Digital transmission in the presence of depolarization crosstalk with four-dimensional constellations
Description
The dual polarization communication system with depolarization crosstalk is studied with various four-dimensional constellations. Specifically, the probability of symbol error (P$\sb{\rm es}$) performances of dual-channel M-QAM (DCM-QAM) and a constellation called GL4-256 are obtained for three types of cancelers--the diagonalizer, the Minimum Mean Square Error (MMSE) canceler, and the Maximum Likelihood Detector (MLD). It is discovered that there are three different diagonalizers, one of which has P$\sb{\rm es}$ performance which grossly outperforms that of the other two. A formula is derived for the weights of the MMSE canceler which is used to show the equivalence of the MMSE with the best diagonalizer, for large signal-to-noise ratios A new measure of P$\sb{\rm es}$ performance for the MLD is introduced, which is called the Crosstalk Asymptotic Estimate (CAE). Monte Carlo simulation results are provided for DC16-QAM, which show excellent agreement between the simulated and analytical results For the best diagonalizer, GL4-256 outperforms DC16-QAM for crosstalk levels below -9.5 dB. Also, for the MLD, GL4-256 outperforms DC16-QAM for crosstalk levels below -12 dB. Furthermore, for DC16-QAM the MLD outperforms the best diagonalizer by about 1.4 dB, for crosstalk levels above -10 dB. However, for GL4-256, the MLD outperforms the best diagonalizer by about 1 dB, only for crosstalk levels above -2 dB The concept of catastrophic constellations is introduced to explain the poor P$\sb{\rm es}$ performance of DCM-QAM and GL4-L, for high crosstalk levels. A new sixteen-symbol non-catastrophic constellation (NC-16) is presented, whose P$\sb{\rm es}$ performance does not deteriorate with crosstalk. A comparison with DC-QPSK shows that NC-16 vastly outperforms DC-QPSK for crosstalk levels above -5 dB Receiver structures for the three diagonalizers are presented, along with a new four-dimensional diagonalizer and a new four-dimensional MMSE canceler. The latter two receivers are used to receive GL4-L, and are extensions to the receivers presently used for DCM-QAM. Both of these use a single four-dimensional detector, for which a new design is given that is well suited to hardware implementation