Dual-Band Doherty DPD

The Doherty amplifier achieves high efficiency through active load modulation between its carrier and peaking amplifiers. In a dual-band Doherty configuration, this load modulation becomes frequency-dependent, creating a nonlinear interaction surface that varies with both the instantaneous envelope of each band and their relative phase. The DPD model must capture these dynamic impedance trajectories to accurately predict and invert the distortion.

Unlike single-band Doherty PAs, the gain and phase response in one band is modulated by the instantaneous power level of the other band. This results in a two-dimensional distortion surface where:

• AM/AM distortion in Band 1 depends on |x1| and |x2|
• AM/PM distortion in Band 1 depends on |x1| and |x2| The DPD must implement a 2D correction function to compensate for this envelope coupling.

The Doherty architecture is biased deeply into Class-AB (carrier) and Class-C (peaking) to maximize power-added efficiency. This aggressive biasing introduces strong gain compression and phase distortion near saturation. In dual-band operation, the composite signal's peak-to-average ratio is higher, pushing the amplifier deeper into compression more frequently. The DPD must provide sufficient expansion gain to linearize without sacrificing the efficiency gains of the Doherty topology.

A 2D Memory Polynomial (2D-MMP) is the foundational model for dual-band Doherty DPD. It extends the standard memory polynomial by including cross-terms that are functions of the envelope magnitudes of both bands:

• y1(n) = Σ a_k,m * x1(n-m) * |x1(n-m)|^k * |x2(n-m)|^l
• These cross-terms capture the intermodulation coupling and cross-band memory effects inherent in the shared Doherty combiner network.

The Doherty output combiner—typically an impedance inverter and quarter-wave transformer—is designed for a single frequency. In dual-band operation, the combiner's frequency-dependent impedance creates additional nonlinear reflections and standing waves. The DPD model must implicitly learn to compensate for these passive network nonlinearities that manifest as memory effects and band-specific impedance mismatches at the transistor current source plane.

The Indirect Learning Architecture (ILA) is adapted for dual-band Doherty DPD by using a 2D post-distorter in the feedback path. The post-distorter estimates the inverse model using the attenuated PA output and the original baseband signals from both bands. The coefficient extraction solves a least-squares problem on the 2D basis matrix. Once converged, the coefficients are copied to the forward predistorter. This architecture handles the non-commutativity of the Doherty nonlinearity and the DPD function.

The core operating principle of the Doherty amplifier where the impedance seen by the carrier amplifier dynamically changes as a function of the peaking amplifier's current contribution. At low power levels, the carrier sees a high impedance for maximum efficiency. As the peaking amplifier turns on, the load line is modulated downward, maintaining saturation and high efficiency. For dual-band DPD, this load modulation becomes frequency-dependent, meaning the impedance trajectory differs at each carrier frequency. The predistorter must account for this frequency-selective nonlinear behavior.

Nonlinear interference products generated by the interaction of two concurrent carrier signals within the Doherty amplifier. These include:

• Intermodulation distortion (IMD) products falling in and around both transmit bands
• Cross-modulation where the envelope of one band transfers onto the other
• Inter-band IMD falling in the gap between the two bands In a Doherty architecture, the peaking amplifier's nonlinear turn-on characteristic generates particularly strong cross-band products that a conventional single-band DPD cannot correct. The dual-band DPD must synthesize correction signals that specifically cancel these products.

A behavioral model that extends the standard memory polynomial to two dimensions by including cross-terms dependent on the instantaneous envelope magnitudes of both concurrent bands. The model structure is:

• Diagonal terms: Standard memory polynomial terms for each band independently
• Cross-terms: Products of one band's sample with the other band's envelope magnitude raised to various powers This captures the cross-band memory effects inherent in dual-band Doherty PAs, where the nonlinear behavior in one band is influenced by the past envelope history of the signal in the other band. The 2D-MMP provides an excellent balance between modeling accuracy and computational complexity.

The rigorous mathematical foundation for dual-band DPD, derived analytically from the passband Volterra series. This model describes the complete baseband nonlinear behavior including all intermodulation and cross-modulation products up to a specified nonlinearity order. Key characteristics:

• Kernel symmetry reduces the number of independent coefficients
• Captures both short-term and long-term memory effects
• Provides the theoretical basis for simplified models like the 2D-MMP The full Volterra model is computationally prohibitive for real-time implementation but serves as the gold standard for offline modeling and as a benchmark for evaluating simplified architectures.

The dominant closed-loop adaptation method for dual-band Doherty DPD. The architecture operates as follows:

1. The attenuated PA output is fed to a post-distorter model
2. The post-distorter coefficients are identified by minimizing the error between the post-distorter output and the original input
3. The identified coefficients are copied directly to the predistorter in the forward transmission path This approach avoids the need for a PA inverse model and converges reliably even with the strong nonlinearities of a Doherty amplifier. The multi-band variant estimates coefficients for both bands and all cross-band terms simultaneously.