Comparison of Different Precoding Techniques for Unbalanced Impairments Compensation in Short-Reach DMT Transmission Systems

Channel independent precoding technique has been widely used in optical discrete multi-tone (DMT) transmission systems to compensate unbalanced impairments induced by bandwidth limitations and imperfect frequency responses of electrical/optical devices and various interferences. However, the comparison of different precoding techniques in terms of peak-to-average power ratio (PAPR) reduction, nonlinear distortion tolerance, implementation complexity, and bit error rate (BER) improvements has not been fully studied. In this article, we comparatively investigate seven most commonly used precoding techniques, i.e., discrete Fourier transform (DFT), orthogonal circulant matrix transform (OCT), constant amplitude zero autocorrelation sequence-based matrix transform (CAZACT), Zadoff-Chu matrix transform (ZCT), discrete cosine transform (DCT), discrete Hartley transform (DHT), and Walsh-Hadamard transform (WHT), through both numerical simulations and offline experiments. Simulations show that the ZCT can achieve the best PAPR reduction, and the OCT cannot reduce the PAPR. Besides, DFT, CAZACT, ZCT, DCT, and DHT precoded DMT signals have superior error vector magnitude performance after passing through nonlinear models. And the corresponding precoded QPSK-DMT signals have better BER performance than both OCT/WHT precoded and conventional ones in the distortion-limited scenarios. However, the precoded 16/64QAM-DMT signals, excluding OCT precoded one, are more sensitive to nonlinear distortions and provide minor BER improvement or even may degrade the BER performance. Complexity analysis exhibits the WHT precoding does not require multiplications and therefore has the lowest implementation complexity. In the inter-symbol interference-limited case, OCT precoding can still achieve a good signal-to-noise ratio (SNR) balance and provide the best BER performance. A simple timing synchronization point adjustment (TSPA) method is employed to enhance SNR balance. Simulated and experimental results exhibit that similar BER performance can be achieved by using these precoding techniques together with TSPA in noise-limited scenarios. Considering the implementation complexity, WHT precoding may be a good option to compensate unbalanced impairments in the short-reach DMT transmission system.