Piggyback search for fast radio bursts using Nanshan 26m and Kunming 40m radio telescopes -- I. Observing and data analysis systems, discovery of a mysterious peryton

We present our piggyback search for fast radio bursts using the Nanshan 26m Radio Telescope and the Kunming 40m Radio Telescope. The observations are performed in the L-band from 1380 MHz to 1700 MHz at Nanshan and S-band from 2170 MHz to 2310 MHz at Kunming. We built the \textsc{Roach2}-based FFT spectrometer and developed the real-time transient search software. We introduce a new radio interference mitigation technique named \emph{zero-DM matched filter} and give the formula of the signal-to-noise ratio loss in the transient search. Though we have no positive detection of bursts in about 1600 and 2400 hours data at Nanshan and Kunming respectively, an intriguing peryton was detected at Nanshan, from which hundreds of bursts were recorded. Perytons are terrestrial radio signals that mimic celestial fast radio bursts. They were first reported at Parkes and identified as microwave oven interferences later. The bursts detected at Nanshan show similar frequency swept emission and have double-peaked profiles. They appeared in different sky regions in about tens of minutes observations and the dispersion measure index is not exactly 2, which indicates the terrestrial origin. The peryton differs drastically from the known perytons detected at Parkes, because it appeared in a precise period of $p=1.71287\pm 0.00004$ s. Its origin remains unknown.