The study deals with the novel polarisation-independent 20-bit chipless radiofrequency identification (RFID) transponder that is based on a circularly arranged array of electrically small dual-spiral capacitively-loaded dipole scatterers with improved robustness of radar cross-section (RCS) response. A single scatterer exhibits a better performance in terms of electrical size and RCS than the earlier introduced U-dipole type scatterers occupying the same footprint area. In order to investigate the frequency stability and amplitude uniformity of RCS curve, two arrangements of scatterer arrays were analysed: rearranged side-by-side and circular. In comparison to the other arrangements, the latter provides an excellent amplitude RCS stability over the whole operational frequency band and, at the same time enables the polarisation independence of identification. However, it requires the two-channel orthogonal polarisation measurement.