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 $b$-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.Comment: Submitted to IEEE Transactions on Information Theor

On the potential of the EChO mission to characterise gas giant atmospheres

Space telescopes such as EChO (Exoplanet Characterisation Observatory) and JWST (James Webb Space Telescope) will be important for the future study of extrasolar planet atmospheres. Both of these missions are capable of performing high sensitivity spectroscopic measurements at moderate resolutions in the visible and infrared, which will allow the characterisation of atmospheric properties using primary and secondary transit spectroscopy. We use the NEMESIS radiative transfer and retrieval tool (Irwin et al. 2008, Lee et al. 2012) to explore the potential of the proposed EChO mission to solve the retrieval problem for a range of H2-He planets orbiting different stars. We find that EChO should be capable of retrieving temperature structure to ~200 K precision and detecting H2O, CO2 and CH4 from a single eclipse measurement for a hot Jupiter orbiting a Sun-like star and a hot Neptune orbiting an M star, also providing upper limits on CO and NH3. We provide a table of retrieval precisions for these quantities in each test case. We expect around 30 Jupiter-sized planets to be observable by EChO; hot Neptunes orbiting M dwarfs are rarer, but we anticipate observations of at least one similar planet.Comment: 22 pages, 30 figures, 4 tables. Accepted for publication in MNRA

THE CONTROL OF ROTATION DURING RUGBY UNION GOAL KICKING

INTRODUCTION: While the basic kicking technique in ball sports is well understood, there has been limited research conducted on the biomechanics of rugby union goal kicking. Specifically, the movement characteristics which contribute to kicking accuracy have not been well defined. It is probable that the control of body rotation plays an important role in determining kicking accuracy. The quantity of rotation is characterised by the extent of angular momentum but surprisingly this quantity has seldom been used in analysis of kicking technique. This study aims to investigate how rugby players control rotation during execution of. the kicking action and to determine the relationship between segmental angular momentum contributions and kicking accuracy