FAST FRB backend; LQ, GH, XYX, QJZ, SD made key contributions to the overall FAST data processing pipelines; LS, MC, MK provided salient information on FRB 121102 from other observatories, particularly Effelsberg, and contributed to the scientific analysis; SC, JMC, DRL made numerous corrections to the writing and analysis. JMC, in particular, pointed out the errors in the noise floor analysis in the original draft. * Uncertainties in parentheses refer to the last quoted digit. † Reduced χ 2 is obtained by the best fitting method with 20 iterations. ‡ Coefficient of determination, R 2 = 1 − S res /S tot , where S tot is total sum of squares from data, and S res is the minimum fitting residual sum of squares.

The polarization of fast radio bursts (FRBs), which are bright astronomical transient phenomena, contains information about their environments. Using wide-band observations with two telescopes, we report polarization measurements of five repeating FRBs and find a trend of lower polarization at lower frequencies. This behavior is modeled as multipath scattering, characterized by a single parameter, σ RM , the rotation measure (RM) scatter. Sources with higher σ RM have higher RM magnitude and scattering time scales. The two sources with the highest σ RM , FRB 20121102A and FRB 20190520B, are associated with compact persistent radio sources. These properties indicate a complex environment near the repeating FRBs, such as a supernova remnant or a pulsar wind nebula, consistent with their having arisen from young stellar populations.