Function Computation via Electromagnetic Superposition

QC 20241014

Abstract

In wireless communication systems, interference is considered one of the main bottlenecks. Because all devices share the same electromagnetic spectrum, communication protocols generally attempt to separate radio resources to avoid interference. In LTE and 5G, devices are not allowed to transmit at their own behest but must receive an uplink grant that dictates which radio resources to use. In Wi-Fi 5, devices are allowed to transmit without a grant from the router, but they have to listen to the channel and wait until it is quiet before transmitting. While these interference-avoiding methods are quite useful, they face the problem of congestion. If too many devices are communicating data simultaneously, the avoidance of interference leads to insufficient spectrum for each user, and quality of service drops dramatically.

In this thesis, we study a novel form of wireless communication that takes a different approach to sharing electromagnetic spectrum. Rather than using orthogonal resources for each device, it schedules devices on the same communication resources, resulting in electromagnetic superposition of their signals. When the receiver listens, the superimposed signal will contain so much interference that it is difficult to distinguish the individual messages. However, it is possible to compute functions of the transmitted messages. Hence, this method is often referred to as Over-the-Air Function Computation (AirComp).

The challenges of AirComp are fundamentally different from those of orthogonal communication. Well-known results on, e.g., phase acquisition, forward error correction, and modulation do not map directly to the AirComp setting. Because of this, the state-of-the-art literature on AirComp usually does not guarantee error-free function computation with a vanishing probability of error but resorts to imperfect function estimation. We have dedicated this thesis to improving the state of estimation algorithms for AirComp. For example, we have developed a power control scheme that eliminates estimation bias for fast-fading channels, and we have leveraged dimensionality-reduction methods to compute certain functions without error.

Our recent work has focused on incorporating realistic assumptions concerning time synchronization and phase acquisition. In orthogonal communication methods, phase alignment is often achieved by careful correction at the receiver side, using reference signals and phase-locked loops. In AirComp, since we are interested in the coherent superposition of signals, the phase cannot be corrected at the receiver side. Transmitter-side phase correction from UEs is challenging, and therefore we have developed non-coherent AirComp methods that avoid this problem. We also specify non-coherent AirComp schemes for digital communication problems in the sparse regime, outperforming orthogonal methods.

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