Out-of-Band DPD

Unlike conventional DPD that minimizes total adjacent channel power, out-of-band DPD applies a spatial weighting to the linearization cost function. The algorithm prioritizes suppressing spectral regrowth in specific angular directions—typically toward adjacent channel licensees or sensitive receivers—while tolerating slightly higher emissions in benign directions. This is achieved by incorporating the array manifold vector into the DPD coefficient optimization, effectively creating a spatial notch in the out-of-band emission pattern.

The optimization objective explicitly separates in-band and out-of-band performance metrics:

• In-band: Error Vector Magnitude (EVM) is allowed to degrade within acceptable limits
• Out-of-band: Adjacent Channel Leakage Ratio (ACLR) is aggressively minimized This is implemented through a frequency-weighted least squares formulation where the error signal is filtered to emphasize spectral components outside the allocated channel bandwidth before coefficient computation.

Out-of-band DPD is primarily motivated by spectrum emission mask requirements defined by 3GPP and ITU-R. In 5G NR deployments with carrier aggregation and dynamic spectrum sharing, the nonlinear products from one carrier can desensitize receivers operating in adjacent bands. The technique ensures compliance without requiring excessive power amplifier back-off, preserving power-added efficiency while meeting the -45 dBc ACLR targets typical of base station specifications.

In massive MIMO arrays, out-of-band DPD solves a joint spatial-spectral optimization problem. The predistorter coefficients are computed to minimize the radiated nonlinear power in specified angular-frequency regions. This requires knowledge of:

• The array steering vector for each beam direction
• The power amplifier nonlinear model for each transmit chain
• The antenna mutual coupling matrix The resulting predistorter simultaneously linearizes the array while steering distortion products away from protected directions.

A fundamental design tension exists between out-of-band suppression and in-band signal quality. Aggressive adjacent channel suppression typically increases in-band distortion due to the nonlinear interaction between the predistorter correction signal and the original waveform. System designers must balance:

• ACLR margin against regulatory limits
• EVM floor against modulation order requirements
• PA efficiency against linearity headroom Advanced implementations use Pareto optimization to find the optimal operating point for a given deployment scenario.

Effective out-of-band DPD requires feedback that captures the far-field radiated spectrum in the protected direction. This is typically achieved through a calibrated observation receiver with a directional antenna placed in the spatial region of interest. The feedback path must have sufficient dynamic range to measure spectral regrowth 45-50 dB below the main channel power. In production systems, this calibration is performed during array commissioning and periodically updated to track environmental changes.

The primary objective of Out-of-Band DPD is to suppress spectral regrowth—the unwanted expansion of a signal's bandwidth caused by power amplifier nonlinearity. This regrowth creates adjacent channel interference that degrades network capacity. Key metrics include:

• ACLR (Adjacent Channel Leakage Ratio): Measures the ratio of power in the main channel to power leaking into adjacent channels
• EVM (Error Vector Magnitude): Quantifies in-band distortion affecting modulation accuracy
• Out-of-Band DPD specifically targets ACLR improvement in directions where regulatory limits are most stringent

Out-of-Band DPD is inherently beamforming-aware, as the nonlinear distortion pattern radiated by an array changes with the beamforming weights. Key interactions:

• Beam-dependent impedance: Each beam steering angle presents different load impedances to individual PAs, altering their nonlinear characteristics
• Spatial distortion directivity: Spectral regrowth is not isotropic—it concentrates in specific spatial directions based on the array geometry and beam pattern
• Joint optimization: The predistorter must adapt coefficients as the beam scans to maintain out-of-band suppression in the target direction

A fundamental physical mechanism that Out-of-Band DPD must compensate for. When beamforming weights change, the active reflection coefficient seen by each PA varies due to:

• Mutual coupling between array elements
• Beam-dependent impedance loading from the phased array combiner network
• This impedance variation directly modulates the PA's AM-AM and AM-PM characteristics, causing the nonlinear distortion profile to shift dynamically
• Out-of-Band DPD must track these impedance-induced changes to maintain spectral mask compliance across all steering angles

A complementary linearization architecture where the far-field radiated signal serves as the feedback reference for DPD training. For Out-of-Band DPD:

• A spatially-placed observation receiver captures the combined array output in the direction of interest
• This captures the aggregate effect of all PAs, mutual coupling, and beamforming in a single measurement
• Enables direction-specific linearization without requiring per-element feedback chains
• Particularly valuable for massive MIMO where per-element observation is impractical

A prerequisite signal conditioning step that Out-of-Band DPD often integrates. Antenna crosstalk creates parasitic signal paths between elements that:

• Introduce linear and nonlinear distortion components that mix with PA-generated regrowth
• Create spatially-dependent interference patterns in the far-field
• Out-of-Band DPD must model and cancel these coupling effects to achieve deep spectral suppression
• Techniques include coupling matrix inversion and spatial decorrelation preprocessing

An advanced framework that incorporates the array manifold vector—the spatial signature of the array—directly into the DPD optimization. This approach:

• Models the radiated field as a function of both element excitations and nonlinear distortion products
• Enables directionally-weighted optimization where out-of-band suppression is prioritized in specific angular sectors
• Uses spatial filtering concepts to project distortion into directions where it causes minimal interference
• Particularly effective for base station arrays serving sectorized coverage patterns