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Real Time Status Updates in Wireless HARQ with Imperfect Feedback Channel

We study the impact of the erroneous wireless control feedback channel on the Age of Information (AoI) performance. We consider a point-to-point communication setup employing packet combining strategies to transmit status update packets over an erroneous wireless data channel. The sender receives the positive acknowledgment (ACK) or negative acknowledgment (NACK) of packet reception over an error-prone wireless feedback channel. To mitigate the impact of the imperfect feedback channel on the system performance, we adopt an asymmetric signal detection model to control the detection accuracy of ACK and NACK signals. We then compute the explicit expressions for the average aoi under preemptive and non-preemptive service management policies. We show the optimum parameter design for the control channel model in order to minimize the average aoi. The numerical results validate the analysis and provide detailed perspectives on the optimal signal detection setup minimizing the average aoi, and the possible trade-off between aoi and resource utilization. Generally, the analysis for a preemption setting illustrates that a better protection for the NACK messages compared to the ACK messages can preserve the minimum aoi performance. Especially, under a high noisy feedback channel setup, we show that the viable solution minimizing the average aoi is a blind transmission mechanism at the cost of increasing unnecessary utilization of the channel resources. Moreover, the analysis for a non-preemptive policy reveals the dependence of the optimal feedback signal detection design on the status packet generation rate at the sensor. Such a dependency makes the feedback signal detection approach to provide a more reliable ACK detection compared to NACK messages under the condition of more frequent packet arrival, whereas the opposite holds under the condition of less frequent packet arrival.