Two-dimensional (2-D) polynomial models are widely used in digital predistortion (DPD) design for dual-band power amplifier (PA) linearization. However, the conventional polynomial model exhibits numerical instabilities when high-order nonlinearities are included. To solve this problem, a closed-form 2-D orthogonal polynomial DPD model is deduced under the assumption of complex Gaussian processes. Compared with the Legendre orthogonal polynomial for uniform distribution, the complex Gaussian assumption is more coincident with practical communication signals. Cutting down the condition number of the input correlation matrix is the most important objective to deduce the new model, and the experiment results show that the condition number of the new model can be significantly decreased both for the Gaussian signal and the practical OFDM signal. The predistortion performance of the OFDM signal is also investigated. In the presence of 32-bit floating point single precision processing, the proposed model is more stable in the least squares (LS) parameter estimation and yield better adjacent channel power ratio (ACPR) and normalized mean square error (NMSE) improvement when compared with the conventional model and the Legendre model. At the same time, the proposed model has fewer polynomial coefficients compared with the Legendre model and accordingly reduce the complexity of coefficient estimation.

二维（2-D）多项式模型广泛用于数字预失真（DPD）设计中，以实现双频功率放大器（PA）线性化。然而，当包含高阶非线性时，传统的多项式模型表现出数值不稳定性。为了解决这个问题，在复杂的高斯过程的假设下，推导了一个封闭形式的二维正交多项式DPD模型。与均匀分布的勒让德正交多项式相比，复杂高斯假设与实际通信信号更加一致。减少输入相关矩阵的条件数是推导新模型的最重要目标，实验结果表明，无论是高斯信号还是实际的OFDM信号，新模型的条件数都可以大大降低。还研究了OFDM信号的预失真性能。在存在32位浮点单精度处理的情况下，与最小二乘（LS）参数估计相比，所提出的模型更加稳定，与之相比，该模型具有更好的相邻信道功率比（ACPR）和归一化均方误差（NMSE）改进。常规模型和Legendre模型。同时，与勒让德模型相比，所提出的模型具有更少的多项式系数，从而降低了系数估计的复杂度。与常规模型和Legendre模型相比，该模型在最小二乘（LS）参数估计中更稳定，并且产生了更好的相邻信道功率比（ACPR）和归一化均方误差（NMSE）改进。同时，与勒让德模型相比，所提出的模型具有更少的多项式系数，从而降低了系数估计的复杂度。与常规模型和Legendre模型相比，该模型在最小二乘（LS）参数估计中更稳定，并且产生了更好的相邻信道功率比（ACPR）和归一化均方误差（NMSE）改进。同时，与勒让德模型相比，所提出的模型具有更少的多项式系数，从而降低了系数估计的复杂度。