Capacity Bounds for Communication Systems with Quantization and Spectral Constraints

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.