Net Residual Dispersion Research Articles

중계 구간이 증가할수록 SMF 길이와 RDPS가 점진적으로 증가하거나 감소하는 분산 제어 광전송 링크

MSSI (mid-span spectral inversion)와 결합된 분산 제어 (DM; dispersion management)는 광섬유가 갖는 색 분산과 비선형 효과에 기인하는 신호 왜곡을 줄일 수 있는 기술이다. 이러한 전송 링크의 융통적 구성을 위해 단일 모드 광섬유 (SMF; single mode fiber)의 길이와 중계 구간 당 잉여 분산 (RDPS; residual dispersion per span)이 중계 구간이 증가할수록 점진적으로 증가되거나 감소되는 인위적 분포 링크에서 전체 잉여 분산 (NRD; net residual dispersion) 제어 위치에 따른 왜곡된 WDM 채널의 보상 특성을 살펴보았다. 각 전송 반 구획 중 WDM 채널의 광 펄스 폭이 가장 좁아지는 중계 구간이 NRD 조절 위치가 되도록 SMF 길이와 RDPS를 점진적 증가 또는 감소 분포 패턴으로 링크를 구성해야 최상의 보상 효과를 얻을 수 있는 것을 확인하였다. Dispersion management (DM) combining with mid-spans spectral inversion (MSSI) is one of the various techniques compensating for the distorted optical signals. For the flexible implementation of this configured link, the compensation characteristics in the optical link with artificial distribution of the gradually ascending and descending of single mode fiber (SMF)'s lengths and residual dispersion per span (RDPS) as the number of fiber spans are assessed as a function of the control positions of net residual dispersion (NRD). It is confirmed that the best compensation is obtained by distributing gradually ascending or descending of SMF's lengths and RDPS capable to place NRD control position at fiber span, in which optical pulse width is most narrow.

랜덤 분포 구조의 분산 제어 광전송 링크에서 RDPS의 편차가 왜곡된 WDM 채널의 보상에 미치는 영향

분산 제어 (DM; dispersion management)와 광 위상 공액 기술이 결합된 전송 링크의 융통적 구성을 위해 중계 구간 당 잉여 분산(RDPS; residual dispersion per span)이 랜덤하게 분포하는 링크에서 RDPS 편차에 따른 WDM 채널의 보상 특성을 살펴보았다. 또한 허용 가능 NRD (net residual dispersion) 관점에서 RDPS 편차에 따른 링크 설계 기준도 제시하였다. RDPS 편차가 적을수록 WDM 채널 보상 효과가 우수하다는 것을 확인하였다. 또한 특정 눈 열림 패널티 (EOP; eye opening penalty)를 얻을 수 있는 허용 가능 NRD가 RDPS 편차에 비례하여 감소하는 것을 확인하였다. 따라서 본 연구 결과는 융통적인 장거리 광전송 링크 설계에 참고 자료가 될 것으로 기대한다. The compensation characteristics of WDM channels depending on residual dispersion per spans (RDPS) deviation in optical links with the randomly distributed RDPS for the adaptive configuration are investigated in this paper. Also, the link design rule related with RDPS deviations is proposed, from the viewpoint of the allowable net residual dispersion (NRD). It is confirmed that the effect of compensation for the distorted WDM channels is more increased as RDPS deviation is smaller. Also, it is confirmed that the decrease of the allowable NRD range for the exact eye opening penalty (EOP) is proportional to RDPS deviation. Therefore, the results of this research is expected to be the design reference for the flexible link configuration of long-haul optical transmission links.

분산 제어와 Mid-Span Spectral Inversion이 적용된 광전송 링크에서 반 전송 구획의 잉여 분산이 전체 잉여 분산에 미치는 영향

분산 제어와 Mid-Span Spectral Inversion이 적용된 광전송 링크에서 반 전송 구획의 잉여 분산이 전체 잉여 분산에 미치는 영향

Dispersion Managed Optical Transmission Links with an Artificial Distribution of the SMF Length and Residual Dispersion per Span

Dispersion management (DM), optical phase conjugation (OPC), and the combination of DM and OPC are promising techniques to compensate for optical signal distortion due to group velocity dispersion and nonlinear Kerr effects. The system performance improvement in DM links combined with OPC has been reported; however, the fixed residual dispersion per span (RDPS) usually used in these links restricts the flexibility of link configuration. Thus, in this paper, a flexible optical link configuration with artificially distributed single-mode fiber (SMF) lengths and RDPS in the combination of DM and OPC is proposed. Simulation results show that the best artificial distribution pattern is the gradually descending distribution of SMF lengths and the gradually ascending distribution of RDPS, as the number of fiber spans is increased, regardless of the average RDPS, the optimal net residual dispersion, and the dispersion coefficient of the dispersion compensating fiber.

Compensation Characteristics of the Distorted WDM Signals Depending on the Variation Degree of RDPS Random Variables in the Optical Links with Dispersion Management and Optical Phase Conjugation

The effects of the variation degree of residual dispersion per span (RDPS) random variables on the compensation characteristics of the distorted signals in optical links with the dispersion management (DM) and the mid-way optical phase conjugator (OPC) are investigated in this paper. In order to obtain this goal, the effective launch power range and the effective net residual dispersion (NRD) range are induced as a function of the variation degree of RDPS random variables. We confirm that it is needed to select the RDPS random variables of the narrow deviation in each fiber spans for implementing the flexible optical links transmitting the relative higher launch power. Also, we confirmed that it is more advantageous to use postcompensation rather than precompensation for expanding the effective NRD range.

RDPS가 랜덤하게 분포하는 분산 제어 광전송 링크에서 전체 전송 거리에 따른 유효 전체 잉여 분산

분산 제어 (DM; dispersion management)와 광 위상 공액 (optical phase conjugation)이 적용된 파장 다중 (WDM; wavelength division multiplexing) 시스템의 유연한 구성을 위하여 중계 구간 당 잉여 분산 (RDPS; residual dispersion per span)이 랜덤하게 분포하는 전송 링크에서 전체 전송 거리에 따른 설계 기준을 도출하였다. 설계기준 분석에 사용된 DM 파라미터는 유효 전체 잉여 분산 (NRD; net residual dispersion)과 유효 입사 전력이다. 단일 모드 광섬유 (SMF; single mode fiber) 기준 전체 전송 거리가 1,000 km 이하인 링크에 랜덤 분포의 RDPS가 적용되는 경우 일정 분포에 비해 시스템 성능이 크게 차이나지 않아 유연한 네트워크 구성이 가능하고, 넓은 범위에 걸쳐 있는 WDM 채널에 대해 하나의 값이 아닌 폭넓은 NRD를 링크에 적용할 수 있다는 것을 확인하였다. The design rule depending on total transmission length is induced in the optical links with residual dispersion per span (RDPS) of the random distribution, which is adopted for implementing the flexible systems of wavelength division multiplexing (WDM) transmission with dispersion management (DM) and optical phase conjugation. DM parameters used for the analysis of the design rule are the effective net residual dispersion (NRD) and the effective launch power. It is confirmed that the flexible optical network configuration with the total transmission length lower than 1,000 km is possible, because the system performance difference between the randomly distribution and the uniform distribution of RDPS is small. And, in the optical links with the randomly distributed RDPS, the wide NRD can be applied for transmitting WDM channels of the relatively wide launch power.

분산 제어 광전송 링크에서 중계 구간의 RDPS 기울기에 따른 WDM 신호의 보상 특성

분산 제어 (DM; dispersion management)와 광 위상 공액 (optical phase conjugation)이 적용된 광전송 링크에서 중계 구간 당 잉여 분산 (RDPS; residual dispersion per span) 기울기 (slope)에 따른 파장 분할 다중 전송 (WDM; wavelength division multiplexed) 채널의 보상 특성을 분석하여 최적의 RDPS 기울기를 도출하였다. RDPS 기울기가 증가할수록 WDM 채널의 유효 입사 전력 범위를 더욱 증가시키고 채널 간 성능 차이를 더욱 감소시키는 것을 확인하였다. 아울러 RDPS 기울기가 증가할수록 유효 전체 잉여 분산 (NRD; net residual dispersion) 범위도 증가하여 큰 RDPS 기울기가 유연한 광전송 링크 구성에 더욱 유리하다는 것을 확인하였다. The optimal residual dispersion per span (RDPS) slope is induced through the analyses of the compensation characteristics of the wavelength division multiplexed (WDM) channels depending on RDPS slope in the optical links with a dispersion management (DM) and an optical phase conjugation. The simulation results show that the effective launch power of WDM is more increased and the performance difference between the channels is more decreased as RDPS slope is more increased. The simulation results also show that the effective net residual dispersion (NRD) range is more increased as RDPS slope is more increased, and consequently, it is more advantageous to use the large RDPS slope for implementing the flexible optical links.

분산 제어가 적용된 WDM 전송 링크에서 집중 RDPS를 통한 시스템 성능 개선

System performance improvement through the concentrated residual dispersion per span (RDPS) in special transmission fiber spans in optical transmission links with dispersion management (DM) for wavelength division multiplexed (WDM) transmission is investigated through the comparison with the performance in optical transmission links with uniform RDPS in every fiber spans. It is confirmed that, in optical links with RDPS of 0 ps/nm uniformly distributed in the rest fiber spans, if RDPS of 300 ps/nm and 1,320 ps/nm are concentrated in 5th-13th fiber spans and 6th-13th fiber spans, respectively, then the best performance is obtained. It is also confirmed that optimal net residual dispersion (NRD) controlled by precompensation and postcompensation are 10 ps/nm and -10 ps/nm, respectively, in all two cases, and the effective launching power range below 1 dB eye opening penalty (EOP) in the concentrated RDPS of 300 ps/nm and 1,320 ps/nm are improved by 2 dB and 6 dB than optical transmission links with the uniformly distributed RDPS, respectively.

Dispersion Management and Optical Phase Conjugation in Optical Transmission Links with a Randomly Distributed Single-Mode Fiber Length

Suppressing or mitigating signal distortion due to group velocity dispersion and optical Kerr effects is necessary in ultra-high speed and long-haul wavelength division multiplexing (WDM) transmission systems. Dispersion management (DM), optical phase conjugation (OPC), and the combination of these two are promising techniques to compensate for signal distortion. In this paper, to implement a flexible optical WDM network, a new optical link configuration with a randomly distributed single-mode fiber (SMF) length and fixed residual dispersion per span in the combination of DM and OPC is proposed and investigated. The simulation results show that the best net residual dispersion (NRD) in the proposed optical links is +10 ps/nm, which is independent of pre- and postcompensation. The effective launch power of the WDM channel is increased more in the optical links with NRD = +10 ps/nm controlled by only precompensation. Furthermore, the system performance difference between the proposed optical link configuration with the best NRD and the conventional optical link with uniform distribution of the SMF length had little significance. Consequently, it is confirmed that the proposed optical link configuration with the best NRD is effective and useful for implementing a reconfigurable long-haul WDM network.

분산 보상 광섬유의 분산 계수와 중계 구간 당 잉여 분산에 따른 WDM 신호의 보상 특성

단일 모드 광섬유의 그룹 속도 분산과 비선형 효과에 의해 왜곡되는 960 Gbps 파장 분할 다중 신호의 보상을 위해 분산 제어 기술이 적용된 광전송 링크에서 분산 보상 광섬유 (DCF; dispersion compensating fiber)의 분산 계수와 중계 구간 당 잉여 분산량 (RDPS; residual dispersion per span)이 왜곡 보상에 미치는 영향을 분석하였다. 우선 왜곡 보상에 큰 영향을 미치는 최적 전체 잉여 분산량 (NRD; net residual dispersion)은 고려한 모든 DCF의 분산 계수와 RDPS에 관계없이 큰 입사 전력에서 구해야 한다는 것을 확인하였다. 중계 구간의 RDPS는 매우 작게, 반면 DCF의 분산 계수는 크게 하여야 시스템 성능이 현저하게 개선되는 것을 확인하였다. The effects of dispersion coefficient of dispersion compensating fiber (DCF) and residual dispersion per span (RDPS) on in the dispersion managed optical links for compensating the distorted 960 Gbps wavelength division multiplexd (WDM) signals due to group velocity dispersion (GVD) and optical nonlinear effects of single mode fiber (SMF) are investigated. It is confirmed that optimal net residual dispersion (NRD), which greatly affects compensating for optical signals, should be induced under the large launch power condition, irrelevant on the considered dispersion coefficient of DCF and RDPS. It is also confirmed that system performances are greatly improved by selecting the very small RDPS and very large dispersion coefficient of DCF.

인위적인 단일 모드 광섬유 길이와 RDPS 분포를 갖는 분산 제어 광전송 링크에서 선치 보상과 후치 보상을 통한 WDM 신호의 성능 개선

단일 모드 광섬유의 그룹 속도 분산과 자기 위상 변조에 의해 왜곡된 파장 분할 다중 신호의 효율적인 보상을 위한 새로운 광전송 링크 기술을 제안하였다. 제안된 전송 링크는 WDM 송신이나 수신단 근처에 광 위상 공액기(OPC; optical phase conjugator)가 위치하고 각 중계 구간의 SMF 길이와 RDPS(residual dispersion per span)가 인위적으로 분포하는 구조이다. 시스템 성능을 개선하여 유효 입사 전력 범위와 유효 전체 잉여 분산 (NRD; net residual dispersion)을 늘릴 수 있는 최적의 링크 구조는 OPC가 WDM 수신단에 가깝게 위치하고 후치 보상(postcompensation)에 의해 NRD를 결정하고 중계 구간이 증가할수록 SMF 길이와 RDPS를 점진적으로 감소시키는 링크라는 것을 확인하였다. New optical transmission links technique for compensating of the distorted wavelength division multiplexed (WDM) signals due to group velocity dispersion (GVD) and self phase modulation (SPM) in single mode fiber (SMF) are proposed. The proposed optical links have optical phase conjugator (OPC) placed at nearby WDM transmitter or receiver and repeater spans with artificial distribution of SMF length and residual dispersion per span (RDPS). It is confirmed that optimal link configuration expanding effective launching power range and effective net residual dispersion (NRD) by improving system performance is that having OPC closely placed at WDM receiver and the gradually descended distribution of SMF length and RDPS of each repeater spans, related with the gradually increased optical link length. And, it is also confirmed that NRD is controlled by postcompensation in optimal optical link with OPC closely placed at WDM receiver.

중계 구간의 SMF 길이와 RDPS 분포가 일정하지 않은 분산 제어 광전송 링크를 통한 왜곡된 WDM 신호의 보상

분산 제어 (DM; dispersion management)은 파장 분할 다중 (WDM; wavelength division multiplexed) 채널의 고품질 전송을 위해 광섬유의 그룹 속도 분산 (GVD; group velocity dispersion)과 비선형 효과의 상호 작용에 의해 왜곡되는 신호의 보상할 수 있는 대표적 기술이다. DM이 적용된 광전송 링크의 유연한 구성에 필요한 중계 구간 (fiber span)을 구성하는 단일 모드 광섬유 (SMF; single mode fiber)의 길이와 중계 구간 당 잉여 분산 (RDPS; residual dispersion per span)을 랜덤하게 분포시키는 구조와 인위적으로 분포시키는 구조에서의 최적 전체 잉여 분산 (NRD; net residual dispersion)의 최적치와 유효 입사 전력 범위를 도출하였다. 고려한 SMF의 길이와 RDPS 분포 패턴 모두 precompensation으로 NRD를 조절하는 경우에서는 +10 ps/nm, postcompensation으로 NRD를 조절하는 경우에서는 -10 ps/nm이 최적 NRD라는 것을 알 수 있었다. 그리고 NRD가 상기 값으로 설정된 경우 중계 구간이 증가할수록 SMF 길이를 감소시키고, RDPS를 증가시키는 인위적인 분포의 전송 링크에서의 시스템 성능이 가장 양호하여 균일한 분포의 링크에 비해 유효 입사 전력 범위가 2 dB 정도 신장되는 것을 확인하였다. Dispersion management (DM) is the typical technique compensating for the distorted signals due to interaction of group velocity dispersion (GVD) and optical nonlinear effects for transmitting wavelength division multiplexed (WDM) channel with the excellent performance. Optimal net residual dispersion (NRD) and effective launching power range of optical transmission links with random distribution and artificial distribution of single mode fiber (SMF) length and residual dispersion per span (RDPS) required to flexibly design of optical links in DM. It is confirmed that optimal net residual dispersion (NRD) are +10 ps/nm and -10 ps/nm controlled by precompensation and postcompensation, respectively, in both of the considered distribution patterns of SMF length and RDPS. And, in optimal NRD, system performance in optical links with the descending distribution of SMF length and the ascending distribution of RDPS among the artificial distribution patterns are more improved, consequently, effective launching power range is expanded by almost 2 dB than those in optical links with the uniform distribution.

전송 반 구획에서만 중계 구간 당 분산이 랜덤하게 분포하는 광 링크에서의 WDM 신호의 성능

그룹 속도 분산 (GVD; group velocity dispersion)과 비선형 효과의 상호 작용에 의해 왜곡되는 파장 분할 다중 (WDM; wavelength division multiplexing) 신호를 보상하기 위해 광 위상 공액기 (OPC; optical phase conjugator)와 분사 제어 (DM; dispersion management)가 적용된 광전송 링크에서의 전체 잉여 분산 (NRD; net residual dispersion)의 최적치와 유효 입사 전력 범위를 도출하였다. 실제 광전송 시스템의 융통적 설계를 위해 한 쪽 반 전송 구획에서의 단일 모드 광섬유 (SMF; single mode fiber) 중계 구간(span) 당 잉여 분산 (RDPS; residual dispersion per span)이 랜덤하게 분포하는 광전송 링크를 고려하였다. precompensation으로 전체 분산을 조절하는 링크의 최적 NRD는 10 ps/nm이고 이 경우 유효 입사 전력 범위는 -8~1 dBm인 것을 확인하였다. 또한 postcompensation으로 전체 분산을 조절하는 링크의 최적 NRD는 -10 ps/nm이고, 유효 입사 전력 범위는 -7.5~1 dBm인 것을 확인하였다. Optimal net residual dispersion (NRD) and effective launching power range of optical transmission links with optical phase conjugator (OPC) and dispersion management (DM) for compensating the distorted wavelength division multiplexing (WDM) signals due to interaction of group velocity dispersion (GVD) and optical nonlinear effects. WDM systems considered in this research have optical links with the random distribution of residual dispersion per span (RDPS) in each single mode fiber (SMF) spans of only one half transmission section for designing the adaptive optical transmission system configurations. It is confirmed that optimal NRD is 10 ps/nm and effective launching power range is obtained to be -8~1 dBm under NRD = 10 ps/nm in optical links with total dispersion controlled by precompensation. And, it is also confirmed that optimal NRD is -10 ps/nm and effective launching power range is obtained to be -7.5~1 dBm under NRD = -10 ps/nm in optical links with total dispersion controlled by postcompensation.

WDM Transmission Using Dispersion Compensation in Optical Transmission Links with Nonuniform Residual Dispersion per Span

The possibility of implementing nonuniform residual dispersion per span (RDPS) in optical links with net residual dispersion (NRD) controlled by precompensation and postcompensation for 960 Gbps WDM transmissions is studied and discussed. The fiber optic communication links investigated in this paper consist of inline dispersion management (DM) for each fiber spans and optical phase conjugator (OPC) at mid-way of total transmission length in order to compensate for WDM signal distortions due to group velocity dispersion (GVD) and nonlinearities. It is confirmed that the effect of nonuniform RDPS distribution on system performance is not significant. It is also confirmed that the optimal NRD is obtained to be one of two values of +10 ps/nm or -10 ps/nm, which depend on the deciding of NRD controlled by precompensation or postcompensation, and the exact RDPS configurations. The effective NRD ranges resulting eye opening penalty (EOP) below 1 dB are independent on the exact RDPS distribution for relative low launch power. Therefore, results show the possibility of implementing the flexible optical links to expand network construction for WDM transmission of high bit-rate capability.

분산 제어와 광 위상 공액이 적용된 광전송 링크에서 총 전송 거리와 중계 간격에 따른 전체 잉여 분산과 입사 전력의 최적화

단일 모드 광섬유 (SMF; single mode fiber)의 색 분산과 자기 위상 변조 (SPM; self phase modulation)에 의한 신호 왜곡을 보상하기 위하여 분산 제어 (DM; dispersion management)와 광 위상 공액 (OPC; optical phase conjugation)이 적용된 파장 분할 다중 (WDM; wavelength division multiplexed) 시스템에서 전송 링크의 설계 기준을 살펴보았다. 본 연구에서 고려한 전송 링크의 설계 기준은 precompensation과 postcompensation에 의해 결정되는 최적 전체 잉여 분산 (NRD; net residual dispersion)과 채널의 최적 입사 전력 범위이다. 최적 NRD는 WDM 시스템의 전체 전송 거리와 중계 간격에 상관없이 precompensation과 postcompensation에 따라 각각 +10 ps/mn와 -10 ps/mn로 얻어졌다. 그러나 전송 거리와 중계 간격이 짧을수록 시스템 성능이 전반적으로 더욱 양호하게 나타나고, 비교적 넓은 유효 입사 전력 범위에 대해 유효 NRD 범위가 넓게 분포한다는 것을 알 수 있었다. Design rules of optical transmission links with dispersion management (DM) and optical phase conjugation (OPC) for compensating optical signal distortion due to chromatic dispersion and self phase modulation (SPM) of single mode fiber (SMF) are investigated in this paper. Design rules consist of optimal net residual dispersion (NRD) and optimal range of launching power of wavelength division multiplexed (WDM) channels as a function of total transmission length and span length. In all considered total transmission length and span length, optimal NRD are obtained to +10 ps/nm and -10 ps/mn for transmission links, which is controlled by precompensation and postcompensation, respectively. It is confirmed that system performances are more improved and effective NRD for wide launching power have wider range as total transmission length and span length are more decreased.

40 Gbps RZ Transmission Using Dispersion Compensation of Single-Span in Optical Transmission Links with Multi-Span of Single Mode Fiber

In dispersion management (DM) and optical phase conjugation applied into optical transmission links with multi fiber spans for minimizing the impact of nonlinearity and group velocity (GVD), implementation possibility of DM using only one fiber span for pre- or postcompensation was assessed as a function of duty cycle of RZ pulse and residual dispersion per span (RDPS). It is confirmed that DM with optimal net residual dispersion (NRD) controlled by only one fiber span could be sufficiently applied into optical transmission links, though optimal NRD is more increased than that in transmission links with the general DM scheme of pre- and postcompensation. Thus, it is expected that optical transmission system is simply designed and implemented by applying the proposed DM scheme into real optical transmission links. Also, it is confirmed that the advantageous duty cycle of RZ is 0.5 and RDPS is setting to be small value for the effective transmitting wide signal wavelength range in optical links with optimal NRD controlled by only one fiber span.

Analytical Design of SPM-Limited Systems With Optical Phase Conjugation

Optical phase conjugation (OPC) is a promising technique to compensate the nonlinear impairment in optical fiber communications. However, the compensation for nonlinearity by use of OPC is limited by the asymmetry of signal power. Thus, the optimization of a link taking advantage of OPC is demanded. In this letter, an analytical model is proposed to optimize the design of self-phase-modulation (SPM)-limited systems in which the nonlinearity is compensated by OPC. Using the model, the optimal location of the phase conjugator can be evaluated, and an analytical expression of optimal net residual dispersion is obtained. Moreover, the SPM-compensation efficiency of OPC can be estimated conveniently.

Optimization of the Net Residual Dispersion for Self-Phase Modulation-Impaired Systems by Perturbation Theory

The performance of self-phase modulation (SPM)-impaired systems can be improved significantly by adjusting the net residual dispersion (NRD) of the systems. In this paper, we propose a novel approach to optimize the NRD for SPM-impaired systems. We find that in SPM-impaired system, the optimal NRD can be obtained by minimizing the output distortion of a single pulse. Using a perturbation theory, a semianalytical expression is derived to calculate the output distortion of a single pulse. With the obtained expression, the NRD of SPM-impaired dispersion-managed systems can be optimized conveniently. Compared to previous methods, the present method is simple and fast. The validity of this method is verified by numerical simulations for various SPM-impaired systems

Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems

Dispersion management is an effective technique to suppress the nonlinear impairment in fiber transmission systems, which includes tuning the amounts of precompensation, residual dispersion per span (RDPS), and net residual dispersion (NRD) of the systems. For self-phase modulation (SPM)-limited systems, optimizing the NRD is necessary because it can greatly improve the system performance. In this paper, an analytical method is presented to optimize NRD for SPM-limited dispersion-managed systems. The method is based on the correlation between the nonlinear impairment and the output pulse broadening of SPM-limited systems; therefore, dispersion-managed systems can be optimized through minimizing the output single-pulse broadening. A set of expressions is derived to calculate the output pulse broadening of the SPM-limited dispersion-managed system, from which the analytical result of optimal NRD is obtained. Furthermore, with the expressions of pulse broadening, how the nonlinear impairment depends on the amounts of precompensation and RDPS can be revealed conveniently.