United States Patent (19)
`Jeckeln et al.
`
`54 ADAPTIVE DIGITAL PREDISTORTION FOR
`POWER AMPLIFIERS WITH REAL TIME
`MODELING OF MEMORYLESS COMPLEX
`GAINS
`
`75 Inventors: Ernesto G. Jeckeln; Fadhel M.
`Ghannouchi, both of Montreal;
`Mohamad A. Sawan, Laval, all of
`Canada
`73 Assignee: Amplix, Montreal, Canada
`
`21 Appl. No.: 08/877,479
`22 Filed:
`Jun. 17, 1997
`(51) Int. Cl. .................................................. HO3F 1/26
`52 U.S. Cl. ............................................. 330/149; 332/103
`58 Field of Search ............................. 330/149; 332/103,
`332/107,123, 159, 160; 375/297; 455/63,
`126
`
`56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`4,291,277 9/1981 Davis et al. ............................ 330/149
`4,700,151 10/1987 Nagata ...................................... 332/18
`4,985,688
`1/1991 Nagata .
`... 332/123
`5,049,832 9/1991 Cavers ......
`... 330/149
`5,113,414 5/1992 Karam et al. ............................. 375/60
`5,119,040 6/1992 Long et al. ...
`... 330/149
`5,148,448 9/1992 Karam et al. ............................. 375/60
`5,237,288 8/1993 Cleveland .....
`... 330/107
`5,262,734 11/1993 Dent et al. ................................ 330/52
`5,396,190 3/1995 Murata .................................... 330/149
`5,404,378 4/1995 Kimura .........
`... 375/296
`5,420,536 5/1995 Faulkner et al.
`... 330/149
`5,491,457 2/1996 Feher ............
`... 332/103
`5,524.285
`6/1996 Wray et al. ............................. 455/126
`5,524,286 6/1996 Chiesa et al. ........................... 455/126
`5,568,088 10/1996 Dent et al. ...
`... 330/151
`5,598,436
`1/1997 Brajal et al. ..
`... 375/297
`5,650,758 7/1997 Xu et al. .......
`... 330/149
`5,699,383 12/1997 Ichiyoshi.
`... 375/297
`OTHER PUBLICATIONS
`E.G. Jeckeln, F.M. Ghannouchi and M. Sawan, “Adaptive
`Digital Predistorter for Power Amplifiers with Real Time
`Modeling of Memoryless Complex Gain", IEEE MTT-S
`
`US006072364A
`Patent Number:
`11
`(45) Date of Patent:
`
`6,072,364
`Jun. 6, 2000
`
`International Microwave Symposium, San Francisco, Jun.
`1996.
`E.G. Jeckeln, F.M. Ghannouchi and M. Sawan, “Adaptive
`Digital Predistorter for Power Amplifiers with Real Time
`Modeling of Memoryless Complex Gain", IEEE Transaction
`on Microwave Theory and Thechniques (submitted, Mar. 29,
`1996).
`J.G. Proakis, “Digital Communications”, McGraw Hill,
`1983.
`J.H. Mathews, “Numerical Methods”, for Computer Sci
`ence, Engineering, and Mathematics, McGraw Hill, 1989.
`“Adaptive Linearization of Power Amplifiers in Digital
`Radio Systems’” Saleh et al., The Bell System Technical
`Journal, vol. 62, No. 4, Apr. 1983 pp. 1019–1033.
`(List continued on next page.)
`Primary Examiner Robert Pascal
`Assistant Examiner Khanh Van Nguyen
`Attorney, Agent, or Firm-Griffin, Butler, Whisenhunt &
`Szipl, LLP
`ABSTRACT
`57
`In an adaptive method and device for predistorting a signal
`to be transmitted, Supplied by a signal Source to an input of
`a power amplifier having a output for delivering an ampli
`fied output Signal, the following Steps are conducted: pre
`distorting the Signal to be transmitted by means of cascaded
`predistortion amplitude and phase look-up tables interposed
`between the Signal Source and the input of the power
`amplifier, producing a first feedback signal in response to the
`predistorted Signal, producing a Second feedback signal in
`response to the amplified output signal from the power
`amplifier, delaying the first feedback Signal for eliminating
`any time lag between the first and Second feedback Signals,
`and real time modeling the predistortion amplitude and
`phase look-up tables in response to the first and Second
`feedback signals in order to update these two tables. The
`position of the delay circuit (delaying step), that permits the
`use of the real time modeling procedure, eliminates the
`convergence time and the requirement for any iterative
`algorithms.
`
`18 Claims, 4 Drawing Sheets
`
`-
`
`--------------
`
`
`
`
`
`14
`
`16QAM
`SOURCE
`
`PULSE
`SHAPING
`FILTER
`
`PREDISTORTER -4.
`TABLE
`
`
`
`
`
`
`
`
`
`
`
`a
`
`m
`
`was
`
`- a--
`
`- -
`
`Vd exp (iid)
`
`6
`
`QUADRATURE
`MODULATOR
`
`
`
`PETITIONERS EXHIBIT 1014
`Page 1 of 13
`
`

`

`6,072,364
`Page 2
`
`OTHER PUBLICATIONS
`
`“A New Baseband Linearizer for More Efficient Utilization
`of Earth Station Amplifiers Used for QPSK Transmissions”
`Girard et al., IEEE J. on Selec. Areas in Comm. Vol. Sac-1,
`No. 1, Jan. 1983, pp. 46-56.
`“Adaptation Behavior of a Feedforward Amplifier Linear
`izer” J.K.Cavers, IEEE Trans. on Vehicular Technology, vol.
`44, No. 1. Feb. 1995, pp. 31-40.
`“A Wide-Band Feedforward Amplifier”. Meyer et al., IEEE
`Journal of Solid-State Circuits vol. SC-9, No. 6, Dec. 1974,
`pp. 422–428.
`“Direct Conversion Transceiver Design for Compact Low
`Cost Portable Mobile Radio Terminals' Bateman et al.,
`Center for Communications Research, U. of Bristol, pp.
`57–62, 1989.
`“Novel Linearizer Using Balanced Circulators aand Its
`Application to Multilevel Digital Radio Systems”. Imai et al.,
`IEEE Trans. on Micro. Theory and Tech. vol. 37, No. 8, Aug.
`1989 pp. 1237–1243.
`
`“An assessment of the Performance of Linearisation
`schemes in the Australian Mobilesat System by simulation”
`T.A.Wilkinson, 6th Int’l Conf. on Mobile Radio and Per
`sonal Comm. UK 1991, pp. 74-76.
`“Linear Amplification Technique for Digital Mobile Com
`munications' Y.Nagata, Comm. Res. Lab. C&C Systems
`Res. Labs. 1989, pp. 159–164.
`“Amplifier Linearization Using a Digital Predisorter with
`Fast Adaptation and Low Memory Requirements' J.K.
`Cavers, IEEE Trans. on Vehic.Tech. vol. 39, No. 4, Nov.
`1990, pp. 374-382.
`“Adaptive Linearisation Using Pre-Distortion” Faulkner et
`al. CH2846–4/90/0000-0035 1990 IEEE, pp. 35–39.
`“Analysis and Compensation of Bandpass Nonlinearities for
`Communications' Kaye et al., IEEE Trans. on Communi
`cations, Oct. 1972, pp. 965–972.
`“Signal Processing WorkSystem' Communications Library
`Reference, Alta Group of Cadence Design Systems, Inc,
`Mar. 1995, pp. i-iii, pp. iv-xiv.
`
`PETITIONERS EXHIBIT 1014
`Page 2 of 13
`
`

`

`U.S. Patent
`U.S. Patent
`
`
`
`Jun. 6, 2000
`
`Sheet 1 of 4
`
`6,072,364
`6,072,364
`
`AYNLVYOVNO
`
`YOLVINGON
`
`
`
`YOLVINGOWS[gry
`SYNLVYCVNO
`
`WVO91
`[oePAPA4
`
`|9}
`
`(Qf)dxawp
`
`ONIdVHS
`
`ysl
`
`Asind
`
`JONNOS
`
`PETITIONERS EXHIBIT 1014
`Page 3 of 13
`
`PETITIONERS EXHIBIT 1014
`Page 3 of 13
`
`

`

`U.S. Patent
`
`Jun. 6, 2000
`Sheet 2 of 4
`FIG2a
`
`6,072,364
`
`- 0.18
`
`0. O 9
`
`O
`
`O 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
`input Vrms
`
`FIG.2b
`
`0.18
`
`0. O 9
`
`0.35
`0.3
`
`0.25
`
`0. 2
`
`O 15
`
`0. 1
`
`O
`
`-0.05
`
`0.35
`
`0.3
`
`0.25
`
`0. 2
`
`O 15
`
`0. 1
`
`0.05
`
`-0.05
`
`O
`
`0.05
`
`0.15
`0.1
`Input Vrms
`
`0.2
`
`0.25
`
`- AM-AM
`- - - - AM-PM
`RTM
`
`PETITIONERS EXHIBIT 1014
`Page 4 of 13
`
`

`

`U.S. Patent
`
`Jun. 6, 2000
`Sheet 3 of 4
`FIG.3a
`
`6,072,364
`
`0.25
`
`0.2
`
`2 0.15
`S 0.1
`O
`
`0.05
`
`O
`-0.05
`
`O
`
`0.15
`0.1
`0.05
`Input Vrms
`
`0.2
`
`0.25
`
`ooo RTM23 samples
`Pred function
`
`FG.3b
`
`
`
`o
`
`0.05
`
`0.15
`0.
`input Vrms
`
`0.2
`
`0.25
`
`ooo RTM23 samples
`Pred function
`
`PETITIONERS EXHIBIT 1014
`Page 5 of 13
`
`

`

`U.S. Patent
`
`Jun. 6, 2000
`
`Sheet 4 of 4
`
`6,072,364
`
`
`
`
`
`s
`
`º? HEIHOISIGEdd
`
`PETITIONERS EXHIBIT 1014
`Page 6 of 13
`
`

`

`6,072,364
`
`1
`ADAPTIVE DIGITAL PREDISTORTION FOR
`POWER AMPLIFIERS WITH REAL TIME
`MODELING OF MEMORYLESS COMPLEX
`GAINS
`
`BACKGROUND OF THE INVENTION
`
`2
`Techniques, vol. 37, no. 8, pp. 1237-1243, August
`1989), this technique has historically been the most
`common method in analog implementation. This
`method uses a nonlinear element which precedes the
`device to be compensated, its gain-expansion charac
`teristic cancels the gain compression of the amplifier.
`Like feed-forward, it has an open loop configuration
`and therefore is very sensitive to drifts.
`In recent years, the technology progreSS of Digital Signal
`Processors (DSP) has been one of the motive of the immi
`nent course toward digital modulation techniques. Actually,
`the digital Signal can be processed in Such a way that greater
`bandwidth efficiency and Voice quality can be obtained. In
`addition various applications Such as generation of accurate
`gain and phase matching in two quadrature modulating
`Signals, real-time compensation for channel impairments
`and the benefits of fast computational machines have moti
`Vated the use of these processors in Several methods of
`linearization. These techniques are called Digital Lineariza
`tion Techniques.
`One of the features of the digital techniques is the control
`against the effects of drift. It is well known, that the power
`amplifier characteristic are quite Sensitive to temperature
`variation and Some unbalance in the linearization proceSS
`can be occurred. In order to overcome this problem and
`avoid the effect of device power Supply precision and drifts
`produced by Switching between channels, adaptability is
`needed. In this way, an adaptive digital predistorter is the
`most promising technique that can be applied to narrow
`band Personal Communication Service using a DSP. The
`first Successful work was presented by Y. Nagata, "Linear
`Amplification Technique for Digital Mobile
`Communications', in Proc. IEEE Veh. Technol. Conf. Sans
`Francisco, Calif., pp. 159-164, 1989 using a two
`dimensional Look-Up Table (LUT) technique with adaptive
`digital feedback at baseband and pulse shaping filter prior to
`predistortion. This technique has shown the advantage that
`any order of nonlinearity and any modulation format can be
`supported. Followed later by J. Cavers, “Amplifier Linear
`ization Using a Digital Predistorter with Fast Adaptation and
`Low Memory Requirement”, IEEE Transactions on Vehicu
`lar Technology, vol.39, no. 4, pp. 374-382, November 1990
`and M. Faulkner, T. Mattsson and W. Yates, “Adaptive
`Linearization Using Predistortion”, in Proc. 40th IEEE Veh.
`Technol. Conf. pp. 35-40, 1990, several drawbacks were
`eliminated using a one-dimensional table. This has made
`possible that leSS memory is needed and therefore, the
`convergence time has been reduced. These previous tech
`niques were based on iterative algorithms.
`An interesting idea was proposed by T. Wilkinson, “An
`Assessment of the Performance of Linearization Schemes in
`the Australian Mobilsat System by Simulation', IEE 6th Int.
`Conf. on Mobile Radio, London, pp. 74-76, 1991 using two
`look-up tables, one for the amplitude and the Second for the
`phase. Each LUT includes one hundred entries covering the
`range of input levels and linear interpolation is used to
`determine values between entries. This later technique does
`not consider any adaptability dedicated to drift correction.
`OBJECTS OF THE INVENTION
`An object of the present invention is therefore to eliminate
`the above described drawbacks of the prior art, in particular
`to eliminate the convergence time and the need for iterative
`algorithms.
`SUMMARY OF THE INVENTION
`More Specifically, in accordance with the present
`invention, there is provided an adaptive method for predis
`
`1. Field of the Invention
`The present invention relates to an adaptive predistortion
`method and device for power amplifiers dedicated in par
`ticular but not exclusively to spectrally efficient microwave
`mobile communication equipments.
`2. Brief Description of the Prior Art
`With the increasing demand on the RF and microwave
`Spectrum, caused by the proliferation of wireleSS commu
`nications and Satellite networks, more Spectrally efficient
`modulation techniques will have to be developed. Linear
`modulation methods, like M-ary QAM, meet this require
`ment with high units of bits per second per Hertz. But since
`it has a high envelope variation, their performance is
`Strongly dependent on the linearity of the transmission
`System. In addition, modern wireleSS radio Systems like
`mobile cellular and emerging Personal Communication SyS
`tems (PCS) require a high power efficiency to extend the
`battery life of the portables. To maximize the power added
`efficiency and the power output, the power amplifier is often
`operated near Saturation where the input/output power char
`acteristics become nonlinear. Unfortunately, if linear modu
`lation with fluctuating envelope is used in conjunction with
`a highly efficient nonlinear amplification, distortion and
`Spectral spreading into adjacent channels will occur. In order
`to reduce these undesired effects and meet the desired power
`and spectral efficiency, linearization techniques have been
`introduced.
`A variety of linearization methods have been reported and
`many different ways can be used to Segment this topic.
`FactorS Such as average transmitter power, operating
`bandwidth, power efficiency, adaptability and complexity
`are Significant considerations in design compromises that
`can be used to categorize the different techniques. In general,
`all these techniques are, by any measure, derived from three
`main types named:
`i) Feed-forward (R. Meyer, R. Eschenbach and W.
`Edgerley, Jr. “A wide-Band Feedforward Amplifier”,
`IEEE J. of Solid-State Circuits, vol. Sc-9, no. 6, pp.
`442-428, December 1974), which includes an open
`loop configuration, can handle a multicarrier Signal but
`can not easily be controlled against the effects of drift.
`Moreover, their low power efficiency make it suitable
`in base Station only. A good analysis of adaptation
`behavior has been presented in J. Cavers, "Adaptation
`Behavior of a Feed forward Amplifier Linearizer”,
`IEEE Transactions on Vehicular Technology, vol. 44,
`no. 1, pp. 31-40, February 1995;
`ii) Feedback (A. Bateman & D. Haines, “Direct Conver
`sion Transceiver Design for Compact Low-Cost Por
`table Mobile Radio Terminals.” IEEE Conf. pp. 57–58,
`1989), which presents an excellent reduction of out
`of-band emissions, is relatively easy to implement.
`However, stability requirement limits its bandwidth
`because of its critical dependence on the loop delay;
`and
`iii) Predistortion (N. Imai, T. Nojima and T. Murase,
`“Novel Linearizer Using Balanced Circulators and Its
`Application to Multilevel Digital Radio Systems”,
`IEEE Transactions on Microwave Theory and
`
`15
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`PETITIONERS EXHIBIT 1014
`Page 7 of 13
`
`

`

`6,072,364
`
`15
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`3
`torting a signal to be transmitted, Supplied by a signal Source
`to an input of a power amplifier having an output for
`delivering an amplified output Signal. This method com
`prises the Steps of predistorting the Signal to be transmitted
`by means of predistortion amplitude and phase look-up table
`means interposed between the Signal Source and the input of
`the power amplifier, producing a first feedback Signal in
`response to the predistorted Signal, producing a Second
`feedback signal in response to the amplified output Signal
`from the power amplifier, delaying at least one of the first
`and Second feedback signals for eliminating any time lag
`between these first and Second feedback Signals, and updat
`ing the predistortion amplitude and phase look-up table
`means in response to the first and Second feedback signals.
`Preferably, the delaying Step comprises delaying the first
`feedback signal in order to eliminate any time lag between
`the first and Second feedback Signals, the updating Step
`comprises real time modeling the predistortion amplitude
`and phase look-up table means in response to the first and
`Second feedback Signals, the real time modeling comprises
`using a linear or third-order cubic spline interpolation, and
`the predistorting Step comprises predistorting the Signal to
`be transmitted by means of cascaded one-dimensional pre
`distortion amplitude and phase look-up tables.
`Also in accordance with the present invention, there is
`provided an adaptive device for predistorting a Signal to be
`transmitted, Supplied by a Signal Source to an input of a
`power amplifier having an output for delivering an amplified
`output signal. The device comprises predistorter means
`comprising predistortion amplitude and phase look-up table
`means interposed between the Signal Source and the input of
`the power amplifier for amplitude and phase predistorting
`the signal to be transmitted, means for producing a first
`feedback signal in response to the predistorted Signal from
`the predistorter means, means for producing a Second feed
`back signal in response to the amplified output Signal from
`the power amplifier, delay means for eliminating any time
`lag between the first and Second feedback signals, and means
`for updating the predistortion amplitude and phase look-up
`table means in response to the first and Second feedback
`Signals.
`Advantageously, the updating means comprises means for
`real time modeling the predistortion amplitude and phase
`look-up table means in response to the first and Second
`feedback Signals, the predistortion amplitude and phase
`look-up table means comprises, in cascade, a one
`dimensional predistortion amplitude look-up table and a
`one-dimensional predistortion phase look-up table, and the
`delay means comprises means for delaying the first feedback
`Signal in order to eliminate any time lag between the first and
`Second feedback Signals.
`In accordance with a preferred embodiment:
`the Signal to be transmitted is a digital Signal;
`the predistortion amplitude and phase look-up table
`means are digital predistortion amplitude and phase
`look-up table means for producing a digital predistorted
`Signal;
`the adaptive signal predistorting device comprises a
`digital-to-analog converter for converting the digital
`predistorted Signal into an analog predistorted Signal
`and a quadrature modulator for converting the analog
`predistorted Signal into a microwave Signal Supplied to
`the input of the power amplifier; and
`the means for producing a Second feedback Signal com
`65
`prises a microwave coupler for Supplying a portion of
`the amplified output Signal of the power amplifier to a
`
`4
`quadrature demodulator producing, in response to this
`portion of the amplified output signal of the power
`amplifier, a demodulated analog signal and an analog
`to-digital converter for converting the demodulated
`analog signal into the Second feedback Signal, in digital
`form.
`According to another preferred embodiment of the
`invention, the Signal to be transmitted comprises an ampli
`tude component and a phase component, and the predistorter
`means comprises:
`the one-dimensional predistortion amplitude look-up
`table for producing a predistorted amplitude in
`response to the amplitude component of the Signal to be
`transmitted;
`the one-dimensional predistortion phase look-up table for
`producing a predistorted phase in response to the
`predistorted amplitude; and
`means for combining the phase component of the Signal
`to be transmitted, the predistorted amplitude and the
`predistorted phase into the predistorted Signal at the
`output of the predistorter means.
`Thanks to the position of the delay circuit, the conver
`gence time and the requirement for any iterative algorithms
`are eliminated through real time modeling and by using a
`linear or third-order cubic spline interpolation.
`The objects, advantages and other features of the present
`invention will become more apparent upon reading of the
`following non restrictive description of a preferred embodi
`ment thereof, given by way of example only with reference
`to the accompanying drawings.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`In the appended drawings:
`FIG. 1 is a block diagram of an adaptive digital predis
`torting device in accordance with the present invention,
`comprising a predistorter;
`FIG. 2a is a graph showing the AM-AM and AM-PM
`characteristics of a microwave power amplifier of class AB;
`FIG.2b is a graph comparing the AM-AM and AM-PM
`characteristics of a microwave power amplifier of class AB
`obtained by measurements and RealTime Modeling (RTM);
`FIG. 3a is a graph showing an interpolated amplitude
`predistortion function and 23 amplitude Samples obtained by
`Real Time Modeling;
`FIG. 3b is a graph showing an interpolated phase predis
`tortion function and 23 phase samples obtained by Real
`Time Modeling; and
`FIG. 4 is a block diagram of the predistorter of the
`adaptive digital predistorting device of FIG. 1.
`
`DETAILED DESCRIPTION OF THE
`PREFERRED EMBODIMENT
`Referring to FIG. 1 of the appended drawings, a preferred
`embodiment of the adaptive digital predistorting device
`according to the invention is presented. This adaptive digital
`predistorting device is generally identified by the reference
`1.
`As shown in FIG. 1, the amplifier system 17 includes an
`adaptive digital predistorting device 1 comprising: a predis
`torter 2 including a one-dimensional predistortion amplitude
`look-up table 3 and a one-dimensional predistortion phase
`look-up table 4; a digital-to-analog (D/A) converter 5; a
`quadrature modulator 6; a microwave coupler 7; a quadra
`ture demodulator 8; an oscillator 9; an analog-to-digital
`
`PETITIONERS EXHIBIT 1014
`Page 8 of 13
`
`

`

`6,072,364
`
`6
`Then, the memoryleSS complex gain of the power ampli
`fier 13 is given by the following relation:
`
`5
`
`Now, considering the complex gain of the predistorter 2 in
`a Sub-System whose output is the input Signal of the micro
`wave power amplifier 13, the resulting predistorted Signal
`can be written as follows:
`
`S
`(A/D) converter 10; a delay circuit 11; and a Real Time
`Modeling (RTM) circuit 12.
`The amplifier system 17 further comprises a microwave
`power amplifier 13 to amplify the microwave Signal from
`the quadrature modulator 6.
`In the illustrated example, the Spectrally efficient
`16-QAM modulation method is used by a source 14 to
`produce a 16-QAM modulated signal 15 to be transmitted.
`Of course, it is within the Scope of the present invention to
`use another type of Source. Signal 15 is passed through a
`pulse shaping circuit 16 ensure Free-Symbol-Interference
`(FSI).
`A microwave power amplifier used in mobile
`communication, Such as power amplifier 13 of FIG. 1, must
`operate close to Saturation to achieve both high power
`efficiency and high transmitted power. The microwave
`power amplifier 13 is Said to be Saturated when its output
`power level no longer increases in response to an increase of
`its input power level. Close to the Saturation region, the
`input/output characteristic of the microwave power ampli
`fier 13 becomes nonlinear and, therefore, amplitude and
`phase distortion are generated when digital modulation with
`fluctuating envelope is used. These effects are identified
`within the modulated Signal as additional amplitude and
`phase modulations that may degrade the Bit-Error-Rate
`(BER) performance of the modulation scheme. In addition,
`a time invariant microwave power amplifier can be classified
`as having either Zero memory or non Zero memory. If the
`microwave amplifier 13 is wideband in comparison to the
`input Signal, it is considered as having Zero memory and its
`input-output characteristic can be given by the following
`relation:
`
`(5)
`where V(t) and CIV(t) are the predistorted amplitude and
`phase respectively.
`Then, the output signal of the power amplifier 13 will be:
`
`From equations (2) and (6), one can see that the conditions
`that must be satisfied to properly correct the AM and PM
`distortions are:
`
`where K is the expected constant gain of the power amplifier
`13 and V(t) is the amplitude modulation of the input signal
`to be amplified, i.e. Supplied to the power amplifier 13.
`A) Equivalent Low Pass Signal
`The complex envelope method as described by Signal
`Processing WorkSystem (SPW), Alta Group of Cadence
`Design System, Inc., 1996, using the concepts of equivalent
`lowpass signals and Systems, has been used to analyse and
`simulate the amplifier system 17. More specifically, the
`representation of bandpass Signals and Systems can be given
`in terms of equivalent lowpass waveforms under the condi
`tion that their bandwidths are much smaller than the carrier
`frequency (J. G. Proakis, “Digital Communications”,
`McGraw Hill, 1983). In this case, the equivalent lowpass
`Signal must be derived from their modulated passband
`counterparts. The modulated carrier Signal x(t) can be writ
`ten aS:
`
`(9)
`x(t)=ReV(t)ei2 "?et" (O-ReV(t)eice?? "fe
`where V(t) is the amplitude modulation, p(t) is the phase
`modulation, f is the carrier frequency, and Redenotes the
`real part of the quantity in brackets. The complex envelope
`of the bandpass signal or the equivalent lowpass complex
`Signal S(t) is given by:
`
`This is an equivalent polar representation where V(t) is the
`amplitude modulation and p(t) is the phase modulation of
`the baseband Signal. The advantage to model the microwave
`Signal and the linearized power amplifier 13 at baseband is
`that it simplifies the analysis and reduces dramatically the
`number of iterations during Simulation when the amplifier
`system 17 is analysed.
`In this manner, equation (10) can be treated as an equiva
`lent lowpass signal. Then, in order to map the information
`into a corresponding Set of discrete amplitudes and phases,
`the Signal waveforms may be represented as:
`
`15
`
`25
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`where y(t) is the output signal of the microwave power
`amplifier, X(t) is the input signal of the same amplifier, and
`T is the memoryleSS complex gain of that microwave power
`amplifier.
`In this way, a memoryleSS nonlinearity of the microwave
`power amplifier 13 can be considered because of the narrow
`band of the baseband signal relative to the bandwidth of the
`power amplifier 13. Then, the memoryleSS complex gain T
`is expressed as a function of the amplitude only, hence the
`possibility to use a one-dimensional look-up table during the
`predistortion procedure; this means that the nonlinearity of
`the power amplifier 13 is independent of the frequency and
`phase of the microwave signal. Therefore, the memoryleSS
`complex gain T is modeled through the amplitude transfer
`characteristic AM-AM of the power amplifier 13 and the
`AM-PM conversion factor of the same amplifier as shown in
`FIG. 2a. Let the input signal of the microwave power
`amplifier 13 be:
`(2)
`S(t)=V(t) coscot--0(t)
`where V(t) is a time-dependent amplitude, () is the angular
`frequency of the input signal, t is a time variable, and 0(t) is
`a time-dependent phase shift of the input Signal.
`The output signal may then be expressed as follows:
`
`where:
`GIV(t) is the AM-AM amplitude transfer characteristic
`of the power amplifier 13; and
`(pV(t) is the AM-PM conversion factor of the power
`amplifier 13.
`
`65
`
`where Vcp,m=1,2,3,....M represent the M possible
`Symbols in the signal-space diagram and u(t) is the wave
`form impulse response of the pulse Shaping filter 16. The
`
`PETITIONERS EXHIBIT 1014
`Page 9 of 13
`
`

`

`6,072,364
`
`7
`term u(t) is Selected to control the spectral characteristics of
`the transmitted Signal. In general, the equivalent lowpass
`complex Signal that must be transmitted over the power
`amplifier 13 can be written in time domain as:
`
`&
`S(t) = X. V, en u(t-nT)
`
`=l
`
`(12)
`
`where {V.cp, represents the sequence of transmitted infor
`mation Symbols that change at the Signalling intervals nT,
`n=1,2,3,..., and T is the Symbol period.
`B) Real Time Modeling (RTM)
`In order to capture and eliminate the higher intermodu
`lation levels generated by the power amplifier 13, equation
`(12) must be oversampled according to the bandwidth to be
`compensated. To Simplify the analysis, we can model a
`discrete Signal through the impulse Sampling representation
`considering the Sample-data as a number occurring at a
`Specific instant of time. In this case, the discrete Signal may
`be represented as a Sequence of impulse functions of the
`form:
`
`15
`
`&
`
`S(n) =XVey(n - iT)
`
`i-l
`
`(13)
`
`25
`
`where y(n-iT) represents the impulse sampling at the Sig
`nalling intervals iT" (i=1,2,3,....), T is the sampling period
`and {V, p, are the discrete amplitudes and phases of the
`Signal trajectory in the Signal-space diagram.
`In this manner, using the equation (13), the equivalent
`lowpass of the amplifier input signal Ve', and the feedback
`signal (1/K)V'e' (FIG. 1), are oversampled to provide a
`number of data Samples. These pairs of complex Samples
`correspond to an ascending list of values of the amplitude of
`the input signal. These values must be spread out to cover
`the overall range of the input envelope levels and must
`Satisfy:
`(14)
`0s Vog Val-Voz. ... <V.
`Then, the Sequences of complex Samples can be written as:
`
`35
`
`40
`
`8
`Then, the memoryleSS complex gain of the power amplifier
`13 can be expressed as an equivalent complex envelope
`transfer function as follows:
`
`(20)
`T(t)=GV(t) lea
`where GIV(t) is obtained from the normalized gV(t)).
`FIG. 2b shows a comparison between the measured
`AM-AM and AM-PM characteristics and the Real Time
`Modeling (RTM) results of a class AB power amplifier 13.
`To this end, 23 complex samples of Real Time Modeling
`were used to interpolate the Memoryless Complex Gains
`(MCG) function. Of course, the present invention is usable
`with other classes of amplifiers.
`C) Predistortion
`Based on the above equations (7) and (8) that must be
`satisfied to ideally correct the AM and PM distortion, the
`optimal compensation made by predistortion can be
`achieved when the compensation envelope transfer function
`is given by:
`
`and the compensation phase characteristic is given by:
`
`Under these conditions, the Set of data points of amplitudes
`(V, V") from (15) and (16) are interchanged as (V.", V)
`and the Set of data points of phase distortion are put in
`opposition according to (22). Then, the updating of the
`one-dimensional amplitude and phase look-up tables 3 and
`4 is made in a form in which there is correspondence
`between input and output values of the look-up tables as
`illustrated by the following relation (23). It is important to
`note that the input amplitude V(t) and the predistorted input
`amplitude V(t) are used to point to an address of the look-up
`tables 3 and 4, respectively. These look-up tables 3 and 4
`implement a mapping from the input to the output, according
`to the number of Sampled pairs, using linear or cubic spline
`interpolation. If cubic spline interpolation is used, only a
`Small number of Sampled pairs are needed.
`
`W(t) -->
`
`V
`V2
`
`V
`
`| -
`
`Wii
`V2
`:
`
`Vaa
`
`-> V(t)
`
`(23)
`
`g
`
`XValealy(n-IT)
`
`=
`
`g
`
`X. Viety(n - IT)
`
`p
`
`(15)
`
`45
`
`(16)
`
`50
`
`V(t) - ||
`
`d
`Wii
`O2
`V2
`|-| |- a
`Vaa
`Ca
`
`=
`
`where q is the number of samples and V"=(1/K)V".
`From (15) and (16), the samples of phase distortion can be
`obtained as:
`
`(17)
`
`55
`
`Then, the set of data points (V1,V"), (V, V."), ... (V,
`60
`V") and (V1, (pl), (V2, p2), . . . (V. (P) are used to
`perform interpolations. These interpolations permit to deter
`mine both the relative envelope transfer functions gV(t)
`and the envelope dependent phase shift (pV(t) which are
`expressed as:
`
`65
`
`(18)
`(19)
`
`Referring to FIGS. 1 and 4, the 16-QAM modulated
`Signal from the pulse shaping filter 16 is Supplied to the
`predistorter 2. FIG. 4 is a Schematic block diagram showing
`a possible configuration of the predistorter 2 to obtain the
`predistorted power amplifier input Signal. In the case of FIG.
`2, a polar representation was chosen to configure the one
`dimensional predistortion amplitude and phase look-up
`tables 3 and 4 and these can be accessed in cascade form
`where the first and the Second tables generate the predis
`torted amplitude and phase respectively.
`As shown in FIG. 4, the 16-QAM modulated signal from
`the pulse Shaping circuit 16 has a phase component 0 and an
`amplitude component V(t). The phase component 0 is
`Supplied to a magnitude/phase-to-complex converter 19.
`
`PETITIONERS EXHIBIT 1014
`Page 10 of 13
`
`

`

`6,072,364
`
`1O
`
`15
`
`9
`The amplitude component V(t) is Supplied to the one
`dimensional predistortion amplitude look-up table 3 which
`then outputs the predistorted amplitude V(t).
`The predistorted amplitude V(t) is Supplied to the con
`verter 19 along with the phase component 0 to produce the
`signal V(t)e'. The predistorted amplitude V(t) is also
`Supplied as input signal of the one-dimensional predistortion
`phase look-up table 4 to produce the predistorted phase C.
`The predistorted phase C. is Supplied to one input of a
`multiplier 20 through a phase-to-complex converter 21. The
`other input of the multiplier 20 is supplied with the signal
`V(t)e'to produce the predistorted input signal V(t)e'
`(FIG. 1).
`The predistorted input signal V(t)e' is digital-to-analog
`converted by the D/A converter 5 and the digital-to-analog
`converted signal VA(t)e' is proces