Open-Loop Digital Predistortion Using Cartesian Feedback for

Open-Loop Digital Predistortion Using Cartesian Feedback for Adaptive RF Power Amplifier Linearization SungWon Chung, Jack W. Holloway, and Joel L. Dawson Massachusetts Institute of Technology, Cambridge, MA 02139 Abstract— We present a new adaptive power amplifier (PA) linearization technique. We leverage analog Cartesian feedback (CFB) to train a Cartesian look-up table, reducing DSP and power amplifier modeling requirements to a min- imum and eliminating model convergence as a design issue. Because the CFB system does not continuously operate, we overcome the bandwidth limitation traditionally associated with this technique. In addition, we exploit sample averaging to greatly relax the noise requirements of the analog feed- back path. We implemented a prototype 900-MHz direct- conversion transmitter with a class-A PA. We measured a 10-dB reduction of out-of-band distortion products with no noise floor degradation for 40-MHz-bandwidth, 16-QAM test signals. Index Terms— wideband systems, predistortion, adaptive predistortion, digital predistortion, Cartesian feedback, PA linearization, adaptive linearization, power amplifiers. I. INTRODUCTION Streaming video applications in portable units will require dense channel spacings to accommodate simul- taneously operating multiple terminals. In addition, the need for energy-efficient communication naturally leads to a spectrally efficient modulation. The combination of dense channel spacings and spectrally efficient modulation techniques imposes severe linearity requirements on the power amplifier (PA). The problem is that stringent linearity requirements take the PA from being merely power-hungry to being incredibly inefficient. In theory, linear PAs can achieve 50% drain efficiency at maximum output swing. However, realistic linearity requirements force a back-off from the maximum swing, cutting the PA drain efficiency to under 20% in general OFDM-based transmitters. A powerful alternative to power back-off is to employ some form of PA linearization. A number of linearization solutions can be found in the literature. Static digital predistortion is a classic method, in which a detailed power amplifier model is captured as a static look-up table (LUT) or mathematical model [3]. The drawback to this method is that it is not robust to variations in process, supply voltage, temperature, and aging effects. Cartesian feedback (CFB) is also a classic solution, in which continuous analog feedback makes the PA output linearly follow the input [1]. Despite the excellent energy efficiency of CFB for PA linearization, and the natural robustness to variations in the PA model, the bandwidth ( , ) f pd pd Nonlinear Power Amplifier PA Q III Q RX constellation Q Cartesian LUT Q Ipd TX constellation pd Fig. 1. Cartesian LUT, which is trained at low symbol by analog Cartesian feedback loop before transmitters start to communicate with receivers. of CFB transmitters is fundamentally and severely limited by the group delay of any SAW filters in the transmit paths. Finally, adaptive digital predistortion is an effort to combine the best of both solutions, employing a LUT or PA model that is continuously updated by digital feedback [2]. The shortcoming here is the power overhead incurred by the digital signal processing (DSP) involved. This overhead grows with the transmission signal rate. We build on the previous work by combining the simplicity and robustness of CFB with the high bandwidth capability and low DSP overhead of static digital predistor- tion: We use an analog Cartesian feedback loop to train a Cartesian predistortion LUT. LUT training is performed by CFB only when necessary, and after the training is completed, the CFB loop is turned off. Then, open- loop digital predistortion (ODPD) starts using the LUT newly adapted for PA’s current characteristics. Training the LUT at low symbol rates renders a high-speed DSP unnecessary. Furthermore, the Cartesian LUT (organized according to (I,Q) Cartesian baseband pairs) inherently allows for nonlinear transmit path characteristics that are not rotationally symmetric with respect to the baseband constellation. We organize this paper as follows. In Section II we de- scribe the principles and merits of open-loop digital predis- tortion using Cartesian feedback. Section III highlights a wideband transmitter architecture deploying the proposed technique. We present measured results in Section IV, and provide our concluding remarks in Section V. II. ADVANTAGES OF OPEN-LOOP DIGITAL PREDISTORTION USING CFB Fig. 1 illustrates our open-loop digital predistortion con- cept. The Cartesian LUT directly transforms a baseband constellation into a predistorted constellation, which can- cels out the PA nonlinearity. When necessary, the analog CFB is used to train the Cartesian LUT during a pause in data transmission. 14491-4244-0688-9/07/$20.00 ©2007 IEEE (a) (b) Fig. 2. Demodulated 900-MHz transmitter output using a class-A power amplifier for a rectangular baseband constellation: (a) below PA 1-dB compression point, (b) at PA 1-dB compression point (27dBm). A key advantage of our system is that, compared to other forms of adaptive predistortion, it uses an absolute minimum of digital signal processing. A Cartesian, versus polar, LUT also expands our technique to cover nonlin- earities that are not rotationally symmetric, another key advantage. Finally, using the CFB only for training means that this loop does not need to be fast, a tradeoff that we exploit to achieve greater accuracy. We discuss the first two advantages in the following paragraphs, and show in section III how we exploit the lax bandwidth requirements of the CFB loop itself. A. Adaptation with Minimal Digital Signal Processing Most of the DSP reduction comes from using analog feedback, and from using a Cartesian instead of a polar LUT. Analog CFB finds the unique solution [IpdQpd]′ to a static nonlinear vector equation fPA ( [ Ipd Qpd ]′ ) = [ I Q ]′ (1) where PA gain is modeled as the memoryless function fPA. The solution is stored into the Cartesian LUT and there is no conversion from Cartesian to polar when the solution is accessed. Additionally, there is no parameterized model of the nonlinearity to fit to the acquired data. There are therefore no convergence issues, and a corresponding reduction in DSP required. At the present time, our system cannot compensate for memory effects that are observable in some power amplifiers [5]. It has been shown in [4] that these effects may become important when the transmit SNR exceeds 40dB. For the WiMAX/WLAN standards, however, it appears from our measurements that a memoryless model for the PA is sufficient. We regard expanding our technique to account for memory effects as a key problem in our ongoing research. B. Compensation of Non-symmetric Nonlinearity in the Transmit Path Predistortion systems that use polar look-up tables (of- ten described in terms of AM-AM and AM-PM distortion) assume a form for the nonlinearity that is rotationally sym- metric with respect to the baseband constellation. While this is often a good approximation, our measurements D/A D/A ωt −φtωcos SAW PA D/A L(s) L(s) Itrim Qtrim Q I index index RCF cos Attn A/D data Cartesian Look-Up Table Fig. 3. Open-loop digital predistortion transmitter architecture with feed- back training. Transmitter has two separate operation modes: feedback training and open-loop digital predistortion (ODPD). in Fig. 2 show a departure from true symmetry that, left unchecked, would ultimately limit performance. Our measurements also show that the amount of asymmetry in the PA output increases as output power grows. These effects cannot be captured in a polar look-up table, which is used in conventional digital predistortion systems. The reason for this non-symmetric nonlinearity is warp- ing of the constellation due to IQ mismatches. The IQ mismatches include the amplitude and gain mismatch of all circuit blocks in transmit path: loop filters, variable gain amplifiers, and upconversion mixers. In general, these IQ mismatches should be tightly regulated to meet the requirements of the transmit spectrum mask and EVM re- quirements. Furthermore, while these mismatches are mit- igated by Cartesian feedback, they cannot be completely overcome by conventional digital predistortion techniques [6]. The Cartesian LUT predistortion approach is particu- larly attractive because it can compensate for the non- symmetric nonlinearity with no additional circuitry. Be- cause the Cartesian LUT contains a complete 2D charac- terization of the transmit path nonlinearity, any rotational asymmetry is automatically compensated for. III. DESIGN OF THE PROTOTYPE SYSTEM To test our concept, we created a discrete component prototype 900-MHz transmitter using a class-A PA (Mini- Circuits ZHL-0812-HLN), whose architecture is illustrated in Fig. 3. A GSM/900 SAW filter (ECS DSF947.5B-21) is placed between the preamplifier and the PA to provide a quiet noise floor. The transmitter has two separate and exclusive operation modes. In feedback training mode, the transmitter closes the analog feedback loop during a pause in data trans- mission. Training constellation inputs let the predistorted constellation be available at the input of the upconversion mixer. The A/D samples the predistorted constellation points and stores them into the Cartesian LUT. In open- loop digital predistortion (ODPD) mode, the analog CFB loop is disconnected and turned off. Then, the Cartesian 1450 m A f L(s) Y(s)X(s) n nf np Fig. 4. Simplified transmitter noise model. LUT entry Predistorted vector signal Baseband vector signal Q I PA baseband signal modulated RF signal Cartesian Look-Up Table Unwanted high frequency signal (interpolation noise) Predistorted signal Fig. 5. Interpolation noise generated by coarse LUT entries. LUT directly predistorts baseband digital signals. The two upconversion mixers modulate the predistorted IQ signals and deliver the upconverted RF signals to the preamplifier. Beyond the basic predistortion concept, there are a number of design issues that must be considered when putting together the overall system. The fact that the analog feedback loop no longer needs to be fast permits some simplification, and some optimizations to improve accuracy. The total training time is determined by the speed of the analog loop, and by the coarseness of the LUT that we populate. In the following sections, we treat these issues in detail. A. Downconversion Path Noise Averaging Feedback can linearize a PA, but sometimes at the cost of a reduced SNR. In turn, both noise floor and linearization performance become poor. In the open-loop digital predistotion mode, the upconversion mixer noise, which is modeled as nm in Fig. 4, dominates the noise floor of PA output spectrum. In the feedback training mode, upconversion mixer noise is suppressed by loop gain, and downconversion mixer noise nf appears at PA output without any attenuation. Significant downconversion path noise reduction can be accomplished by a simple method. Averaging several measurements for each LUT entry greatly reduces the impact of downconversion mixer noise. Fig. 6(a) shows a measured result with an excessive noise injected into the feedback path. Downconversion noise averaging in the feedback training mode reduced the noise floor by 10dB in ODPD mode. We averaged 32 samples to obtain each of the 1024 LUT entries. (a) (b) Fig. 6. Two noise sources in ODPD system: (a) downconversion noise, (b) LUT interpolation noise. B. Analog Loop Speed and Training Time The minimum LUT training time using feedback train- ing is primarily limited by SAW filter delay. The SAW filter delays place an upper limit on the bandwidth at which we can close a feedback loop with acceptable stability margins. The SAW filter (ECS DSF947.5B-21) in the prototype has a maximum group delay of 149ns in passband. For our prototype, we chose a dominant- pole compensated loop filter with 40dB of DC gain. Our simulation results showed that if we placed the dominant pole such that the closed-loop bandwidth was 2MHz, the delay of the SAW filter caused unacceptably low stability margins. This was evinced by severe peaking in the closed- loop frequency response. In the final design the dominant pole was placed such that the closed-loop bandwidth was approximately 100kHz. This led to acceptable stability margins, and allowed us to run our training sequence at a rate of 5ksym/sec. The A/D conversion process exploits the fact that the training sequence is slow in two ways. First, as we described in section III-A, we have time to do digital averaging, which buys us immunity to noise in the down- conversion process. This is an important advantage for CFB systems, which typically rely on a highly accurate and noise-free downconversion path. Second, it allows us to use a low power A/D with a compact silicon footprint. Sub-1mW power dissipation, which is negligible to the power saving obtained by linearizing PAs, is enough for 12bit 100ksps SAR A/D converters. C. Interpolation Noise Reduction The Cartesian LUT measurements should be as sparse as possible in order to reduce the training time, with simple linear interpolation used to fill in the rest of the elements. However, the linear interpolation introduces numerical noise in the predistorted baseband IQ signals, as shown in Fig. 5. Unwanted high frequency components are added to the PA output when the upconversion mixer cannot filter the interpolation noise. A measured result, shown in Fig.6(b), shows that the noise floor increases by around 10dB in the open-loop predistortion mode while linearity improvement is still effective. 1451 947.49 947.495 947.5 947.505 947.51 −60 −50 −40 −30 −20 −10 0 10 20 30 MHz dB m fundamental LO feedthrough third fifth SFDR 27dB (a) 947.49 947.495 947.5 947.505 947.51 −60 −50 −40 −30 −20 −10 0 10 20 30 MHz dB m LO feedthrough fundamental third fifth SFDR 37dB (b) Fig. 7. DSB transmission spectrum of a 1-kHz sinusoid: (a) open-loop transmission without predistortion, (b) open-loop digital predistortion. (a) (b) Fig. 8. Measured EVM of open-loop 16-QAM at 28-dBm PA output: (a) 5.98% (without predistortion), (b) 2.22% (with predistortion). To filter out the interpolation noise generated by coarse LUT, an upsampling raised cosine filter is added between the LUT and the D/A as seen in Fig. 3. IV. MEASURED RESULTS Fig. 7 shows the linearization performance of open-loop digital predistortion after CFB training for a 1-kHz double- side band sinusoid. The nonlinearity reduction is 10dB with 26-dBm PA output (1-dB power back-off). When PA output goes beyond a correctable level, the loop filter output saturates since a large error signal forces the CFB to compensate for PA nonlinearity. Once the saturation happens, finite slew rate of the loop filter prevents a correct LUT entry sampling of subsequent training constellations. Fig. 8 shows an EVM performance measured at 28- dBm PA output for 2-MHz bandwidth 16-QAM signals. The EVM improved from 5.98% in unlinearized open-loop mode to 2.22% in open-loop predistortion mode. Fig. 9 shows the linearization performance of open- loop digital predistortion on 16-QAM signals. An ap- proximately 10-dB reduction of out-of-band distortion products is measured for both 5-MHz and 40-MHz band- width signals. The maximum linearizable bandwidth in the prototype transmitter is limited by upconversion mixer frequency response. Because the predistorted signals in- clude 7th-order harmonics, the 280-MHz flat frequency response of the upconversion mixer is required for 40- MHz bandwidth 16-QAM signals. A small mixer output swing allows a wider flat frequency band. Therefore, a preamplifier is placed between the mixer and the PA to reduce the mixer output swing, and 35-MHz bandwidth SAW filter could not be used with the 40-MHz bandwidth signals. Table I summarizes the power consumption of major modules and maximum linearizable bandwidth for a stan- dard open-loop, a CFB, and an open-loop digital predis- 930 940 950 960 970 −60 −50 −40 −30 −20 −10 0 10 20 30 MHz dB m Open−loop With ODPD 5MHz Channel Power: 27.6 dBm (a) 860 880 900 920 940 −60 −50 −40 −30 −20 −10 0 10 20 30 MHz dB m Open−loop With ODPD 40MHz Channel Power: 27.1 dBm (b) Fig. 9. Open-loop digital predistortion on 16-QAM signals: (a) 5-MHz bandwidth with SAW filter (b) 40-MHz bandwidth without SAW filter. TABLE I POWER CONSUMPTION AND MAXIMUM LINEARIZABLE BANDWIDTH Overall Power Saved Power Linearizable BW Open-loop 9980 mW - - CFB 6990 mW 2990 mW 10 kHz ODPD 7635 mW 2345 mW 40 MHz tortion system. To have the same level of nonlinearity at 25-dBm PA output, the ODPD technique saves 2.3W. This represents an overall power reduction of 23%. V. CONCLUSION We have presented an efficient adaptive PA linearization technique suitable for wideband portable communication units. This technique replaces a high performance DSP with a Cartesian LUT and analog Cartesian feedback. The result is a minimum of power overhead associated with linearization, a minimum of PA modeling, and no model convergence issues. In addition, we have avoided the bandwidth limitation traditionally associated with CFB systems: our prototype provides linearization at symbol rates over two orders of magnitude higher than is possible with conventional analog feedback. ACKNOWLEDGMENT This work was funded in part by the FCRP Focus Center for Circuit & System Solutions (C2S2), under contract 2003-CT-888, as well as KOSEF. REFERENCES [1] J. L. Dawson and T. H. Lee, “Automatic phase alignment for a fully integrated Cartesian feedback power amplifier system,” IEEE J. of Solid-State Circuits, vol. 38, pp. 2269-2279, Dec. 2003. [2] F. Wang, A.H. Yang, D.F. Kimball, L.E. Larson, and P.M. Asbeck, “Design of wide-bandwidth envelope-tracking power amplifiers for OFDM applications,” IEEE Trans. on Microwave Theory and Tech- niques, vol. 53, pp. 1244-1254, Apr. 2005. [3] R.B. Staszewski, J.L. Wallberg, S. Rezeq, C.-H. Hung, O.E. Eliezer, S.K. Vemulapalli, C. Fernando, K. Maggio, R. Staszewski, N. Barton, M.-C. Lee, P. Cruise, M. 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