Comparison of Real- and Complex-Valued NN Equalizers for Photonics-Aided 90-Gbps D-band PAM-4 Coherent Detection

Abstract

5G defines below 100 GHz as the millimeter-wave bands, whereas 100 GHz - 3 THz is categorized as THz band in 6G. Deep leraning (DL) is expected to enable a significant paradigm shift in 6G wireless networks. In this paper, D-band 90-Gbps single channel PAM-4 signal generation and transmission over 10-km SMF and 3-m wireless link at 140-GHz can be achieved. A novel complex-valued neural network (CVNN) equalizer using &#x2018;&Copf;ReLU&#x2019; activation function to directly recover PAM-4 signals from received noised signals is demonstrated. There are three DSP options in the experiment. In <i>Opt</i>.1, firstly conducted cascaded multi-modulus algorithm (CMMA) pre-equalization (pre-EQ) at transmitter, then processed via frequency offset estimation (FOE), carrier phase recovery (CPR) and finally real-valued neural network (RVNN) equalization at receiver. Here, the RVNN equalizers include DNN with a softmax output layer, two-step joint-DNN equalizer and LSTM. The experimental results show that LSTM-based equalizer outperforms the other real NN-based equalizers by average 0.5 to 1.5 dB at BER of 10^&#x2212;3 magnitude. Differently from <i>Opt</i>. 1, real-valued CMMA pre-EQ at transmitter is unexpected for CVNN in the other two options. In <i>Opt</i>. 2, we only combine down-conversion and CVNN regarded as &#x2018;pure data-driven&#x2019; training at receiver. This pure data-driven CVNN equalizer improves BER a lot and also has a larger computation burden, especially BER is as low as 1 &#x00D7; 10^&#x2212;4 with <i>n</i>₀ &#x003D; 571 and <i>n</i>₁ &#x003D; 200 training cells and the time complexity reaches 350000 in one iteration. Thanks to the aid of traditional mathematical-oriented models including FOE and CPR, the computation burden of CVNN in <i>Opt</i>. 3 is released significantly. Furthermore, we compare the performance of CVNN and RVNN in terms of BER decision accuracy, time complexity and receiver sensitivity. Followed by the same DSP with the same complexity, the comparison result between DNN and CVNN in the same structure of [371-260-1] with 11000 samples and 300 epochs shows that CVNN performs better due to its reservation of phase information. Therefore, we believe that the joint use of model-based, e.g., FOE, CPR steps and complex DL-based techniques has a potential for the future 6G wireless physical layer algorithms.