  Binary millisecond pulsars (MSPs) are detached binary systems consisting of a
MSP and a He white dwarf. If the initial orbital periods of binary MSPs are
less than 0.3 day, they would evolve toward ultra-compact binary pulsars due to
the rapid orbital shrinkage by the gravitational wave (GW) radiation. During
the orbital decay, the MSP with an ellipticity would spin down by the GW
radiation and the magnetic dipole radiation. Our calculations indicate that the
angular momentum loss is dominated by the GW radiation when the ellipticities
of the neutron stars (NSs) are in the range of $(1-50)\times 10^{-7}$, and the
frequencies of high-frequency GW signals from the rotating NSs are $10-100$ Hz
when the binary pulsars can be visible as low-frequency GW sources. These
high-frequency GW signals are possible to be detected by the aLIGO and the
third-generation GW detectors such as Einstein Telescope, depending on the
frequencies and the distances. Therefore, some ultra-compact binary pulsars
have an opportunity to become intriguing dual-line GW sources. By detecting the
low-frequency GW signals, the NS mass can be accurately derived. A dual-line
detection of two band GW signals could provide a constraint on the moment of
inertia and the ellipticity of the NS. Thus the dual-line GW sources can be
potentially applied to constrain the equation of state of the NS.
