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Multiple-input multiple-output (MIMO) techniques have become an essential part of broadband wireless communications systems. For example, the recently developed IEEE 802.16e specifications for broadband wireless access include three MIMO profiles employing 2x2 space-time codes (STCs) and two of those are mandatory on the downlink of Mobile WiMAX systems. Conventional approaches to STC design are based on performance criteria such as coding gain, diversity gain, multiplexing gain, and ignore the decoder complexity. In this paper, we take an alternative approach and present a full-rate full-diversity 2x2 STC design leading to substantially lower complexity of the optimum detector than existing schemes. This makes the implementation of high performance full-rate codes realistic in practical systems.