  We consider communication over the block noncoherent AWGN channel with
low-precision Analog-to-Digital Converters (ADCs) at the receiver. For standard
uniform Phase Shift Keying (PSK) modulation, we investigate the performance of
a receiver architecture that quantizes only the phase of the received signal;
this has the advantage of being implementable without automatic gain control,
using multiple 1-bit ADCs preceded by analog multipliers. We study the
structure of the transition density of the resulting channel model. Several
results, based on the symmetry inherent in the channel, are provided to
characterize this transition density. A low complexity procedure for computing
the channel capacity is obtained using these results. Numerical capacity
computations for QPSK show that 8-bin phase quantization of the received signal
recovers more than 80-85 % of the capacity attained with unquantized
observations, while 12-bin phase quantization recovers above 90-95 % of the
unquantized capacity. Dithering the constellation is shown to improve the
performance in the face of drastic quantization.
