Research On Frequency Domain Equalization In Mode Division Multiplexing System

With the rapid development of the information society,the global data traffic is increasing exponentially at a rate estimated to exceed 50% annually.It brings that the capacity of the traditional single-mode fiber(SMF)communication system is approaching its nonlinear Shannon limit.As a new capacity expanding method,mode division multiplexed(MDM)transmission in few-mode fiber(FMF)can achieve ultra-high capacity beyond the capacity bottleneck of the single-mode fiber.Utilizing the spatial modes as new degree of freedom,a MDM system,in which each channel is on one orthogonal spatial mode ideally,can increase the capacity of long-haul communication systems with the number of modes proportionally.However,impairments in a real FMF transmission system,such as chromatic dispersion(CD),mode dependent loss(MDL),random mode coupling and differential mode group delay(DMGD),can degenerate the system performance.Especially the interplay between random mode coupling among different spatial modes and accumulated DMGD can cause severe channel crosstalk and inter-symbol interference,which will deteriorate the transmission performance and limit the transmission distance.Therefore,it is a key issue for MDM system to develop an effective digital signal processing algorithm to mitigate those impairments and implement mode demultiplexing successfully.This paper mainly discusses mode demultiplexing for MDM system.We analyze the transmission characteristics of spatial modes,generation mechanisms of the impairments and their effects on MDM system.The mathematical model of MDM system is established on the basis of considering those impairments synthetically,and set up the MDM simulation system with on-line digital signal processing(DSP).Then,the time domain multimodulus algorithm(TD-MMA)and the frequency domain multimodulus algorithm(FD-MMA)are used for compensating the channel crosstalk and inter-symbol interference,respectively.At last,frequency domain joint decision MMA(FD-JDMMA)is proposed to improve the convergence speed,and hybrid time-frequency domain sign-sign JDMMA(Hybrid-SJDMMA)is also proposed to reduce the computational complexity.The details of this paper are as follows.1.The basic conception of FMF is introduced briefly and the orthogonality of modes in the ideal FMF is demonstrated to confirm the physical background of mode division multiplexing.The impairments in MDM system,mode coupling,DMGD and MDL are discussed and the generation mechanisms of those impairments are studied.2.By adopting the combination approach of matrix propagation model and nonlinear Schr?dinger equation,the mathematical model of MDM system is established.The 3×3 single polarization and 6×6 dual polarization MDM simulation systems are set up with the VPI Transmission Maker 8.7 and Matlab.And the effects of DMGD and mode coupling are studied in the former simulation system.3.The principles of TD-MMA and FD-MMA are introduced separately,and the mathematic relation between the computational complexity of the two algorithms and the number of modes or the total DMGD for MDM system is analyzed.To verify the effectiveness of the two algorithms,the simulations for mQAM signals(m=4 and 16)are performed in the 6×6 dual polarization MDM simulation system.The simulation results show that FD-MMA leads to low computational complexity while maintaining similar transmission performance as TD-MMA.4.Two improved algorithms called FD-JDMMA and Hybrid-SJDMMA,respectively,are proposed for mode demultiplexing in MDM system.In the proposed FD-JDMMA algorithm,the statistical modulus error(SME)and the decision modulus error(DME)are calculated to obtain the combined error on the basic of the error calculation formula of FD-MMA.Then,the combined error is used for updating the tap weights to improve the convergence speed of the coefficients of the equalizers.In the proposed Hybrid-SJDMMA algorithm,the equalizer tap weight updates are simplified by discarding all of the information about the error term,and keeping only the sign of the error term on the basic of FD-JDMMA.The equalizer tap weights are updates in time domain and complex multiplications are not required,which will reduce the computational complexity of frequency domain equalization.The two proposed algorithms are used for the 6×6 dual polarization MDM simulation system and the performance is compared with FD-MMA.The simulation results show that FD-JDMMA has a better BER performance for 16 QAM signals and maintains similar computational complexity as FD-MMA.And for 4QAM and 16 QAM signals,the number of symbols for FD-JDMMA is reduced by about 50% than that for FD-MMA to achieve BER of 0.001.Hybrid-SJDMMA can achieve similar BER performance and convergence speed as FD-MMA.Meanwhile,the computational complexity of Hybrid-SJDMMA is almost one half of that of FD-MMA.Hybrid-SJDMMA has certain advantage of lower computational complexity.