We propose a multichannel feedback protocol to enable local scheduling with channel state information for wireless networks with orthogonal frequency division multiplexing (OFDM). In our proposed protocol, the frequency subcarrier domain is shared by multiple control channels, on which request-to-send (RTS) and clear-to-send (CTS) are exchanged. These control channels are created using random spreading signatures. Channel state information of the simultaneous transmissions, which defines the gains of these channels, is exchanged on these control channels and channel state information tables that contain the channel information of both the desired link and the interfering links are created at the transmit nodes, then scheduling decisions are made based on the channel information tables. We show that the proposed protocol improves the network throughput compared to IEEE 802.11 style protocols for a wireless local area network topology.