  Light travel time changes due to gravitational waves may be detected within
the next decade through precision timing of millisecond pulsars. Removal of
frequency-dependent interstellar medium (ISM) delays due to dispersion and
scattering is a key issue in the detection process. Current timing algorithms
routinely correct pulse times of arrival (TOAs) for time-variable delays due to
cold plasma dispersion. However, none of the major pulsar timing groups correct
for delays due to scattering from multi-path propagation in the ISM. Scattering
introduces a frequency-dependent phase change in the signal that results in
pulse broadening and arrival time delays. Any method to correct the TOA for
interstellar propagation effects must be based on multi-frequency measurements
that can effectively separate dispersion and scattering delay terms from
frequency-independent perturbations such as those due to a gravitational wave.
Cyclic spectroscopy, first described in an astronomical context by Demorest
(2011), is a potentially powerful tool to assist in this multi-frequency
decomposition. As a step toward a more comprehensive ISM propagation delay
correction, we demonstrate through a simulation that we can accurately recover
impulse response functions (IRFs), such as those that would be introduced by
multi-path scattering, with a realistic signal-to-noise ratio. We demonstrate
that timing precision is improved when scatter-corrected TOAs are used, under
the assumptions of a high signal-to-noise and highly scattered signal. We also
show that the effect of pulse-to-pulse "jitter" is not a serious problem for
IRF reconstruction, at least for jitter levels comparable to those observed in
several bright pulsars.
