  The spectrum scarcity at sub-6 GHz spectrum has made millimeter-wave (mmWave)
frequency band a key component of the next-generation wireless networks. While
mmWave spectrum offers extremely large transmission bandwidths to accommodate
ever-increasing data rates, unique characteristics of this new spectrum need
special consideration to achieve the promised network throughput. In this work,
we consider the off-grid problem for mmWave communications, which has a
significant impact on basic network functionalities involving beam steering and
tracking. The off-grid effect naturally appears in compressed sensing (CS)
techniques adopting a discretization approach for representing the angular
domain. This approach yields a finite set of discrete angle points, which are
an approximation to the continuous angular space, and hence degrade the
accuracy of related parameter estimation. In order to cope with the off-grid
effect, we present a novel parameter-perturbation framework to efficiently
estimate the channel and the covariance for mmWave networks. The proposed
algorithms employ a smart perturbation mechanism in conjunction with a
low-complexity greedy framework of simultaneous orthogonal matching pursuit
(SOMP), and jointly solve for the off-grid parameters and weights. Numerical
results show a significant performance improvement through our novel framework
as a result of handling the off-grid effects, which is totally ignored in the
conventional sparse mmWave channel or covariance estimation algorithms.
