2D-DPD (Two-Dimensional DPD)

The core innovation of 2D-DPD is its two-dimensional indexing structure. Unlike conventional 1D DPD that relies solely on the magnitude of a single signal, 2D-DPD constructs a 2D address from the instantaneous magnitudes |x₁(n)| and |x₂(n)| of two concurrent baseband signals. This allows the predistorter to uniquely map a correction coefficient for every combination of signal envelope levels across both bands, directly addressing the cross-band modulation that a 1D model cannot see.

A primary function of 2D-DPD is the suppression of cross-band intermodulation distortion (IMD). When two signals are amplified concurrently, the PA nonlinearity generates distortion products that fall into both transmit bands and the gap between them. The 2D model includes cross-terms that are functions of the envelope of one band acting on the signal of the other. This allows the predistorter to synthesize a cancellation signal specifically for these cross-modulated components, dramatically improving adjacent channel leakage ratio (ACLR) in both bands.

The 2D Memory Polynomial is the most widely adopted behavioral model for 2D-DPD. It extends the standard memory polynomial by adding cross-band memory terms. The model includes:

• In-band terms: Standard memory polynomial terms for each band individually.
• Cross-band terms: Products of the current signal sample in one band with the past envelope magnitudes of the other band. This structure captures both static nonlinearity and cross-band memory effects while maintaining a linear-in-parameters structure for robust coefficient extraction.

For hardware-efficient implementation on FPGAs or ASICs, the 2D-DPD function is often realized as a 2D Look-Up Table (2D-LUT). The instantaneous magnitudes of the two baseband signals are quantized to form a 2D address that indexes a table of complex gain correction values. Bilinear interpolation between adjacent table entries ensures smooth correction. This approach replaces computationally expensive polynomial evaluation with a simple memory access, making it suitable for high-speed, real-time applications in base stations and user equipment.

The parameters of a 2D-DPD model are estimated using joint coefficient extraction. The input and output waveforms of both bands are captured simultaneously from the PA. A single least-squares estimation problem is formulated that includes all in-band and cross-band model terms. This joint approach is critical because the cross-band terms couple the two bands; estimating coefficients independently for each band would fail to capture the inter-band nonlinear interactions. The resulting model is then copied to the predistorter in the forward path.

The theoretical basis for 2D-DPD lies in the dual-band Volterra series. Starting from the passband Volterra series, a baseband equivalent is derived by selecting only those nonlinear terms whose frequencies fall around the two carrier frequencies. This analytical derivation reveals the exact structure of in-band and cross-band kernels. Simplified models like the 2D-MMP and 2D-GMP are pruned versions of this full Volterra series, retaining only the most significant terms to balance modeling accuracy with computational feasibility.