  Low-resolution digital-to-analog and analog-to-digital converters (DACs and
ADCs) have attracted considerable attention in efforts to reduce power
consumption in millimeter wave (mmWave) and massive MIMO systems. This paper
presents an information-theoretic analysis with capacity bounds for classes of
linear transceivers with quantization. The transmitter modulates symbols via a
unitary transform followed by a DAC and the receiver employs an ADC followed by
the inverse unitary transform. If the unitary transform is set to an FFT
matrix, the model naturally captures filtering and spectral constraints which
are essential to model in any practical transceiver. In particular, this model
allows studying the impact of quantization on out-of-band emission constraints.
In the limit of a large random unitary transform, it is shown that the effect
of quantization can be precisely described via an additive Gaussian noise
model. This model in turn leads to simple and intuitive expressions for the
power spectrum of the transmitted signal and a lower bound to the capacity with
quantization. Comparison with non-quantized capacity and a capacity upper bound
that does not make linearity assumptions suggests that while low resolution
quantization has minimal impact on the achievable rate at typical parameters in
5G systems today, satisfying out-of-band emissions are potentially much more of
a challenge.
