In this paper we present a new set of blind equalization algorithms for multicarrier CDMA systems with receiver diversity. We first re-examine the cost function in the well-known subspace method and interpret it in terms of the noise projector, which can be effectively approximated by a special weighted spectral decomposition of the data autocorrelation matrix. By adding a user-specific cost term to the common cost function, we show that all user channel responses can be estimated in parallel. A block algorithm with lower complexity is derived first, followed by a recursive algorithm using RLS-type matrix updating. Our new approach treats additional antennas in the same way as a higher processing gain and provides a programmable structure to compromise between spectral and spatial diversity. Simulations show our method is near-far resistant, and our adaptive algorithm has fast convergence.