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This paper discusses the problem of Non Data Aided (NDA) Signal to Noise Ratio (SNR) estimation of Binary Phase Shift keying (BPSK) modulated signals using the Expectation Maximization (EM) Algorithm. In addition, the Cramer-Rao Lower Bounds (CRLB) for the estimation of Data Aided (DA) and Non Data Aided (NDA) Signal to Noise Ratio (SNR) estimation is derived. Multiple Input Single Output (MISO) channels with Space Time Block Codes (STBC) is used. The EM algorithm is a method that finds the Maximum Likelihood (ML) solution iteratively when there are unobserved (hidden or missing) data. Extension of the proposed approach to other types of linearly modulated signals in estimating SNR is straight forward. The performance of the estimator is assessed using the NDA CRLBs. Alamouti coding technique is used in this paper with two transmit antennas and one receive antenna. The authors' assumption is that the received signal is corrupted by additive white Gaussian noise (AWGN) with unknown variance, and scaled by fixed unknown complex channel gain. Monte Carlo simulations are used to show that the proposed estimator offers a substantial improvement over the conventional Single Input Single Output (SISO) NDA SNR estimator due to the use of the statistical dependences in space and time. Moreover, the proposed NDA SNR estimator works close to the NDA SNR estimator over Single Input Multiple Output (SIMO) channels.