Minimum energy to send k bits over Rayleigh-fading channels
Author(s)
Yang, Wei; Durisi, Giuseppe; Polyanskiy, Yury
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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)[superscript 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.
Date issued
2015-10Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
2015 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Yang, Wei et al. “Minimum Energy to Send k Bits over Rayleigh-Fading Channels.” 2015 IEEE International Symposium on Information Theory (ISIT) June 14-19 2015, Hong Kong, China, Institute of Electrical and Electronics Engineers (IEEE), October 2015: 2959-2963 © 2015 Institute of Electrical and Electronics Engineers (IEEE)
Version: Author's final manuscript
ISBN
978-1-4673-7704-1
ISSN
2157-8095
2157-8117