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.
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