DocumentCode :
3663529
Title :
Minimum energy to send k bits over Rayleigh-fading channels
Author :
Wei Yang;Giuseppe Durisi;Yury Polyanskiy
Author_Institution :
Chalmers University of Technology, 41296 Gothenburg, Sweden
fYear :
2015
fDate :
6/1/2015 12:00:00 AM
Firstpage :
2959
Lastpage :
2963
Abstract :
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 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 → ∞ compared to the case of perfect receiver CSI. Specifically, we show that in the noCSI 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). 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 × 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.
Keywords :
"Rayleigh channels","Receivers","Error probability","AWGN channels","Decoding","Transmitters"
Publisher :
ieee
Conference_Titel :
Information Theory (ISIT), 2015 IEEE International Symposium on
Electronic_ISBN :
2157-8117
Type :
conf
DOI :
10.1109/ISIT.2015.7282999
Filename :
7282999
Link To Document :
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