Chipless radio frequency identification (RFID) technology is expected to replace barcode technology due to its ability to read in non-line-of-sight (NLOS) situations, long reading range, and low cost. Currently, there is extensive research being conducted on frequency-coded (FC) co-polarized radar cross-section (RCS)-based tags, which are widely used. However, detecting co-polarized chipless RFID tags in cluttered environments is still a challenge, as confirmed by measuring two co-polarized tags in front of a perfect metal reflector (30.5cm×22.5cm). To address this challenge, a realistic mathematical model for a chipless RFID system has been developed that takes into account the characteristics of the reader and the tag, as well as reflections from cluttered objects. This extensive mathematical model developed for linear chipless RFID systems in clutter scenarios holds the potential to greatly assist researchers in their exploration of RCS-based tags. By relying solely on simulations, this model provides a tool to effectively analyze and understand RCS-based tags, ultimately simplifying the process of generating more authentic tag designs. This model has been simulated and verified with measurement results by placing a single flat metal reflector behind two co-polarized one-bit designs: a dipole array tag and a square patch tag. The results showed that the interfering signal completely overlaps the ID of the co-polarized tag, severely limiting its detectability. To solve this issue, the proposed solution involves reading the tag in cross-polarization mode by etching a diagonal slot in the square patch tag. This proposed tag provides high immunity to the environment and can be detected in front of both dielectric and metallic objects.