Research

My research interests lie at the intersection of high-dimensional statistics, information theory, signal processing, and optimization. I am particularly interested in the design and analysis of scalable inference algorithms, especially message-passing and spectral methods, with an emphasis on precise asymptotic characterization and optimality in high dimensions.

A Unified Framework of AMP Algorithms

This line of work studies the construction of AMP-type algorithms for rotationally invariant models from a unified perspective. The current paper shows how a broad class of such algorithms can be derived by reducing them to long-memory OAMP, which leads to a systematic way to identify the corresponding Onsager terms. The framework also recovers an existing rotationally-invariant AMP algorithm in a more transparent form, clarifies the role of free cumulants in the derivation, and suggests new algorithmic variants for spiked-model estimation.

  1. Unifying AMP Algorithms for Rotationally-Invariant Models, Songbin Liu and Junjie Ma, arXiv:2412.01574, 2024.

Spiked Matrix Models under Rotationally Invariant Noise

This line of research studies spiked matrix models under rotationally invariant noise, with the goal of understanding the fundamental limits of statistical inference and the optimality of efficient algorithms in non-i.i.d. settings. An overview of this work was recently featured in the newsletter of the IEEE Information Theory Society, Guangzhou Chapter. Newsletter Article

  1. Optimality of Approximate Message Passing for Spiked Matrix Models with Rotationally Invariant Noise, Rishabh Dudeja, Songbin Liu, and Junjie Ma, Annals of Statistics, 54(1): 466--489, 2026.
  2. Orthogonal Approximate Message Passing with Optimal Spectral Initializations for Rectangular Spiked Matrix Models, Haohua Chen, Songbin Liu, and Junjie Ma, arXiv 2502.05524.

Discrete Precoding for Massive MIMO

This line of work studies low-complexity precoding algorithms for massive MIMO systems under discrete or quantized signaling constraints motivated by practical hardware limitations. A central theme is the asymptotic analysis and optimization of practically relevant precoding schemes. The first paper puts on rigorous footing a Bussgang-decomposition-based technique that has been widely used in the study of quantized massive MIMO systems. The second paper develops an asymptotic analysis for a commonly used nonlinear one-bit precoding method, and provides theoretical insights into the selection of optimal regularization parameters.

  1. Asymptotic SEP Analysis and Optimization of Linear-Quantized Precoding in Massive MIMO Systems, Zheyu Wu, Junjie Ma, Ya-Feng Liu, and A. Lee Swindlehurst, IEEE Transactions on Information Theory, 70(4): 2566--2589, 2024.
  2. Asymptotic Analysis of Nonlinear One-Bit Precoding in Massive MIMO Systems via Approximate Message Passing, Zheyu Wu, Junjie Ma, Ya-Feng Liu, and Bruno Clerckx, IEEE Transactions on Information Theory, 2026+.

Activity Detection in Grant-Free Random Access

This line of work studies covariance-based activity detection for massive MIMO grant-free random access. A central question is the identifiability of maximum-likelihood formulations, which determines whether the underlying activity pattern can in principle be recovered from the sample covariance. The current paper provides a precise asymptotic characterization of the associated phase transition for commonly used random signature models, via a tractable semi-random surrogate. It also points to a universality conjecture for the Kronecker-product-type random matrices arising in the original model.

  1. Precise Analysis of Covariance Identifiability for Activity Detection in Grant-Free Random Access, Shengsong Luo, Junjie Ma, Chongbin Xu, and Xin Wang, arXiv:2406.01138, 2024.

Phase Retrieval

Phase retrieval concerns the recovery of a signal from magnitude-only measurements and arises in a range of imaging and sensing applications. Our work develops and analyzes spectral methods and message-passing algorithms for phase retrieval, with an emphasis on sharp asymptotic analysis, information-theoretic limits, and the role of structured sensing matrices.

  1. Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems, Junjie Ma, Ji Xu, and Arian Maleki, IEEE Transactions on Information Theory, vol. 70, no. 1, pp. 482--508, 2023.
  2. Spectral Method for Phase Retrieval: an Expectation Propagation Perspective, Junjie Ma, Rishabh Dudeja, Ji Xu, Arian Maleki, and Xiaodong Wang, IEEE Transactions on Information Theory, vol. 67, no. 2, pp. 1332--1355, 2021.
  3. Information-Theoretic Limits for Phase Retrieval with Subsampled Haar Sensing Matrices, Rishabh Dudeja, Junjie Ma, and Arian Maleki, IEEE Transactions on Information Theory, vol. 66, no. 12, pp. 8002--8045, 2020.
  4. Analysis of Spectral Methods for Phase Retrieval with Random Orthogonal Matrices, Rishabh Dudeja, Milad Bakhshizadeh, Junjie Ma, and Arian Maleki, IEEE Transactions on Information Theory, vol. 66, no. 8, pp. 5182--5203, 2020.
  5. Optimization-Based AMP for Phase Retrieval: The Impact of Initialization and ℓ2-Regularization, Junjie Ma, Ji Xu, and Arian Maleki, IEEE Transactions on Information Theory, vol. 65, no. 6, pp. 3600--3629, 2019.

Orthogonal AMP

Approximate message passing (AMP) is a powerful class of iterative algorithms for signal recovery and high-dimensional inference with large random matrices. One of its most appealing features is that, in the high-dimensional limit, its dynamics can often be characterized exactly by state evolution. Orthogonal AMP (OAMP) extends this framework beyond the standard i.i.d. Gaussian setting, allowing state-evolution analysis for a much broader class of random matrix ensembles and leading to new algorithms for compressed sensing and coded linear systems.

  1. Orthogonal AMP, Junjie Ma and Li Ping, IEEE Access, vol. 5, pp. 2020--2033, 2017.
  2. Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis, Zhuohang He, Junjie Ma, and Xiaojun Yuan, IEEE Transactions on Information Theory, vol. 71, no. 2, pp. 1323--1361, 2025.
  3. On Orthogonal AMP in Coded Linear Vector Systems, Junjie Ma, Lei Liu, Xiaojun Yuan, and Li Ping, IEEE Transactions on Wireless Communications, vol. 18, no. 12, pp. 5658--5672, 2019.
  4. Denoising-based Turbo Compressed Sensing, Zhipeng Xue, Junjie Ma, and Xiaojun Yuan, IEEE Access, vol. 5, pp. 7193--7204, 2017.
  5. On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices, Junjie Ma, Xiaojun Yuan, and Li Ping, IEEE Signal Processing Letters, vol. 22, no. 10, pp. 1580--1584, 2015.
  6. Turbo Compressed Sensing with Partial DFT Sensing Matrix, Junjie Ma, Xiaojun Yuan, and Li Ping, IEEE Signal Processing Letters, vol. 22, no. 2, pp. 158--161, 2015.
  7. Energy-Spreading-Transform-Based MIMO Systems: Iterative Equalization, Evolution Analysis, and Precoder Optimization, Xiaojun Yuan, Junjie Ma, and Li Ping, IEEE Transactions on Wireless Communications, vol. 13, no. 9, pp. 5237--5250, 2014.