WO2001029963A1

WO2001029963A1 - Adaptive digital predistortion for amplifier linearization

Info

Publication number: WO2001029963A1
Application number: PCT/US2000/029346
Authority: WO
Inventors: Rajeev Khrishnamoorthy
Original assignee: Lucent Technologies, Inc.
Priority date: 1999-10-20
Filing date: 2000-10-20
Publication date: 2001-04-26
Also published as: AU1342101A

Abstract

The invention provides techniques for performing predistortion for a power amplifier in order to compensate for amplifier nonlinearities. The cost function to determine the performance includes constellation distortion as well as spectral regrowth. Quasi-optimum techniques are described which are simple to implement and introduce negligible degradation relative to the optimum approach. Approximation approaches allow trade offs between memory, complexity, and performance. Finally, adaptive algorithms are to allow adaptation to changing signal and power amplifier characteristics.

Description

ADAPTIVE DIGITAL PREDISTORTION FOR AMPLIFIER LINEARIZATION

Rajeev Krishnamoorthy

This application claims the benefit of U.S. Provisional Application No. 60/160,607 filed 20 October 1999.

BACKGROUND OF THE INVENTION

1. Field of the Invention. This invention relates to power amplifiers and, more particularly, to techniques for linearization of power amplifiers in communication systems.

2. Prior Art. Previously, attempts to linearize power amplifiers have generally focused on the reduction of spectral regrowth, and have been driven by regulatory constraints regarding limits on the out-of-band emissions that are permissible. Further, the majority of linearization techniques that have been implemented have been analog techniques; while digital techniques have been described in the open literature these have also, generally, focused on the spectral regrowth issues, including out-of-band emissions.

SUMMARY OF THE INVENTION

The present invention accounts for signal distortion as well as spectral regrowth into the design of power amplifiers. The tradeoffs between amplifier efficiency, distortion, and spectral regrowth are quantified. Using these, simple, easily implementable, controlled suboptimal predistortion techniques are provided to enhance the performance of communication systems using such power amplifiers.

BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention:

FIG. 1 shows a block diagram of a conventional transmitter.

FIG 2 shows a block diagram of a transmitter that incorporates baseband predistortion.

FIG. 3 shows the power characteristics of an amplifier.

FIG. 4 illustrates the basic idea of predistortion.

FIG. 5 shows a mapping function.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Reference is now made in detail to preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention is described in conjunction with the preferred embodiments, it will be understood that it is not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention as defined by the appended claims.

1. Models

1.1 Transmitter

Figure 1 shows a block diagram of a conventional transmitter 10. In a digital section 12 of the conventional transmitter 10, input data bits d are mapped in a constellation mapper 14 onto a symbol constellation. A resulting complex data stream x is then convolved with a pulse-shaping filter 16 to produce samples v. In an analog section 17, the discrete, complex sample stream is then converted by an analog circuit 18 to an analog signal via a D/A converter, quadrature modulated, and upconverted to RF frequencies. This analog signal is the amplified in a power amplifier 20 and transmitted as a signal u.

FIG. 1 also shows that the analog section 17 of the transmitter described above is modeled as a linear circuit h( ), followed by a nonlinear transfer function, a( •), according to a paper by Maas titled "Nonlinear Microwave Circuits", Reprinted by IEEE, August ,1996. An assumption is made that the frequency response, H(ω), of the linear circuit is flat in the region of interest and is sufficiently broadband that it introduces negligible distortion into the signal v. The linear circuit h( ) is typically composed of image rejection filters and a matching network, and so this assumption holds quite well for narrowband signals, such as those used in cellular networks. The transfer function a(-) is the response of the power amplifier 20. Note that there could also be an output-matching network following the nonlinear section which can be modeled as a linear circuit so that the previous comments apply.

Figure 2 shows the block diagram of a transmitter 20 that incorporates baseband predistortion in a predistorter 24, according to the invention. Note that the transmitter 20 now incorporates a receiver block 22 that includes attenuation, down-conversion, and demodulation functions to produce a recovered data signal v*. The output of the pulse shaping filter v and the recovered data signal v* are processed with a predistortion algorithm as indicated by block 26 to provide a distortion error control signal on a control line 28 to the predistorter 24. Note that since, in practice, the predistorter 24 is adapted only infrequently, a loopback from the output of the amplifier into an existing receiver path could be used to perform predistortion updates.

Let v be a discrete sampled stream, which is the output of the pulse-shaping filter 16. Passing v through the predistorter function, f( ), results in r, which is quadrature modulated and upconverted in the analog circuitry 18. For simplicity and taking the comments about the linear circuit h(-) into account, we shall assume that r is the input to the amplifier. The output of a non-linear power amplifier 30 is u=a(r), the transmitter signal. 1.2 Power Amplifier

A power amplifier is typically described by its AM- AM and AM-PM characteristics as illustrated in FIG. 3. In FIG. 3, -7 is the efficiency of the amplifier, and Δφ is the phase rotation in degrees. The output power, P_out has been normalized so that the gain is unity (0 dB) when P,„ =0 dB.

We see from the figure that while the amplifier response to low amplitude signals is fairly clean with constant gain and very little phase distortion, this does not hold true at higher values of P_m On the other hand, we also note that the efficiency, η, increases with increasing input power. The problem, therefore, is to operate the power amplifier 30 as efficiently as possible while containing the distortion introduced by the nonlinear amplifier 30.

1.3 Performance Metrics

Traditionally, out-of-band spectral regrowth has been used as the metric for determining the backoff of the input signal to the power amplifier. This is certainly a necessary condition, since regulatory constraints regarding the out-of-band power of a transmitted signal must be met. However, little consideration has been given to the in-band distortion introduced by the nonlinearity of the power amplifier. If out-of-band distortion were the only criterion, then performance goals could be met by simply adding a filter at the output of the power amplifier to attenuate the out- of-band emissions. This approach would, however, increase the distortion in the desired signal.

The approach that is disclosed by the present invention is to factor in constellation distortion, that is the in-band signal-to-distortion ratio and the resulting efficiency of the power amplifier, in addition to the out-of-band emissions, when determining the predistortion technique and input backoff level to be used. This integrated approach allows designers of communication systems to tailor the complexity of the predistortion algorithms to fit the desired spectral mask and the bit error rate performance of the system as determined by the SDR.. Method

In the predistortion techniques that are described, a reduction in constellation distortion always results in a reduction in spectral regrowth. Consequently, it suffices to measure the constellation distortion. FIG. 2 illustrates that this can be done in a predistortion algorithm block 26 by passing the recovered data signal v* through a receiver, slicing the resulting filtered signal, and subtracting the sliced value from the constellation point. Doing this for a large number of points will result in a complete characterization of the distortion.

Algorithm for Determining Performance Metrics

One implementation of an algorithm for determining performance metrics is as follows:

1. Perform timing recovery on the received sample stream, v*. Let the delay be t.

2. For a specified number of symbols, N,

2.1 Slice v* at the appropriate sampling instant. Let x* (k) = slice (v*kT + t))-

2.2 Find the error vector, ε=x(k) -x*(k). 2.3 Collect error statistics (e.g. sum, histogram, exceeds threshold, etc.)

3. Return desired error statistics

For all the predistortion techniques described below, the transceiver measures the constellation distortion for a variety of input backoff values, and settles on an acceptable level.

1.4 Tradeoff between Efficiency and Constellation Distortion

The constellation distortion technique described above is a function of the input backoff level. For each input backoff level, the system estimates the efficiency, η. Given this efficiency estimate, the system determines a required backoff level at which to operate in order to satisfy given performance requirements, such as maximum allowable distortion, minimum required efficiency, or a combination of these two performance requirements that results in optimizing system performance.

2. Description of Techniques FIG. 4 illustrates the basic idea of predistortion. Consider the scenario depicted in FIG. 4. Let r_raw be the amplitude of the input. The desired output is a _es- The output due to the amplifier, however, is a_amP. In order to obtain the desired output, therefore, the input signal has to be r_Pd.

2.1 Look-Up Table Approaches

One commonly used technique for accomplishing predistortion is by using a table of predistortion values. Values of r, A(r), Δφ(r) are stored in the table. For every complex input, r, the predistorter 24 looks up the closest value of A(r) available in the table, then looks up the resulting phase distortion, Δφ(r), based on this predistorted value, and puts out a complex predistorted sample.

For the look-up table technique, the parameters among which a tradeoff is to be accomplished are:

(1) the size of the look-up table;

(2) the complexity of the algorithm to be used in calculating the input spacing of the table;

(3) the adaptation capability of (2);

(4) the minimum in-band output IBO required to meet out-of-band emissions criteria, resulting from (1) & (2), and

(5) the performance: resulting efficiency and signal-to-distortion ratio SDR resulting from (1), (2), and (3).

The spacing of the input levels in the look-up table is derived via a companding function, s(r). Equally-spaced amplitude input levels, for example, corresponds to s(r)=r, equi-spacing by power levels corresponds to s(r)=τ . If a(r) is the response of the amplifier to the input, r, following an approach according to a paper by J.K. Cavers titled "Optimum Indexing in Predistorting Amplifier Linearizers", IEEE 47^th Vehicular Technology Conference, 1997, let g(r)=a(r)/r be the (complex) transfer characteristic of the power amplifier. If f(r) is the transfer characteristic of the predistorter, then f₀pt(r)gop_t (r)=C, where C, a constant, is the "linear gain" of the predistorter/amplifier combination. Given a power amplifier, look-up table size, N, and signal power distribution function PDF, p(r), let the optimum compander (where optimum is used in a minimum mean-squared error sense), be s_opt. Then the derivative can be expressed according to Cavers as

s_opt . [INSERT EQUATION HERE]

where [INSERT EQUATION HERE].

The optimum companding function takes both the derivative of the amplifier gain as well as the (power) weighted PDF of the signal. A sub-optimum approach, but one which reduces the complexity of estimating the spacing, and which works well for amplifier over the quasi-linear range, is to use

[INSERT EQUATION HERE]

One way of implementing this is as follows:

Algorithm for Finding Input Spacing

0. Input parameters: 0.1. Backoff level

0.2. r_mj_π and r_max are the minimum and maximum input values of the signal amplitude. For M-PSK and M-QAM constellations, r_mi_n will be 0.

0.3 Number of bins, N_bi_ns, into which the interval [r_mj_n , r_ma will be divided (i.e., size of the memory in which statistics are collected) 0.4 Number of look-up table points NLUT

1. For a number of symbols, N_symbois

1.1 For each received sample, r, find the appropriate bin, k 1.2 Add r² to the k^th bin (results in w(r) when properly normalized)

2. Find the cube root of the values in each bin (results in w(r)^{1 3}).

3. Sum the values of w(r)^1/3 -results in an approximation for |w(r)^1/3 )

4. Divide the values obtained in step 4 by the result of step 5 (results in s(r)).

5. Obtain the values of s(r) by summing the values of s(r) obtained in step 6

5.1 s_mj_n and s_max are, respectively, the minimum and maximum values of s(r)

6. Divide the interval [s_mill , s_max] into N_Luτ points, {si, S₂,...,S_NLUT}

7. Find the points, {r_l5 r₂,...,r_NLUτ}, corresponding to {s_1? S₂,...,S_NLUT} - This is the result.

The look-up procedure requires a search among the table entries to determine which entry is appropriate. If input values {v_ls V ,...,V_N} are stored, then the first step in the procedure is to determine k, such that V_k = min( Iv-v ). FIG. 5 shows that this could be done by a mapping function. If there is no mapping function, this step involves a search. Following this, the appropriate value is output. This could either be a complex number, or an amplitude and phase pair, which will have to be converted to a complex sample.

The mapping function can be implemented in a variety of ways. In the case of equally-spaced amplitude points, let Δv so that v_m = mΔv + vj. Then m(v) = round (v-vj) / Δv. For other companding functions, the tradeoff will have to be made between the length required for a search, the memory required for the mapping function, and the complexity of implementing the mapping function.

2.2 Linear Polynomial Approximation In this technique, the predistorter multiplies the sample inputs with a polynomial that corrects the nonlinearity of the amplifier. The novelty introduced here is the choice of data points to which the polynomial is fit. We use the "Algorithm for Finding Input Spacing" to find the set of input values and the corresponding output values. Following this, we solve for the polynomial. One way to implement this is: Algorithm to Find a Linear Polynomial to carry out Predistortion

0. Input parameters:

0.1 Same as for "Algorithm for Finding Input Spacing" 0.2 Degree of Polynomial, N_Poiy

1. Get Spacing using "Algorithm for Finding Input Spacing". We now have the input points, {r_l5 r₂,...,r»χuτ}, and the corresponding output values {s_1?

S ,...,SNLUT

2. Form the set of linear equations, S = Pfø) =[INSERT

3. Solve for the set of coefficients, {p_m}- This can be done in a number of standard ways, for example by using Singular Value Decomposition, Cholesky Factorization, etc.

2.3 Rational Approximation of Predistortion Function

This technique is similar to that described in the "Linear Polynomial Approximation" section, but it attempts to approximate the predistortion using the quotient of two polynomials, P(r) and Q(r), i.e., the predistorter multiplies the sample inputs, r, by P(r) / Q(r).

Here again, the choice of data points to which the polynomial is fit is determined by using the "Algorithm for Finding Input Spacing" to find the set of input values and the corresponding output values. Following this, we solve for two polynomials. One way to implement this is: Algorithm to Find a Linear Polynomial to carry out Predistortion

4. Input parameters:

4.1 Same as for "Algorithm for Finding Input Spacing"

4.2 Degree of Numerator Polynomial N_num and Denominator Polynomial,

Nden 5. Get Spacing using "Algorithm for Finding Input Spacing". We now have the input points, , {x , Γ₂,...,Γ_NLUT}, and the corresponding output values {s_{l 5} S₂,...,SNLUT- 6. Form the set of equations,

sk = [INSERT EQUATION HERE]

7. Solve for the set of coefficients,. {p_m, q_m}- This can be, for example, by using the Pade approximation technique.

3. Adaptation

3.1 Varying Signal and Power Amplifier Characteristics

The need for the predistorter to dynamically adapt to changing system characteristics arises when either the signal characteristics (i.e., the PDF) or the power amplifier characteristics (e.g., as a function of temperature) change.

There are a number of situations in which the need for adaptation arise. Some of them include: Dynamic modulation schemes: based on the feedback regarding the

Signal-to-Noise plus Interference Ratio, a variety of constellations can be used to maximize data throughput. For example, in a TDMA system, each time slot could carry a different modulation scheme.

Multi-Carrier Systems: In systems which use multi-carrier modulation (e.g., OFDM), the number of transmitted carriers can vary depending on the traffic load. This will change the distribution of the transmitted signal.

CDMA: Base stations in a CDMA system can transmit one to several signals, each one convolved with a distinct PN spreading sequence. The number of such signals will, again, depend on the traffic load. This will change the distribution of the transmitted signal.

Time and Temperature Variation of the Power Amplifier Characteristics: Both temperature and aging cause the PA characteristics to change. The temperature variation occurs during a single usage session, as the components heat up, whereas the aging dynamic occurs over a period of months and years.

No single technique will be suited to handle all these situations. We describe some techniques, and discuss the applicability of each to the various cases.

3.2 Separate Lists & Coefficient Sets

In this case of differing modulation schemes, keeping separate sets of coefficients for the polynomial (or table values for the look-up table approach) is the simplest. The appropriate set is accessed depending on the modulation scheme being used. This technique can also be used for multi-carrier and CDMA systems , where the number of states over which PDF ranges is finite. This assumes that the power amplifier characteristics are not varying.

3.3 Linked Lists

In the standard table lookup technique, the table is simply arranged in ascending value. Based on the input sample (with no mapping function implemented) the table is searched until the closest stored input value is found.

If we wish to insert or delete an input/output pair, this will affect the memory location of all entries which follow this pair. With a linked list, each entry has a pointer to the previous and succeeding entry's memory location (the first and last entries have specific, reserved values for the previous and succeeding location, which indicate the head and tail of the list). In this manner, we achieve two objectives:

1. the ordering of the list is not linked to memory locations

2. changes in the table can be achieved by simply changing the appropriate pointers, thereby removing the need for reordering the table. Note that once an entry is changed or deleted, its location is declared free, and future updates can be overwritten on this location. Consequently, in addition to providing a smooth way of updating the look-up table, this procedure reduces the memory requirement for doing updates by not requiring an entirely separate table to be generated before removing the outdated one.

This technique is useful for temporal and temperature changes of the amplifier, as well as a signal whose PDF changes slowly over time. It could be used for the multi-carrier or the CDMA case where the system is willing to accept a degradation in performance for short periods of time while the predistortion values are updated to reflect the changes in the signal characteristics.

3.4 Adaptive Approximation Algorithms

Calculating and updating the polynomial coefficients can be done in one of two ways: 1. With a series of random input values and using an adaptive technique such as steepest descent, LMS, or RLS. The advantage of such a technique is that it is simple to implement. There are two drawbacks: first, the convergence speed could be slow (especially with LMS). Second, since the input values are not chosen in an optimum or quasi-optimum fashion, the solution could have a large error (see, for example, the constellation distortion in figure 10 due to using equi- amplitude spacing.)

2. By using a quasi-optimum such as the r PDF companding approach to finding a set of input points, and then calculating or updating the polynomial to fit the inverse function. By performing an SVD or a recursive QR decomposition on the desired points, the calculation of the polynomial coefficients can be done simply. The performance of this substantially outperforms the first alternative.

4. Conclusions

Techniques for performing predistortion at baseband have been described.

We started with defining the cost function, over which the optimization is performed, to include constellation distortion as well as spectral regrowth. A quasi- optimum look-up table technique was described that is simple to implement and introduces negligible degradation relative to the optimum. We also described polynomial approximation approaches, which allow designers of communication systems to trade off between memory, complexity, and performance. Finally, adaptive algorithms were described which allow the various techniques to adapt to changing signal and power amplifier characteristics.

The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.

Claims

I CLAIM:

1. A system for providing predistortion to a power amplifier to compensate for power amplifier nonlinearities, comprising: a predistorter that is controlled by a a distortion error control signal and that receives a discrete sampled data stream signal v which is passed through the predistorter function, f( ), to provide a predistorted output signal r for driving the power amplifier; and means for implementing a predistortion algorithm from the a discrete sampled data stream signal v and a recovered data signal v* from the output of the power amplifier and for providing the distortion error control signal to the predistorter.

2. The system of Claim 1 wherein the means for implementing the predistortion algorithm includes passing the recovered data signal v* through a receiver, slicing the resulting filtered signal, and subtracting the sliced value from a constellation point for the discrete sampled data stream signal v for a number of constellation points to provide characterization of the distortion.

3. The system of Claim 3 wherein the means for implementing the predistortion algorithm uses adaptive look-up tables to provide for dynamically adjusting to changing amplifier and signal modulation characteristics.

4. The system of Claim 1 wherein the means for implementing the predistortion algorithm uses Polynomial approximation.

5. The system of Claim 1 wherein the means for implementing the predistortion algorithm uses an adaptive polynomial approximation to dynamically adjust to changing amplifier and modulation characteristics.

6. The system of Claim 1 wherein the means for implementing the predistortion algorithm uses look-up tables.

7. The system of Claim 1 including means estimating the efficiency η of the power amplifier for each input backoff level of the power amplifier and for providing a tradeoff between amplifier efficiency and constellation distortion, where the constellation distortion technique described above is a function of the input backoff level, in order to satisfy given performance requirements, including maximum allowable distortion, minimum required efficiency, or a combination of thereof that provides a desired power amplifier performance level.

8. The method of Claim 7 wherein the tradeoff includes a cost function that includes an in-band signal-to-distortion ratio as well as a spectral regrowth value.