It is one of the biggest challenges of distributed cooperative antenna (COOPA) systems to provide base stations (BSs) with downlink channel information for transmit filtering (precoding). In this paper, we propose a novel feedback scheme via a subspace-based channel quantization method. The proposed scheme adopts the chordal distance as a channel quantizer criterion so as to capture channel characteristics represented by subspaces spanned by the channel matrix. We also propose a combined feedback scheme which is based on the hierarchical codebook construction method in an effort to reduce the feedback overhead by exploiting the temporal correlation of the channel. The proposed methods are tested for distributed COOPA systems in terms of simulations. Simulation results show that the proposed subspace-based channel quantization method outperforms the analog pilot retransmission method, and the combined feedback scheme performs as well as the permanent full-feedback scheme with a much smaller amount of uplink resources.