Minimum Energy to Send k Bits Over Multiple-Antenna Fading Channels
Artikel i vetenskaplig tidskrift, 2016

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 the lack of CSI at the receiver causes a slowdown in the speed of convergence to 1.59 dB as k -> infinity compared with the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to 1/root k dB is proportional to ((log k)/ k)(1/3), whereas when perfect CSI is available at the receiver, this gap is proportional to lksa. 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 x 10(7) information bits, whereas 6 x 10(4) bits suffice for the case of perfect CSI at the receiver.

acta scientiarum mathematicarum

multiple-antenna fading channels

minimum energy per bit





Computer Science

coding rate


Channel coding

finite blocklength

energy efficiency


ekopa a


Wei Yang

Princeton University

Giuseppe Durisi

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Yury Polyanskiy

Massachusetts Institute of Technology (MIT)

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 62 12 6831-6853 7585063


Informations- och kommunikationsteknik


Grundläggande vetenskaper


Elektroteknik och elektronik



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