Inter-Band IMD

Inter-band IMD products fall between the two fundamental transmit bands, not adjacent to them. For two carriers at frequencies f₁ and f₂, the critical third-order products appear at 2f₁ - f₂ and 2f₂ - f₁, which land in the frequency gap when the carrier spacing is sufficiently wide. This distinguishes inter-band IMD from in-band distortion and adjacent channel leakage.

• Example: With carriers at 2.1 GHz and 2.6 GHz, the 2f₁ - f₂ product appears at 1.6 GHz
• These products cannot be filtered by bandpass filters tuned to either carrier
• The wider the carrier separation, the further inter-band IMD falls from the transmit bands

The instantaneous envelope of one carrier modulates the nonlinear characteristics experienced by the other carrier. This cross-modulation effect means the distortion in Band 1 is not solely a function of Band 1's signal—it depends on the magnitude and phase of Band 2's envelope at every instant.

• The PA's AM-AM and AM-PM responses become functions of a composite envelope
• Memory effects in one band influence distortion in the other band
• Requires 2D behavioral models where predistortion is indexed by both |x₁(n)| and |x₂(n)|

Capturing inter-band IMD for DPD adaptation demands an observation receiver with bandwidth spanning from the lowest IMD product to the highest transmit carrier. For widely spaced carriers, this can exceed 1 GHz of instantaneous bandwidth.

• Observation bandwidth = f₂ + (f₂ - f₁) for upper IMD3 capture
• Requires high-speed, high-dynamic-range ADCs
• Often necessitates sub-sampling or multi-path receiver architectures
• Feedback linearity must exceed the target linearization performance by 10-15 dB

Unlike in-band DPD which corrects distortion co-located with the signal, inter-band IMD cancellation requires generating a predistortion signal in the gap region where no original transmission exists. This is fundamentally a signal injection problem rather than a pre-correction problem.

• The predistorter must synthesize a cancellation signal at frequencies where the input is zero
• Requires separate cross-band predistorter (CB-DPD) blocks
• Cancellation signal must be phase-aligned with the IMD product at the PA output
• Typically implemented as an additive feedforward or feedback-assisted architecture

While third-order inter-band IMD is dominant, fifth and seventh-order products also fall within the inter-band gap and can limit achievable linearization. As carrier spacing increases, higher-order products spread across a wider spectral range.

• 5th-order: 3f₁ - 2f₂, 3f₂ - 2f₁
• 7th-order: 4f₁ - 3f₂, 4f₂ - 3f₁
• Odd-order products dominate due to PA transfer function symmetry
• Volterra series models naturally capture all intermodulation orders

Inter-band IMD is exacerbated when the PA operates near compression for efficiency. Multi-band signals have a higher composite peak-to-average power ratio (PAPR) than single-band signals, forcing operation further into back-off or requiring joint crest factor reduction.

• Composite PAPR increases with the number of aggregated carriers
• Doherty PAs exhibit stronger inter-band IMD due to load modulation interactions
• Multi-band CFR reduces PAPR before the PA, indirectly reducing IMD
• Envelope tracking supplies introduce additional cross-band dynamics

The active process of generating a correction signal equal in amplitude but opposite in phase to inter-band IMD products. This technique specifically targets distortion falling in the frequency gap between two transmit bands, neutralizing interference without affecting the main carrier signals. Implementation typically requires a dedicated cross-band predistorter block with high dynamic range.

A behavioral model extending the memory polynomial to two dimensions by including cross-terms dependent on the envelope magnitudes of both concurrent bands. Key characteristics:

• Captures cross-band memory effects where past envelope history in one band influences nonlinear behavior in another
• Uses a two-dimensional indexing structure based on instantaneous magnitudes of both baseband signals
• Balances modeling accuracy with computational complexity for dual-band scenarios

A nonlinear phenomenon where the modulation envelope of a strong interfering signal is transferred onto a desired signal. Unlike simple intermodulation, cross-modulation causes the amplitude and phase variations of one carrier to appear on another, even when their frequency separation is large. This effect is particularly problematic in carrier aggregation scenarios where component carriers have different modulation schemes and power levels.

A key performance metric measuring the ratio of power leaked into adjacent channels relative to the power in the main channels for a multi-band transmitter. For inter-band IMD analysis, MB-ACLR is extended to include:

• Inter-band gap measurements: Quantifying distortion power in the frequency gap between transmit bands
• Cross-band leakage: Power from one carrier appearing in the adjacent channel of another carrier
• Regulatory compliance requires meeting ACLR specifications across all bands simultaneously

A predistortion technique applying independent linearization processing to different frequency sub-bands of a wideband signal. This approach is critical for inter-band IMD because:

• It can target specific frequency regions where distortion products fall
• Allows different linearization bandwidths for in-band versus inter-band correction
• Reduces computational overhead by focusing processing power only where needed
• Particularly effective when combined with subband DPD architectures for managing wideband nonlinearities

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. For inter-band IMD mitigation:

• The post-distorter captures both in-band and cross-band distortion products
• Joint coefficient estimation simultaneously identifies all model parameters including cross-band terms
• The architecture inherently accounts for cross-band memory effects through its feedback structure
• Enables real-time adaptation to changing PA characteristics without interrupting transmission