Minimum Energy to Send $k$ Bits Over Multiple-Antenna Fading Channels
Name
isit15_noncoh_ebno.pdf
Description
Accepted version
Size
354.53 KB
Format
Adobe PDF
Checksum (MD5)
934954878b4e420b8dca88221ab68e45
Author(s)
Polyanskiy, Yury
Date Issued
June 2015
Journal
2015 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Yang, Wei, Giuseppe Durisi and Yury Polyanskiy. "Minimum energy to send k bits over Rayleigh-fading channels." 2015 IEEE International Symposium on Information Theory (ISIT), Hong Kong, China, 14-19 June 2015.
Version
Author's final manuscript
Abstract
This paper investigates the minimum energy required to transmit k information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to 1:59 dB as k goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that lack of CSI at the receiver causes a slowdown in the speed of convergence to -1:59 dB as k → ∞ compared to the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to -1:59 dB is proportional to ((log k)/k)1/3, whereas when perfect CSI is available at the receiver, this gap is proportional to 1/√k. In both cases, the gap to -1:59 dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of -1:5 dB in the no-CSI case, one needs to transmit at least 7×107 information bits, whereas 6 × 104 bits suffice for the case of perfect CSI at the receiver (same number of bits as for nonfading AWGN channels). Interestingly, all results (asymptotic and numerical) are unchanged if multiple transmit antennas and/or block fading is assumed.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tit.2016.2615629
