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We propose a closed loop space time block coding technique using four antennae at the transmitter for the enhancement of link layer performance of orthogonal frequency division multiplexing (OFDM) based broadband wireless access systems such as wireless local area networks (WLANs) and wireless metropolitan area networks (WMANs). Since full code rate and complex valued space-time block codes (STBCs) do not exist for more than two transmit antennae, we propose two feedback based STBC schemes. In the first scheme, phases of certain symbols in each sub carrier are rotated according to the feedback from the receiver. In the second scheme, best two out of four antennae are activated for transmission based on the associated channel gains in each subcarrier. In both schemes, the channel perceived at the receiver becomes orthogonal and the transmit diversity gain is maximized. One of the major challenges associated with the closed loop STBC schemes in OFDM systems as compared to CDMA systems is the requirement for extensive channel state information feedback as channel orthogonalization is performed in each subcarrier. However, by exploiting the feedback correlation among subcarriers, we have proposed a group based quantization technique to reduce feedback overhead significantly, making this scheme very attractive to broadband wireless access systems.