METHOD AND SYSTEM FOR BASEBAND PREDISTORTION LINEARIZATION IN MULTI-CHANNEL WIDEBAND COMMUNICATION SYSTEMS

Abstract

An efficient baseband predistortion linearization method for reducing the spectral regrowth and compensating memory effects in wideband communication systems using effective multiplexing modulation technique such as wideband code division multiple access and orthogonal frequency division multiplexing is disclosed. The present invention is based on the method of piecewise pre-equalized lookup table based predistortion, which is a cascade of a lookup table predistortion and piecewise pre-equalizers.

Claims

1. A method comprising: providing a pre-distortion lookup table (LUT) having N first entries, N being an integer equal to or greater than unity; providing a pre-equalization lookup table (LUT) having M second entries, M being an integer equal to or greater than unity, the pre-equalization LUT being associated with a pre-equalizer; determining an index based on a magnitude of a baseband input signal; generating a sample by multiplying the baseband input signal with an entry of the N first entries in accordance with the index; and pre-equalizing the sample using an entry of the M second entries in accordance with the index to generate a pre-equalized signal, wherein the baseband input signal is a digital complex signal, and each entry of the pre-distortion LUT comprises complex coefficients, and wherein the complex coefficients are obtained by: converting the sample to an analog baseband signal by an analog-to-digital converter while bypassing the pre-equalizer; frequency upconverting the analog baseband signal to an upconverted signal; amplifying the upconverted signal by a power amplifier to obtain an amplified signal; attenuating the amplified signal to an attenuated signal; frequency downconverting the attenuated signal to a baseband signal; and performing an indirect learning least mean square (LMS) algorithm using the baseband signal and the baseband input signal to obtain the complex coefficients.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a schematic diagram showing a piecewise pre-equalized LUT predistortion system in accordance with the invention.

[0013] FIG. 2 is a schematic diagram showing a polynomial-based embodiment of the equalizer 107 of FIG. 1.

[0014] FIG. 3A is a graph showing complex gain adjuster response.

[0015] FIG. 3B is a graph showing piecewise equalizer response in accordance with the invention.

[0016] FIG. 3C is a graph showing response of the cascade of complex gain adjuster and piecewise equalizers in accordance with the invention.

[0017] FIG. 3D is a graph showing a power amplifier response

[0018] FIG. 3E is a graph showing detailed response from the response of the cascade of complex gain adjuster and piecewise equalizers and the complex gain adjuster response.

[0019] FIG. 4A is a graph showing representative linearization results before and after linearization with an embodiment of a memoryless LUT PD using an eight tone test signal with 500 kHz spacing.

[0020] FIG. 4B is a graph showing representative linearization results before and after linearization with a LUT Hammerstein PD using an eight tone test signal with 500 kHz spacing.

[0021] FIG. 4C is a graph showing representative linearization results before and after linearization with a piecewise pre-equalized PD of the present invention using an eight tone test signal with 500 kHz spacing.

[0022] FIG. 4D is a graph showing representative linearization results before and after linearization with a memory polynomial PD using an eight tone test signal with 500 kHz spacing.

[0023] FIG. 5 is a graph showing representative linearization results for the four types of PDs consisting of a memoryless LUT PD, a LUT Hammerstein PD, a piecewise pre-equalized PD of the present invention, and a memory polynomial PD using a sigble W-CDMA carrier, respectively.

[0024] FIG. 6 is a graph showing performance comparisons of the simulation results of the ACPR for the four types of PD consisting of a memoryless LUT PD, a LUT Hammerstein PD, a piecewise pre-equalized PD of the present invention, and a memory polynomial PD using a single W-CDMA carrier, respectively.

[0025] FIG. 7 is a graph showing measured linearization results for the 4 types of PD consisting of a memoryless LUT PD, a LUT Hammerstein PD, a piecewise pre-equalized PD of the present invention, and a memory polynomial PD using a single W-CDMA carrier, respectively.

[0026] FIG. 8 is a graph showing performance comparisons of the measurement results of the ACPR for the 4 types of PD consisting of a memoryless LUT PD, a LUT Hammerstein PD, a piecewise pre-equalized PD of the present invention, and a memory polynomial PD using a single W-CDMA carrier, respectively.

[0027] FIG. 9 is a graph showing complexity estimation of the piecewise pre-equalized PD of the present invention.

[0028] FIG. 10 is a graph showing complexity estimation of the memory polynomial PD.

DETAILED DESCRIPTION OF THE INVENTION

[0029] To overcome the computational complexity and numerical instability of the memory polynomial PD found in the prior art, The present invention, therefore, utilizes an adaptive LUT-based digital predistortion system with a LUT that has been pre-equalized to compensate for memory effects, so as to achieve less computational load than the prior art while also reducing the adjacent channel power ratio (ACPR) to substantially the same degree as the memory polynomial PD has achieved. The system provided by the present invention is therefore referred as a piecewise pre-equalized, lookup table based predistortion (PELPD) system hereafter.

[0030] Preferred and alternative embodiments of the PELPD system according to the present invention will now be described in detail with reference to the accompanying drawings.

[0031] FIG. 1 is a schematic diagram showing an embodiment of a PELPD system in accordance with the invention. As illustrated, the linear magnitude addressing method for the LUT 106 indexing is used as follows:

m=round(|u(n)|.Math.N),

where u (n) is the input signal 101 and the round function returns the nearest integer number which is the index (m) and N is the LUT 106 size.

[0032] The digital complex baseband input signal samples 101 are multiplied prior to pre-equalization 107 by complex coefficients 102 drawn from LUT entries as follows

x(n)=u(n).Math.F.sub.m(|u(n)|),

where F.sub.m(|u(n)|) is the complex coefficient 102 corresponding to an input signal 101 magnitude for compensating AM to AM and AM to PM distortions of the PA 110.

[0033] N by K−1 filter coefficients in the LUT of the piecewise pre-equalizer 107 are used to compensate for memory effects, where N is the depth of the LUT and the FIR filter has K taps. In some embodiments, the piecewise pre-equalizers 107 use a FIR filter rather than an infinite impulse response (IIR) filter because of stability issues, although a FIR filter is not necessarily required for all embodiments. The output 104 of the pre-equalizers can be described by

[00001]$\begin{array}{c}z\left(n\right)=\underset{k=0}{\overset{K-1}{.Math.}}{W}_k^m\left(.Math.u\left(n\right).Math.\right).Math.x\left(n-k\right)\\ =\underset{k=0}{\overset{K-1}{.Math.}}{W}_k^m\left(.Math.u\left(n\right).Math.\right).Math.u\left(n-k\right).Math.F_m\left(.Math.u\left(n-k\right).Math.\right),\end{array}$

[0034] where W.sub.k.sup.m(|u(n)|) is the k-th tap and m-th indexed coefficient corresponding to the magnitude of the input signal, u(n) 101. Also, W.sub.k.sup.m(|u(n)|) is a function of |u(n)| and F.sub.m 102 is a function of (|u(n−k)|. For analysis purposes, the memoryless LUT 106 (F.sub.m) structure can be replaced by a polynomial model as follows:

[00002]$F_m\left(.Math.u\left(n\right).Math.\right)=\underset{p-1}{\overset{P}{.Math.}}{b}_{2p-1}.Math.{.Math.u\left(n-k\right).Math.}^{2\left(p-1\right)}$

[0035] where 2p−1 is the polynomial order and b is a complex coefficient corresponding to the polynomial order. Moreover, it is noted that the tap coefficients and memoryless LUT coefficients (Fm) 102 depend on u(n) and u(n−k), respectively.

[0036] Therefore, each piece of the equalizer can be expressed using a polynomial equation by

[00003]$z\left(n\right)=\underset{k=0}{\overset{K-1}{.Math.}}{W}_k^m\left(.Math.u\left(n\right).Math.\right).Math.\underset{p=1}{\overset{P}{.Math.}}{b}_{2p-1}.Math.u\left(n-k\right).Math.{.Math.u\left(n-k\right).Math.}^{2\left(p-1\right)}$

[0037] where W.sub.k.sup.m(|u(n)|) is the k-th tap coefficient with the m-th index being a function of |u(n)|. Without loss of generality, the piecewise pre-equalizers 107 can be defined similarly using a 1-th order polynomial,

[00004]$z\left(n\right)=\underset{k=0}{\overset{K-1}{.Math.}}\underset{p=1}{\overset{L-1}{.Math.}}{w}_{k,2l-1}.Math.{.Math.u\left(n\right).Math.}^{2\left(l-1\right)}\times \stackrel{P}{\underset{p-1}{.Math.}}{b}_{2p-1}.Math.u\left(n-k\right).Math.{.Math.u\left(n-k\right).Math.}^{2\left(p-1\right)}$

where w.sub.k,l is the k-th tap and 1-th order coefficient.

[0038] After digital-to-analog converting 108 of z(n)104, this signal is up-converted 109 to RF, amplified by the PA 110 generating distortions, attenuated 113, down-converted 114 to baseband, and then finally analog-to-digital converted 115 and applied to the delay 116 estimation algorithm 117. The feedback signal, that is, the output of the PA 110 with delay, y(n−Δ) 105 can be described by

[00005]$y\left(n-\Delta \right)=G\left(.Math.z\left(n-\Delta \right).Math.\right).Math.e^{j.Math.\Phi \left(\left|z\left(n\Delta \right)\right|\right)}$

[0039] where G(⋅) and Φ(⋅) is AM/AM and AM/PM distortions of the PA 110, respectively and A is the feedback loop delay. For estimating Δ, a correlation technique was applied as follows:

[00006]$R\left(d\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{.Math.}}z\left(n\right).Math.y^{*}\left(n+d\right)$

where d is the delay variable and N is the block size to correlate.

[0040] After delay 116 estimation, the memoryless LUT 106 coefficients can be estimated by the following equation which is the least mean square (LMS) algorithm with indirect learning.

F.sub.m(|u(n+I)|)=F.sub.m(|u(n)|)+μ.Math.u(n).Math.e(n)

where n is the iteration number, μ is the stability factor and e(n) is x(n)−y(n).Math.F.sub.m(|x(n)|).

[0041] It should be pointed out that addressing already generated can be reused for indexing y(n)105 which is a distorted signal able to cause another error due to incorrect indexing. During this procedure, the samples, x(n) 103, should bypass by the piecewise pre-equalizers 107. After convergence of this indirect learning LMS algorithm, the equalizers 107 are activated. An indirect learning method with an LMS algorithm has also been utilized for adaptation of the piecewise filter coefficients. The input of the multiple equalizers 107 in the feedback path is written in vector format as

[00007]$y_{FI}\left(n\right)=\left[y_F\left(n\right)y_F\left(n-1\right)\mathrm{.Math.}{y}_F\left(n-K+1\right)\right]$

[0042] where y.sub.F(n) is the post LUT output, that is, y(n).Math.F.sub.m(|y(n)|).

[0043] Therefore, the multiple FIR filter outputs, yFO(n), can be derived in vector format using the following equations.

[00008]$y_{FO}\left(n\right)=W^m.Math.{y_{FI}\left(n\right)}^T$$W^m=\left[W_0^m{W}_1^m\mathrm{.Math.}{W}_{k-1}^m\right]$

[0044] where T is a transpose operator.

[0045] Adaptation of the tap coefficients of the pre-equalizers 107 can be obtained as follows:

W.sup.m(|u(n+1)|)=W.sup.m(|u(n)|)+μ.Math.(y.sub.F1(n).sup.T)*.Math.E(n)

[0046] where E(n) is the error signal between z(n) and yFO(n), and μ is the step size (* represents the complex conjugate). The adaptation algorithm determines the values of the coefficients by comparing the feedback signal and a delayed version of the input signal.

[0047] Referring to the feedback path beginning at output 111, it will be appreciated that several alternatives exist for using such feedback to update the LUT values or polynomial coefficients. In some embodiments, the output of the PA is converted to baseband, and the resulting baseband signal is compared to the input signal. The resulting error is used to correct the LUT values and coefficients. In other embodiments, the output from the PA is spectrally monitored and the out of band distortion is monitored using a downconverter, bandpass filter and power detector. The power detector value is then used to adjust the LUT values or polynomial coefficients.

[0048] FIG. 2 illustrates the corresponding block diagram of the piecewise pre-equalizers 107 PD when polynomial equations are utilized. The polynomial representation requires too many complex multiplications similar to the Volterra series. The complexity is reduced when a PELPD-based approach, as shown in FIG. 1, is utilized, because fewer calculations are required, although more memory may be required. It will be appreciated from the discussion herein that the pre-equalizing portion is adaptive and designed to correct memory effects, while the lut serves primarily to pre-distort to correct the other nonlinearities found in commercial PA's.

[0049] FIGS. 3A-3D are graphical explanations of the PELPD of the present invention. A typical memoryless predistorter response is shown in FIG. 3A. FIG. 3B demonstrates the hysteresis created by the piecewise pre-equalizers divided into N pieces. Since the hysteresis of the power amplifier is not necessarily uniformly distributed over the whole input magnitude range, the piecewise pre-equalizers are applied to achieve a uniform compensation across the entire input range. The output of the PELPD of the present invention is illustrated in FIG. 3C, which can be thought of as resulting from a cascade of FIGS. 3A and 3B. FIG. 3D shows the response of a typical power amplifier response and FIG. 3B results in the PELPD of the present invention as represented in FIG. 3C. FIG. 3D shows the response of a typical power amplifier response with memory. The desired linear response in FIG. 3E is achieved after FIG. 3C and FIG. 3D are cascaded.

[0050] In order to examine the performance of the PELPD of the present invention, the behavioral modeling of a PA based on time domain measurement samples was first carried out. The behavioral model was based on the truncated Volterra model. A 300 W peak envelope power (PEP) Doherty PA using two 170 W push-pull type laterally diffused metal oxide semiconductors (LDMOS) at the final stage was designed. This Doherty PA operates at 2140 MHz band and has 61 dB of gain and 28% power added efficiency (PAE) at an average 30 W output power. To construct the PA model based on measurements of the actual PA, the test bench was utilized [K. Mekechuk, W. Kim, S. Stapleton, and J. Kim, “Linearinzing Power Amplifiers Using Digital Predistortion, EDA Tools and Test Hardware,” High Frequency Electronics, pp. 18-27, April 2004]. Based on the behavioral model, various types of PDs including a memoryless LUT PD, a Hammerstein PD, the PELPD of the present invention and a memory polynomial PD have been simulated and the adjacent channel power ratio (ACPR) performances are compared. The LUT size was fixed to 128 entries through all simulations, which is a compromise size considering quantization effects and memory size. Those skilled in the art will recognize that the amount of compensation for nonlinearities is related to the size of the LUT 106. Increases in LUT size, while yielding a more accurate representation of the nonlinearities, comes at the cost of more effort in the adaptation. Thus, selection of LUT size is a trade-off between accuracy and complexity.

[0051] As a test signal, a single downlink W-CDMA carrier with 64 dedicated physical channels (DPCH) of Test Mode based on 3rd Generation Partnership Project (3GPP) standard specifications, which has 3.84 Mchips/s and 9.8 dB of a crest factor. First, an eight tone signal with 500 kHz spacing which has 9.03 dB of PAR and 4 MHz bandwidth, which is comparable to a W-CDMA signal, was used for verifying the proposed method.

[0052] FIGS. 4A-4D are graphs showing representative linearization results before and after linearization of the four types of PD. As shown in FIG. 4A, a conventional memoryless LUT PD was able to improve the linearity and also compensate for the memory effects. FIG. 4B shows a conventional Hammerstein PD which deteriorates the performance above 10 MHz and improves it within a 10 MHz bandwidth. If the RF frequency response in the main signal path is quite flat, the Hammerstein PD is not able to correct any other memory effects except for frequency response memory effects. There is also no obvious improvement for reducing spectral regrowth using the conventional Hammerstein PD. It is very clear that the ability of the Hammerstein PD for suppressing distortions coming from memory effects is quite limited. FIG. 4C shows the performance of the PELPD of the present invention (with 2 taps). FIG. 4D illustrates the performance of a conventional memory polynomial PD (with 5th order and two memory terms). By comparing FIGS. 4A-4D, it can be seen that the PELPD of the present invention is comparable to the memory polynomial PD in terms of ACPR performance.

[0053] FIG. 5 is a graph showing linearization results for the four types of PD mentioned above. A single W-CDMA carrier was applied to the LUT PD, the LUT Hammerstein PD, the PELPD of the present invention, and the memory polynomial PD.

[0054] FIG. 6 is a graph showing performance comparisons of the simulation results of the ACPR for the 4 types of, respectively. The conventional Hammerstein PD was unable to improve any distortions coming from memory effects over the memoryless PD. The PELPD of the present invention could suppress distortions due to nonlinearities as well as memory effects of the PA.

[0055] After verifying the ACPR performance of the PELPD of the present invention in the simulations based on the behavioral PA model, an experiment was performed using the actual Doherty PA in the test bench. The transmitter prototype consists of an ESG which has two digital to analog converters (DACs) and a RF up-converter, along with the PA. The receiver comprises an RF down-converter, a high speed analog to digital converter, and a digital down-converter. This receiver prototype can be constructed by a VSA. For a host DSP, a PC was used for delay compensation and the predistortion algorithm. As a test signal, two downlink W-CDMA carriers with 64 DPCH of Test Model 1 which has 3.84 Mchips/s and 9.8 dB of a crest factor was used as the input signal in the measurements in order to verify the compensation performance of the different PDs. All coefficients of PDs are identified by an indirect learning algorithm which is considered to be inverse modeling of the PA. During the verification process, a 256-entry LUT, 5 taps FIR filter for Hammerstein PD, the PELPD of the present invention (with 2 taps), and a 5th order-2 delay memory polynomial were used. The choice of the number of taps was optimized from several measurements.

[0056] FIG. 7 is a graph showing the measured linearization results before and after linearization of the 4 types of PD using a single W-CDMA carrier, respectively. ACPR calculation at the output of the prototype transmitter, is performed at a frequency offset (5 MHz and −5 MHz) from the center frequency.

[0057] FIG. 8 is a graph showing performance comparisons of the measurement results of the ACPR for the 4 types of PD using a single W-CDMA carrier, respectively. The ACPR value for the transmitter with the Hammerstein PD having a 5 tap FIR filter is about 1 dB better than a LUT PD on the upper ACPR (5 MHz offset) and the same at the lower ACPR (−5 MHz offset). The PELPD of the present invention and a 5th order-2 memory polynomial PD show close compensation performance in terms of ACPR. Both are able to improve the ACPR about 4 dB and 6 dB more than Hammerstein PD and a memoryless LUT PD, for the lower and upper ACPR, respectively.

[0058] The complexity of the PELPD method of the present invention and the memory polynomial method is also evaluated (neglecting LUT readings, writings, indexing, and calculation of the square root (SQRT) of the signal magnitude, because LUT indexing depends not only on the methods, but also on the variable, for example, magnitude, logarithm, power, and so on and the SQRT operation can be implemented in different ways). Therefore, the complexity is only estimated by counting the number of additions (subtractions) and multiplications per input sample. In order to consider a real hardware implementation, complex operations are converted into real operations and memory size is also considered. For example, one complex multiplication requires two real additions and four real multiplications. If N is the number of LUT entries, memory size required is 2N (I&Q LUTs).

[0059] FIG. 9 is a graph showing complexity estimation of the PELPD of the present invention. If the LUT has 256 entries and the filters have 2 taps, the PD requires 40 real additions (subtractions), 54 real multiplications per sample, and a memory size of 1542. The PELPD of the present invention requires the same number of additions and multiplications as the traditional Hammerstein PD, but requires more memory.

[0060] FIG. 10 is a graph showing complexity estimation of the memory polynomial PD using an RLS indirect learning algorithm. The number of arithmetic operations are given in FIG. 11, where O is equal to P(K+1). For example, P=5 and K=1 require 1342 real additions (subtractions), 1644 real multiplications per sample, and memory size of 24. In a comparison of the number of multiplications with the PELPD of the present invention, the memory polynomial PD requires 300 times more real multiplications per sample. Therefore, the complexity is significantly reduced by the PELPD method. In addition, the number of real multiplication for the memory polynomial method grows as the square power of the polynomial order and memory length.

[0061] In summary, the PELPD of the present invention, compared to the conventional Hammerstein approach, could reduce spectral regrowth more effectively and achieve a similar correction capability with the memory polynomial PD, but requires much less complexity.

[0062] Although the present invention has been described with reference to the preferred and alternative embodiments, it will be understood that the invention is not limited to the details described thereof. Various substitutions and modifications have been suggested in the foregoing description, and others will occur to those of ordinary skill in the art. Therefore, all such substitutions and modifications are intended to be embraced within the scope of the invention as defined in the appended claims.