Capacity Bounds and Spectral Constraints for Transceivers With Finite Resolution Quantizers

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 finite 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 a discrete Fourier transform (DFT) matrix, the model naturally captures filtering and spectral constraints. In particular, this model allows studying the impact of quantization on out-of-band (OOB) emission constraints. The out-of-band emission constraints are defined using a "spectrum mask" in practical wireless systems. All transmissions need to meet the OOB constraint to allow other services and technologies to operate in adjacent bands.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, satisfying OOB emissions is potentially much more of a challenge.