Toward Optimal Rate-Delay Tradeoff for Computation Over Multiple Access Channel

Computation over multiple access channel (CoMAC) scheme provides a promising solution to future large-scale wireless networks by utilizing the superposition property of the wireless channel to compute a class of functions with a summation structure (e.g., mean, norm, etc.). However, its implementation usually requires all nodes' channel state information (CSI) and its performance is limited by the channel condition of the worst node. In order to avoid massive CSI aggregation and improve the limited performance, we propose an automatic repeat request (ARQ)-aided CoMAC scheme in this paper. The transmitters and signaling procedures are designed to achieve the tradeoff between the achievable function rate and the transmission delay. The corresponding performance of the proposed ARQ-aided CoMAC scheme and the traditional ARQ-aided communication scheme are compared for both homogeneous networks and heterogeneous networks. By optimizing the ARQ level, we further maximize the achievable function rate of the proposed scheme. Asymptotic closed-form expressions are derived by resorting to the extreme value theory and point mass approximation. Monte Carlo simulations are given to illustrate and verify the performance of the proposed designs.