This work proposes a low-complexity blind adaptive reduced-rank method (BARC) for symbol estimation using an adaptive decimation and interpolation scheme based on diversity-combining and the constant modulus criterion for interference suppression. The proposed approach employs an iterative procedure to jointly optimize the interpolation, decimation and estimation tasks for blind reduced-rank parameter estimation. We describe joint iterative estimators based on the constrained constant modulus (CCM) criterion, introduce alternative decimation structures, including the optimal decimation scheme, and develop low-complexity stochastic gradient adaptive algorithms for the proposed structure. Simulations for a CDMA interference suppression application show an excellent performance and substantial gains over prior art.