  We propose a fermionic dark matter model by extending Standard Model with a
Dirac fermion and a real pseudoscalar. The fermion dark matter particle
interacts with the Standard Model sector via the Higgs portal through a
dimension five interaction term as also through a pseudoscalar interaction
term. The parameter space of the model is then constrained by using the vacuum
stability and perturbativity condition as also with the LHC constraints. They
are finally constrained by the PLANCK results for dark matter relic densities.
The direct detection limits are then ensured to have satisfied by the model. We
then explore within the framework of the model, the possible signatures of
synchrotron radiation from the annihilations of dark matter in the Galactic
Centre region when the end product is $e^+e^-$. We consider the observational
data from the radio telescopes namely SKA, GMRT and Jodrell Bank telescopes and
compare our calculated synchrotron flux density with them and also with the
results predicted by these experiments. We predict that if the low frequency
radio telescopes like GMRT, SKA operate at the peak frequencies obtained from
our calculations should get a better r.m.s sensitivity.
