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An adaptive protocol based on minimizing a tight approximate symbol-error-rate (SER) significantly improves a performance of full-rate cooperative communication systems in comparison with existing protocols. This protocol crucially requires a short-term channel variance for computing such approximate SER, used in an adaptation process. In this paper, we propose a least square (LS) approach to estimate that of short-term channel variance, and the pilot transmission strategy. A mean square error (MSE) for such estimation is also derived. Simulation results indicate that the adaptive protocol employing the LS channel variance estimation performs essentially similar to an ideal adaptive protocol for quasi-static fading channels, where a lower SER compared with existing protocols is achieved. For nonquasistatic fading channels, the proposed scheme is still able to work acceptably with a SER penalty in high signal-to-noise ration (SNR) regimes. In addition, the analytical MSE is close to the simulated MSE as well.