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In this paper, we formulate the problem of blind equalization of constant modulus (CM) signals as a convex optimization problem. The convex formulation is obtained by performing an algebraic transformation on the direct formulation of the CM equalization problem. Using this transformation, the original nonconvex CM equalization formulation is turned into a convex semidefinite program (SDP) that can be efficiently solved using interior point methods. Our SDP formulation is applicable to baud spaced equalization as well as fractionally spaced equalization. Performance analysis shows that the expected distance between the equalizer obtained by the SDP approach and the optimal equalizer in the noise-free case converges to zero exponentially as the signal-to-noise ratio (SNR) increases. In addition, simulations suggest that our method performs better than standard methods while requiring significantly fewer data samples.