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A systematic micromagnetic modeling study on the spin transfer induced noise in CCP (current-confined-path )/CPP (current-perpendicular-to-plane) spin valve and magnetic tunnel junction (MTJ) heads is presented. Both CCP/CPP spin valve and MTJ read heads are modeled using previously developed micromagnetic model. Abutted permanent magnet longitudinal bias scheme is assumed. The Landau-Lifshitz-Gilbert equation is modified to include the spin transfer torque. The current-confined-path is modeled with randomly distributed conducting channels in the Cu interlayer of a CPP spin valve stack. Exact current distribution in the stack is solved by using a 3-dimensional resistors network model. The size and density of the channels are varied in the simulation study. Thermally excited magnetization gyro-motion is also included in the model. Random fields simulating the thermal excitation are added to the effective field in the spin-transfer modified LLG equation by applying the fluctuation-dissipation theorem. The narrow conducting channels in the CCP/CPP spin valve stack formed by the porous conducting layer significantly reduces the current threshold for spin transfer excited noise. It is also found that the noise characteristics strongly depend on the actual distribution of the narrow conducting channels and the size of these channels.