Evaluating the Impact of QAM Constellation Subset Selection on the Achievable Information Rates of Multidimensional Formats in Fully Loaded Systems

An efficient procedure is presented for evaluating the performance of multidimensional modulation formats in terms of the achievable information rate (AIR). It allows the explicit properties of signal constellations to be captured and is applicable to fully loaded dense wavelength-division multiplexed transmission systems. The efficiency of the procedure facilitates formulating multidimensional quadrature amplitude modulation (QAM) constellation subset selection as a combinatorial optimization problem. The attained solutions for the quadrature phase shift keying (QPSK) 8D constellation subset selection suggest that a known 8D power and polarization balanced constellation (PPB constellation, 4 bits/8D symbol) and its different variations are the closest 8D QPSK subsets to the Shannon limit at 4 bits/8D symbol. 8D constellation subset selection of a QPSK constellation at 6 bits/8D symbol allows obtaining an 8D polarization balanced version of polarization-switched QPSK (PB-PS-QPSK). Using the proposed procedure, the performance of these constellations and their nonpolarization balanced counter parts, i.e., dual polarization binary phase shift keying (DP-BPSK) and PS-QPSK, is assessed in terms of the estimated AIR. The results exhibit good agreement with those of full system simulations for a single channel and five channels. Moreover, the impact of QAM constellation subset selection on the system performance is evaluated by comparing the reduction in information rate for a symbol rate of 35 Gbaud as a function of the number of channels. For 41 channels, the PPB constellation outperforms DP-BPSK by 2 Gb/s in information rate for a 12,000 km dispersion-managed (DM) link due to the improved linear and nonlinear constellation properties. Finally, PB-PS-QPSK enables an increase of 1.5 Gb/s in information rate compared to PS-QPSK for a 10,000 km DM link.