Bias in mean SNR and SNR differences - how to avoid

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Bias in mean SNR and SNR differences - how to avoid

When using WSPR SNR to compare the performance of two stations, receivers or antennas we look at graphs or we calculate the means and form the difference. Curious slow changes in SNR differences filtered with a five day moving average between me and G4HZX for spots from North America were discovered to be an artefact due to the effect of the WSPR decoding threshold of about -29dB truncating the probability distributions of the SNRs at each station, leading to a positive bias in the SNR difference that increased as the SNR itself decreased.

Here is the Abstract of our report on this topic. A pdf of the report is too large to attach, please email me to request a copy as comments are most welcome.

When forming the mean SNR of WSPR spots received, and when forming the difference between SNR at two receivers, care needs to be taken to avoid the positive bias introduced due to WSPR's ca. -29dB decoding threshold. This threshold has the effect of truncating the lower tail of the probability distribution of the SNR of received spots. The greater the standard deviations of the received SNR and the SNR difference, and the greater the mean SNR difference, the higher the SNR at which the bias becomes important. For a mean SNR difference of 5dB and a combined standard deviation of 5dB the bias in the mean difference will be ca. +1dB at an SNR of -18dB at the receiver with highest SNR.
Our motivating question was to understand the observed correlation between mean SNR differences at G3ZIL and G4HZX for spots from North America and the daily mean solar flux. We show that the causal link was the relationship between solar flux and mean SNR and then the bias on the SNR difference with SNR, as described here, which reached 10dB. Our analysis is based on Monte Carlo simulations with parameters drawn from our observations and an analytical approach based on the verified assumption that the mean SNR and the mean differences have Normal distributions. Further work is needed to establish the probability of successful decoding as the SNR approaches the threshold.

Gwyn G3ZIL