Carrier Aggregation DPD

Carrier aggregation DPD extends traditional single-band models by constructing multi-dimensional basis functions that capture cross-band interactions. The predistorter input is a vector of baseband signals from each component carrier, and the nonlinear model includes:

• Intra-band terms: Standard memory polynomial terms for each carrier independently
• Cross-band envelope coupling terms: Products of envelope magnitudes from different carriers (e.g., |x₁|²·|x₂|²)
• Cross-modulation terms: Phase-dependent interactions where the modulation of one carrier transfers onto another

This multi-dimensional indexing creates a combinatorial explosion of basis functions, requiring careful pruning strategies to maintain computational feasibility.

Two fundamental topologies exist for carrier aggregation DPD:

Joint DPD Architecture:

• A single unified predistorter processes the composite multi-carrier signal before upconversion
• Captures all cross-band interactions natively within one model
• Requires wider observation bandwidth to capture intermodulation products
• Higher computational complexity but superior linearization performance

Separate Per-Carrier DPD:

• Independent predistorters applied to each component carrier before combining
• Lower complexity but cannot fully cancel cross-band distortion products
• Often augmented with cross-band predistorter blocks that inject correction signals into adjacent carriers
• Suitable when carriers are widely spaced and cross-band IMD is manageable

The feedback observation receiver in carrier aggregation DPD must capture all distortion products that fall within or near the transmit bands. Key requirements include:

• Observation bandwidth ≥ 5× total signal bandwidth to capture third and fifth-order intermodulation products
• For two 20 MHz carriers with 40 MHz spacing, the observation path may need 200+ MHz of instantaneous bandwidth
• Multi-rate observation architectures can reduce ADC requirements by using parallel narrowband receivers tuned to specific IMD zones
• Spectral stitching techniques combine multiple narrowband captures to reconstruct wideband distortion spectra

Insufficient observation bandwidth leads to aliased distortion products and degraded linearization performance.

For dual-carrier aggregation, 2D-DPD uses a two-dimensional indexing scheme based on the instantaneous magnitudes of both baseband signals:

• 2D Look-Up Table (2D-LUT): Complex gain correction values indexed by (|x₁|, |x₂|), enabling hardware-efficient implementation
• 2D Memory Polynomial (2D-MMP): Extends memory polynomial with cross-terms dependent on both envelope magnitudes to capture cross-band memory effects
• Model includes terms like x₁(n-m)·|x₁(n-m)|ᵏ·|x₂(n-m)|ˡ for various k,l combinations
• 2D Generalized Memory Polynomial adds sample-crossing terms between carriers for enhanced accuracy

These models balance modeling fidelity against the exponential growth in coefficient count as more carriers are added.

Carrier aggregation creates unique distortion products that require targeted cancellation:

• Inter-band IMD: Distortion falling in the gap between carriers, often requiring dedicated cancellation signals
• Cross-modulation compensation: Correcting envelope transfer from strong to weak carriers
• Frequency-selective DPD: Applying independent linearization to different sub-bands to manage frequency-dependent nonlinearities
• Subband DPD decomposition: Splitting wideband signals into narrowband sub-signals, applying independent DPD, and recombining

Advanced implementations use dedicated cross-band predistorter blocks that generate correction signals specifically targeting IMD products falling into adjacent transmit bands, rather than relying solely on a unified model.

Parameter estimation for carrier aggregation DPD requires specialized algorithms:

• Joint coefficient estimation: Simultaneously identifies all model coefficients including cross-band terms in a single optimization step using least-squares or iterative methods
• Multi-Band Indirect Learning Architecture (MB-ILA): A post-distorter is identified from the attenuated PA output and copied to the forward-path predistorter
• Sequential extraction: Coefficients for individual carriers are extracted first, then cross-band terms are identified in subsequent stages
• Online adaptation must track changes in cross-band behavior due to thermal drift and antenna loading variations

Real-time coefficient updates require matrix inversion operations that scale with the cube of the coefficient count, making dimensionality reduction critical for embedded implementation.

A digital predistortion architecture designed to linearize a single power amplifier that is simultaneously transmitting two or more widely spaced component carriers. Unlike traditional single-band DPD, this approach synthesizes a composite correction signal that accounts for cross-band intermodulation distortion (IMD).

• Key Challenge: Nonlinear mixing between carriers generates distortion products that fall both in-band and out-of-band
• Architecture: Employs a multi-dimensional predistorter function indexed by the instantaneous envelopes of all concurrent carriers
• Application: Essential for intra-band and inter-band carrier aggregation in 4G LTE-Advanced and 5G NR base stations

A behavioral model that extends the classical memory polynomial to two dimensions by incorporating cross-terms dependent on the envelope magnitudes of both concurrent bands. This structure captures the nonlinear interaction and memory effects between two carrier signals amplified through a common power amplifier.

• Formulation: Includes terms for self-distortion (each band independently) and cross-distortion (envelope coupling between bands)
• Advantage: Balances modeling accuracy with computational tractability compared to full 2D Volterra series
• Implementation: Coefficients are typically extracted using least-squares estimation on observed input-output waveforms

The process of actively generating a correction signal equal in amplitude but opposite in phase to intermodulation products that fall into adjacent transmit bands. This is critical when component carriers are closely spaced and nonlinear mixing creates interference that cannot be filtered without affecting the desired signals.

• Mechanism: A dedicated cross-band predistorter block synthesizes cancellation signals based on the envelope coupling between carriers
• Target: Inter-band IMD products that land in the gap between carriers or directly on top of neighboring allocations
• Benefit: Enables tighter carrier spacing and improved spectral efficiency in carrier aggregation deployments

A predistortion topology where a single, unified predistorter block processes the composite multi-band signal before digital-to-analog conversion and upconversion. This contrasts with separate predistorters applied independently to each carrier.

• Signal Flow: Individual baseband carriers are combined, then passed through a single multi-dimensional predistorter
• Advantage: Naturally accounts for all cross-band interactions within the composite signal
• Trade-off: Requires a higher digital sampling rate to cover the full multi-band bandwidth, increasing FPGA resource utilization
• Use Case: Preferred when carriers are closely spaced and cross-band effects dominate

A closed-loop adaptive DPD training method where a post-distorter model is identified from the attenuated power amplifier output and then copied to the predistorter in the forward transmission path. This architecture avoids the need for a direct inverse model of the PA.

• Training Loop: The post-distorter coefficients are estimated to minimize the error between the post-distorter output and the original input
• Copy Step: Once converged, coefficients are transferred to the identical predistorter block upstream of the PA
• Advantage: Robust to PA characteristic changes over time and temperature
• Multi-Band Extension: Joint coefficient estimation captures all cross-band terms simultaneously

A hardware-efficient predistorter implementation where complex gain correction values are indexed by a two-dimensional address derived from the instantaneous magnitudes of two concurrent input signals. This replaces computationally expensive polynomial evaluation with simple memory lookups.

• Addressing: The 2D index is formed by quantizing the envelope magnitudes of both carriers
• Content: Each LUT entry stores a complex gain value that pre-distorts the composite signal
• Adaptation: Table entries are updated using feedback from the PA output, often via interpolation to handle sparse table coverage
• Benefit: Dramatically reduces real-time computational load on FPGA or ASIC implementations