1. Digital Predistortion Techniques

2. Adaptive Digital Feedback Predistortion (DFBPD) Technique

2.1 Operation of DFBPD

 The 1st term is the fundamental signal amplification, the 2nd term is the IM signal cancellation, and the 3rd term is the feedback loop distortion. The approximation clearly shows the feedback operation of the system; the overall gain of the FBPD, G_PD is determined by the feedback loop gain only, i.e., 1/G_y, which is independent of the amplifier gain fluctuation due to temperature variation, etc. The (1-G_u) term indicates that the predistortion signal is extracted from the loop and is injected into the main amplifier. For accurate predistortion, G_u should be adjusted close to the 1. The IM component is further suppressed by a factor of closed loop gain G_yG_m due to the negative feedback operation. Therefore, the system is named FBPD. However, the detector circuit error X_f is forwarded to the output, and significant improvements of the error are not effected compared to the conventional digital PD algorithm.

The structure of the proposed digital FBPD is the same as analog feedback except that the feedback signal e(t) in the cancellation loop constructs a LUT in the digital domain, and the gain factors, G_u and G_y, of the signal cancelling and feedback paths are adjusted by the digital signal processor (DSP) instead of using vector modulators (VMs) in the RF domain. The predistortion signal is extracted directly from the LUT, which has been updated using the error signal extracted at the signal cancellation loop beforehand. Thus, the time delay through the loop is eliminated, and the bandwidth limitation does not exist. The oscillation tendency of the feedback circuit can be suppressed easily by digital control of the feedback component. Moreover, the abundant advantages of the FBPD circuit mentioned above can be utilized for the linearization. The distortion correction of the PD is carried out by the digital PD and further enhanced by the feedback linearization. Another merit of the digital FBPD is rapid convergence due to efficient PD signal extraction by the feedback circuit. And the initial condition for the PD signal has little effect on the convergence behavior.

2.2 Equivalent Models and Adaptive Alogrithms

Above figures show the equivalent models of conventional digital PD and the proposed DFBPD. Each model includes several error models for the detector, a modulator, a delay mismatch block, a predistortion signal error, and quantizer blocks to test performance and check tolerances under various conditions. As shown in figures, the additive white Gaussian noise (AWGN) and 3rd-order nonlinear elements G_n(·) are used as error sources for the detection and modulation parts, modeling the thermal noise and mixer nonlinearity, respectively. The delay mismatch blocks are added to represent the overall loop delay mismatches. Also, the quantizer blocks are included to analyze the quantization errors of the source signal, LUT, and PD output. The digital PD employs the recurisive least-square (RLS) adaptive algorithm to extract the error signal to provide fast convergence. The extracted error signal is stored into a LUT, and a stored value multiplies the input signal to generate a PD signal. For the FBPD, we can directly extract an accurate error from the feedback loop (cancellation loop), and the error signal is stored into the LUT. Then, the stored error signal is added to the input as a predistortion signal without any loop delay. The PD signal generation and the adaptation algorithms of the digital FBPD are quite different from conventional digital PD. The RLS adaptive algorithm is initialized by

where a is a small positive constant, is a K X 1 vector, where K is the size of the LUT, and I is the K X K identity matrix. Next, for each time, n = 1, 2, ..., computed as

where λ is the forgetting factor (a scalar value) and P(n) is a K X K matrix. Both π(n) and K_v(n) are the K X 1 matrices. The LUT is constructed and updated by each successive iteration. On the other hand, the DFBPD algorithm is very simple and expressed as

where v_d(n) is the predistorted input signal, v_a(n) is the final output signal, and G_PD is the overall PD system gain. The LUT is constructed by this error signal v_e(n).

2.3 Experimental Results

In order to validate the proposed digital FBPD technique, we have employed the ADS-ESG-VSA connected solution as an experimental setup for quick and exact verification, and used the Doherty power amplifier (DPA) module shown above figure with 180-W of peak envelope power (PEP) and 20-W average power for a single-carrier forward-link WCDMA signal. The main amplifier of the DPA module consists of two Freescale MRF5S21090 LDMOSFETs, and the uneven power drive technique is applied to improve the performance. The signal used is a 2.14-GHz forward WCDMA signal with a 3.84-MHz of chip rate and 9.8-dB PAR at 0.01% complementary cumulative distribution function (CCDF), generated using the 3GPP WCDMA library of ADS. The conventional digital PD and the proposed digital FBPD have two 256-entry AM/AM and AM/PM LUTs, which are programmed by MATLAB using the RLS and FBPD algorithms, respectively.

Above figure shows the measured spectra before and after linearization by the digital PD and FBPD for the WCDMA signal. The ACLRs at 2.5-MHz offset for the two techniques are nearly the same, -58 dBc, which is an improvement of 15 dB at an average output power of 43 dBm. These experimental results demonstrate that the both predistortion techniques can successfully compensate for the nonlinear characteristics of the Doherty amplifier.

3. Weighted Polynomial Digital Predistortion (DPD) Technique

As shown in above figure, the proposed weighted polynomial algorithm is consisted of the weighting, polynomial and de-weighting blocks. The weighting is introduced to get an ideal error function for the least square fit algorithm. The weighting function describes the statistical characteristics of the modulation signal and the harmonic generation property of an amplifier at a high power level. Then, the weighted polynomial PD signals are generated by using a polynomial least square fit algorithm. Finally, the generated PD signals are de-weighted and applied to the PA. These procedures are iterated using the indirect learning architecture until we get the linear output.

The least square fit algorithm is employed to optimize the coefficients with a minimum square error for a sequential ramp training signal. For the modulated signal, the error function is not accurate since the occurrence of the data point, i.e. probability density function (p.d.f.) is different. In case of the forward-link WCDMA signal, the p.d.f. of the amplitude response has the Rayleigh distribution as shown in below figure.

We can estimate the overall error, which is sum of differences between modeled responses (y_i) and desired responses (d_i) of the modulated signal, with the least square fit optimized polynomial coefficients. The overall error can be calculated by integrating the product of the average error distribution at each amplitude (error_avg(x)), which is determined by the least square fit model, by the Rayleigh p.d.f. as follows:

The non-weighted ramp training signal has an uniform average error distribution, and it is not the optimum for the minimum overall error of the WCDMA signal. Therefore, the Rayleigh distribution weighting is applied to the least square fit error function for the ramp training signal. Another point is that the PD signal at the peak power region, which is dominant for harmonic generation, should to be emphasized more than the other power regions. Therefore, we have implemented an increasing exponential weight to improve accuracy at the peak power region and to describe the harmonic generation property accurately as follows:

The above equation shows that it can represent the harmonic generation property of an amplifier, and as a becomes large, the high order terms have more weighting than the low order terms. As a consequence, the exponential function raises the accuracy at a higher power region, and a=1 provides a good weighting function.

2.1 Experimental Results

Above figure shows the measured power spectral densities obtained using the proposed optimum weighted polynomial algorithm and the non-weighted polynomial algorithm. The proposed optimum weighting algorithm could deliver a good ACLR of -60 dBc at an average power of 43 dBm, which is a cancellation of 16 dB with PAE of about 29%, while the non-weighted polynomial case has a poor ACLR cancellation of 4 dB at the same average power.

Above figure shows AM/AM curves with the optimum weighting algorithm and the non-weighting case. These results show clearly the improved accuracy of the optimum weighted polynomial fit.