Tri-Band DPD

The predistorter synthesizes correction signals based on a three-dimensional function of the instantaneous envelope magnitudes |x₁|, |x₂|, and |x₃|. This 3D indexing captures the composite nonlinear behavior where the amplifier's response to one carrier depends simultaneously on the amplitude states of the other two.

• 3D-LUT implementation: Correction values indexed by a 3D address derived from all three envelope signals
• Volterra kernel selection: Only cross-terms involving products of all three bands are retained to manage complexity
• Dimensionality challenge: A naive 3D table grows exponentially; sparse indexing and interpolation are essential for hardware feasibility

Tri-band operation generates third-order and fifth-order intermodulation products that fall within or near the three transmit bands. The DPD must actively cancel these products, which result from nonlinear mixing of all three carriers.

• IMD3 triple-beat products: Arise from f₁ ± f₂ ± f₃ combinations, potentially landing directly on a desired channel
• Cross-modulation correction: The modulation envelope of band 1 transferring onto band 2 via amplifier nonlinearity must be pre-compensated
• Band-gap IMD: Products falling between bands still require management to meet spectral mask requirements

The Tri-Band Generalized Memory Polynomial (3B-GMP) extends the dual-band model by adding cross-terms that couple all three envelope magnitudes and their delayed samples. This captures both static nonlinearities and dynamic memory effects across bands.

• Cross-band memory terms: |x₁(n-m)|ᵏ · x₂(n) · x₃(n) type terms capture how past envelope states in one band affect current distortion in another
• Lagging envelope coupling: Delayed envelope products model thermal and trapping memory effects that span multiple symbol periods
• Coefficient pruning: Basis function selection algorithms eliminate redundant terms to keep the model tractable for real-time adaptation

All predistorter coefficients—including cross-band terms—are estimated simultaneously using a joint optimization procedure. This ensures that correcting distortion in one band does not inadvertently degrade linearization in the other two.

• Least-squares formulation: A single large regression matrix incorporates all three bands' basis functions and cross-terms
• QR decomposition: Used for numerically stable coefficient solving on embedded processors
• Indirect learning architecture: A tri-band post-distorter is identified from the attenuated PA output and then copied to the forward predistorter path

Tri-band DPD demands three to nine times the computational throughput of single-band DPD, depending on model complexity. FPGA and ASIC implementations must balance linearization performance against power and silicon area constraints.

• Multi-rate processing: Each band's DPD can operate at its own sample rate, with cross-band terms computed at the lowest common rate to save power
• Time-interleaved LUT access: 3D look-up tables are partitioned across parallel memory banks to achieve required throughput
• Pipelined basis function generation: Nonlinear terms for all three bands are computed in parallel pipelines before the final summation stage

Linearization effectiveness is measured per-band and across the composite spectrum. Key metrics include per-band ACLR, composite error vector magnitude (EVM), and total wideband spectral mask compliance.

• MB-ACLR: Adjacent channel leakage ratio measured individually for each of the three carriers
• Cross-band cancellation depth: The reduction in IMD products falling into adjacent bands, typically targeting 20-25 dB of suppression
• Composite EVM: The combined modulation quality across all three bands, ensuring no band suffers degradation during joint linearization

The generalized predistortion framework that synthesizes a correction signal based on a multi-dimensional function of the instantaneous amplitudes of three or more concurrent transmit signals. For tri-band scenarios, this involves a 3D indexing space where the predistorter gain is a function of |x1|, |x2|, and |x3|. This architecture directly addresses the combinatorial explosion of cross-band intermodulation products generated when three carriers interact in a single power amplifier.

An extension of the generalized memory polynomial model that incorporates cross-band envelope and sample-crossing terms to capture complex nonlinear interactions in multi-band transmitters. For tri-band operation, the MB-GMP includes:

• Type 1 terms: Self-band memory polynomials for each of the three carriers
• Type 2 terms: Cross-band envelope coupling between pairs of bands
• Type 3 terms: Tri-band envelope interactions where the instantaneous gain depends on all three signal magnitudes simultaneously This model balances modeling accuracy with computational tractability.

Nonlinear interference products generated by the interaction of multiple carrier signals within a power amplifier, falling on top of or near the desired transmit bands. In tri-band systems, the distortion landscape becomes significantly more complex than dual-band:

• Third-order IMD: Products like 2f1±f2, f1±f2±f3 appear across the spectrum
• Fifth-order IMD: Higher-order mixing creates additional spectral regrowth
• Cross-modulation: The modulation envelope of one carrier transfers onto another Effective tri-band DPD must model and cancel all these distortion mechanisms simultaneously.

A parameter identification technique that simultaneously estimates all coefficients of a multi-band predistorter model, including cross-band terms, in a single optimization step. For tri-band DPD, this involves solving a large least-squares problem where the observation matrix includes basis functions from all three bands and their interactions. Key considerations include:

• Ill-conditioning: Cross-band basis functions can be highly correlated, requiring regularization
• Computational load: Matrix dimensions grow cubically with the number of bands
• Adaptation rate: Joint estimation provides faster convergence than sequential band-by-band approaches

A closed-loop DPD adaptation method where a post-distorter model is identified from the attenuated PA output and then copied to the predistorter in the forward path. In tri-band operation, the MB-ILA requires:

• Tri-band feedback receiver: Captures all three bands simultaneously with sufficient bandwidth
• Time alignment: Precise synchronization between transmitted and observed waveforms across all three carriers
• Post-distorter training: A tri-band model is trained to invert the PA nonlinearity, then used as the predistorter This architecture avoids the need for a direct PA model and is robust to PA parameter drift.

A key performance metric measuring the ratio of power leaked into adjacent channels to the power in the main channels for a multi-band transmitter. For tri-band systems, ACLR must be measured:

• Per band: Each of the three carriers has its own adjacent channel requirements
• Inter-band regions: Spectral regrowth in the gaps between carriers must be quantified
• Composite metric: Overall system compliance often requires all individual ACLR measurements to meet regulatory masks Typical targets for base station transmitters are -45 dBc to -50 dBc per adjacent channel.