PhaseMax: Convex Phase Retrieval via Basis Pursuit

We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is Basis Pursuit, which implies that phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice

PAR-Aware Large-Scale Multi-User MIMO-OFDM Downlink

We investigate an orthogonal frequency-division multiplexing (OFDM)-based downlink transmission scheme for large-scale multi-user (MU) multiple-input multiple-output (MIMO) wireless systems. The use of OFDM causes a high peak-to-average (power) ratio (PAR), which necessitates expensive and power-inefficient radio-frequency (RF) components at the base station. In this paper, we present a novel downlink transmission scheme, which exploits the massive degrees-of-freedom available in large-scale MU-MIMO-OFDM systems to achieve low PAR. Specifically, we propose to jointly perform MU precoding, OFDM modulation, and PAR reduction by solving a convex optimization problem. We develop a corresponding fast iterative truncation algorithm (FITRA) and show numerical results to demonstrate tremendous PAR-reduction capabilities. The significantly reduced linearity requirements eventually enable the use of low-cost RF components for the large-scale MU-MIMO-OFDM downlink.Comment: To appear in IEEE Journal on Selected Areas in Communication

MIMO Transmission with Residual Transmit-RF Impairments

Physical transceiver implementations for multiple-input multiple-output (MIMO) wireless communication systems suffer from transmit-RF (Tx-RF) impairments. In this paper, we study the effect on channel capacity and error-rate performance of residual Tx-RF impairments that defy proper compensation. In particular, we demonstrate that such residual distortions severely degrade the performance of (near-)optimum MIMO detection algorithms. To mitigate this performance loss, we propose an efficient algorithm, which is based on an i.i.d. Gaussian model for the distortion caused by these impairments. In order to validate this model, we provide measurement results based on a 4-stream Tx-RF chain implementation for MIMO orthogonal frequency-division multiplexing (OFDM).Comment: to be presented at the International ITG Workshop on Smart Antennas - WSA 201

On the Performance of Mismatched Data Detection in Large MIMO Systems

We investigate the performance of mismatched data detection in large multiple-input multiple-output (MIMO) systems, where the prior distribution of the transmit signal used in the data detector differs from the true prior. To minimize the performance loss caused by this prior mismatch, we include a tuning stage into our recently-proposed large MIMO approximate message passing (LAMA) algorithm, which allows us to develop mismatched LAMA algorithms with optimal as well as sub-optimal tuning. We show that carefully-selected priors often enable simpler and computationally more efficient algorithms compared to LAMA with the true prior while achieving near-optimal performance. A performance analysis of our algorithms for a Gaussian prior and a uniform prior within a hypercube covering the QAM constellation recovers classical and recent results on linear and non-linear MIMO data detection, respectively.Comment: Will be presented at the 2016 IEEE International Symposium on Information Theor