PMM Amplitude Estimation for SDR Baseband Under Non-Gaussian Radio-Frequency Noise

Abstract

Amplitude estimation from Software-Defined Radio (SDR) baseband recordings becomes unreliable when the additive Radio-Frequency (RF) noise departs from the Gaussian model assumed by Ordinary Least Squares (OLS). Rather than comparing estimators one by one, this paper treats OLS, the Polynomial Maximization Method of orders two and three (PMM2, PMM3) and the fractional branch of the Parametrically Adaptive Transition Polynomial (PATP) as members of a single continuously parameterised family, and states the problem as the synthesis of a decision rule that selects a member from the cumulants of one finite block, minimising the regret with respect to an oracle choice. The protocol combines synthetic polygaussian noise, real RF residuals from RadioML2018 over-the-air recordings, controlled heavy-tailed and platykurtic regimes, and leptokurtic blocks from two drone recordings. Per-block PMM2 is unstable at N=1024 because the skewness estimate has a low signal-to-noise ratio; pooling the cumulants over calibration blocks returns it to the OLS baseline. On real platykurtic RF noise PMM3 lowers the mean squared error from 3.28 × 10^-3 to 2.76 × 10^-3, and Newey–West HAC standard errors raise the empirical 95% coverage of all three point estimators from about 0.72 to 0.920–0.924 — PMM3 included (0.922) — which is still about three percentage points below nominal. In the heavy-tailed regime relative efficiency is reported as a ratio of medians of squared errors with paired bootstrap intervals, because the mean-based figure does not converge under infinite variance: at α_s = 1.2 the oracle bound PATP* reaches 38.8 [33.8; 44.5] while the practically achievable adaptive rule AUTO_EXT reaches 6.41 [4.96; 8.26]. The family is two-sided — it gains on both non-Gaussian edges and returns exactly OLS on the Gaussian controls — unlike the one-sided Huber M-estimator, which loses 2–12% on platykurtic noise. Finally, we quantify what the dispatch rule costs: against a per-block oracle it selects a suboptimal member in 65.0% of the synthetic and 69.9% of the real-noise blocks, with regret 16.19 and 1.220 respectively, and on the synthetic set it is 10.7х worse than plain OLS. The resulting operational recommendation is therefore conditional, not unconditional dispatch: PMM3 for nearly symmetric platykurtic RF residuals, pooled calibration for PMM2, the fractional branch for heavy tails, and OLS whenever the block cumulants do not clearly indicate otherwise.