Phase Retrieval Motivated Nonlinear MIMO Communication With Magnitude Measurements

Abstract

This paper proposes a multiuser magnitude-only (MO-)MIMO, whose base station acquires quantized magnitudes of the complex baseband signals through envelop detectors and low-resolution ADCs. Consequently, MO-MIMO enjoys much lower circuit power and cost in comparison with the conventional MIMO. Because the phase information is unavailable, all the existing MIMO baseband algorithms cannot be applied into MO-MIMO. Therefore, two types of channel estimators and multiuser detectors are constructed by first categorizing the channel estimation and multiuser detection problems as a quantized phase retrieval (PR) problem, and then solving the latter by developing two methods under the framework of generalized approximate message passing (GAMP). The first method directly applies GAMP to solve the quantized PR problem by exploiting the probability relationships between the quantized magnitude measurements and unknown complex signals. The second method iterates between the missing phase estimation and signal recovery, where the latter calls for GAMP to handle a linear mixing problem with quantized observations. The developed estimators and detectors call for matrix-vector multiplications and nonlinear function calculations as the most complex operations, handle the nonlinear quantization loss specially, and exploit the signal prior probability distributions. Finally, their effectiveness is validated experimentally.