  Millimeter (mm) wave massive MIMO has the potential for delivering orders of
magnitude increases in mobile data rates, with compact antenna arrays providing
narrow steerable beams for unprecedented levels of spatial reuse. A fundamental
technical bottleneck, however, is rapid spatial channel estimation and beam
adaptation in the face of mobility and blockage. Recently proposed compressive
techniques which exploit the sparsity of mm wave channels are a promising
approach to this problem, with overhead scaling linearly with the number of
dominant paths and logarithmically with the number of array elements. Further,
they can be implemented with RF beamforming with low-precision phase control.
However, these methods make implicit assumptions on long-term phase coherence
that are not satisfied by existing hardware. In this paper, we propose and
evaluate a noncoherent compressive channel estimation technique which can
estimate a sparse spatial channel based on received signal strength (RSS)
alone, and is compatible with off-the-shelf hardware. The approach is based on
cascading phase retrieval (i.e., recovery of complex-valued measurements from
RSS measurements, up to a scalar multiple) with coherent compressive
estimation. While a conventional cascade scheme would multiply two measurement
matrices to obtain an overall matrix whose entries are in a continuum, a key
novelty in our scheme is that we constrain the overall measurement matrix to be
implementable using coarsely quantized pseudorandom phases, employing a virtual
decomposition of the matrix into a product of measurement matrices for phase
retrieval and compressive estimation. Theoretical and simulation results show
that our noncoherent method scales almost as well with array size as its
coherent counterpart, thus inheriting the scalability and low overhead of the
latter.
