DPD Coefficient Estimator

Wireless communication transmissions commonly require wide bandwidth signal transmission over a wide signal dynamic range. To transmit signals over a wide dynamic range and achieve high efficiency, RF power amplifiers (PAs) commonly operate in their nonlinear region. As this constellation diagram shows, the nonlinear behavior of a PA causes signal constellation distortions that pinch the amplitude (AM-AM distortion) and twist phase (AM-PM distortion) of constellation points proportional to the amplitude of the constellation point.

The goal of digital predistortion is to find a nonlinear function that linearizes the net effect of the PA nonlinear behavior at the PA output across the PA operating range. When the PA input is x(n), and the predistortion function is f(u(n)), where u(n) is the true signal to be amplified, the PA output is approximately equal to G×u(n), where G is the desired amplitude gain of the PA.

The digital predistorter can be configured to use a memory polynomial with or without cross terms.

Estimating Predistortion Function and Coefficients

The DPD coefficient estimation uses an indirect learning architecture to find function f(u(n)) to predistort input signal u(n) which precedes the PA input.

The DPD coefficient estimation algorithm models nonlinear PA memory effects based on the work in reference papers by Morgan, et al [1], and by Schetzen [2], using the theoretical foundation developed for Volterra systems.

Specifically, the inverse mapping from the PA output normalized by the PA gain, {y(n)/G}, to the PA input, {x(n)}, provides a good approximation to the function f(u(n)), needed to predistort {u(n)} to produce {x(n)}.

Referring to the memory polynomial equations above, estimates are computed for the memory-polynomial coefficients:

The memory-polynomial coefficients are estimated by using a least squares fit algorithm or a recursive least squares algorithm. The least squares fit algorithm or a recursive least squares algorithms use the memory polynomial equations above for a memory polynomial with or without cross terms, by replacing {u(n)} with {y(n)/G}. The function order and dimension of the coefficient matrix are defined by the degree and depth of the memory polynomial.

For an example that details the process of accurately estimating memory-polynomial coefficients and predistorting a PA input signal, see Digital Predistortion to Compensate for Power Amplifier Nonlinearities.

For background reference material, see the works listed in [1] and [2].

The DPD coefficient estimator based on [1] offers one specific indirect learning architecture, and may not be an optimal estimator. Other estimators, such as those using a direct learning architecture, may achieve better DPD results.

With the indirect learning architecture coefficient estimator, choosing the optimal degree and memory depth for the DPD coefficient estimator is a manual and iterative process. Consider starting by using a DPD coefficient estimator that has the same degree and the memory depth as that of the PA model, and check the DPD results. Assuming the results look promising, try reducing the degree and the memory depth for the DPD coefficient estimator. If DPD results are roughly the same or better, consider using the smaller degree and a smaller memory depth for the DPD coefficient estimator because it will be less computationally intensive. You should also experiment with degrees and memory depths above the degree and the memory depth of the PA model. If DPD performance improves using a higher degree or a larger memory depth for the DPD coefficient estimator may be desirable.

Regardless of the polynomial degree used for the estimator, you must control the bandwidth of the DPD input signal to avoid aliasing due to nonlinearities. As a rule of thumb, set the oversampling ratio of the DPD input signal equal to or greater than the degree of the DPD memory polynomial.