  We consider joint channel estimation and faulty antenna detection for massive
multiple-input multiple-output (MIMO) systems operating in time-division
duplexing (TDD) mode. For systems with faulty antennas, we show that the impact
of faulty antennas on uplink (UL) data transmission does not vanish even with
unlimited number of antennas. However, the signal detection performance can be
improved with a priori knowledge on the indices of faulty antennas. This
motivates us to propose the approach for simultaneous channel estimation and
faulty antenna detection. By exploiting the fact that the degrees of freedom of
the physical channel matrix are smaller than the number of free parameters, the
channel estimation and faulty antenna detection can be formulated as an
extended atomic norm denoising problem and solved efficiently via the
alternating direction method of multipliers (ADMM). Furthermore, we improve the
computational efficiency by proposing a fast algorithm and show that it is a
good approximation of the corresponding extended atomic norm minimization
method. Numerical simulations are provided to compare the performances of the
proposed algorithms with several existing approaches and demonstrate the
performance gains of detecting the indices of faulty antennas.
