We present an expression for the shot noise power spectral density in
quasi-one dimensional conductors electrostatically controlled by a gate
electrode, that includes the effects of Coulomb interaction and of Pauli
exclusion among charge carriers. In this sense, our expression extends the well
known Landauer-Buttiker noise formula to include the effect of Coulomb
interaction through induced fluctuations in the device potential. Our approach
is based on the introduction of statistical properties of the scattering matrix
and on a second-quantization many-body description. From a quantitative point
of view, statistical properties are obtained by means of Monte Carlo
simulations on a ensemble of different configurations of injected states,
requiring the solution of the Poisson-Schrodinger equation on a
three-dimensional grid, with the non-equilibrium Green functions formalism. In
a series of example, we show that failure to consider the effects of Coulomb
interaction on noise leads to a gross overestimation of the noise spectrum of
quasi-one dimensional devices