Joint PAPR Reduction and Over-the-Air Computing in Multi-User OFDMA Systems

We consider the peak-to-average power ratio (PAPR) reduction challenge of orthogonal frequency division multiplexing (OFDM) systems utilizing tone reservation (TR) under an over-the-air computing constraint, such that the signals placed in the reserved tones simultaneously enable distributed computation at the receiver. To that end, the problem is cast as a fractional programming problem and solved via the iterative quadratic transform (QT), which guarantees convergence to a stationary point. A key contribution is the decomposition of the reserved-tone vector into an orthogonal pair of components: one satisfying the sum-computation constraint and the other providing the remaining degrees of freedom for PAPR reduction. This decomposition reveals that the proposed method and the benchmark sacrifices the same number of degrees of freedom. However, the proposed design distributes the computational payload across all reserved tones, yielding superior robustness against multi-user interference and quantization noise. Analytical and simulation results confirm that the proposed method matches the benchmark in PAPR reduction while outperforming it in computation accuracy, particularly in multi-user scenarios.