FER Estimation in a Memoryless BSC With Variable Frame Length and Unreliable ACK/NAK Feedback

We consider the problem of estimating the frame error rate (FER) of a given memoryless binary symmetric channel by observing the success or failure of transmitted packets. Whereas FER estimation is relatively straightforward if all observations correspond to packets with equal length, the problem becomes considerably more complex when this is not the case. We develop FER estimators when transmissions of different lengths are observed, together with the Cramer-Rao lower bound (CRLB). Although the main focus is on maximum likelihood (ML) estimation, we also obtain low-complexity schemes performing close to optimal in some scenarios. In a second stage, we consider the case in which FER estimation is performed at a node different from the receiver, and incorporate the impairment of unreliable observations by considering noisy ACK/NAK feedback links. The impact of unreliable feedback is analyzed by means of the corresponding CRLB. In this setting, the ML estimator is obtained by applying the expectation-maximization algorithm to jointly estimate the error probabilities of the data and feedback links. Simulation results illustrate the benefits of the proposed estimators.