  Channel estimation (CE) for millimeter-wave (mmWave) lens-array suffers from
prohibitive training overhead, whereas the state-of-the-art solutions require
an extra complicated radio frequency phase shift network. By contrast,
lens-array using antenna switching network (ASN) simplifies the hardware, but
the associated CE is a challenging task due to the constraint imposed by ASN.
This paper proposes a compressive sensing (CS)-based CE solution for
full-dimensional (FD) lens-array, where the mmWave channel sparsity is
exploited. Specifically, we first propose an approach of pilot training under
the more severe haraware constraint imposed by ASN, and formulate the
associated CE of lens-array as a CS problem. Then, a redundant dictionary is
tailored for FD lens-array to combat the power leakage caused by the continuous
angles of multipath components. Further, we design the baseband pilot signals
to minimize the total mutual coherence of the measurement matrix based on CS
theory for more reliable CE performance. Our solution provides a framework for
applying CS techniques to lens-array using simple and practical ASN. Simulation
results demonstrate the effectiveness of the proposed scheme.
