Digital Pre-Distortion

1. ?Introduction?

A typical block diagram of the Open RAN (ORAN) Split 7.2 Low PHY,DFE(digital front end) in O-RU including the DPD block is shown below.?

PA is implemented in a wireless base station transmitter. The gain of power amplifiers is, in general, nonlinear. The nonlinearity in the PA-boosted signal spreads the spectrum of transmit signal (spectral regrowth) and hence increases its interference on the neighboring bands (adjacent channel leakage, ACL). It also includes memory effects i.e, the gain depends on the past signal. The memory effects can be due to thermal effects, electron trapping in the transistors, etc. The short-term memory effects are quite significant when the input signal does not have a constant envelope. For example, the peak of an OFDM signal, whose power can be significantly higher than the average power, rises the temperature of transistors transiently and till they touch normal temperatures, the transistors operate on a different non-linear curve.?

2 Digital Predistortion

Digital Pre-Distortion (DPD) is one of the most fundamental building blocks in wireless communication systems today. It is used to increase the efficiency of Power Amplifiers. By reducing the distortion created by running Power Amplifiers in their non-linear regions, Power Amplifiers can be made to be far more efficient. Wireless base stations not employing CFR (crest factor reduction) or DPD algorithms typically exhibit low efficiency, and therefore high operational and capital equipment costs. A typical Class AB LDMOS Power Amplifier with WCDMA waveforms may have approximately 15-20% efficiency. With CFR and DPD turned on, this efficiency can grow to as much as 40%, resulting in tremendous savings in CapEx and OpEx for network operators. With later generations of Power Amplifier design leveraging Doherty architectures, efficiencies in the 50%+ range?are possible, as claimed by vendors like Xilinx. Thus, using the pre-distorter block, the power amplifier can be utilized up to its saturation point while still maintaining good linearity, thereby significantly increasing its efficiency.

The memory effects and non-linearity can be addressed in both analog and digital domain.? In the digital domain, the signal that is fed to PA is pre distorted such that, the PA response to the distorted signal has a linear relationship with the actual input signal. The nonlinearity of power amplifiers (PA) can be modelled as a Volterra series, Wiener, Hammerstein, Wiener-Hammerstein, Memory polynomial model, etc.

The DPD first estimates the coefficients of the polynomial, and memory length and compensates for the distortions before PA. i.e., it acts as the inverse function of PA non-linearity. The combined response of PA and an ideal digital pre-distorter (DPD) should be linear and independent of past inputs.

?The DPD algorithm needs to model the PA behavior accurately and efficiently for successful DPD deployment.

A typical DPD setup is as follows.

2.1 DPD models

? DPD implementations can be classified into memoryless models and models with memory. In this section, description of both models is provided.

2.2 Memoryless models

Memoryless models focus on the power amplifier that has a memoryless nonlinearity, that is, the current output depends only on the current input through a nonlinear mechanism. This instantaneous non-linearity is usually characterized by the AM/AM and AM/PM responses of the power amplifier, where the output signal amplitude and phase deviation of the power amplifier output are given as functions of the amplitude of its current input. Both memoryless polynomial algorithm and Look-Up Table (LUT) based algorithm are two key algorithms for memoryless models.?

Let x(n) and y(n) be the input and output of the PA respectively; if the signal is a narrow band, memory effects can be ignored. The input-output relation would be a polynomial, in such a case as follows.

Let T be the length of training signal, then the above equation can be rewritten as ?

Vector c can be estimated by the Least Squares (LS) method as SNR is very high, for there is no wireless path. Here, H:--Hermitian operator(conjugate transpose)

Above method works well when the polynomial degree is no more than 4 or 5. The higher the degree, the higher the condition number (due to properties of the Vandermonde matrix), and hence estimates could be inaccurate if one tries to estimate c when K > 4. ??

2.3 Memory Model

Memory model is commonly used as the signal bandwidth gets wider, such as for WCDMA, 3GPP LTE, LTE-Advanced,5GNR systems. For wider bandwidths, power amplifiers begin to exhibit memory effects. This is especially true for those high-power amplifiers used in wireless base stations. The causes of the memory effects can be attributed to thermal constants of the active devices or components in the biasing network that have frequency dependent behaviors. As a result, the current output of the power amplifier depends not only on the current input, but also on the past input values. In other words, the power amplifier becomes a nonlinear system with memory. For such a power amplifier, memoryless pre-distortion can achieve only very limited linearization performance. Therefore, such digital pre-distorters must have memory structures.

To construct digital pre-distorters with memory structures, there are two types of approaches. One type of approach is to first identify the power amplifier and then find the inverse of the power amplifier directly. This approach is named as direct learning architecture (DLA). However, obtaining the inverse of a nonlinear system with memory is generally a difficult task. Another type of approach is to use the indirect learning architecture (IDLA) to design the pre-distorter directly. The advantage of this type of approach is that it eliminates the need for model assumption and parameter estimation of the power amplifier.

?Generalized Memory Polynomial

A kth memory polynomial component is written as?

??? A more generalized memory polynomial can be represented as?

Where Ka, La are the number of coefficients for an aligned signal and envelope (memory polynomial); Kb, Lb, Mb are the number of coefficients for signal and? lagging? envelope;? and? Kc, Lc, Mc? are? the number of coefficients for signal and leading envelope. Coefficients have linear relation which can estimated by least squares.

2.4 DPD algorithm Implementation approaches

DPD algorithms are computationally complex and consume a lot of memory too, especially for the memory models.

Polynomials with Memory and memoryless versions can be efficiently implemented on FPGAs or on ASIPs(Application specific instruction processor) having specialized vector DSP instruction set for polynomial evaluation using Horner’s method which is an efficient way of evaluating polynomials and their derivatives at a given point. It is also used for a compact presentation of the long division of a polynomial by a linear polynomial. The method is named after the British mathematician William George Horner. More information about this approach can be found at: --

https://www.cut-the-knot.org/Curriculum/Calculus/HornerMethod.shtml

?3 Challenges for a DPD solution

The challenges for a high performance practical DPD solution can be summarized in these requirements:

·??????? Static performance (compliance testing or where the BTS traffic load is approximately constant)

·??????? ACLR, considering LTE example, Adjacent Channel Leakage Ratio (ACLR) is defined as the ratio of the in-band power to the power in adjacent LTE carriers. Typical values should be around 60 dB.

·??????? EVM, ie. error vector magnitude (including GaN as a special case). Charge trapping in GaN is a long-term memory effect, where there is a trap and then a thermal de-trap. GMP-based DPD corrects some of the error. However, there is residual error that continues to impact signal quality. This distortion induces a corresponding rise in EVM.

EVM: --The error vector refers to the vector between the actual constellation point as seen by a receiver and the ideal constellation point. An intuitive way to interpret EVM is simply (1/SNR); i.e., in dB scale EVM (dB) = -SNR (dB). If we measure SNR directly at any radio transmitter, it is difficult to get more than 40 dB as the value, but considering the ideal scenario it should be infinite.

·??????? Dynamics

·??????? Robustness

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