thus the compensating apparatus can be configured to emulate the models in both  FIGS. 8 and 11 .  
      As remarked earlier, one preferred embodiment of the compensating apparatus is as an RF-ASIC, also referred to as an APE.  
      It has been realised that the block diagram in  FIG. 11  and the block diagram in  FIG. 8  can be constructed using the same RF-ASIC components. Each block diagram can be emulated as a special case (see  FIGS. 14 and 15  respectively).  
      The APE provides predistortion and equalisation in Feed Forward loops. The benefits of this solution are summarised as follows:  
      Firstly the predistortion, improves both the efficiency and the spectral purity of the main amplifier.  
      Secondly, the non-linear equalisation can adapt to the frequency-variant compression characteristics of the main amplifier.  
      Thirdly, the error power is reduced; smaller error amplifier is required which has larger bandwidth and smaller electrical delay and delay ripple.  
      Finally, very short output matching delay is needed, hence the output loss is lower, and the cancellation is better. The filter delay line may be replaced with low cost coax or a printed track.  
      A further advantage of the present invention is that the same RF-ASIC can be configured either as a 5 th  order predistorter or as a 3 rd  order non-linear equaliser.  
      The structure of one implementation of the APE RF-ASIC can be described with reference to either of FIGS.  14  or  15 , the same reference numerals are used in both Figures for like components. An RF signal  1002  is phase-split into an in-phase  1006  and a quadrature component  1008  (I and Q) by a phase-splitter  1004 . The two components  1006 , 1008  are input into respective multipliers  1010 , 1010 ′. Each multiplier squares the amplitude value for the corresponding component and the squared amplitudes are summed at an adder  1030  to give an X 2  signal. The X 2  signal itself is fed to a further multiplier  1020  where the X 2  value is squared again to give a X 4  signal.  
      Consider now the treatment of the in-phase component  1006  only. A symmetrical treatment is given to the quadrature phase component  1008 . Three combiners  1040 , 1050 , 1060  are provided each suitable for combining an RF signal with a corresponding coefficient provided by a controller device (not shown). The first of these combiners  1040  takes a first coefficient  1102  and the X 2  signal as input and generates a first combined signal  1202 . The second combiner  1050  takes a second coefficient  1104  and an external signal  1025  as input and generates a second combined signal  1204 . The first and second combined signals  1202 , 1204  are added by an adder  1070  to give a sum  1076 . The sum  1076  and the in-phase component  1006  are input into a multiplier  1080 : the result being a first summand  1086 .  
      The in-phase component  1006  is also input into the third combiner  1060  where it is combined with a third coefficient  1106 . The output of the third combiner  1060  is a second summand  1206 . The symmetrical quadrature path results in two further summands  1088 ,  1216 . All four summands are summed in an adder  1090 . The output of the adder  1090  is a predistorted signal  1092 . Provided the input coefficients are appropriate to a given PA, the predistorted signal  1092  should be compensated for at least some of the dominant mixing products in the PA transfer characteristics.  
      For completeness the quadrature path is also described. There are three more combiners  1040 ′,  1050 ′,  1060 ′, each suitable for combining an RF signal with a corresponding coefficient provided by a controller device (not shown). The fourth combiner  1040 ′ takes a first coefficient  1112  and the X 2  signal as input and generates a fourth combined signal  1212 . The fifth combiner  1050 ′ takes a second coefficient  1114  and the external signal  1025  as input and generates a fifth combined signal  1214 . The fourth and fifth combined signals  1212 , 1214  are added by an adder  1070 ′ to give a sum  1078 . The sum  1078  and the quadrature component  1008  are input into a multiplier  1080 : the result being the third summand  1088 .  
      The quadrature component  1008  is also input into the sixth combiner  1060 ′ where it is combined with a sixth coefficient  1116 . The output of the sixth combiner  1060 ′ is the fourth summand  1216 .  
      In the examples of configurations of the RF-ASIC, the first and fourth coefficients  1102 , 1112  are 3 rd  order coefficients K ( 3) x1 . Likewise the third and sixth coefficients  1106 , 1116  are 1 st  order coefficients K (1)   x .  
      The RF-ASIC is thus, with little rearrangement, configurable as either a 5th order polynomial predistorter, in which case the external signal  1025  is the X 4  signal generated at the multiplier  1020 , or a 3rd order equaliser, in which case the external signal  1025  is the X 2  signal delayed by an external circuit  1502 . The second and fifth coefficients  1104 , 1114  supplied to the second and fifth combiners  1050 , 1050 ′ are 5 th  order K ( 5) x  or 3 rd  order K ( 3) 1  respectively.  
      Note that the X 2  and X 4  signals are taken off-chip and the X 4  signal is routed back in the  FIG. 14  arrangement.  
      For narrowband applications (BW 5 MHz to 20 MHz), the dispersion of the non-linearity in the PA over frequency may be negligible. In this case, it is advantageous to configure the RF-ASIC as a 5th order polynomial predistorter. This configuration is shown in  FIG. 14 .  
      For wider bandwidth applications (BW=30 MHz-100 MHz), the compression characteristics of the main amplifier may vary over frequency. In these cases, better cancellation is achieved by configuring the RF-ASIC for 3rd order equalisation of the transfer function. This arrangement is shown in  FIG. 15 .  
      This arrangement implements the envelope-dependent term in equation 2 described above and is equivalent to the model in  FIG. 11 . T 1  delay is realised by an external LC circuit  1502  in this example.  
      It should be noted, that two or more APE RF-ASIC circuits can be cascaded to realise more complicated impulse responses. It is also possible to include carrier frequency dependent terms in the RF-ASIC.  
      In a further embodiment of the present invention, two RF-ASIC blocks are arranged to compensate for both envelope and carrier frequency effects. An illustration of such a configuration is shown in  FIG. 16 .  
      In yet another embodiment of the present invention, an APE is incorporated in a feed forward loop. This embodiment is illustrated is shown in  FIG. 17 .  
      The error signal is detected and applied to a microcontroller (PIC). The search algorithm (e.g. perturbation loop) may be coded into the PIC, which also includes all the necessary ADC/DAC converters.  
      The APE also fulfils the functionality of the vector modulator in the cancellation loop. This is accomplished by the complex K1 coefficient.  
      It has been shown that memory effects are generally weak in well-designed power amplifiers. The carrier frequency dependent terms can usually be neglected. The APE predistorter can compensate for the envelope frequency dependent terms, if necessary.  
      The APE technique improves both the bandwidth and the efficiency of feed forward amplifiers whilst also reducing the costs of hardware. The APE is a key technique for the implementing multi-carrier power amplifier that simultaneously covers the full RF DCS/PCS/FDD bandwidths.