Systematic variation of the residual of PSR B1937+21, the trace of its companion star?

PSR B1937+21 was the first millisecond pulsar ever measured. Which has been appeared as a singular pulsar. The high-precision observation of this pulsar shows systemic long-term variation in the residual of time of arrivals. This paper modelled the secular variation by the orbital precession induced time delay of a binary pulsar system. The fitting requires that as a binary pulsar, PSR B1937+21 should have small companion star, $m_2\sim 10^{-2}M_{\odot}$, and projected semi-major axis, $x\sim 10^{-4}$s to $10^{-3}$s. Which corresponds to ignorable radial velocity of the pulsar to the line of sight. This might explain why it has been measured as a singular pulsar instead of a binary pulsar.