  Receiver sensitivity is a particularly important metric in optical
communication links operating at low signal-to-noise ratios (SNRs), for example
in deep-space communication, since it directly limits the maximum achievable
reach and data rate. Pulse position modulation (PPM) with direct detection
photon-counting detectors are the most power-efficient solution known, however,
the sensitivity gain comes at the expense of reduced spectral efficiency. We
show that quadrature phase-shift keying (QPSK) modulation with a
phase-sensitive ultralow noise pre-amplified coherent receiver outperforms
other well-known power-efficient multi-dimensional coherent modulation formats,
while simultaneously having higher spectral efficiency. It also results in
better sensitivity than PPM for orders up to 64 with ideal direct detection
using photon-counting receivers. This is because of the bit error rate
characteristics favoring the QPSK format when forward error correction with a
large overhead is considered.
