  We propose and investigate a compressive architecture for estimation and
tracking of sparse spatial channels in millimeter (mm) wave picocellular
networks. The base stations are equipped with antenna arrays with a large
number of elements (which can fit within compact form factors because of the
small carrier wavelength) and employ radio frequency (RF) beamforming, so that
standard least squares adaptation techniques (which require access to
individual antenna elements) are not applicable. We focus on the downlink, and
show that "compressive beacons," transmitted using pseudorandom phase settings
at the base station array, and compressively processed using pseudorandom phase
settings at the mobile array, provide information sufficient for accurate
estimation of the two-dimensional (2D) spatial frequencies associated with the
directions of departure of the dominant rays from the base station, and the
associated complex gains. This compressive approach is compatible with coarse
phase-only control, and is based on a near-optimal sequential algorithm for
frequency estimation which can exploit the geometric continuity of the channel
across successive beaconing intervals to reduce the overhead to less than 1%
even for very large (32 x 32) arrays. Compressive beaconing is essentially
omnidirectional, and hence does not enjoy the SNR and spatial reuse benefits of
beamforming obtained during data transmission. We therefore discuss system
level design considerations for ensuring that the beacon SNR is sufficient for
accurate channel estimation, and that inter-cell beacon interference is
controlled by an appropriate reuse scheme.
