Open-Loop DPD

In an open-loop topology, the predistorter coefficients are calculated offline during a one-time characterization or factory calibration procedure. Once loaded into the transmit path, these coefficients remain fixed regardless of changes in the PA's operating conditions.

• No observation receiver or feedback ADC is required
• Eliminates the computational overhead of real-time coefficient updates
• The predistorter acts as a static nonlinear function applied directly to the baseband I/Q samples

The defining architectural feature is the absence of a transmit observation receiver (TOR) . Unlike closed-loop systems that require a dedicated coupler, mixer, and ADC to sample the PA output, open-loop DPD operates entirely in the forward path.

• Reduces bill of materials (BOM) cost and PCB complexity
• Eliminates feedback loop stability concerns
• Avoids the latency penalty associated with ADC conversion and signal alignment

The primary limitation of open-loop DPD is its inability to track time-varying nonlinearities. Changes in PA behavior caused by temperature fluctuation, device aging, supply voltage variation, or channel frequency switching are not compensated.

• Thermal memory effects accumulate without correction
• Linearization performance degrades as the PA deviates from its characterized state
• Best suited for environments with tightly regulated temperature and stable VSWR

Open-loop predistorters are frequently implemented using pre-computed look-up tables indexed by instantaneous signal magnitude. The LUT stores complex gain values that invert the PA's AM/AM and AM/PM distortion curves.

• Extremely low computational complexity — a single table lookup per sample
• Ideal for FPGA and ASIC implementations with limited DSP slices
• LUT entries are populated from a one-time model extraction procedure using a vector network analyzer or offline simulation

Deployment follows a characterize-then-apply methodology. The PA is stimulated with a known training signal, its output is captured on a benchtop, and an inverse model is fitted using batch processing.

• Typical workflow: Stimulus → Capture → Model Fitting → Coefficient Extraction → LUT Programming
• Leverages high-precision lab equipment unavailable in the field
• Coefficients are burned into non-volatile memory on the radio unit

Open-loop DPD achieves excellent linearization when the PA operates in a narrow, predictable envelope. It is commonly deployed in cost-sensitive or latency-intolerant applications where the operational environment is controlled.

• ACPR improvement of 15-20 dB is achievable under nominal conditions
• Typical applications: small cells, indoor femtocells, satellite transponders, and low-power IoT transmitters
• Often paired with analog pre-distortion for additional margin

An adaptive predistortion topology that continuously updates coefficients based on real-time feedback from the transmit observation path. Unlike open-loop systems, closed-loop architectures sample the PA output through a feedback receiver, compare it with the desired signal, and iteratively minimize the error. This enables compensation for time-varying effects such as temperature drift, device aging, and channel loading changes. The trade-off is increased hardware complexity and power consumption from the observation receiver chain.

A postdistorter-based training architecture where the predistorter coefficients are copied from a separately trained postdistorter placed after the power amplifier. The ILA identifies the PA's inverse transfer function by training a model in the feedback path to reproduce the original input signal. Once converged, coefficients are transferred to the forward predistorter. This architecture avoids the need for explicit PA model inversion but can suffer from bias in the coefficient estimate when measurement noise is present in the feedback loop.

A closed-loop training architecture that directly estimates the predistorter coefficients by minimizing the error between the desired input and the actual PA output. DLA treats the PA and predistorter as a cascaded system and computes the error gradient through the combined transfer function. This approach is theoretically more accurate than ILA because it optimizes the true linearization objective rather than an intermediate postdistorter model. However, it requires knowledge of the PA model or its instantaneous linearization for gradient computation.

The algorithmic process of determining the optimal parameters for a digital predistorter model to minimize nonlinear distortion. In open-loop DPD, estimation occurs offline during characterization or factory calibration using batch least squares or iterative optimization. Key techniques include:

• Least Squares Estimation: Minimizes sum of squared residuals
• LMS (Least Mean Squares): Stochastic gradient descent for online adaptation
• RLS (Recursive Least Squares): Faster convergence with higher computational cost
• QR-RLS: Numerically stable variant using QR decomposition for ill-conditioned problems

A direct learning technique that mathematically inverts the power amplifier behavioral model to derive the predistorter transfer function. Given an accurate forward PA model f(·), the ideal predistorter is the inverse function f⁻¹(·) such that the cascade produces linear gain. Practical challenges include:

• Non-invertible regions where the PA characteristic is not strictly monotonic
• Numerical instability when the PA model is ill-conditioned
• Memory effects that make exact inversion computationally intractable Approximate inversion using iterative methods or constrained optimization is common in practice.

A self-adjusting signal processing framework where filter coefficients are automatically updated to minimize a cost function in response to changing conditions. While open-loop DPD uses fixed coefficients, adaptive filtering forms the mathematical foundation for closed-loop alternatives. Core concepts include:

• Cost Function: Typically mean squared error between desired and actual output
• Convergence Rate: Speed at which coefficients approach optimal values
• Misadjustment: Excess error beyond theoretical minimum due to gradient noise
• Coefficient Drift: Gradual deviation from optimal values due to temperature or aging These concepts define the performance envelope of any adaptive DPD system.