Cross-Band Distortion

Cross-band distortion is fundamentally caused by intermodulation distortion (IMD). When two or more signals at frequencies f1 and f2 are amplified by a nonlinear device, they mix to produce sum and difference products (e.g., 2f1 - f2, 2f2 - f1). In a multi-band context, these products can fall directly on top of or adjacent to the desired transmit bands, making them impossible to filter without also removing the signal of interest.

• Third-order products (IMD3) are typically the strongest and most problematic
• Products fall both in-band and out-of-band
• The number of distortion products grows factorially with the number of carriers

Cross-modulation occurs when the amplitude envelope of a strong signal in one band is transferred onto a weaker signal in another band due to amplifier nonlinearity. This is distinct from simple intermodulation because it involves the actual modulation content being impressed upon the victim signal, causing intelligible crosstalk and severe error vector magnitude (EVM) degradation.

• The modulation envelope of Band A appears as amplitude variation on Band B
• Particularly damaging for signals with high peak-to-average power ratios
• Cannot be corrected by conventional single-band DPD

Cross-band memory effects describe the phenomenon where the nonlinear behavior in one frequency band is influenced by the past envelope history of a signal in a different band. These arise from shared physical mechanisms in the amplifier, such as dynamic drain bias modulation, thermal coupling, and charge trapping in semiconductor materials.

• Long-term thermal memory: Temperature changes from one band's activity alter the gain and phase response for all bands
• Electrical memory: Shared bias networks and power supply impedance create envelope-frequency-dependent interactions
• Requires multi-dimensional memory polynomial models for accurate compensation

Cross-band distortion causes spectral regrowth—the broadening of the transmitted spectrum beyond the allocated channel bandwidth. This directly degrades the Adjacent Channel Leakage Ratio (ACLR), a critical regulatory compliance metric. In multi-band transmitters, distortion products from one band can regrow into the adjacent channel of another band, creating a complex interference landscape.

• ACLR degradation can exceed 10-15 dB without proper linearization
• Regulatory masks (3GPP, FCC) mandate strict ACLR limits
• Multi-band ACLR (MB-ACLR) must be measured across all band combinations

Conventional single-dimensional DPD models based solely on the instantaneous magnitude of one signal are incapable of predicting cross-band distortion. Two-dimensional (2D) models index the predistortion correction by the instantaneous envelope magnitudes of both concurrent baseband signals, creating a 2D basis function space that captures the joint nonlinearity.

• 2D Memory Polynomial (2D-MMP) includes cross-terms dependent on |x1(n)| and |x2(n)|
• 2D Look-Up Tables (2D-LUT) use a 2D address derived from both signal magnitudes
• Model complexity scales quadratically with the number of bands

Two architectural philosophies exist for mitigating cross-band distortion. Joint DPD uses a single unified predistorter processing a composite multi-band signal before upconversion, inherently capturing cross-band interactions. Separate DPD applies independent predistorters to each band but requires explicit cross-band predistorter blocks that generate correction signals targeting intermodulation products falling into adjacent bands.

• Joint DPD requires higher sampling rates to cover the full multi-band bandwidth
• Separate DPD with cross-band blocks offers more modular implementation
• The choice impacts FPGA resource utilization and power consumption

The fundamental physical mechanism behind cross-band distortion. When two or more signals pass through a nonlinear device like a power amplifier, they mix to produce unwanted spectral components at sum and difference frequencies. Third-order intermodulation products (IMD3) are particularly problematic because they fall close to the original carriers and are difficult to filter. In a dual-band scenario, the nonlinear interaction generates not only in-band IMD but also cross-modulation products that land directly on top of the second transmit band, corrupting its error vector magnitude (EVM).

A dedicated signal processing block that generates a correction waveform specifically targeting intermodulation products falling into an adjacent transmit band. Unlike a conventional single-band DPD that only linearizes its own channel, a cross-band predistorter:

• Synthesizes cancellation signals equal in amplitude but opposite in phase to the predicted cross-band distortion
• Operates in the digital baseband before upconversion, injecting the correction into the victim band's transmit path
• Relies on 2D or multi-dimensional LUTs indexed by the instantaneous amplitudes of both aggressor and victim signals This approach is critical when the distortion bandwidth exceeds the linearization capability of a single wideband predistorter.

A unified linearization topology where a single, composite predistorter processes the combined multi-band signal before digital-to-analog conversion and upconversion. This contrasts with separate predistorters that operate independently on each carrier. Advantages include:

• Inherent cross-band compensation: The joint model naturally captures inter-band interactions within its coefficient structure
• Single feedback path: Simplifies the observation receiver design
• Wideband DAC requirement: Demands a digital-to-analog converter with sufficient bandwidth to cover all carriers plus the distortion spread The Multi-Band Generalized Memory Polynomial (MB-GMP) is a common model structure used within joint architectures.

The dominant adaptive coefficient estimation framework for multi-band DPD. The MB-ILA operates by:

1. Capturing the PA output through a feedback receiver and time-aligning it with the input
2. Training a post-distorter in the feedback path to invert the PA's nonlinear characteristic
3. Copying the converged coefficients to the forward-path predistorter This indirect approach avoids the need to solve a nonlinear optimization problem directly on the transmit path. For cross-band distortion, the post-distorter model must include cross-band basis functions to learn the inter-band interaction, ensuring the copied predistorter cancels distortion in all bands simultaneously.

A hardware-efficient implementation of a dual-band predistorter where complex gain correction values are stored in a two-dimensional memory. The LUT is addressed by a composite index derived from the instantaneous magnitudes of both baseband signals: Address = f(|x₁|, |x₂|). Key implementation considerations:

• Addressing granularity: Uniform vs. non-uniform spacing to minimize quantization error
• Interpolation: Bilinear interpolation between adjacent table entries to reduce required memory depth
• Adaptation: The LUT contents are updated by the coefficient extraction algorithm, often using a copy-back mechanism from the post-distorter 2D-LUTs offer a compelling balance between linearization performance and FPGA resource utilization for real-time cross-band cancellation.