The invention relates to an improved antenna system and antenna module incorporating same. The antenna system comprises a first antenna element adapted to a first frequency band and a second antenna element adapted to a second frequency band. The radiation pattern of the second antenna is improved because the first antenna element comprises: a radiating structure provided on a first side of a dielectric substrate, and at least one resonant structure provided, at least in part, on a second, reverse side of the dielectric substrate. The at least one resonant structure is an open-loop type resonator adapted to resonate at a frequency in the second frequency band. The at least one resonant structure is provided at close proximity to the radiating structure on the reverse sides of the dielectric substrate, occupying, on the second side of the dielectric substrate, an area which is only in part covered by the radiating structure on the first side of the dielectric substrate.
