In this paper, we consider distributed estimation of an unknown random scalar by using wireless sensors and a fusion center (FC). We adopt a linear model for distributed estimation of a scalar source where both observation models and sensor operations are linear, and the multiple access channel (MAC) is coherent. We consider a fusion center with multiple antennas and single antenna. In order to estimate the source, best linear unbiased estimation (BLUE) is adopted. Two cases are considered: Minimization of the mean square error (MSE) of the BLUE estimator subject to network power constraint, and minimization of the network power subject to the quality of service (QOS). For a fusion center with multiple antennas, iterative solutions are provided and it is shown that the proposed algorithms always converge. For a fusion center with single antenna, closed-form solutions are provided, and it is shown that the iterative solutions will reduce to the closed-form solutions. Furthermore, the effect of noise correlation at the sensors and fusion center is investigated. It is shown that knowledge of noise correlation at the sensors will help to improve the system performance. Moreover, if correlation exists and not factored in, the system performance might improve depending on the correlation structure. We also show, by simulations, that when noise at the fusion center is correlated, even with knowing the correlation structure, the system performance degrades. Finally, simulations are provided to verify the analysis and present the performance of the proposed schemes.