We study the current noise spectra of a tunnel junction of a metal withstrong pairing phase fluctuation and a superconductor. It is shown that thereis a characteristic peak in the noise spectrum at the intrinsic Josephsonfrequency $\omega_J=2eV$ when $\omega_J$ is smaller than the pairing gap butlarger than the pairing scattering rate. In the presence of an AC voltage, thetunnelling current noise shows a series of characteristic peaks with increasingDC voltage. Experimental observation of these peaks will give direct evidenceof the pair fluctuation in the normal state of high-$T_c$ superconductors andfrom the half width of the peaks the pair decay rate can be estimated.
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