  We perform a detailed theoretical-experimental study of the dynamical
decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate
the DD sequences applied to suppress the dephasing of the electron spin of the
NV center induced by the coupling to a spin bath composed of the substitutional
nitrogen atoms. The decoupling efficiency of various DD schemes is studied,
including both periodic and periodic pulse sequences. For ideal control pulses,
we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing
of the pulses provides best performance. We show that, as the number of control
pulses increases, the decoupling fidelity scaling differs qualitatively from
the predictions of the Magnus expansion, and explain the origin of this
difference. In particular, more advanced symmetrized or concatenated protocols
do not improve the DD performance. Next, we investigate the impact of the
systematic instrumental pulse errors in different periodic and aperiodic pulse
sequences. The DD protocols with the single-axis control do not preserve all
spin components in the presence of the pulse errors, and the two-axis control
is needed. We demonstrate that the two-axis control sequence with the CPMG
timing is very robust with respect to the pulse errors. The impact of the pulse
errors can be diminished further by symmetrizing this protocol. For all
protocols studied here, we present a detailed account of the pulse error
parameters which make strongest impact on the DD performance. In conclusion, we
give specific recommendations about choosing the decoupling protocol for the
system under investigation.
