Volterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of nonlinear calibration, and improve stability and speed, while preserving accuracy. Several techniques (LASSO, DOMP and OBS) and their variants (WLASSO and OBD) are compared in this paper for the experimental calibration of an IF amplifier. The results show that Volterra models can be simplified, yielding models that are 4–5 times sparser, with a limited impact on accuracy. About 6 dB of improved Error Vector Magnitude (EVM) is obtained, improving the dynamic range of the amplifiers. The Symbol Error Rate (SER) is greatly reduced by calibration at a large input power, and pruning reduces the model complexity without hindering SER. Hence, pruning allows improving the dynamic range of the amplifier, with almost an order of magnitude reduction in model complexity. We propose the OBS technique, used in the neural network field, in conjunction with the better known DOMP technique, to prune the model with the best accuracy. The simulations show, in fact, that the OBS and DOMP techniques outperform the others, and OBD, LASSO and WLASSO are, in turn, less efficient. A methodology for pruning in the complex domain is described, based on the Frisch–Waugh–Lovell (FWL) theorem, to separate the linear and nonlinear sections of the model. This is essential because linear models are used for equalization and cannot be pruned to preserve model generality vis-a-vis channel variations, whereas nonlinear models must be pruned as much as possible to minimize the computational overhead. This methodology can be extended to models other than the Volterra one, as the only conditions we impose on the nonlinear model are that it is feedforward and linear in the parameters.

中文翻译：

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使用 Volterra 内核的放大器非线性校准的模型复杂度降低方法

Volterra 模型允许对非线性动力系统进行建模，即使它们需要估计大量参数并且因此具有潜在的巨大计算成本。因此，Volterra 模型的修剪对于降低非线性校准的计算成本、提高稳定性和速度，同时保持准确性至关重要。本文比较了几种技术（LASSO、DOMP 和 OBS）及其变体（WLASSO 和 OBD）用于中频放大器的实验校准。结果表明，Volterra 模型可以简化，生成的模型稀疏 4-5 倍，对准确性的影响有限。获得了大约 6 dB 的改进误差矢量幅度 (EVM)，从而提高了放大器的动态范围。通过在大输入功率下进行校准，大大降低了符号错误率（SER），并且剪枝降低了模型复杂度而不妨碍 SER。因此，修剪可以提高放大器的动态范围，模型复杂度几乎降低了一个数量级。我们提出了用于神经网络领域的 OBS 技术，与更为人所知的 DOMP 技术相结合，以最佳精度修剪模型。事实上，模拟表明 OBS 和 DOMP 技术优于其他技术，而 OBD、LASSO 和 WLASSO 反过来效率较低。基于 Frisch-Waugh-Lovell (FWL) 定理，描述了一种在复杂域中进行剪枝的方法，以分离模型的线性和非线性部分。这是必不可少的，因为线性模型用于均衡并且不能被修剪以保持模型相对于信道变化的通用性，而必须尽可能修剪非线性模型以最小化计算开销。这种方法可以扩展到 Volterra 模型以外的模型，因为我们对非线性模型施加的唯一条件是它在参数中是前馈和线性的。