Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing

We propose a novel quadrature over-the-air computing (Q-OTAC) framework that enables the simultaneously computation of two independent functions and/or data stream within a single transmission. In contrast to conventional OTAC schemes, where a single function is computed by treating each complex signal as a single component, the proposed Q-OTAC exploits both in-phase and quadrature (IQ) components of a complex signal, encoding two distinct functions and/or data streams at the edge devices (EDs) and employing a novel low-complexity IQ-decoupled combiner at the access point (AP) to independently recover each stream, which effectively doubles the computation rate. A key strength of this framework lies in its simplicity and broad compatibility: the extension into the quadrature domain is conceptually straightforward, yet remakably powerful, allowing seamless integration into existing OTAC techniques. Simulation results validate the effectiveness of this approach, including the first demonstration of dual-function aggregation (e.g., parallel summation and product), highlighting the potential of Q-OTAC for enabling multi-modal and high-efficiency beyond fifth generation (B5G) applications.

💡 Research Summary

The paper introduces a novel Quadrature Over‑the‑Air Computing (Q‑OTAC) framework that doubles the computational capacity of conventional over‑the‑air computing (OTAC) by exploiting both the in‑phase (I) and quadrature (Q) components of a complex wireless symbol. Traditional OTAC maps data only onto the real part of a complex symbol, allowing a single nomographic function (e.g., sum, average, product) to be computed per transmission resource. This underutilizes the two‑dimensional complex signal space and limits the computation rate to one function per resource block.

In the proposed Q‑OTAC, each edge device (ED) processes two independent data streams, (d_f) and (d_g), through pre‑processing functions (\phi_f(\cdot)) and (\phi_g(\cdot)) to obtain real symbols (s_f) and (s_g). These are then combined into a single complex transmit symbol (s = s_f + j s_g). Over the multiple‑access channel, the superposition of all ED transmissions yields a received vector (\mathbf{y}= \mathbf{H}( \mathbf{s}_f + j\mathbf{s}_g) + \mathbf{w}), where (\mathbf{H}) is the K‑by‑N channel matrix and (\mathbf{w}) is AWGN.

At the access point (AP), the complex received signal is split into its real and imaginary parts, forming a real‑valued system of dimension (2N). Two linear combiners, (\mathbf{u}_f) and (\mathbf{u}_g), are designed to independently estimate the two target functions (f) and (g). By formulating a minimum‑mean‑square‑error (MMSE) problem for each stream, closed‑form solutions are derived: \