  The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the
antenna outputs are processed by an analog linear combining network and
quantized by a set of threshold quantizers is studied. The linear combining
weights and quantization thresholds are selected from a set of possible
configurations as a function of the channel matrix. The possible configurations
of the combining network model specific analog receiver architectures, such as
single antenna selection, sign quantization of the antenna outputs or linear
processing of the outputs. An interesting connection between the capacity of
this channel and a constrained sphere packing problem in which unit spheres are
packed in a hyperplane arrangement is shown. From a high-level perspective,
this follows from the fact that each threshold quantizer can be viewed as a
hyperplane partitioning the transmitter signal space. Accordingly, the output
of the set of quantizers corresponds to the possible regions induced by the
hyperplane arrangement corresponding to the channel realization and receiver
configuration. This connection provides a number of important insights into the
design of quantization architectures for MIMO receivers; for instance, it shows
that for a given number of quantizers, choosing configurations which induce a
larger number of partitions can lead to higher rates.
