Simultaneous Signal-and-Interference Alignment for Two-Cell Over-the-Air Computation

Abstract

The next-generation wireless networks are envisioned to support large-scale sensing and distributed machine learning, thereby enabling new intelligent mobile applications. One common network operation will be the aggregation of distributed data (such as sensor observations or AI-model updates) for functional computation (e.g., averaging) so as to support large-scale sensing and distributed machine learning. An efficient solution for data aggregation, called over-the-air computation (AirComp), embeds functional computation into simultaneous access by many edge devices. Such schemes exploit the waveform superposition of a multi-access channel to allow an access point to receive a desired function of simultaneous signals. In this work, we aim at realizing AirComp in a two-cell multi-antenna system.To this end, a novel scheme of simultaneous signal-and-interference alignment (SIA) is proposed that builds on classic IA to manage interference for multi-cell AirComp. The principle of SIA is to divide the spatial channel space into two subspaces with equal dimensions: one for signal alignment required by AirComp and the other for inter-cell IA. As a result, the number of interference-free spatially multiplexed functional streams received by each AP is maximized (equal to half of the available spatial degrees-of-freedom). Furthermore, the number is independent of the population of devices in each cell.In addition, the extension to SIA for more than two cells is discussed.

Cooperative Interference Management for Over-the-Air Computation Networks

“…Cooperative interference management for AirComp networks remains a largely uncharted area. Recently, an initial study in this area was reported in [26], where a scheme called simultaneous signal-and-interference alignment is proposed to maximize the number of interference-free aggregated data streams in a two-cell AirComp network. In this work, we study the same theme of multi-cell cooperation but from a different perspective, namely power control.…”

“…We denote {Q opt2 k } k∈K ℓ and ν opt2 ℓ as the optimal solution to problem (P2.2.ℓ). Let λ ℓ,j ≥ 0 denote the dual variable associated with the j-th IT constraint in (26) for problem (P2.2.ℓ). Then the partial Lagrangian of problem (P2.2.ℓ) is given by…”

“…where {λ opt2 ℓ,j } is the optimal dual variables associated with the constraints in (26) of problem (P2.2.ℓ) and ν opt ℓ is the optimal solution to problem (P2.2.ℓ). Furthermore, we have…”

“…Combining with IT constraints in (26), it is worth to point out that if γ 0 ≥ 1 B 1 , then the IT levels are unreasonably low, or the power budgets are unreasonably high, for which case all the power constraints become inactive. This case does not make sense in practice and thus is excluded in the sequence discussion, and we hence assume the case with practical power budgets and the IT levels satisfying γ 0 ≤ 1 B 1 .…”

“…In this case, we have ν ℓ,0 ≥ 1 B 1 accordingly. Furthermore, with the IT constraint in (26), there exists a possible solution in which only the IT constraint is tight instead of the power budget constraints. Thus, we correspondingly have the following potential constraints:…”