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On the Capacity-Achieving Input of Channels With Phase Quantization
- Source :
- IEEE Transactions on Information Theory. 68:5866-5888
- Publication Year :
- 2022
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2022.
-
Abstract
- 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. However, an exact characterization of the capacity-achieving input distribution for channels with multi-bit phase quantization has not been provided. In this paper, we consider four different channel models with multi-bit phase quantization at the output and identify the optimal input distribution for each channel model. We first consider a complex Gaussian channel with $b$-bit phase-quantized output and prove that the capacity-achieving distribution is a rotated $2^b$-phase shift keying (PSK). The analysis is then extended to multiple fading scenarios. We show that the optimality of rotated $2^b$-PSK continues to hold under noncoherent fast fading Rician channels with $b$-bit phase quantization when line-of-sight (LoS) is present. When channel state information (CSI) is available at the receiver, we identify $\frac{2\pi}{2^b}$-symmetry and constant amplitude as the necessary and sufficient conditions for the ergodic capacity-achieving input distribution; which a $2^b$-PSK satisfies. Finally, an optimum power control scheme is presented which achieves ergodic capacity when CSI is also available at the transmitter.<br />Comment: 23 pages, 4 figures, Accepted for publication in IEEE Transactions on Information Theory
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 68
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi.dedup.....92e9868bd6826a66258f86e1636e29f6