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We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n /spl times/ n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex …