  We study the problem of localizing multiple sources of forced oscillations
(FOs) and estimating their characteristics, such as frequency, phase, and
amplitude, using noisy PMU measurements. For each source location, we model the
input oscillation as a sum of unknown sinusoidal terms. This allows us to
obtain a linear relationship between measurements and the inputs at the unknown
sinusoids' frequencies in the frequency domain. We determine these frequencies
by thresholding the empirical spectrum of the noisy measurements. Assuming
sparsity in the number of FOs' locations and the number of sinusoids at each
location, we cast the location recovery problem as an $\ell_1$-regularized
least squares problem in the complex domain -- i.e., complex-LASSO (linear
shrinkage and selection operator). We numerically solve this optimization
problem using the complex-valued coordinate descent method, and show its
efficiency on the IEEE 68-bus, 16 machine and WECC 179-bus, 29-machine systems.
