Adaptive digital linearization of RF power
`amplifiers
`
`Linearisation adaptative numerique
`d'amplificateurs de puissance RF
`
`Anit Lohtia, Paul A. Goud and Colin G. Englefield,
`TR Labs and Department of Electrical Engineering, University of Alberta, Edmonton, Alta. T6G 2G7
`
`The performance of an adaptive digital technique for the linearization of RF power amplifiers is investigated. Cubic spline interpolation is used to estimate
`the amplifier's AM-AM and AM-PM characteristics. Using the computed characteristic coefficients, the baseband input signal is appropriately predistorted
`to compensate for the amplifier nonlinearity. This method has significantly better suppression of the intermodulation products than other predistortion
`techniques. The out-of-band power emission is also significantly reduced. The performance of baseband predistortion linearization techniques is adversely
`affected by modulator and demodulator impairments. A digital correction technique is presented to compensate for these imperfections. In this technique,
`part of the RF signal is fed to an envelope detector. The detector output and the baseband signal are used to estimate the impairment values, using the
`Newton-Raphson method. The estimated impairment values are then used to compensate for the modulator/demodulator impairments. Spurious signals can
`be suppressed by more than 30 dB using this technique.
`
`Cet article traite de la performance d'une technique adaptative numlrique pour la linearisation d'amplificateurs de puissance RF. Une interpolation spline
`cubique est utilised pour estimer les caractlristiques AM-AM et AM-PM de l'ampliflcateur. A partir des coefficients calculus, le signal d'entrle en bande
`de base est prfctistorsionne' en vue de compenser la non-linlarite' de l'ampliflcateur. Cette m&hode rlsulte en une suppression significativement meilleure
`des produits d'intermodulation que d'autres techniques de prldistorsion, et la puissance 6mise hors bande est Igalement rlduite de maniere significative.
`La performance des techniques de linearisation par prldistorsion en bande de base est affectle par les imperfections du modulateur et du dlmodulateur, et
`une technique de correction numlrique est prlsentle pour leur compensation, dans laquelle une partie du signal RF est envoyle a un dltecteur d'enveloppe.
`La sortie du dltecteur et le signal en bande de base sont utilises pour estimer la valeur des imperfections avec la mlthode Newton-Raphson, et pour
`compenser les imperfections du modulateur/dlmodulateur. Le niveau des signaux non-dlsires peut £tre r£duit de plus de 30 dB.
`
`I. Introduction
`
`Analogue wireless cellular telephone systems, specifically, AMPS
`(Advanced Mobile Phone Service), NMT (Nordic Mobile Telephone)
`and TACS (Total Access Communication System), all use frequency
`modulation. Since a frequency-modulated signal has a constant enve­
`lope, a power-efficient RF amplifier can be used to amplify the signal
`without generating intermodulation distortion products. However,
`frequency modulation is not spectrally efficient. Linear modulation
`techniques are spectrally more efficient than frequency modulation.
`The North American interim standard (IS-54) specifies jrV4-shifted
`differentially encoded quadrature phase-shift keying (rc/4-DQPSK) as
`the modulation method for digital cellular systems [1]. While jt/4-
`DQPSK modulation is spectrally efficient, it also gives rise to an RF
`signal that has a fluctuating envelope. Nonlinear amplification of such
`a modulated signal leads to intermodulation distortion products and
`spectral spreading. Therefore, to keep the out-of-band power emission
`below the limits specified by the IS-54 standard, a highly linear RF
`power amplifier is required to amplify a TT/4-DQPSK modulated signal.
`
`A simple way to achieve linear amplification is to back off the
`amplifier, so that it operates in the linear region of its transfer charac­
`teristic. However, using an amplifier in this way provides a low dc-to-
`RF conversion efficiency. A main challenge in RF power amplifier
`design is to maintain linearity without compromising the power effi­
`ciency of the amplifier.
`
`A number of techniques for the linearization of RF power amplifi­
`ers have been reported in the literature. These techniques normally fall
`into one of the following categories: 1) feedforward, 2) linear amplifi­
`cation using nonlinear components (LINC), 3) negative feedback, and
`4) predistortion. Feedforward correction [2] has an open-loop configu­
`ration; hence, it is unconditionally stable and is inherently capable of
`
`Can. J. Elect. & Comp. Eng., Vol. 20, No. 2,1995
`
`wide-band signal amplification. However, this technique cannot adapt
`to drifts in the amplifier characteristic which may occur due to tem­
`perature variation, change in power supply voltage, frequency change,
`etc. The LINC method [3]-[4] uses two well-matched amplifiers. The
`input signal is split into two constant-amplitude phase-modulated
`signals which are then amplified separately using two nonlinear RF
`amplifiers. These signals are then passively summed in such a way
`that their undesired components are in anti-phase, so that they cancel.
`LINC requires two well-matched amplifiers, which may not be easy to
`obtain. Also, this method cannot adapt to drifts in the amplifier charac­
`teristics. A modification of the LINC technique, the Combined Ana­
`logue Locked Loop Universal Modulator (CALLUM) [5], uses
`feedback from the output to compensate for drifts in the characteristics
`of the amplifiers. Cartesian coordinate negative feedback linearization
`[6]-[7] uses synchronously demodulated signals as the feedback infor­
`mation. These signals are subtracted from the baseband input signals
`to generate loop error signals. If the loop gain is sufficiently high, the
`feedback loop will continuously correct for the nonlinearity. This tech­
`nique is comparatively simple to implement, but the resulting linearity
`and bandwidth are critically dependent on the loop time delay.
`Predistortion techniques [8]-[ll] operate on the basis of providing an
`appropriately distorted signal to the amplifier, so that the amplifier
`output is simply a scaled replica of the original input signal. Some
`predistortion techniques use fixed signal predistortion circuits prior to
`amplification. Such circuits cannot compensate for drifts in the ampli­
`fier nonlinearities. Several transmitter-based recursive algorithms have
`been developed to adapt to drifts in the amplifier characteristics. Cavers
`[10] proposed a complex gain predistorter that takes advantage of the
`amplitude dependence of the amplifier distortion. This technique uses
`the secant method to obtain and update the predistortion coefficients.
`This algorithm, however, is sensitive to the initial conditions, which
`can prevent convergence [11].
`
`Authorized licensed use limited to: James Proctor. Downloaded on December 18,2024 at 23:18:19 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1021
`Page 1 of 7
`
`

`

`66
`
`CAN. J. ELECT. & COMP. ENG., VOL. 20, NO. 2, 1995
`
`This paper presents a new adaptive predistortion technique for RF
`power amplifier linearization. The AM-AM and AM-PM characteris­
`tics of the amplifier are estimated using cubic spline interpolation,
`from a look-up table of distortion values that are obtained directly
`from the amplifier itself using synchronous demodulation. These esti­
`mated characteristics are then used to predistort the input signal. In
`this paper, the performance of this technique is compared with that of
`the cartesian coordinate negative feedback and complex gain
`predistortion techniques, using intermodulation products and out-of-
`band power emission as the key criteria.
`
`A quadrature modulator is required to generate the modulated RF
`signal for transmission. As well, a quadrature demodulator recovers
`the baseband feedback signal from the output RF signal. Analogue
`quadrature modulators and demodulators have three major impair­
`ments; namely, gain imbalance, phase imbalance and dc offset. These
`impairments generate spurious signals that will degrade the perform­
`ance of a baseband feedback linearization method. This paper also
`presents a technique for compensating these quadrature modulator and
`demodulator impairments. For representative modulator/demodulator
`impairment values, the overall improvement of amplifier linearity is
`also presented.
`
`II. Proposed RF power amplifier linearizer
`
`A block diagram of a transmitter with the proposed linearizer is
`shown in Fig. 1. The signal source bits, generated as a pseudorandom
`sequence of length 231 - 1, are encoded, in pairs, into the in-phase (/*)
`and quadrature (qj) components of the transmitted symbols. An over
`sampling rate of 16 samples/symbol was used. The i* and qk compo­
`nents pass through a pulse-shaping filter. The square of the magnitude
`of the resulting complex signal, | v*|2, is a pointer to a look-up table
`that contains predistortion coefficients for the i and q channels. The
`signal (/*, qk) is a vector multiplied by the appropriate complex
`predistortion coefficient to generate the predistorted signal (ip, qp),
`which in turn is converted to two analogue signals by a pair of D/A
`converters. These analogue signals drive a quadrature modulator that
`generates the RF signal. The input to the amplifier can be written as
`
`2)m cos (a>c* - <$>p),
`2 + qp
`x(t) = (ip
`(1)
`where <J>p = \axrx[qplip], and <oc is the carrier frequency. A portion of
`the amplifier output is synchronously demodulated to generate a pair
`of baseband signals, which are converted to digital signals, id and qd,
`using A/D converters. The quadrature demodulator outputs, id and q&
`are compared with the inputs to the quadrature modulator, ip and qp.
`To estimate the AM-AM and AM-PM characteristics, let
`
`v,= [«>2 + ?„2],/2.
`
`fa = tan-1 [#*/«*],
`
`<t> = 4>rf- 4>p, the phase distortion introduced by the amplifier.
`
`For a small number of values of vp, corresponding values of vd and
`3> are stored in memory. These values of vp are sampled in predeter­
`mined intervals. From trial simulations, it was found that 30 different
`values of vp were sufficient to accurately define the amplifier's ampli­
`tude and phase characteristic. Note that the points do not need to be
`equally spaced; they must, however, be spread over the entire range of
`the input signal. Since there is delay in the feedback path, the input
`signal must be delayed by the same amount. Methods of measuring
`and implementing this delay are discussed in [8] and [11]. Using these
`stored values, cubic spline interpolation [12] is used to estimate the
`AM-AM and AM-PM characteristics for any particular | v* |2 value.
`For equivalent accuracy using a single polynomial fit, a high-order
`polynomial would be required. Predistortion coefficients are computed
`using the estimated AM-AM and AM-PM characteristics. For a given
`input power level, xm, the desired output power level, yc, is known
`from the required linear characteristic, as shown in Fig. 2. If the input
`signal, xm
`is fed to the amplifier without predistortion, the output
`power would be ya, which does not lie on the linear characteristic. To
`obtain the desired output power, yC9 the input to the amplifier should
`be xp. The inverse AM-AM characteristic is directly computed from
`the measured distortion values. For the corrected value of magnitude,
`xp, the corresponding value of phase distortion ($) can be read from
`the estimated AM-PM characteristic.
`
`The proposed linearizer makes use of the fact that the amplitude
`and phase distortion of a narrow-band RF power amplifier are depend­
`ent only upon the amplitude of the input signal and are independent of
`the phase of the input signal [10]. In other words, input signals with
`equal magnitude suffer identical amplitude and phase distortion. How­
`ever, analogue quadrature modulator and demodulator impairments
`can introduce phase-dependent distortion into the system and can de­
`grade the performance of the linearizer.
`
`III. Quadrature modulator and demodulator impairments
`
`Fig. 3 shows a schematic diagram of a typical quadrature modula­
`tor. The modulator consists of four components; namely, two mixers,
`a quadrature hybrid and an in-phase power combiner. These compo­
`nents are not ideal, resulting in a collective effect that can be repre­
`sented by gain imbalance, phase imbalance and dc offset [13]-[16].
`Gain imbalance represents the gain mismatch between the i and q
`channels. Ideally, the gains in the i and q channels are equal. If the
`phase difference between the local oscillator signals for the i and q
`channels is not exactly 90°, phase imbalance exists. A difference in the
`lengths of the two RF paths can result in a frequency-dependent phase
`imbalance. Lastly, carrier feedthrough gives an unwanted RF compo­
`nent at the carrier frequency. The quadrature demodulator suffers from
`similar impairments. The gain and phase errors result in image signals
`
`A A
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`
`Authorized licensed use limited to: James Proctor. Downloaded on December 18,2024 at 23:18:19 UTC from IEEE Xplore. Restrictions apply.
`Figure 1: Block diagram of a n/4-DQPSK transmitter with the proposed linearizer.
`Figure 2: Power transfer characteristic of an amplifier.
`
`Input power
`
`PETITIONERS EXHIBIT 1021
`Page 2 of 7
`
`

`

`LOHTIA / GOUD / ENGLEFIELD: ADAPTIVE DIGITAL LINEARIZATION OF RF POWER AMPLIFIERS
`
`67
`
`that are independent of dc offset. The image signals due to the gain
`and phase error are 90° out of phase. Self-mixing of the carrier in the
`mixer can cause dc offset.
`
`For a single-tone input signal to the modulator with frequency fmt
`gain and phase imbalance will generate a spurious tone at frequency fm
`below the carrier frequency. The dc offset generates a spurious signal
`at the carrier frequency. These spurious signals can add to the inter-
`modulation distortion products when the composite signal is passed
`through the amplifier nonlinearity. Therefore, spurious signals must
`be kept at the minimum level possible. Gain imbalance distorts a cir­
`cular modulation constellation into an elliptical constellation. Phase
`imbalance causes rotation of the axes of this ellipse. The dc offset
`shifts all constellation points by an equal amount.
`
`A. Quadrature modulator and demodulator
`impairment compensators
`The output of an ideal quadrature modulator can be written as
`
`s(t) = i(t) cos cocf + <?(0 s in <M >
`where i(t) and q(t) are the in-phase and quadrature-phase components
`respectively. However, a practical quadrature modulator has gain im­
`balance, phase imbalance and dc offset. Therefore, the output of a
`practical quadrature modulator would be given by
`
`(2)
`
`are stored in memory. There are five unknowns in (5); namely, a\, a2,
`b\, b2, and <(>. Therefore, five independent equations are needed to
`solve for these unknowns. Five sets of values of m, id and qd, obtained
`at five different time instants, are used to generate five independent
`equations that are solved using the multivariate Newton-Raphson
`method [12]. In the actual computations, m2 is used in order to avoid
`taking the square root. To generate independent equations and ensure
`convergence of the Newton-Raphson method, the values of m, id and
`qd should be well spread out over the signal constellation. The initial
`values for the Newton-Raphson iterations are taken to be no gain im­
`balance, no dc offset, and no phase imbalance (i.e., the ideal values a\
`= a2 =1, b\ = b2 = 0, <(> = 0). With these initial conditions, the Newton-
`Raphson iterations always converged for reasonable impairment val­
`ues. With the impairment values known, the i and q signals are
`predistorted to correct for the modulator imperfections. To update the
`estimated values of the impairments, a new set of values of m, id and qd
`is measured and stored in memory, and the impairment values esti­
`mated as before.
`
`The structure of the demodulator impairment compensator is simi­
`lar to that of the modulator impairment compensator, as shown in
`Fig. 5. The input to the envelope detector is a portion of the RF signal,
`s(t). If s(t) is given by (2), then the outputs of an ideal quadrature
`demodulator would be i and q. However, the outputs of a practical
`quadrature demodulator will be
`
`s(t) = [axi(t) + bx ] cos (cocr + <)>) + [a2q{t) + b2 ] sin (Oct,
`
`(3)
`
`where «i, a2 are gains, and b\9 b2 are dc offsets for the i and q channels
`respectively, and <\> is the phase imbalance between the / and q chan­
`nels.
`
`Equation (3) can be simplified to
`
`s(t) = m(t) cos [cocf + 9(0] >
`
`(4)
`
`where
`
`/' (t) = a3 [i(t) cos <|> + q(t) sin (-()))] + b3 ,
`
`q'{t) = a4q{t) + b4.
`
`The envelope detector output is given by
`
`'
`
`1 <
`(r-b3)
`
`COS(|>
`
`«3
`
`+
`
`(q>-b4)
`a4
`
`.
`sin $
`
`fl4
`
`(7)
`
`(8)
`
`Vz
`
`■
`
`(9)
`
`(0={[M<)+*1 )cos*]2 +[(fl!i(0+*i )sin(-4>)+(«2*(f)+*2 )f } 2 (5)
`
`The digitized detector output, m, along with the corresponding de­
`modulated values /' and q\ are stored in memory. As in the case of the
`
`and
`
`9(0 = tan_1
`
`( M Q + f r )sin(-4>)+(fl2g(0+62)
`(fl1i(r) + 61)cos(()
`
`(6)
`
`Input
`
`A block diagram of the proposed compensator for the modulator
`impairments is shown in Fig. 4. A portion of the modulator output is
`fed to an envelope detector. The digitized detector output, m, and the
`corresponding values of the quadrature inputs (id, qd) to the modulator
`
`j
`
`q
`
`Processor
`
`[
`
`L
`
`si (t)
`
`Quadrature
`Modulator
`
`>
`
`m
`
`H
`
`Envelope
`Detector
`
`A/D
`
`l-lnput ■£> t
`
`fi\ w Quadrature
`Hybrid
`
`In-phase Power
`Combiner
`
`RF Output
`
`Q-lnput ^a>
`
`Figure 4: Quadrature modulator impairment compensator.
`
`Quadrature
`- Demodulator
`
`|s(t)
`J RF Input
`
`i
`
`q
`
`Processor
`t K
`m
`
`^
`
`r
`
`q'
`
`A/D -
`
`Envebpe
`Detector
`
`|
`
`Authorized licensed use limited to: James Proctor. Downloaded on
`Figure 3: Schematic diagram of an analogue quadrature modulator.
`
`Figure 5: Quadrature demodulator impairment compensator.
`
`PETITIONERS EXHIBIT 1021
`Page 3 of 7
`
`

`

`68
`
`CAN. J. ELECT. & COMP. E N G, VOL. 20, NO. 2, 1995
`
`modulator, there are five unknowns in (9); namely: a3, a4, b3, b* and cj>.
`Therefore, five independent equations are needed to solve for these
`unknowns. Five sets of values of m, V and q\ obtained at five different
`time instants, are used to generate five independent equations that are
`then solved using the Newton-Raphson method. As previously, m2 is
`used in (9). The estimated impairment values are used to post-distort V
`and q' in order to correct for the demodulator impairments.
`
`IV. Simulation models
`
`A complex envelope simulation model has been used to compare
`the performance of the different linearization techniques. Band-pass
`signals are represented by equivalent low-band signals. Simulation
`models include a random data source, a TE/4-DQPSK modulator and a
`square-root raised cosine pulse-shaping filter (n = 0.35). The param­
`eters used for the amplifier models were obtained from actual meas­
`urements of the AM-AM and AM-PM characteristics of nonlinear
`
`power amplifiers that were tested in the laboratory. The characteristics
`for the class AB and class B amplifiers are shown in Figs. 6 and 7
`respectively. The class AB amplifier is an Avantek 6-W amplifier
`specially designed for the North American cellular frequency band.
`The class B amplifier uses a Philips BLV93 transistor, with a nominal
`maximum output power of 8 W.
`
`The performance of different linearization techniques has been
`evaluated using the power spectral density (PSD) and intermodulation
`distortion product power levels as the performance criteria. The output
`data are windowed by a Blackman window to reduce the spectral leak­
`age. Overlapping sets of data are averaged together to reduce the vari­
`ance in each frequency sample. The intermodulation distortion
`products have been evaluated using a two-tone input signal. The test
`signal has two complex tones, one at 20 kHz and one at 25 kHz, a
`cosine wave being used for the i component, and a sine wave for the q
`component.
`
`V. Results
`
`A comparison of the performance of the proposed linearization
`technique with cartesian coordinate negative feedback and complex
`gain predistortion linearization is shown in Fig. 8. For the cartesian
`coordinate negative feedback technique, a loop gain of 25 dB and
`
`1
`
`B 1
`
`1
`
`9
`
`M
`
`T
`
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`Input power (dB)
`
`Figure 6: Transfer characteristics of the experimental class AB amplifier.
`
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`Input power (dB)
`
`Figure 8: Linearized class AB amplifier performance: (a) intermodulation products IM3
`at 15 and 30 kHz and IM5 at 10 and 15 kHz; (b) power spectral density.
`Authorized licensed use limited to: James Proctor. Downloaded on December 18,2024 at 23:18:19 UTC from IEEE Xplore. Restrictions apply.
`Figure 7: Transfer characteristics of the experimental class B amplifier.
`
`PETITIONERS EXHIBIT 1021
`Page 4 of 7
`
`

`

`LOHTIA / GOUD / ENGLEFIELD: ADAPTIVE DIGITAL LINEARIZATION OF RF POWER AMPLIFIERS
`
`69
`
`bandwidth of 100 kHz were used. For the complex gain predistortion
`technique, 64 points were used. For the cubic spline interpolation tech­
`nique, 30 spline points were used. In all the tests, the peak RF ampli­
`fier power was set at the 1-dB gain compression point. This point
`corresponds to the 0-dB input level in Figs. 6 and 7. The third-order
`(IM3) and fifth-order (IM5) intermodulation distortion products for
`the uncompensated class AB amplifier were found to be -29.6 dB and
`-31.8 dB respectively. The proposed technique reduces IM3 and IM5
`to -80.3 dB and -81.2 dB respectively. The better performance
`observed in the cubic spline interpolation is due to better curve fitting
`of the AM-AM characteristic than the complex gain predistortion that
`uses a linear interpolation technique. The IM3 and IM5 are -62 dB and
`-69 dB respectively when complex gain predistortion is used. The
`cartesian coordinate negative feedback reduces IM3 and IM5 to -49 dB
`and -54 dB respectively. Fig. 8(b) shows the output power spectral
`density for the three linearization methods. The proposed technique is
`seen to have significantly better performance than cartesian coordinate
`negative feedback in the first and second adjacent channels, and simi­
`lar performance in the third adjacent channel. A comparison of results
`for the class B amplifier is shown in Fig. 9.
`
`1
`
`1 1
`
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`* Cartesian Coordinate
`O Complex Gain
`0 Uncompensated
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`
`- 8 0-
`
`-100 -
`
`25
`15
`Frequency (kHz)
`(a)
`
`C
`3
`
`3
`I
`)
`(
`
`i
`
`^
`
`1
`0
`
`:
`3
`c
`)
`i
`k
`
`35
`
`40.
`Frequency
`(b)
`
`60.
`(kHz)
`
`Fig. 10 shows the level of the undesired sideband in a quadrature
`modulator with and without an impairment compensator. The input
`test signal is a 20-kHz complex tone. The sideband level is shown as a
`function of gain imbalance, with phase imbalance as a parameter. The
`undesired sideband is seen to be about 70 dB below the desired
`sideband level when the compensator is used. There is a variation of
`about 25 dB in the suppressed sideband. This variation is attributable
`to the convergence characteristics of the iterative process in the New-
`ton-Raphson method. The convergence is not monotonic, and depends
`on the starting value. As a result, the undesired sideband level for a
`higher gain and/or phase imbalance can actually be less than that for a
`smaller imbalance. It should be noted, however, that convergence is
`always obtained for small impairment values, and that decreasing the
`convergence bound leads to improved performance. This is demon­
`strated in Fig. 11, which shows the undesired sideband level of a
`modulator compensator as a function of the convergence bound for
`Newton-Raphson iterations. It is seen that decreasing the convergence
`bound increases the suppression of the undesired sideband. Decreas­
`ing the convergence bound, however, requires more iterations of the
`convergence algorithm. With a convergence factor of 10"3, the number
`of iterations is normally less than 20. (A convergence factor of 10~3
`implies that the iteration is stopped when the fractional change of each
`parameter during one iteration is less than this value. Each iteration is
`one pass through all five equations.) The compensator works well for
`up to about 12% gain imbalance, 12° phase imbalance and 12% dc
`offset. For greater values of the impairments, the Newton-Raphson
`iterations do not converge. The failure of the compensator correction
`algorithm is thus sudden, rather than a smooth deterioration.
`
`Without compensator
`
`-100
`
`1
`
`3
`2
`Gain imbalance (%)
`
`Figure 10: Undesired sideband level versus gain imbalance.
`
`-40 '
`
`-60 "
`
`-80 "
`
`-100 '
`
`-120
`
`-140 ^
`0.00 01
`
`*
`
`CO
`<D
`
`3
`3
`
`Gain imbalance = 3%
`Phase imbalance = 3°
`
`^^~~*
`
`0.001
`Convergence bound
`
`0 .01
`
`Figure 11: Undesired sideband level versus convergence bound of modulator compensa­
`Figure 9: Linearized class B amplifier performance: (a) intermodulation products IM3 at
`tor.
`15 and 30 kHz and IM5 at 10 and 15 kHz; (b) power spectral density.
`Authorized licensed use limited to: James Proctor. Downloaded on December 18,2024 at 23:18:19 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1021
`Page 5 of 7
`
`

`

`70
`Similar results are obtained for the quadrature demodulator impair­
`ment compensator; these are shown in Figs. 12 and 13.
`
`CAN. J. ELECT. & COMP. ENG., VOL. 20, NO. 2, 1995
`
`o.
`
`-t
`
`Tfein
`"channel
`-J
`
`-20.
`
`Adjacent
`channel 1
`
`Adjacent
`channel 2
`
`I Adjacent
`I channel 3
`
`£ -40.
`
`!
`
`-60. -I
`
`-80.
`
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`0.
`
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`
`80.
`
`1
`
`' 1
`40.
`40.
`Frequency
`
`0.001
`T—i—|—i—r
`60.
`60.
`(kHz)
`
`Legend:
`a) Linearized amplifier with no mod/demod compensator
`b) Uncompensated amplifier
`c) Three different values of convergence bound for
`mod/demod compensator
`d) No mod/demod impairments
`
`Figure 14: Overall system performance for three different values of convergence bound
`for the modulator and demodulator impairment compensator.
`
`that, if no compensation is used to correct for these errors, then the
`overall performance of the linearizer is actually worse than if the am­
`plifier is unlinearized. A modest degree of modulator and demodulator
`compensation results in a significant improvement in the performance
`of the linearized amplifier. If the convergence bound for the modulator
`and demodulator compensation is set at 0.05, then the out-of-band
`power for the overall amplifier drops by about 30 dB; for convergence
`bounds of 0.01 and 0.001, there are further improvements of 6 dB.
`
`These simulations did not investigate the effects of noise on the
`performance of the technique. However, since all the circuitry is within
`the transmitter, the only significant sources of noise are the A/D and
`D/A converters. Envelope detector inaccuracy will affect the modula­
`tor and demodulator impairment compensator performance.
`
`VII. Conclusion
`
`An improved adaptive technique for the linearization of RF power
`amplifiers with narrowband signals has been evaluated. The linearizer
`can compensate for slow drifts of the amplifier characteristics. The
`IM3 and IM5 can be suppressed about 80 dB below the tone levels
`using this linearization method. The technique has been used to
`linearize both class AB and class B amplifiers.
`
`An adaptive technique for the compensation of quadrature modula­
`tor and demodulator impairments has also been studied. The technique
`works well for up to about 12% gain imbalance, 12° phase imbalance
`and 12% dc offset. The spurious signals generated by the quadrature
`modulator can be suppressed by more than 30 dB using the modulator
`impairment compensation technique.
`
`Acknowledgements
`
`The authors thank NovAtel Communications Ltd., especially Dr.
`Andrew Wright, for providing the amplifier distortion measurements,
`and for helpful discussions. The assistance of Mr. Timothy Neufeld
`with computer simulations is also acknowledged.
`
`VI. Discussion
`
`The proposed linearizer is suitable for baseband implementation.
`Since it is basically an open-loop configuration, it is unconditionally
`stable. The feedback loop is closed only during updating of the
`predistortion coefficients. This linearization method is not restricted
`by the modulation format, because the signal is predistorted after the
`pulse-shaping filter. Although the AM-AM and AM-PM characteris­
`tics of the class AB and class B amplifiers are significantly different
`(see Figs. 6 and 7), the linearizer performs almost equally well for
`both amplifiers.
`
`The linearizer assumes the distortion to be dependent only on the
`magnitude of the input signal. However, phase-dependent distortion
`can occur due to the quadrature modulator and demodulator impair­
`ments. The performance of the proposed linearizer is critically de­
`pendent on the quadrature modulator and demodulator performance.
`The quadrature modulator and demodulator impairments need to be
`compensated for to ensure satisfactory performance of the amplifier
`linearizer. The overall linearized system with the quadrature modula­
`tor and demodulator impairment compensator will be a multiple-loop
`system. The effect of modulator and demodulator impairments on the
`performance of the linearized amplifier is illustrated in Fig. 14. For
`both the modulator and demodulator the impairments are taken to be
`3% gain imbalance, 3° phase imbalance, and 3% dc offset. These val­
`ues are fairly typical for practical modems. It is seen from the figure
`
`f
`1
`
`|
`
`1
`
`m
`
`I »-5U
`-20
`f
`U=3°
`[♦.1°
`m -40 1
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`
`75
`.§>
`CO
`
`-80
`
`H
`'
`
`Without compensator
`
`<b <o
`With compensator
`Y = '
`> < C ^ ^c :* - ^^
`
`-100
`I
`
`1
`
`i
`i
`3
`2
`Gain imbalance (%)
`
`i
`4
`
`Figure 12: Image signal level versus gain imbalance.
`
`OA m
`
`I "90"
`
`/ Gain imbalance = 3%
`/
`Phase imbalance = 3°
`
`signal level
`
`o o
`
`I -110-
`
`-120"'
`0 .001
`
`0.01
`Frequency (kHz)
`
`c
`).1
`
`Figure 13: Image signal level versus convergence bound of demodulator impairment
`compensator. Authorized licensed use limited to: James Proctor. Downloaded on December 18,2024 at 23:18:19 UTC from IEEE Xplore. Restrictions apply.
`
`PETITIONERS EXHIBIT 1021
`Page 6 of 7
`
`

`

`LOHTIA / GOUD / ENGLEFIELD: ADAPTIVE DIGITAL LINEARIZATION OF RF POWER AMPLIFIERS
`References
`
`71
`
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`tion Compatibility Standard, IS-54, Electronic Industries Association, Washington,
`D.C., May 1990.
`[2] R.D. Stewart and F.F. Tusubira, "Feedforward linearization of 950 MHz amplifiers,"
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`[3] D.C. Cox, "Linear amplification with nonlinear components," IEEE Trans. Comm.,
`vol. COM-22, no. 12, Dec. 1974, pp. 1942-1945.
`[4] F.H. Raab, "Efficiency of outphasing RF power-amplifier systems," IEEE Trans.
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`[6] A. Bateman, R.J. Wilkinson and J.D. Marvill, "The application of digital signal
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`Stockholm, Sweden, June 1988, pp. 64-67.
`[7] M. Johansson and T. Mattsson, "Transmitter linearization using cartesian coordinate
`negative