For a planar FEL configuration we study stimulated coherent spontaneous
emission driven by a gradient of the bunch current in the presence of different
levels of noise in bunches. To perform a vast amount of simulations required
for obtaining statistically valid results, we developed a memory and time
efficient one-dimensional simulation code based on the integral solution to a
Klein-Gordon equation describing the field evolution. The longitudinal
granularity of the electron bunch density originating from shot noise is
maintained throughout the analysis. Three-dimensional effects like transverse
emittance and diffraction are taken into account in simulations via an
effective FEL parameter calculated from Xie's fitting formula. Calculations are
performed for an FEL model with the SwissFEL injector bunch parameters. It
turns out that a reduction of noise by several orders of magnitude below the
level of shot noise is required to mitigate the noise effect. We propose a
novel scheme that allows for formation of electron bunches with a reduced level
of noise and a high gradient of the current at the bunch tail to enhance
coherent spontaneous emission. The presented scheme uses effects of noise
reduction and controlled microbunching instability and consists of a laser
heater, a shot noise suppression section as well as a bunch compressor. The
noise factor and microbunching gain with and without laser heater are
estimated. We found that shot noise reduction by three orders of magnitude can
be achieved for a finite transverse size electron bunch
