  For the laser interferometer space antenna (LISA) to reach it's design
sensitivity, the coupling of the free running laser frequency noise to the
signal readout must be reduced by more than 14 orders of magnitude. One
technique employed to reduce the laser frequency noise will be arm locking,
where the laser frequency is locked to the LISA arm length. This paper details
an implementation of arm locking, studies orbital effects, the impact of errors
in the Doppler knowledge, and noise limits. The noise performance of arm
locking is calculated with the inclusion of the dominant expected noise
sources: ultra stable oscillator (clock) noise, spacecraft motion, and shot
noise. Studying these issues reveals that although dual arm locking [A. Sutton
& D. A Shaddock, Phys. Rev. D 78, 082001 (2008).] has advantages over single
(or common) arm locking in terms of allowing high gain, it has disadvantages in
both laser frequency pulling and noise performance. We address this by
proposing a hybrid sensor, retaining the benefits of common and dual arm
locking sensors. We present a detailed design of an arm locking controller and
perform an analysis of the expected performance when used with and without
laser pre-stabilization. We observe that the sensor phase changes beneficially
near unity-gain frequencies of the arm-locking controller, allowing a factor of
10 more gain than previously believed, without degrading stability. We show
that the LISA frequency noise goal can be realized with arm locking and
Time-Delay Interferometry only, without any form of pre-stabilization.
