We present nonasymptotic upper and lower bounds on the maximum coding rateachievable when transmitting short packets over a Rician memorylessblock-fading channel for a given requirement on the packet error probability.We focus on the practically relevant scenario in which there is no emph{apriori} channel state information available at the transmitter and at thereceiver. An upper bound built upon the min-max converse is compared to twolower bounds: the first one relies on a noncoherent transmission strategy inwhich the fading channel is not estimated explicitly at the receiver; thesecond one employs pilot-assisted transmission (PAT) followed bymaximum-likelihood channel estimation and scaled mismatched nearest-neighbordecoding at the receiver. Our bounds are tight enough to unveil the optimumnumber of diversity branches that a packet should span so that the energy perbit required to achieve a target packet error probability is minimized, for agiven constraint on the code rate and the packet size. Furthermore, the boundsreveal that noncoherent transmission is more energy efficient than PAT, evenwhen the number of pilot symbols and their power is optimized. For example, forthe case when a coded packet of $168$ symbols is transmitted using a channelcode of rate $0.48$ bits/channel use, over a block-fading channel with blocksize equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy perinformation bit to achieve a packet error probability of $10^{-3}$ compared toa suitably designed noncoherent transmission scheme. Finally, we devise a PATscheme based on punctured tail-biting quasi-cyclic codes and ordered statisticsdecoding, whose performance are close ($1$ dB gap at $10^{-3}$ packet errorprobability) to the ones predicted by our PAT lower bound. This shows that thePAT lower bound provides useful guidelines on the design of actual PAT schemes.
展开▼
