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An LMMSE channel prediction algorithm based on sinusoidal modeling is proposed for SIMO systems, assuming random amplitudes and equal mean powers. The potentially ill-conditioned LS estimates of the complex amplitudes is mitigated by regularization. This is interpreted as an LMMSE prediction, where the complex amplitudes are modeled as random (Rayleigh fading). Evaluated by simulations in SISO scenarios without loss of generality the LMMSE predictor presents a similar performance to the non-regularized LS prediction. The CRB of the frequency estimate of the sinusoidal modeling is derived. The performance of the LMMSE prediction with frequencies estimated by Unitary-ESPRIT is very close to those using the "best possible" frequency estimates according to the CRB. It also outperforms by far the AR modeling based linear prediction in the investigated scenarios.