In the context of wave propagation in periodic media (e.g., composite or architected materials), recent studies have underlined the relevance of subspace identification algorithms to identify wave propagation properties and, thus, to characterize a complex structure experimentally. While such algorithms are usually applied to data sampled in the discrete time domain, as in Operational Modal Analysis (OMA), here the data are collected in the frequency domain from successive periodic unit cells, in the case of 1D-periodic waveguides. Instead of the modal parameters estimated in OMA, such as natural frequencies, the aim here is to estimate the real and imaginary parts of the structural wavenumber (related to the wavelength and the spatial decay, respectively) and the Bloch wave modes (physical wave modes, such as torsional and compressional). These wave-related invariant parameters describe the vibrational behavior of the waveguide, since the displacement field can be represented by wave-mode superposition. The number of measurement points per unit cell is rapidly increasing with the development of full-field vibration measurement techniques. Taking advantage of this data abundance to counterbalance the usually low number of unit cells (a few periods) in the collected data is not of common practice in the community. This paper proposes a subspace identification framework to benefit from multiple points measurements inside each unit cell for periodic waveguides. The approach is illustrated with a simulated periodic beam.