Short Packets Over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

Abstract

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no a priori channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, in Rayleigh fading, for the case when a coded packet of 168 symbols is transmitted using a channel code of rate 0.48 bits/channel use, over a block-fading channel with block size equal to 8 symbols, PAT requires an additional 1.2 dB of energy per information bit to achieve a packet error probability of 10 −3 compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance is close (1 dB gap at 10 −3 packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.

Wireless Access in Ultra-Reliable Low-Latency Communication (URLLC)

“…Alternatively, the transmission can be carried out in a non-coherent way. Rigorous studies that take a holistic view on channel estimation and packet transmission are presented in [20], [21].…”

“…, x n ), which now becomes a random variable. According to (20), every R yields specific outage probability; hence, the sequence of random variables X n induces a distribution over F and the transmitter can no longer guarantee that the outage probability under transmission rate R(X n ) will be equal of less than .…”

Uplink Grant-Free Access Solutions for URLLC services in 5G New Radio

“…Note that user activity detection and channel estimation are required before the data detection, but this may also be done jointly [13]. For block-fading channels, there is further a tradeoff between the diversity achieved by using multiple slots and the required channel estimation overhead [14]. These practical issues are facilitated by the sparse resource allocation.…”

Saddlepoint Approximations for Short-Packet Wireless Communications

“…This coding scheme is denoted as "OSD-REE" and is depicted in green. The derivation and design of these codes can be found in [25]. Observe that, for this scenario, the error-exponent approximation "L − 1+τ 2 +EEA" is not as accurate as the saddlepoint approximations.…”