2 research outputs found
On the Capacity-Achieving Input of Channels with Phase Quantization
Several information-theoretic studies on channels with output quantization
have identified the capacity-achieving input distributions for different fading
channels with 1-bit in-phase and quadrature (I/Q) output quantization. But can
analytical results on the capacity-achieving input also be obtained for
multi-bit quantization? We answer the question in the affirmative by
considering multi-bit phase quantization. We first consider a complex Gaussian
channel with -bit phase-quantized output and prove that the
capacity-achieving distribution is a rotated -phase shift keying (PSK).
The analysis is then extended to multiple fading scenarios. We show that the
optimality of rotated -PSK continues to hold under noncoherent fast fading
Rician channels with -bit phase quantization when line-of-sight (LoS) is
present. When channel state information (CSI) is available at the receiver, we
identify -symmetry and constant amplitude as the necessary
and sufficient conditions for the ergodic capacity-achieving input
distribution; which a -PSK satisfies. Finally, an optimum power control
scheme is presented which achieves ergodic capacity when CSI is also available
at the transmitter.Comment: Submitted to IEEE Transactions on Information Theor