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We carry out a comparative analysis of the performance of three algorithmswidely used to identify significant periodicities in radial-velocity (RV)datasets: the Generalised Lomb-Scargle Periodogram (GLS), its modified versionbased on Bayesian statistics (BGLS), and the multi-frequency periodogram schemecalled FREquency DEComposer (FREDEC). We apply the algorithms to a suite ofnumerical simulations of (single and multiple) low-amplitude Keplerian RVsignals induced by low-mass companions around M-dwarf primaries. The globalperformance of the three period search approaches is quite similar in the limitof an idealized, best-case scenario (single planets, circular orbits, whitenoise). However, GLS, BGLS and FREDEC are not equivalent when it comes to thecorrect identification of more complex signals (including correlated noise ofstellar origin, eccentric orbits, multiple planets), with variable degrees ofefficiency loss as a function of system parameters and degradation incompleteness and reliability levels. The largest discrepancy is recorded in thenumber of false detections: the standard approach of residual analyses adoptedfor GLS and BGLS translates in large fractions of false alarms ($\sim30\%$) inthe case of multiple systems, as opposed to $\sim10\%$ for the FREDEC approachof simultaneous multi-frequency search. Our results reinforce the need for thestrengthening and further development of the most aggressive and effective {\itab initio} strategies for the robust identification of low-amplitude planetarysignals in RV datasets, particularly now that RV surveys are beginning toachieve sensitivity to potentially habitable Earth-mass planets aroundlate-type stars.

Searching for planetary signals in Doppler time series: a performance evaluation of tools for periodograms analysis