We carry out a comparative analysis of the performance of three algorithms widely used to identify significant periodicities in radial-velocity (RV) data sets: the generalized Lomb-Scargle (GLS) periodogram, its modified version based on Bayesian statistics (BGLS) and the multifrequency periodogram scheme called FREquency DEComposer (FREDEC). We apply the algorithms to a suite of numerical simulations of (single and multiple) low-amplitude Keplerian RV signals induced by low-mass companions around M-dwarf primaries. The global performance of the three period search approaches is quite similar in the limit of an idealized, best-case scenario (single planets, circular orbits, white noise). However, GLS, BGLS and FREDEC are not equivalent when it comes to the correct identification of more complex signals (including correlated noise of stellar origin, eccentric orbits, multiple planets), with variable degrees of efficiency loss as a function of system parameters and degradation in completeness and reliability levels. The largest discrepancy is recorded in the number of false detections: the standard approach of residual analyses adopted for GLS and BGLS translates in large fractions of false alarms (∼30 per cent) in the case of multiple systems, as opposed to ∼10 per cent for the FREDEC approach of simultaneous multifrequency search. Our results reinforce the need for the strengthening and further development of the most aggressive and effective ab initio strategies for the robust identification of low-amplitude planetary signals in RV data sets, particularly now that RV surveys are beginning to achieve sensitivity to potentially habitable Earth-mass planets around late-type stars.
