  Massive binary black holes (MBBHs) in nearby galactic centers, if any, may be
nano-Hertz gravitational wave (GW) sources for pulsar timing arrays (PTAs) to
detect. Normally the objective GWs for PTA experiments are approximated as
plane waves because its sources are presumably located faraway. For nearby GW
sources, however, this approximation may be inaccurate due to the curved GW
wave front and the GW strength changes along the paths of PTA pulsar pulses. In
this paper, we analyze the near-field effect in the PTA detection of nearby
sources and find it is important if the source distance is less than a few tens
Mpc, and ignoring this effect may lead to a significant signal-to-noise
underestimation especially when the source distance is comparable to the pulsar
distances. As examples, we assume a nano-Hertz MBBH source located at either
the Galactic Center (GC) or the Large Magellanic Cloud (LMC) according to the
observational constraints/hints on the MBBH parameter space, and estimate its
detectability by current/future PTAs. We find that the GC MBBH may be
detectable by the Square Kilometer Array (SKA) PTA. It is challenging for
detecting the LMC MBBH; however, if a number ($N\gtrsim10$) of stable
millisecond pulsars can be found in the LMC center, the MBBH may be detectable
via a PTA formed by these pulsars. We further illustrate the near-field effects
on the PTA detection of an isotropic GW background contributed mainly by nearby
GW sources, and the resulting angular correlation is similar to the
Hellings-Downs curve.
