A Study on the Uncertainty in Estimation for Short-Length Communication

This work discusses the block error probability of an uncoded and single-carrier data communication system when short and finite-length blocks of symbols are transmitted and both the average energy and the additive noise variance need to be estimated at the receiver side. The lack of relevant information introduces more uncertainty at the receiver side, and a stochastic formulation needs to be adopted in order to characterize such randomness based on the availability of a short-length block of received symbols. Closed-form expressions for the probabilistic model are presented for both M-PAM and M-QAM constellations and flat fading channel. Finally, numerical results show that, to ensure a target block error probability, a trade-off between block length and a proposed uncertainty factor must be carefully considered for performing data communication under such constraint.