  Distributed antenna arrays have been proposed for many applications ranging
from space-based observatories to automated vehicles. Achieving good
performance in distributed antenna systems requires stringent synchronization
at the wavelength and information level to ensure that the transmitted signals
arrive coherently at the target, or that scattered and received signals can be
appropriately processed via distributed algorithms. In this paper we address
the challenge of high precision time synchronization to align the operations of
elements in a distributed antenna array and to overcome time-varying bias
between platforms due to oscillator drift. We use a spectrally sparse two-tone
waveform, which obtains approximately optimal time estimation accuracy, in a
two-way time transfer process. We also describe a technique for determining the
true time delay using the ambiguous two-tone matched filter output, and we
compare the time synchronization precision of the two-tone waveform with the
more common linear frequency modulation (LFM) waveform. We experimentally
demonstrate wireless time synchronization using a single pulse 40$\,$MHz
two-tone waveform over a 90$\,$cm 5.8$\,$GHz wireless link in a laboratory
setting, obtaining a timing precision of 2.26$\,$ps.
