  Adaptive interference cancellation is rapidly becoming a necessity for our
modern wireless communication systems, due to the proliferation of wireless
devices that interfere with each other. To cancel interference, digital
beamforming algorithms adaptively adjust the weight vector of the antenna
array, and in turn its radiation pattern, to minimize interference while
maximizing the desired signal power. While these algorithms are effective in
ideal scenarios, they are sensitive to signal corruptions. In this work, we
consider the case when the transmitter and receiver in a communication system
cannot be synchronized, resulting in a carrier frequency offset that corrupts
the signal. We present novel beamforming algorithms that are robust to signal
corruptions arising from this time-variant carrier frequency offset. In
particular, we bring in the Discrete Prolate Spheroidal Sequences (DPSS's) and
propose two atomic-norm-minimization (ANM)-based methods in both 1D and 2D
frameworks to design a weight vector that can be used to cancel interference
when there exist unknown time-varying frequency drift in the pilot and
interferer signals. Both algorithms do not assume a pilot signal is known.
Noting that solving ANM optimization problems via semi-definite programs can be
a computational burden, we also present a novel fast algorithm to approximately
solve our 1D ANM optimization problem. Finally, we confirm the benefits of our
proposed algorithms and show the advantages over existing approaches with a
series of experiments.
