光传送网建模与价值评估

Modeling and Value Evaluation of Optical Transport Network

针对第十五届中国研究生数学建模B题展开研究,对光纤通信网络工作原理以及价值评估体系进行分析和建模.首先从底层物理原理探究了三种调制方式,即QPSK,8QAM和16QAM,误比特率和信噪比的关系,并从仿真实验角度验证了理论推导合理性,得出三种调制方式在BER=0.02时的SNR容限点分别为6.68dB,10.80dB,12.68dB.接着以单跨为单位对光传输链路建模,计算最优传输功率并求得链路距离最优解:当单跨光纤长度分别为80和100 km时,最远传输为19跨和7跨;基于光纤的信息容量和传输距离,建立网络价值优化模型,结合贪心法和局部三节点系统特征分析法,求解得最优网络规划方案:当最大连接数分别为16和33时,网络价值为5432mTb/s和8923mTb/s;最后探究改变星座图位置,编码方式,概率等方式对光链路传输性能的优化,得到了一组优于原始星座图的结果,以及一组介于8QAM与16QAM之间的结果.

According to B problem in 15th National Graduate Mathematical Contest,this paper aims at the study and modeling of optical fiber communication networks and their value evaluation.Firstly,we theoretically investigate the relationship between Bit Error Ratio(BER)and Signal-to-Noise Ratio(SNR)under three different modulations,that is QPSK,8 QAM and 16 QAM.And the results obtained by simulation verify the reasonability of the theoretical ones.The final tolerance points of SNR are 6.68 dB,10.80 dB and 12.68 dB respectively for the three modulation when BER is 0.02.Then,optical communication link is modelled in span to find the the furthest distance.When the single span is 80 km and 100 km in length,the spans are 19 and 7 at most.Baesd on the results,we model the value evaluation of optical networks and figure it through greedy algorithm and local-three-points algorithm proposed by us.The optimal solution we obtain is that the network values are 5432 mT/s and8923 mT/s when the connections are 16 and 33.Finally,the effects of map location,encoding modes and probilities on transmission performance of optical networks are studied.One result better than the original map is obtained and one result better than 16 QAM but worse than8 QAM is also found.