  We show how to estimate the covariance of the power spectrum of a
statistically homogeneous and isotropic density field from a single periodic
simulation, by applying a set of weightings to the density field, and by
measuring the scatter in power spectra between different weightings. We
recommend a specific set of 52 weightings containing only combinations of
fundamental modes, constructed to yield a minimum variance estimate of the
covariance of power. Numerical tests reveal that at nonlinear scales the
variance of power estimated by the weightings method substantially exceeds that
estimated from a simple ensemble method. We argue that the discrepancy is
caused by beat-coupling, in which products of closely spaced Fourier modes
couple by nonlinear gravitational growth to the beat mode between them.
Beat-coupling appears whenever nonlinear power is measured from Fourier modes
with a finite spread of wavevector, and is therefore present in the weightings
method but not the ensemble method. Beat-coupling inevitably affects real
galaxy surveys, whose Fourier modes have finite width. Surprisingly, the
beat-coupling contribution dominates the covariance of power at nonlinear
scales, so that, counter-intuitively, it is expected that the covariance of
nonlinear power in galaxy surveys is dominated not by small scale structure,
but rather by beat-coupling to the largest scales of the survey.
