This invention relates to digital compensation of a non-linear circuit, for instance linearization of a transmitter chain which may include a non-linear power amplifier, and more particularly relates to techniques for configuring or adapting a configuration used for such compensation.
A concept of applying a digital compensation to restore the quality of an original signal passed through a circuit may be well-known. A power amplifier in a radio of a wireless base station or handset may be compensated digitally in the baseband to minimize the spectral leakage into adjacent channels. An audio amplifier in a speaker may be compensated digitally to achieve high fidelity. In many such examples, variants of Volterra series have been adopted to account for dynamical nature of nonlinearity. Wiener, Wiener-Hammerstein, General Memoryless Polynomial are popular structures for digital pre-distorters, which are used to modify an input signal prior to passing through a non-linear circuit. In general, these structures have an exponential complexity if the polynomial order exceeds 3 to 5, as well as robustness issues due to sensitivity of compensator parameters to variations of a particular device (Device Under Test, DUT), including process, temperature, supply voltage, and other operating conditions.
Referring to
y[n]=h0+ΣpΣτ
In some examples, the non-linear function is reduced set of Volterra terms, for example a delay polynomial:
y[n]=h0+ΣpΣτhp(τ)x[n−τ]|x[n−τ]|(p-1)
In order to invert the non-linear effects of the transmit chain, in general, a relatively large number of terms of such a series representation are needed, and the coefficients of those terms (e.g., the hp terms) must be accurately set. In general, the coefficients in such approaches are continually updated to maintain good linearization. Various approaches to such continual updating are used, for example, based on incremental updates using y[n] and observation of p(t) (e.g., after demodulation).
A number of techniques are known for determining values of the coefficients for such linearization system. However, many such techniques suffer from aspects such as poor convergence in iterative computation of the values, and in lack of robustness of the coefficient values to changes in operating conditions.
In a general aspect, a linearization system computes a robust set of quantities characterizing a nonlinearity of a transmit chain including a power amplifier by combining a current set of quantities characterizing the nonlinearity of the transmit chain with a weighted combination of prior sets of quantities characterizing the nonlinearity of the transmit chain.
In another aspect, in general, a method for digital compensation of a signal chain comprising at least one analog electronic amplification element comprises receiving an input signal to the signal chain. The input signal comprising a plurality of batches of the input signal, each batch corresponding to a different time interval of the input signal. An output signal of the signal chain is also received. The output signal comprising a plurality of batches of the output signal, each batch of the output signal corresponding to a different batch of the input signal. The method includes computing coefficient values for a digital compensator from the plurality of batches of the input signal and the corresponding batches of the output signal. This computing of the coefficient values includes evaluating for each batch of the input signal output of application of a plurality of basis functions to said batch of the input signal, computing a first average over the plurality of batches of the input signal of a first function of the output of the application of the plurality of basis functions to corresponding batches of the input signal, computing a second average over the plurality of batch the input signal of a second function the output of the application of the plurality of basis functions to corresponding batches of the input signal and corresponding batches of the output signal, and computing the coefficient values from the first average and the second average. A desired input signal is processed with the digital compensator configured according to the coefficient values to produce an input signal for the signal chain.
Aspects may include one or more of the following features.
The first average comprises a decaying average, and the second average comprises a decaying average. For instance, each decaying average corresponds to an exponentially decaying average according to weighting proportional to λ−i where i is an increasing index of the batches over time and 0<λ<1 is a real quantity characterizing the rate of exponential decay.
Application of the plurality of basis functions to an ith batch of the input signal is equivalent to a matrix Ai having a number of columns equal to a number of the basis functions and a number of rows equal to a number of samples in the batch of the input signal, and the first function is equivalent to AiHAi+ρI, where AiH is a transpose of complex conjugate of Ai and I is an identity matrix, where ρ is a real number that is zero or is positive.
Computing the first average includes updating the first average using the nth batch using an previous value of the first average, GLn-1 computed without the nth batch according to an update equation GLn=λGLn-1+(1−λ) (AnHAp+ρI).
An ith batch of the output signal is equivalent to a vector bi, having a number of rows equal to a number of samples in the batch of the output signal, and the second function is equivalent to AiHbi
Computing the second average includes updating the second average using the nth batch using an previous value of the first average, GRn-1 computed without the nth batch according to an update equation GRn=λGRn-1+(1−λ) AnHbn.
Computing the coefficient values from the first average, GLn, and the second average, GRn, is according to an equation α=(GLn)−1GRn.
Computing the coefficient values from the first and the second averages includes determining said values according to the equation α=(GLn)−1 GRn subject to bounds on the magnitudes of the coefficient values, αL≤α≤αU.
Each batch of the input signal corresponds to a time interval of the input signal having a same duration.
The plurality of basis functions comprise products of delayed values or conjugates or magnitudes of delayed values.
Processing a desired input signal with the digital compensator configured according to the coefficient values includes weighting the outputs of application of the basis functions to the desired input signal by the computed coefficient values.
Other features and advantages of the invention are apparent from the following description, and from the claims.
As introduced above, a digital compensator may be configurable with values of a set of coefficients that determine how the compensator operates, and in particular, that determine the non-linear function implemented by the compensator as part of the linearization approach. Example of such compensators are described above and in U.S. Pat. No. 9,590,668, “Digital Compensator,” issued on Mar. 7, 2017, which is incorporated herein by reference.
Referring to
When an intermediate input signal, y is provided to the transmit chain 106, the transmit chain 106 generates an output signal, z as an amplified version of the intermediate input signal, y. In general, the output signal, z includes nonlinear distortion due to the nonlinear input/output power characteristic of the transmit chain 106.
Without compensation, the output signal, z would not be an accurate amplified reproduction of the input signal, x. The system 100 includes the DPD 108 to compensate for the nonlinear distortion introduced by the transmit chain 106. In particular, the DPD 108 receives the input signal, x and “predistorts” the signal to generate the intermediate input signal, y. Ideally, the intermediate input signal, y includes an “inverse nonlinear distortion” (i.e., an inverse of the nonlinear distortion introduced by the transmit chain 106), such that the nonlinear distortion introduced by the transmit chain 106 is substantially cancelled by the inverse nonlinear distortion. The output signal, z is therefore substantially free of nonlinear distortion.
In some examples, the DPD 108 operates according to an inverse model of the nonlinear distortion of the transmit chain 106 such that providing the input signal, x to the DPD 108 causes the DPD 108 to generate the intermediate input signal, y as follows:
where fi(⋅) is the ith basis function of n basis functions and αi is the ith parameter (e.g., the ith weight) corresponding to the ith basis function. Each basis function is a linear function (e.g., x(t−1)) or a non-linear function (e.g., |x(t)|2) of the input, x, which may include memory (e.g., x(t)*x(t−1)).
In general, the nonlinear input/output characteristic of the transmit chain 106 may change over time. The parameters, a used by the DPD 108 to generate the intermediate input signal, y are there therefore iteratively updated to reflect the changes in the nonlinear input/output characteristic of the transmit chain 106.
To update the parameters, a used by the DPD 108, the predictor module 110 processes the intermediate input signal, y and a sensed version of the output signal, b∝z to generate an updated set of parameters, a′. In one example, the predictor module 110 determines an updated set of parameters a′ that, in combination with the basis functions and the intermediate input signal, y generate a predicted signal that is as close as possible to the sensed signal, b (e.g., in a least mean squared error sense):
P:y→b
which can be restated as
In some examples, the predictor parameters a are determined using techniques described in the “Parameter Update” section below.
The predictor, P is provided to a DPD update module 112 which processes the predictor, P to update the DPD 108. In some examples, for the predictor, P described above, the DPD update module 112 configures the DPD 108 to perform according to an approximate inverse of the predictor, P as follows:
or by explicitly setting the DPD parameters as: αi=−αi.
In another example, the predictor module 110 determines an updated set of parameters {circumflex over (α)} that, in combination with the basis functions and the sensed signal, b generate a predicted signal, ŷ that is as close as possible to the intermediate input signal, y (e.g., in a least mean squared error sense):
P:b→ŷ
which can be restated as
That is, P is an estimate of a (post) inverse of the nonlinearity of the transmit chain 106. In some examples, the updated set of parameters α is determined using techniques described in the “Parameter Update” section below.
The predictor, P is provided to a DPD update module 112 which processes the predictor, P to update the DPD 108. In some examples, for the predictor, P described immediately above, the DPD update module 112 configures the DPD 108 to perform according to the predictor, P as follows:
or essentially αi=αi.
Referring to
An intermediate input signal, y is provided to the transmit chain 206, which outputs an output signal, z (i.e., an amplified version of the amplifier input signal), which is distorted due to the nonlinear input/output power characteristic of the transmit chain 206.
As was the case above, without compensation, the output signal, z would not be an accurate amplified reproduction of the input signal, x. The system 200 includes the DPD 208 to compensate for the nonlinear distortion introduced by the transmit chain 206. In particular, the DPD 208 receives the input signal, x and “predistorts” the signal to generate the intermediate input signal, y. Ideally, the intermediate input signal, y includes an “inverse nonlinear distortion” (i.e., an inverse of the nonlinear distortion introduced by the transmit chain 206), such that the nonlinear distortion introduced by the transmit chain 206 is substantially cancelled by the inverse nonlinear distortion. The output signal, z is therefore substantially free of nonlinear distortion.
In general, the nonlinear input/output characteristic of the transmit chain 206 may change over time. The parameters, α used by the DPD 208 to generate the intermediate input signal, y are there therefore iteratively updated reflect the changes in the nonlinear input/output characteristic of the transmit chain 206.
In the system of
P:x→{circumflex over (b)}
which can be restated as
The parameters α in combination with the basis functions represent the difference between the model of the nonlinear input/output characteristic of the transmit chain 206 currently being used by the DPD 208 and the current nonlinear input/output characteristic of the transmit chain 206 because the effects both the DPD 208 and the transmit chain 206 on the input signal, x are represented in the sensed signal, b.
In some examples, the set of parameters a is determined using techniques described in the “Parameter Determination” section below.
The predictor P is provided to a DPD update module 212 which processes the predictor, P to update the DPD 208. In some examples, for the predictor, P described immediately above, the DPD update module 212 configures the DPD 208 to combine an approximate inverse of the predictor with the existing DPD 208 as follows:
α′i←αi+αi.
This essentially approximates a cascade of the approximate inverse of the predictor, P−1 with the previous DPD configuration to yield the new DPD configuration.
The above process is performed iteratively and therefore the coefficients are expected to be small in a steady state of the system.
In another example, the predictor module 210 determines a set of parameters a that, in combination with the basis functions and the sensed signal, b generate a predicted signal, {circumflex over (x)} that is as close as possible to the input signal, x (e.g., in a least mean squared error sense):
P:b→{circumflex over (x)}
which can be restated as
In some examples, the updated set of parameters α is determined using techniques described in the “Parameter Determination” section below.
The predictor, P is provided to a DPD update module 212 which processes the predictor, P to update the DPD 208. In some examples, for the predictor, P described immediately above, the DPD update module 212 configures the DPD 208 to combine an approximation of the predictor with the existing DPD 208 as follows:
α′i←αi+αi.
Parameter Determination
In some examples, the predictor P: x→{circumflex over (b)} parameters, α described above are determined in batches using a least squares algorithm as follows:
α=argmin|Aα−b|22=argmin(αHAHAα−2AHbα+bHb)
where b is a vector of sensed signal samples and A is a matrix where each column includes the samples of the basis function, fi(x). The solution for α is therefore:
α=(AHA)−1AHb.
That is, in this formulation, the samples of the sensed signal and the basis function are used once for the batch, and not used in subsequent determination of future coefficient values α.
A number of improvements make use of generally smaller batches of samples of the signals, but each sample is used repeatedly for a number of determinations of the coefficient values. The approach that implements this repeated use of the smaller batches can improve robustness such that any one of the smaller batches, even if having unusual or non-representative data for some reason (e.g., a “glitch”), does not have as significant and impact as compared to a computation on a larger batch.
Anther improvement makes use of a “regularization” of the criterion for determining the coefficient values to bias the result away from coefficient values with large magnitudes. This feature also provides robustness by being less sensitive to batches of data that might result in unusually large and likely not robust coefficient values.
In some examples, the technical improvements include robustness, reliability, and/or improved convergence of coefficients, α. The improvements involve modifying the least squares optimization problem to incorporate a history of previous batches of the input as follows:
where Ai and bi correspond to inputs and outputs for batch i=1, . . . and α depends on the samples from all batches 1 to n. The above equation is subject to αL≤α≤αU, 0<λ<1, and ρ>0.
In the above optimization problem, the large batch term (a Gramian)
AHA
is replaced with
which is a “memory Gramian.” Use of the memory Gramian improves the convergence properties of the optimization process, safeguards against glitches in system behavior, and improves overall performance of the system. Note that each smaller batch of samples of the basis functions Ai contributes at a decaying weight the more distant in the past the smaller batch. Although it should be clear that various forms for averaging of the smaller batches (i.e., averaging over i) may be used (e.g., sliding rectangular window, etc.), a decaying exponential window proportional to λn-i allows iterative updating of the averages as described below.
A similar averaging is used replacing the large batch term with AHb
which is also provides the decaying average of the small batch contributions. Similarly,
bHb
is replaced with the equivalent expression
Finally, a new term
ραHα
is added such that with ρ>0, large magnitude elements of α are biased against in the optimization.
As introduced above, an advantage of using an exponential decaying average of the contributions of the smaller batches is that an iterative updating of the parameters may be used. In particular, at the nth update of the predictor parameters, α is determined based on retaining quantities GLn-1 and GRn-1 from the previous iteration (i.e., from after updating on the previous small batch), computing GLn and GRn from the retained quantities and the new small batch data, and computing a as
α=(GLn)−1GRn.
Note that a best solution that satisfies αL≤α≤αU (elementwise) may be used rather than exact solution using the matrix inverse.
This iteration may be initialized at the first small batch (n=1) as
GL1=A1HA1+ρI,
GR1=A1Hb1,
and updated at each iteration as
GLn=λGLn-1+(1-λ)(AnHAn+ρI),
GRn=λGRn-1+(1λ)AnHbn.
thereby converging to the optimal solution for the coefficient values α.
Optionally, the resulting coefficient values are further modified to improve the stability to produce the actual predictor parameters, αA according to:
αA+αA+η(α-αA)
The values of the parameters, αA are then used as the predictor parameters as described in the approaches above.
In some implementations, a computer accessible non-transitory storage medium includes a database representative of a system including some or all of the components of the linearization system. Generally speaking, a computer accessible storage medium may include any non-transitory storage media accessible by a computer during use to provide instructions and/or data to the computer. For example, a computer accessible storage medium may include storage media such as magnetic or optical disks and semiconductor memories. Generally, the database representative of the system may be a database or other data structure which can be read by a program and used, directly or indirectly, to fabricate the hardware comprising the system. For example, the database may be a behavioral-level description or register-transfer level (RTL) description of the hardware functionality in a high-level design language (HDL) such as Verilog or VHDL. The description may be read by a synthesis tool which may synthesize the description to produce a netlist comprising a list of gates from a synthesis library. The netlist comprises a set of gates which also represent the functionality of the hardware comprising the system. The netlist may then be placed and routed to produce a data set describing geometric shapes to be applied to masks. The masks may then be used in various semiconductor fabrication steps to produce a semiconductor circuit or circuits corresponding to the system. In other examples, Alternatively, the database may itself be the netlist (with or without the synthesis library) or the data set.
It is to be understood that the foregoing description is intended to illustrate and not to limit the scope of the invention, which is defined by the scope of the appended claims. Other embodiments are within the scope of the following claims.
This application claims the benefit of U.S. Provisional Application No. 62/517,380, file on Jun. 9, 2017, which is incorporated herein by reference.
Number | Name | Date | Kind |
---|---|---|---|
4979126 | Pao et al. | Dec 1990 | A |
5819165 | Hulkko et al. | Oct 1998 | A |
5980457 | Averkiou | Nov 1999 | A |
6052412 | Ruether et al. | Apr 2000 | A |
6240278 | Midya et al. | May 2001 | B1 |
7295815 | Wright et al. | Nov 2007 | B1 |
7529652 | Gahinet et al. | May 2009 | B1 |
7599431 | Anderson et al. | Oct 2009 | B1 |
7904033 | Wright et al. | Mar 2011 | B1 |
8446979 | Yee | May 2013 | B1 |
9130628 | Mittal et al. | Sep 2015 | B1 |
9226189 | Kularatna et al. | Dec 2015 | B1 |
9337782 | Mauer et al. | May 2016 | B1 |
9590668 | Kim et al. | Mar 2017 | B1 |
9749161 | Gal | Aug 2017 | B1 |
9973370 | Langer et al. | May 2018 | B1 |
10080178 | Stapleton et al. | Sep 2018 | B2 |
10141896 | Huang | Nov 2018 | B2 |
20020080891 | Ahn et al. | Jun 2002 | A1 |
20030184374 | Huang et al. | Oct 2003 | A1 |
20030207680 | Yang et al. | Nov 2003 | A1 |
20040076247 | Barak et al. | Apr 2004 | A1 |
20040116083 | Suzuki et al. | Jun 2004 | A1 |
20040142667 | Lochhead et al. | Jul 2004 | A1 |
20040196922 | Leffel | Oct 2004 | A1 |
20050001684 | Braithwaite | Jan 2005 | A1 |
20050163251 | McCallister | Jul 2005 | A1 |
20050163252 | McCallister et al. | Jul 2005 | A1 |
20050180527 | Suzuki et al. | Aug 2005 | A1 |
20050190857 | Braithwaite | Sep 2005 | A1 |
20060022751 | Fuller et al. | Feb 2006 | A1 |
20060154622 | Piirainen | Jul 2006 | A1 |
20060229036 | Muller et al. | Oct 2006 | A1 |
20060276147 | Suzuki et al. | Dec 2006 | A1 |
20070091992 | Dowling | Apr 2007 | A1 |
20070230557 | Balasubramonian et al. | Oct 2007 | A1 |
20070241812 | Yang et al. | Oct 2007 | A1 |
20070247487 | Nakamura et al. | Oct 2007 | A1 |
20080019453 | Zhao et al. | Jan 2008 | A1 |
20080039045 | Filipovic et al. | Feb 2008 | A1 |
20080057882 | Singerl et al. | Mar 2008 | A1 |
20080101502 | Navidpour et al. | May 2008 | A1 |
20080268795 | Saed | Oct 2008 | A1 |
20080285640 | McCallister et al. | Nov 2008 | A1 |
20090201084 | See et al. | Aug 2009 | A1 |
20100026354 | Utsunomiya et al. | Feb 2010 | A1 |
20100048149 | Tang et al. | Feb 2010 | A1 |
20100225390 | Brown et al. | Sep 2010 | A1 |
20110044158 | Tao et al. | Feb 2011 | A1 |
20110085490 | Schlee | Apr 2011 | A1 |
20110098011 | Camp, Jr. et al. | Apr 2011 | A1 |
20110128992 | Maeda et al. | Jun 2011 | A1 |
20110135035 | Bose et al. | Jun 2011 | A1 |
20110150130 | Kenington | Jun 2011 | A1 |
20110163806 | Hongo | Jul 2011 | A1 |
20110187437 | Perreault et al. | Aug 2011 | A1 |
20110255627 | Gotman et al. | Oct 2011 | A1 |
20110273234 | Heijden et al. | Nov 2011 | A1 |
20110273236 | Heijden et al. | Nov 2011 | A1 |
20120093210 | Schmidt et al. | Apr 2012 | A1 |
20120108189 | McCallister et al. | May 2012 | A1 |
20120119810 | Bai | May 2012 | A1 |
20120119811 | Bai et al. | May 2012 | A1 |
20120119831 | Bai | May 2012 | A1 |
20120154033 | Lozhkin | Jun 2012 | A1 |
20120154430 | Matsushima et al. | Jun 2012 | A1 |
20120176195 | Dawson et al. | Jul 2012 | A1 |
20120200355 | Braithwaite | Aug 2012 | A1 |
20120219048 | Camuffo et al. | Aug 2012 | A1 |
20120286865 | Chandrasekaran | Nov 2012 | A1 |
20120286985 | Chandrasekaran et al. | Nov 2012 | A1 |
20120293252 | Sorrells et al. | Nov 2012 | A1 |
20120295558 | Wang et al. | Nov 2012 | A1 |
20130033317 | Hawkes | Feb 2013 | A1 |
20130034188 | Rashev et al. | Feb 2013 | A1 |
20130044791 | Rimini et al. | Feb 2013 | A1 |
20130094610 | Ghannouchi et al. | Apr 2013 | A1 |
20130094612 | Kim et al. | Apr 2013 | A1 |
20130163512 | Rexberg et al. | Jun 2013 | A1 |
20130251065 | Bai | Sep 2013 | A1 |
20130259159 | McCallister et al. | Oct 2013 | A1 |
20130329833 | Bai | Dec 2013 | A1 |
20140161159 | Black et al. | Jun 2014 | A1 |
20140161207 | Teterwak | Jun 2014 | A1 |
20140177695 | Cha et al. | Jun 2014 | A1 |
20140187182 | Yan et al. | Jul 2014 | A1 |
20140254716 | Zhou et al. | Sep 2014 | A1 |
20140274105 | Wang | Sep 2014 | A1 |
20140347126 | Laporte et al. | Nov 2014 | A1 |
20150043323 | Choi et al. | Feb 2015 | A1 |
20150043678 | Hammi | Feb 2015 | A1 |
20150049841 | Laporte et al. | Feb 2015 | A1 |
20150061761 | Wills et al. | Mar 2015 | A1 |
20150103952 | Wang et al. | Apr 2015 | A1 |
20150123735 | Wimpenny | May 2015 | A1 |
20150171768 | Perreault | Jun 2015 | A1 |
20150325913 | Vagman | Nov 2015 | A1 |
20150326349 | Yang et al. | Nov 2015 | A1 |
20150333781 | Alon et al. | Nov 2015 | A1 |
20150358039 | Xiong et al. | Dec 2015 | A1 |
20150381216 | Shor et al. | Dec 2015 | A1 |
20150381220 | Gal et al. | Dec 2015 | A1 |
20160028433 | Ding et al. | Jan 2016 | A1 |
20160087604 | Kim et al. | Mar 2016 | A1 |
20160094253 | Weber et al. | Mar 2016 | A1 |
20160095110 | Li et al. | Mar 2016 | A1 |
20160100180 | Oh | Apr 2016 | A1 |
20160112222 | Pashay-Kojouri et al. | Apr 2016 | A1 |
20160191020 | Velazquez | Jun 2016 | A1 |
20160241277 | Rexberg et al. | Aug 2016 | A1 |
20160249300 | Tsai et al. | Aug 2016 | A1 |
20160285485 | Fehri | Sep 2016 | A1 |
20160308577 | Molina et al. | Oct 2016 | A1 |
20160373072 | Magesacher et al. | Dec 2016 | A1 |
20170005627 | Zhao et al. | Jan 2017 | A1 |
20170033969 | Yang et al. | Feb 2017 | A1 |
20170041124 | Khandani | Feb 2017 | A1 |
20170047899 | Abdelrahman et al. | Feb 2017 | A1 |
20170077981 | Tobisu et al. | Mar 2017 | A1 |
20170176507 | O'Keeffe et al. | Jun 2017 | A1 |
20170237455 | Ye et al. | Aug 2017 | A1 |
20170302233 | Huang | Oct 2017 | A1 |
20170338841 | Pratt | Nov 2017 | A1 |
20180097530 | Yang et al. | Apr 2018 | A1 |
20180167092 | Hausmair et al. | Jun 2018 | A1 |
20180287569 | Xu et al. | Oct 2018 | A1 |
20180337700 | Huang et al. | Nov 2018 | A1 |
20190238204 | Kim et al. | Aug 2019 | A1 |
20190260401 | Megretski et al. | Aug 2019 | A1 |
20190260402 | Chuang | Aug 2019 | A1 |
Number | Date | Country |
---|---|---|
WO2012154430 | Nov 2012 | WO |
WO2018156932 | Aug 2018 | WO |
WO2018213558 | Nov 2018 | WO |
WO2018227093 | Dec 2018 | WO |
WO2018227111 | Dec 2018 | WO |
WO2019014422 | Jan 2019 | WO |
WO2019070573 | Apr 2019 | WO |
WO2019094713 | May 2019 | WO |
WO2019094720 | May 2019 | WO |
Entry |
---|
Aguirre, et al., “On the Interpretation and Practice of Dynamical Differences Between Hammerstein and Wiener Models”, IEEE Proceedings on Control Theory Appl; vol. 152, No. 4, Jul. 2005, pp. 349-356. |
Barradas, et al. “Polynomials and LUTs in PA Behavioral Modeling: A Fair Theoretical Comparison”, IEEE Transactions on Microwave Theory and Techniques; vol. 62, No. 12, Dec. 2014, pp. 3274-3285. |
Bosch, et al. “Measurement and Simulation of Memory Effects in Predistortion Linearizers,” IEEE Transactions on Mircrowave Theory and Techniques; vol. 37. No. 12; Dec. 1989, pp. 1885-1890. |
Braithwaite, et al. “Closed-Loop Digital Predistortion (DPD) Using an Observation Path with Limited Bandwidth” IEEE Transactions on Microwave Theory and Techniques; vol. 63, No. 2; Feb. 2015, pp. 726-736. |
Cavers, “Amplifier Linearization Using a Digital Predistorter with Fast Adaption and Low Memory Requirements”, IEEE Transactions on Vehicular Technology; vol. 39; No. 4; Nov. 1990, pp. 374-382. |
D'Andrea et al., “Nonlinear Predistortion of OFDM Signals over Frequency-Selective Fading Channels”, IEEE Transactions on Communications; vol. 49; No. 5, May 2001; pp. 837-843. |
Guan, et al. “Optimized Low-Complexity Implementation of Least Squares Based Model Extraction of Digital Predistortion of RF Power Amplifiers”, IEEE Transactions on Microwave Theory and Techniques; vol. 60, No. 3, Mar. 2012; pp. 594-603. |
Henrie, et al., “Cancellation of Passive Intermodulation Distortion in Microwave Networks”, Proceedings of the 38th European Microwave Conference, Oct. 2008, Amsterdam, The Netherlands, pp. 1153-1156. |
Hong, et al., “Weighted Polynomial Digital Predistortion for Low Memory Effect Doherty Power Amplifier”, IEEE Transactions on Microwave Theory and Techniques; vol. 55; No. 5, May 2007, pp. 925-931. |
Kwan, et al., “Concurrent Multi-Band Envelope Modulated Power Amplifier Linearized Using Extended Phase-Aligned DPD”, IEEE Transactions on Microwave Theory and Techniques; vol. 62, No. 12, Dec. 2014, pp. 3298-3308. |
Lajoinie, et al. “Efficient Simulation of NPR for the Optimum Design of Satellite Transponders SSPAs”, EEE MTT-S International; vol. 2; Jun. 1998; pp. 741-744. |
Li et al. “High-Throughput Signal Component Separator for Asymmetric Multi-Level Outphasing Power Amplifiers”, IEEE Journal of Solid-State Circuits; vol. 48; No. 2; Feb. 2013; pp. 369-380. |
Liang, et al. “A Quadratic-Interpolated LUT-Based Digital Predistortion Techniques for Cellular Power Amplifiers”, IEEE Transactions on Circuits and Systems; II: Express Briefs, vol. 61, No. 3, Mar. 2014; pp. 133-137. |
Liu, et al. “Digital Predistortion for Concurrent Dual-Band Transmitters Using 2-D Modified Memory Polynomials”, IEEE Transactions on Microwave Theory and Techniques, vol. 61, No. 1, Jan. 2013, pp. 281-290. |
Morgan, et al. “A Generalized Memory Polynomial Model for Digital Predistortion of RF Power Amplifiers”, IEEE Transactions of Signal Processing; vol. 54; No. 10, Oct. 2006; pp. 3852-3860. |
Naraharisetti, et al. “Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems”, IEEE Transactions on Microwave Theory and Techniques, vol. 63; No. 7, Jul. 2015; pp. 2199-2210. |
Naraharisetti, et a., “2D Cubic Spline Implementation for Concurrent Dual-Band System”, IEEE, 2013, pp. 1-4. |
Muta et al., “Adaptive predistortion linearization based on orthogonal polynomial expansion for nonlinear power amplifiers in OFDM systems”, Communications and Signal Processing (ICCP), International Conference on, IEEE, pp. 512-516, 2011. |
Panigada, et al. “A 130 mW 100 MS/s Pipelined ADC with 69 SNDR Enabled by Digital Harmonic Distortion Correction”, IEEE Journal of Solid-State Circuits; vol. 44; No. 12; Dec. 2009, pp. 3314-3328. |
Peng, et al. “Digital Predistortion for Power Amplifier Based on Sparse Bayesian Learning”, IEEE Transactions on Circuits and Systems, II: Express Briefs; 2015, pp. 1-5. |
Quindroit et al. “FPGA Implementation of Orthogonal 2D Digital Predistortion System for Concurrent Dual-Band Power Amplifiers Based on Time-Division Multiplexing”, IEEE Transactions on Microwave Theory and Techniques; vol. 61; No. 12, Dec. 2013, pp. 4591-4599. |
Rawat, et al. “Adaptive Digital Predistortion of Wireless Power Amplifiers/Transmitters Using Dynamic Real-Valued Focused Time-Delay Line Neural Networks”, IEEE Transactions on Microwave Theory and Techniques; vol. 58, No. 1; Jan. 2010; pp. 95-104. |
Safari, et al. “Spline-Based Model for Digital Predistortion of Wide-Band Signals for High Power Amplifier Linearization”, IEEE; 2007, pp. 1441-1444. |
Sevic, et al. “A Novel Envelope-Termination Load-Pull Method of ACPR Optimization of RF/Microwave Power Amplifiers”, IEEE MTT-S International; vol. 2, Jun. 1998; pp. 723-726. |
Tai, “Efficient Watt-Level Power Amplifiers in Deeply Scaled CMOS”, Ph.D. Dissertation; Carnegie Mellon University; May 2011; 129 pages. |
Tehrani, et al. “Modeling of Long Term Memory Effects in RF Power Amplifiers with Dynamic Parameters”, IEEE; 2012, pp. 1-3. |
Yu, et al. “Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers”, IEEE Transactions of Microwave Theory and Techniques; vol. 60; No. 12; Dec. 2012, pp. 4198-4208. |
Yu, et al. “Digital Predistortion Using Adaptive Basis Functions”, IEEE Transations on Circuits and Systems—I. Regular Papers; vol. 60, No. 12; Dec. 2013, pp. 3317-3327. |
Yu, et al. “A Generalized Model Based on Canonical Piecewise Linear Functions for Digital Predistortion”, Proceedings of the Asia-Pacific Microwave Conference; 2016, pp. 1-4. |
Zhang et al. “Linearity Performance of Outphasing Power Amplifier Systems”, Design of Linear Outphasing Power Amplifiers; Google e-book; 2003; Retrieved on Jun. 13, 2014; Retrieved from internet <URL: http:www.artechhouse.com/uploads/public/documents/chapters/Zhang-Larson CH2.pdf; pp. 35-85. |
Zhu et al. “Digital Predistortion for Envelope-Tracking Power Amplifiers Using Decomposed Piecewise Volterra Series”, IEEE Transactions on Microwave Theory and Techniques; vol. 56; No. 10; Oct. 2008; pp. 2237-2247. |
Guan et al. “Green communications: Digital predistortion for wideband RF power amplifiers.” IEEE Microwave Magazine 15, No. 7 (2014): 84-99. |
Zhu et al. “Dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers.” IEEE Transactions on microwave theory and techniques 54, No. 12 (2006): 4323-4332. |
Zhu et al. “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series.” IEEE Transactions on Microwave Theory and Techniques 56, No. 7 (2008): 1524-1534. |
Cao et al. “Digital predistortion for high efficiency power amplifier architectures using a dual input modeling approach.” IEEE Transactions on Microwave Theory and Techniques 60, No. 2 (2012): 1-10. |
Naraharisetti. “Linerarization of Concurrent Dual-Band Power Amplifier Using Digital Predistortion.” PhD diss., The Ohio State University, 2014. |
Tehrani et al. “Behavioral modeling of radio frequency transmitters”. Chalmers University of Technology, 2009. |
Molina, et al. “Digital Predistortion Using Lookup Tables with Linear Interpolation and Extrapolation: Direct Least Squares Coefficient Adaptation”, IEEE Transactions on Microwave Theory and Techniques, vol. 65, No. 3, Mar. 2017; pp. 980-987. |
Number | Date | Country | |
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20190260401 A1 | Aug 2019 | US |
Number | Date | Country | |
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62517380 | Jun 2017 | US |