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In this study, the authors present a method to design efficient full-rate linear dispersion space-time block codes (LD-STBCs) in correlated Rayleigh fading channels with simple detection at the receiver. The authors first derive a formula for the achievable capacity of an LD-STBC coded multi-input multiple-output (MIMO) system as a function of correlation at the transmitter and the receiver. Moreover, the authors compute closed-form bit-error rate equations for multiple phase shift keying (M-PSK) and multiple quadrature amplitude modulation (M-QAM) schemes. Then, the authors present a method to construct LD-STBCs over correlated Rayleigh fading MIMO channels. Finally, the authors design LD-STBCs for two and four transmit antennas. The designed LD-STBCs enjoy full-rate, minimum power fluctuation, simple structure, simple processing at the receiver. Moreover, the designed LD-STBCs for two transmit antennas provide better performance than Alamouti and LYC codes and the designed LD-STBCs for four transmit antennas provide better performance than TV codes at practical signal-to-noise ratios. Simulation results show that when the proposed LD-STBC for two transmit antennas is concatenated with an efficient outer channel encoder, it provides better performance than LYC code over correlated fading channels.