Computation Over MAC: Achievable Function Rate Maximization in Wireless Networks

The next generation wireless network is expected to connect billions of nodes, which brings up the bottleneck on the communication speed for distributed data fusion. To overcome this challenge, computation over multiple access channel (CoMAC) was recently developed to compute the desired functions with a summation structure (e.g., mean, norm, etc.) by using the superposition property of wireless channels. This work aims to maximize the achievable function rate of reliable CoMAC in wireless networks. More specifically, considering channel fading and transceiver design, we derive the achievable function rate adopting the quantization and the nested lattice coding, which is determined by the number of nodes, the maximum value of messages and the quantization error threshold. Based on the derived result, the transceiver design is optimized to maximize the achievable function rate of the network. We first study a single cluster network without inter-cluster interference (ICI). Then, a multi-cluster network is further analyzed in which the clusters work in the same channel with ICI. In order to avoid the global channel state information (CSI) aggregation during the optimization, a low-complexity signaling procedure irrelevant with the number of nodes is proposed utilizing the channel reciprocity and the defined effective CSI.