Global optimality conjecture for conventional OFDM in the A-ACF setting

Let $\mathcal{W}_0$ be the class of admissible waveforms without a cyclic prefix, let $x_{\mathrm{OFDM}}\in\mathcal{W}_0$ denote conventional OFDM, and let $\operatorname{EISL}_{\mathrm{A}}(x)$ be the expected integrated sidelobe level computed from the aperiodic autocorrelation function of $x$ , with the expectation taken over sub-Gaussian constellation symbols. The conjecture is that conventional OFDM is globally optimal: $\operatorname{EISL}_{\mathrm{A}}(x_{\mathrm{OFDM}})=\min_{x\in\mathcal{W}_0}\operatorname{EISL}_{\mathrm{A}}(x)$ , equivalently $\operatorname{EISL}_{\mathrm{A}}(x_{\mathrm{OFDM}})\leq\operatorname{EISL}_{\mathrm{A}}(x)$ for every $x\in\mathcal{W}_0$ .

References

Primary source

arXiv

Additional references

Shaping Delay-Doppler Ambiguity in Practical OFDM-ISAC — arXiv

information-theory signal-processing

Posted 4 weeks ago · edited 4 weeks ago

Progress summary

Refreshed 4 weeks ago

Claimed progress

Recent work narrows the competing designs and reports numerical support for conventional OFDM, but its global optimality remains unproved.

The conjecture says conventional OFDM globally minimizes expected integrated sidelobe level among signals without a cyclic prefix under sub-Gaussian constellations. No proposer or original date was identified.

Known results

The statement remains explicitly labeled Conjecture 1 (2024).
Uniform power allocation was proved globally optimal for expected integrated sidelobe level within an OFDM-based model, for periodic and aperiodic autocorrelation and arbitrary constellation mappings (2025); this does not establish the broader waveform-design conjecture.
A related study found normalized periodic ambiguity sidelobe level invariant across orthogonal modulation bases; its separate fast-slow-time formulation reports OFDM optimality for sub-Gaussian constellations (2025), without proving the target A-ACF claim.

September 2026 numerical evidence

A recent report combines invariance arguments with numerical tests supporting the conjectured optimum and says this narrows the design space. It presents evidence, not a proof; global optimality remains conjectural.

Current status (as of September 2026): Related invariance and allocation results, plus numerical evidence, are available, but global optimality of conventional OFDM in the A-ACF setting remains open.

Sources

No solutions have been posted yet.