  We present a new type of search strategy designed specifically to find
continuously emitting gravitational wave sources in known binary systems based
on the incoherent sum of frequency modulated binary signal sidebands. The
search pipeline can be divided into three stages: the first is a wide
bandwidth, F-statistic search demodulated for sky position. This is followed by
a fast second stage in which areas in frequency space are identified as signal
candidates through the frequency domain convolution of the F-statistic with an
approximate signal template. For this second stage only precise information on
the orbit period and approximate information on the orbital semi-major axis are
required apriori. For the final stage we propose a fully coherent Markov chain
monte carlo based follow up search on the frequency subspace defined by the
candidates identified by the second stage. This search is particularly suited
to the low-mass X-ray binaries, for which orbital period and sky position are
typically well known and additional orbital parameters and neutron star spin
frequency are not. We note that for the accreting X-ray millisecond pulsars,
for which spin frequency and orbital parameters are well known, the second
stage can be omitted and the fully coherent search stage can be performed. We
describe the search pipeline with respect to its application to a simplified
phase model and derive the corresponding sensitivity of the search.
