Robust Design for Massive CSI Acquisition in Analog Function Computation Networks

Analog function computation utilizes the superposition property of multi-access channel to compute the target function in an efficient way. However, its corresponding transceiver requires global channel state information (CSI) of the network, which incurs large latency. To tackle this challenge, a novel scheme called over-the-air signaling procedure is proposed by exploiting a defined effective CSI in this paper. We first derive the training complexity of the proposed scheme and compare it with the conventional design. It is shown that the training complexity of the proposed scheme can be greatly reduced for massive CSI acquisition by avoiding collecting individual CSI. To account for the difference of the desired CSI, a corresponding robust model is further discussed. Through modeling the channel uncertainties under the expectation-based model and the worst case model, we formulate the transceiver optimization for both the conventional scheme and the over-the-air signaling procedure. The computational time complexity is derived as a polynomial expression, and it can be significantly reduced for the over-the-air signaling procedure due to its independence of the number of nodes. Finally, the mean-square error improvement and complexity reduction of the proposed design are demonstrated via simulation.