TARA (Telescope Array Radar) is a cosmic ray radar detection experiment colocated with Telescope Array, the conventional surface scintillation detector (SD) and fluorescence telescope detector (FD) near Delta, Utah, U.S.A. The TARA detector combines a 40 kW, 54.1 MHz VHF transmitter and high-gain transmitting antenna which broadcasts the radar carrier over the SD array and within the FD field of view, towards a 250 MS/s DAQ receiver. TARA has been collecting data since 2013 with the primary goal of observing the radar signatures of extensive air showers (EAS). Simulations indicate that echoes are expected to be short in duration (∼ 10 µs) and exhibit rapidly changing frequency, with rates on the order 1 MHz/µs. The EAS radar cross-section (RCS) is currently unknown although it is the subject of over 70 years of speculation. A novel signal search technique is described in which the expected radar echo of a particular air shower is used as a matched filter template and compared to waveforms obtained by triggering the radar DAQ using the Telescope Array fluorescence detector. No evidence for the scattering of radio frequency radiation by EAS is obtained to date. We report the first quantitative RCS upper limits using EAS that triggered the Telescope Array Fluorescence Detector. ; 0 ; SCOPUS: ar.j ; info:eu-repo/semantics/published