Optimizing the architecture for coherent beat-note acquisition in the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) senses gravitational waves by measuring distance fluctuations between three spacecraft (SCs). These measurements rely on precise tracking of a beat-note phase that is formed on a quadrant photodiode (QPD) at each SC by interference of a local laser with a laser sent from a distant SC. The crucial prerequisite of the phase tracking is a successful acquisition of the beat-note frequency. This paper aims to optimize the carrier-to-noise density ratio (CNR) during this process and to evaluate the resulting probability of detection (PD). The CNR is generally lowest during the beat-note acquisition process, since the pointing accuracy relies on coarse acquisition techniques. Based on analytical models, we examine which combinations of QPD segments for the signal readout yield the highest CNR, i.e., are least susceptible to pointing errors. We find from simulations that the highest CNR is ensured by taking the maximum of a combination of two segments in the vertical and horizontal directions. For pointing errors ($3\ensuremath{\sigma}$) of $3.9\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\text{rad}$ and $4.3\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\text{rad}$, this yields an improvement of around 3.7 dB and 5.6 dB in the CNR, respectively, in comparison to a combination of all four segments. In addition, the PD for various configurations of the baselined Fourier-peak detection is analyzed. Here, we find that the PD is most sensitive to the CNR compared to the design parameters of the acquisition scheme, in particular the FFT length. Moreover, it is shown that the aforementioned improvements in the CNR can lead to a significant enhancement of the PD.