The orthogonal frequency-division multiplexing (OFDM) is a widely used modulation scheme in modern digital communication systems. An OFDM signal can be susceptible to channel nonlinearities due to its high peak-to-average power ratio (PAR). This makes estimation and compensation of nonlinear channels particularly vital for OFDM systems. In this paper, we consider identifying cubically nonlinear channels in baseband OFDM systems using minimally sampled input and output signals. Unlike nonlinear channels in bandpass OFDM systems, which can be modeled by a complex baseband equivalent Volterra series with only odd order terms, the nonlinear channel in a baseband OFDM system requires a real Volterra series with both even and odd order terms. The minimally sampled input and output signals of the baseband OFDM system are used to estimate the frequency-domain Volterra kernels of the nonlinear channel. Due to the possible spectral regrowth caused by the channel nonlinearities, the minimally sampled output signal could be aliased. Nevertheless, by conducting higher-order statistical analyses on the OFDM signals, we show that closed form expressions of the Volterra kernels can still be derived. As a result of the closed form expressions, a simple estimate for the Volterra kernels is attained. Furthermore, the derived Volterra kernel estimate is shown to achieve the minimum mean square error (MMSE). Therefore, the proposed approach indeed provides an efficient yet accurate way to estimate nonlinear channels in baseband OFDM systems.

中文翻译：

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最小采样基带 OFDM 系统的非线性信道估计


正交频分复用（OFDM）是现代数字通信系统中广泛使用的调制方案。由于 OFDM 信号具有较高的峰均功率比 (PAR)，因此很容易受到信道非线性的影响。这使得非线性信道的估计和补偿对于 OFDM 系统尤为重要。在本文中，我们考虑使用最小采样输入和输出信号来识别基带 OFDM 系统中的三次非线性信道。与带通 OFDM 系统中的非线性信道不同，带通 OFDM 系统中的非线性信道可以通过仅具有奇数阶项的复杂基带等效 Volterra 级数进行建模，而基带 OFDM 系统中的非线性信道需要具有偶数和奇数阶项的实数 Volterra 级数。基带 OFDM 系统的最小采样输入和输出信号用于估计非线性信道的频域 Volterra 核。由于通道非线性可能导致频谱再生，最小采样输出信号可能会出现混叠。尽管如此，通过对 OFDM 信号进行高阶统计分析，我们表明仍然可以导出 Volterra 内核的封闭形式表达式。作为闭合形式表达式的结果，获得了 Volterra 核的简单估计。此外，导出的 Volterra 核估计可实现最小均方误差 (MMSE)。因此，所提出的方法确实提供了一种有效而准确的方法来估计基带 OFDM 系统中的非线性信道。