  Joint-channel carrier-phase estimation can improve the performance of
multichannel optical communication systems. In the case of pilot-aided
estimation, the pilots are distributed over a two-dimensional channel--time
symbol block that is transmitted through multiple channels. However, suboptimal
pilot distributions reduce the effectiveness of the carrier-phase estimation
and thus result in unnecessary pilot overhead, which reduces the overall
information rate of the system. It is shown that placing pilots identically in
all channels is suboptimal in general. By instead optimizing the pilot
distribution, the mean squared error of the phase-noise estimates can be
decreased by over 90% in some cases. Moreover, it is shown that the achievable
information rate can be increased by up to 0.05, 0.16, and 0.41 bits per
complex symbol for dual-polarization 20 GBd transmission of 64-ary, 256-ary,
and 1024-ary quadrature amplitude modulation over 20 four-dimensional channels,
respectively, assuming a total laser linewidth of 200 kHz.
