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A sensor network is used for distributed SNR estimation. Sensors observe a signal embedded in noise. These observations are phase modulated using a constant-modulus scheme and transmitted over a Gaussian multiple-access channel to a fusion center. At the fusion center, the location parameter and scale parameter are estimated using a minimum-variance estimator as well as computationally simple alternatives. Performance evaluated using the asymptotic variance of the estimators shows that the computationally simple estimators have the same asymptotic performance as the minimum-variance estimators. The optimal phase transmission parameters are also determined for different sensing noise distributions. Simulation results corroborate analytical results.