Robust Analog Function Computation via Wireless Multiple-Access Channels

By Mario Goldenbaum, Slawomir Stanczak. 2012

200 citations recorded by the source corpus.

Wireless sensor network applications often involve the computation of pre-defined functions of the measurements such as for example the arithmetic mean or maximum value. Standard approaches to this problem separate communication from computation: digitized sensor readings are transmitted interference-free to a fusion center that reconstructs each sensor reading and subsequently computes the sought function value. Such separation-based computation schemes are generally highly inefficient as a complete reconstruction of individual sensor readings at the fusion center is not necessary to compute a function of them. In particular, if the mathematical structure of the channel is suitably matched (in some sense) to the function of interest, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. This paper proposes an analog computation scheme that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. A match between the channel and the function being evaluated is thereby achieved via some pre-processing on the sensor readings and post-processing on the superimposed signals observed by the fusion center. After analyzing the estimation error for two function examples, simulations are presented to show the potential for huge performance gains over time- and code-division multiple-access based computation schemes.

Subfields: Artificial Intelligence, Computer Networks and Communications

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Citations in the corpus

Over-the-air Function Computation in Sensor Networks (2016, background): “Function Computation: There has been a lot of recent interest in distributed function computation from the information theory community [10, 28, 3, 22, 11].”
Broadband Analog Aggregation for Low-Latency Federated Edge Learning (2018, background): “In [23], the authors proposed to modulate the data into transmission power to relax the synchronization requirement such that only coarse block-synchronization is required for AirComp.”
One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis (2020, background): “in [24] to wireless MACs and a more general class of non-linear functions.”
Federated Learning: A signal processing perspective (2021, methodology): “These include the analog modulation method proposed in [49], or the broadcasting of a shared cloak during the model distributing step as proposed in [50].”
Federated Learning via Over-the-Air Computation (2018, background): “Recent research works on AirComp have achieved significant progresses from the point of view of information theory [22], signal processing [23], transceiver design [24], [25], channel state information acquisition [26], synchronization issues [27], [28], the AirComp based model aggregation problem p”
Distributed Learning in Wireless Networks: Recent Progress and Future Challenges (2021, background): “OAC is applied to wireless communications in [98]–[100].”
Machine Learning at the Wireless Edge: Distributed Stochastic Gradient Descent Over-the-Air (2019, background): “The transmission of the local gradient computations, gm (θt), m ∈ [M ], to the PS with the goal of PS reconstructing their average can be considered as a distributed function computation problem over a MAC [37].”