Optimized Power Control for Over-the-Air Computation in Fading Channels

Reliable Over-the-Air Computation by Amplify-and-Forward Based Relay

“…Specifically, with the common signal magnitude being α (α = 1/a), the transmission power of node k is computed as b k = min{α/h k , √ P max }, being the former if α/h k is below the power constraint, and otherwise, using the maximal power. In [10], the authors further consider the timevarying channel by regularized channel inversion, aiming at a better tradeoff between the signal-magnitude alignment and noise suppression. Antenna array was also investigated in [19], [20] to support vector-valued AirComp.…”

“…To ensure an unbiased data fusion, it is required that signals from all nodes arrive at the sink, aligned in signal magnitude. This is usually achieved by transmission power control at sensor nodes [9], [10]. Specifically, each node uses a transmission power inversely proportional to the channel gain so as to mitigate the difference in channel gains.…”

Beamforming Design Based on Two-Stage Stochastic Optimization for RIS-Assisted Over-the-Air Computation Systems

“…Hence, as the number of WDs becomes extremely large, the traditional wireless techniques are not energy-efficient in this context and may result in excessive latency. To deal with the above impediments, overthe-air computation (AirComp) has emerged as a promising solution [4]- [8], which finds a way for exploiting the cochannel interference among WDs during its computations. By exploiting the signal superposition imposed by wireless channels, the direct computation of the arithmetic mean, weighted sum, and polynomial of the parameter/data gathered from the WDs is workable at the FC.…”

“…In the literature, there are two lines of research, which focus on digital coded AirComp (see, e.g., [10]- [18]) and analog uncoded AirComp (see, e.g., [4]- [8], [19]- [24]). Simple uncoded transmission was proven to achieve a sufficiently low computation distortion for independent and identically Gaussian distributed data sources [19].…”

“…On the other hand, the computation mean-squared error (MSE) is typically adopted as the accuracy metric for analog AirComp. The optimal power control strategies for AirComp under fading channels and coherent multiple access channels were investigated in [4], [20] and [21] by using convex optimization, respectively. The authors of [22] developed optimal power allocation for minimizing the probability that the computation MSE exceeds a given threshold.…”