Age and Energy Analysis for $L$th Best Relay Enabled Cooperative Status Update Systems With Short Packet Communications

Abstract

In the Internet of Things monitoring systems, the fresh information delivery and efficient energy usage are two significant design concerns. However, they generally cannot be simultaneously achieved. In this paper, we investigate the fundamental tradeoff between the age of information (AoI) and energy consumption (EC) for a generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> th best relay selection policy in two-hop cooperative status update systems with automatic repeat request (ARQ), where the source delivers the sensed status update to the destination through multiple decode-and-forward relays. Among these relays, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> th best relay (i.e., the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> -th earliest one that correctly decodes the update packet) will be selected as a forwarder to relay the data to the sink. When a decoding failure occurs, we can either retransmit the old packet to save sensing EC or sense and transmit a new one to reduce AoI. Accordingly, the classical ARQ and truncated ARQ protocols are employed in the second hop. By considering short packet-based transmissions, the average AoI and average EC expressions are derived, and the weighted combination of them is minimized to attain the tradeoff. Numerical results demonstrate that an optimal packet size that can trade off age and energy always exists. Moreover, the best relay does not always minimize the weighted combination, and the truncated ARQ is superior to the classical one. As a promising candidate, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell$</tex-math></inline-formula> th best relay selection can be implemented when either the system energy resource is limited or the best relay is unavailable.