Minimum Energy to Send k Bits over Rayleigh-Fading Channels
Paper in proceedings, 2015

This paper investigates the minimum energy required to transmit, with a given reliability, k information bits over a stationary memoryless Rayleigh-fading channel, under the assumption that neither the transmitter nor the receiver have \emph{a priori} channel state information (CSI). 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 $k\to\infty$ 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 $1/\sqrt{k}$. Numerically, we observe that to achieve an energy per bit of $ - 1.5$ dB in the no-CSI case, one needs to transmit at least $7\times 10^7$ information bits, whereas $6\times 10^4$ 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.

Author

Wei Yang

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Giuseppe Durisi

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Yury Polyanskiy

Massachusetts Institute of Technology (MIT)

IEEE International Symposium on Information Theory - Proceedings

21578095 (ISSN)

2959-2963 7282999

Areas of Advance

Information and Communication Technology

Subject Categories

Telecommunications

DOI

10.1109/ISIT.2015.7282999

ISBN

978-1-4673-7704-1

More information

Latest update

4/11/2018