1-비트 압축 센싱을 위한 효율적인 알고리즘 = Efficient Algorithm for 1-Bit Compressed Sensing with Multiple Measurement

다국어 초록 (Multilingual Abstract)

In this paper, we consider a compressed sensing (CS) problem with multiple measurement vector (MMV), in which a set of sparse signals with the same support are recovered simultaneously from the corresponding measurements. Many practical problems (e.g., active user detection for massive connectivity, communication-efficient federated learning, and so on) have been formulated in this problem. Also, it is necessary to investigate one-bit CS under the MMV framework, in order to boost communication efficiency.
Unfortunately, the best-known one-bit CS algorithms such as Bayesian matching pursuit (BMP) is not applicable to the emerging one-bit MMV problems. In these problems, we propose novel algorithms, named Turbo-BMP as nontrivial extensions of BMP, respectively. Simulation results demonstrate the superiority of the proposed algorithm.

국문 초록 (Abstract)

본 논문에서는 같은 서포트를 가진 일련의 희소 신호가 해당 측정으로부터 동시에 복구되는 다중 측정 벡터(Multiple Measurement Vector, MMV)를 가진 압축 센싱(Compressive Sensing, CS) 문제를 고려한다. 이 문제에는 많은 실용적인 문제(예: 대규모 연결, 통신 효율 연합 학습 등에 대한 능동적인 사용자 탐지 등)가 형성되었다.
또한 통신 효율을 높이기 위해서는 다중 측정 벡터 프레임워크에서의 1-비트 압축 센싱에 대한 연구가 필요하다.
그러나, 베이지안 매칭 추구(Bayesian Matching Pursuit, BMP)와 같은 잘 알려진 1-비트 압축 센싱 알고리즘은새로운 1-비트 다중 측정 문제에 적용되지 않는다. 이러한 문제에서 우리는 BMP 알고리즘의 확장으로Turbo-BMP(Turbo-Bayesian Matching Pursuit)라는 새로운 알고리즘을 제안한다. 벤치마크 알고리즘으로써, M-BMP(Multiple Measurement Vector-Bayesian Matching Purrsuit)를 비교하여 시뮬레이션을 진행한다. 시뮬레이션 결과는 제안한 알고리즘인 Turbo-BMP의 우수성을 보여준다.

참고문헌 (Reference)

1 J. Chae, "Stacked bayesian matching pursuit for one-bit compressed sensing" 27 (27): 550-554, 2020

2 S. F. Cotter, "Sparse solutions to linear inverse problems with multiple measurement vectors" 53 (53): 2477-2488, 2005

3 Z. Chen, "Sparse activity detection for massive connectivity" 66 (66): 1890-1904, 2018

4 L. Jacques, "Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors" 59 (59): 2082-2102, 2013

5 M. Yan, "Robust 1-bit compressive sensing using adaptive outlier pursuit" 60 (60): 3868-3875, 2012

6 H. M. Shi, "Methods for quantized compressed sensing" 1-9, 2016

7 김도우 ; 문석재 ; 이장원, "Massive MIMO 시스템에서 mMTC를 위한 반직교 랜덤 액세스" 한국통신학회 46 (46): 1164-1172, 2021

8 P. H. Siegel, "Guest editorial —The turbo principle : From theory to practice" 19 : 793-799, 2001

9 J. A. Bazerque, "Distributed spectrum sensing for cognitive radio networks by exploiting sparsity" 58 (58): 1847-1862, 2010

10 F. Zeng, "Distributed compressive spectrum sensing in cooperative multihop cognitive networks" 5 (5): 37-48, 2010

11 Q. Ling, "Decentralized support detection of multiple measurement vectors with joint sparsity" 2996-2999, 2011

12 H. F. Schepker, "Compressive sensing multi-user detection with block-wise orthogonal least squares" 1-5, 2012

13 A. Zymnis, "Compressed sensing with quantized measurements" 17 (17): 149-152, 2010

14 M. Mishali, "Blind multiband signal reconstruction: Compressed sensing for analog signals" 57 (57): 993-1009, 2009

15 Y. Nam, "Bayesian matching pursuit : A finite-alphabet sparse signal recovery algorithm for quantized compressive sensing" 26 (26): 1285-1289, 2019

16 Y. S. Jeon, "A compressive sensing approach for federated learning over massive MIMO communication systems" 20 (20): 1990-2004, 2021