  New developments in detector technology allow for a realistic cost of large
area surface detectors for cosmic ray air showers, with some limitations on
particle identification, energy resolutions, directional information and
dynamic range. In this paper, we present a simulation study using CORSIKA to
quantify the lateral profile of the muons at ground level, characterized by
their energy spectrum and lateral spread, and combine it with the depth at
shower maximum (X$_{max}$) of an EAS initiated by a primary at energies
$10^{16}$ eV - $10^{19}$ eV. Using different primaries, we show that the
combined muon observables and X$_{max}$ can identify the primary in a large
fraction of the events, depending on the energy and the detector performance.
This study provides important input parameters for the design of a future muon
detector for surface array, which will be able to boost the knowledge of
primaries and of the QCD interactions in the atmosphere.
