Abstract: Sparsity-based joint active user detection and channel estimation (JADCE) algorithms are crucial in grant-free massive machine-type communication (mMTC) systems. The conventional compressed sensing algorithms are tailored for noncoherent communication systems, where the correlation between any two measurements is as minimal as possible. However, existing sparsity-based JADCE approaches may not achieve optimal performance in strongly coherent systems, especially with a small number of pilot subcarriers. To tackle this challenge, we formulate JADCE as a joint sparse signal recovery problem, leveraging the block-type row-sparse structure of millimeter-wave (mmWave) channels in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Then, we propose an efficient difference-of-convex function algorithm (DCA) based JADCE algorithm with multiple measurement vector (MMV) frameworks, promoting the row-sparsity of the channel matrix. To mitigate the computational complexity further, we introduce a fast DCA-based JADCE algorithm via a proximal operator, which allows a low-complexity alternating direction multiplier method (ADMM) to resolve the optimization problem directly. Finally, simulation results demonstrate that the two proposed difference-of-convex (DC) algorithms achieve effective active user detection and accurate channel estimation compared with state-of-the-art compressed sensing based JADCE techniques.

大规模机器类型通信的联合活跃用户检测和信道估计：凸差优化视角

[1]Alkhateeb A, El Ayach O, Leus G, et al., 2014. Channel estimation and hybrid precoding for millimeter wave cellular systems. IEEE J Sel Top Signal Process, 8(5):831-846.

[2]Bian XY, Mao YY, Zhang J, 2023. Joint activity detection, channel estimation, and data decoding for grant-free massive random access. IEEE Int Things J, 10(16):14042-14057.

[3]Bian XY, Mao YY, Zhang J, 2024. Joint activity-delay detection and channel estimation for asynchronous massive random access: a free probability theory approach. https://arxiv.org/abs/2402.17996

[4]Boyd S, Parikh N, Chu E, et al., 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn, 3(1):1-122.

[5]Chukhno N, Chukhno O, Moltchanov D, et al., 2024. Models, methods, and solutions for multicasting in 5G/6G mmWave and sub-THz systems. IEEE Commun Surv Tutor, 26(1):119-159.

[6]Cui Y, Li SC, Zhang WQ, 2021. Jointly sparse signal recovery and support recovery via deep learning with applications in MIMO-based grant-free random access. IEEE J Sel Areas Commun, 39(3):788-803.

[7]Djelouat H, Leinonen M, Juntti M, 2022. Spatial correlation aware compressed sensing for user activity detection and channel estimation in massive MTC. IEEE Trans Wirel Commun, 21(8):6402-6416.

[8]Gan X, Zhong CJ, Huang CW, et al., 2021. RIS-assisted multi-user MISO communications exploiting statistical CSI. IEEE Trans Commun, 69(10):6781-6792.

[9]Gao Z, Dai LL, Wang ZC, et al., 2015. Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO. IEEE Trans Signal Process, 63(23):6169-6183.

[10]Gao Z, Ke ML, Mei YK, et al., 2024. Compressive sensing-based grant-free massive access for 6G massive communication. IEEE Int Things J, 11(5):7411-7435.

[11]Ge HM, Li P, 2022. The Dantzig selector: recovery of signal via l1−αl2 minimization. Inv Probl, 38(1):015006.

[12]Guo MQ, Gursoy MC, 2023. Joint activity detection and channel estimation for intelligent-reflecting-surface-assisted wireless IoT networks. IEEE Int Things J, 10(12):10207-10221.

[13]Guo YR, Liu ZJ, Sun YJ, 2024. Low-complexity joint activity detection and channel estimation with partially orthogonal pilot for asynchronous massive access. IEEE Int Things J, 11(1):1773-1783.

[14]Ke ML, Gao Z, Wu YP, et al., 2020. Compressive sensing-based adaptive active user detection and channel estimation: massive access meets massive MIMO. IEEE Trans Signal Process, 68:764-779.

[15]Li S, Xiao LX, Jiang T, 2021. An efficient matching pursuit based compressive sensing detector for uplink grant-free NOMA. IEEE Trans Veh Technol, 70(2):2012-2017.

[16]Li Y, Chen SY, Meng WX, et al., 2024. Correlation aided joint activity detection and channel estimation for multi-device collaborative massive access. IEEE Int Things J, 11(10):18394-18409.

[17]Liu KH, Li XJ, Fang J, et al., 2019. Bayesian mmWave channel estimation via exploiting joint sparse and low-rank structures. IEEE Access, 7:48961-48970.

[18]Liu KH, Wan LT, Sun L, 2022. Fast quadratic sensing via nonconvex optimization. Proc 30^th European Signal Processing Conf, p.2211-2215.

[19]Liu KH, Li XN, Zhao HY, et al., 2023. Joint active user detection and channel estimation for massive grant-free access via difference of convex programming. Proc IEEE Global Communications Conf, p.2335-2340.

[20]Liu L, Yu W, 2018. Massive connectivity with massive MIMO–part I: device activity detection and channel estimation. IEEE Trans Signal Process, 66(11):2933-2946.

[21]Lou YF, Yan M, 2018. Fast L₁-L₂ minimization via a proximal operator. J Sci Comput, 74(2):767-785.

[22]Lou YF, Yin PH, He Q, et al., 2015. Computing sparse representation in a highly coherent dictionary based on difference of L₁ and L₂. J Sci Comput, 64(1):178-196.

[23]Lu HT, Long XZ, Lv JY, 2011. A fast algorithm for recovery of jointly sparse vectors based on the alternating direction methods. Proc 14^th Int Conf on Artificial Intelligence and Statistics, p.461-469.

[24]Ma Z, Wu W, Gao FF, et al., 2024. Model-driven deep learning for non-coherent massive machine-type communications. IEEE Trans Wirel Commun, 23(3):2197-2211.

[25]Marata L, López OLA, Hauptmann A, et al., 2023. Joint activity detection and channel estimation for clustered massive machine type communications. IEEE Trans Wirel Commun, 23(6):5473-5487.

[26]Mei YK, Gao Z, Mi D, et al., 2023. Massive access in extra large-scale MIMO with mixed-ADC over near-field channels. IEEE Trans Veh Technol, 72(9):12373-12378.

[27]Petersen KB, Pedersen MS, 2012. The Matrix Cookbook. http://www2.imm.dtu.dk/pubdb/edoc/imm3274.pdf

[28]Qiao L, Zhang J, Gao Z, et al., 2022. Joint activity and blind information detection for UAV-assisted massive IoT access. IEEE J Sel Areas Commun, 40(5):1489-1508.

[29]Rajoriya A, Budhiraja R, 2023. Joint AMP-SBL algorithms for device activity detection and channel estimation in massive MIMO mMTC systems. IEEE Trans Commun, 71(4):2136-2152.

[30]Shao XD, Chen XM, Jia RD, 2020. A dimension reduction-based joint activity detection and channel estimation algorithm for massive access. IEEE Trans Signal Process, 68:420-435.

[31]Tang ZH, Wang J, Wang JT, et al., 2020. Device activity detection and non-coherent information transmission for massive machine-type communications. IEEE Access, 8:41452-41465.

[32]Tong X, Zhang ZY, Wang J, et al., 2021. Joint multi-user communication and sensing exploiting both signal and environment sparsity. IEEE J Sel Top Signal Process, 15(6):1409-1422.

[33]Wan LT, Liu KH, Zhang W, 2022. Deep learning-aided off-grid channel estimation for millimeter wave cellular systems. IEEE Trans Wirel Commun, 21(5):3333-3348.

[34]Wang BC, Dai LL, Mir T, et al., 2016. Joint user activity and data detection based on structured compressive sensing for NOMA. IEEE Commun Lett, 20(7):1473-1476.

[35]Wang W, Zhang W, Li YJ, et al., 2018. Channel estimation and hybrid precoding for multi-panel millimeter wave MIMO. Proc IEEE Int Conf on Communications, p.1-6.

[36]Wei L, Huang CW, Guo QH, et al., 2022. Joint channel estimation and signal recovery for RIS-empowered multiuser communications. IEEE Trans Commun, 70(7):4640-4655.

[37]Xiu HL, Gao Z, Liao AW, et al., 2023. Joint activity detection and channel estimation for massive IoT access based on millimeter-wave/terahertz multi-panel massive MIMO. IEEE Trans Veh Technol, 72(1):1349-1354.

[38]Yin PH, Lou YF, He Q, et al., 2015. Minimization of l1−2 for compressed sensing. SIAM J Sci Comput, 37(1):A536-A563.

[39]Ying KK, Gao Z, Chen S, et al., 2023. Quasi-synchronous random access for massive MIMO-based LEO satellite constellations. IEEE J Sel Areas Commun, 41(6):1702-1722.

[40]Yu KW, Shen M, Wang R, et al., 2020. Joint nuclear norm and l1−2-regularization sparse channel estimation for mmWave massive MIMO systems. IEEE Access, 8:155409-155416.

[41]Zhang XX, Labeau F, Hao L, et al., 2021. Joint active user detection and channel estimation via Bayesian learning approaches in MTC communications. IEEE Trans Veh Technol, 70(6):6222-6226.

[42]Zhang XX, Fan PZ, Hao L, et al., 2023. Generalized approximate message passing based Bayesian learning detectors for uplink grant-free NOMA. IEEE Trans Veh Technol, 72(11):15057-15061.

[43]Zhang YY, Guo QH, Wang ZY, et al., 2018. Block sparse Bayesian learning based joint user activity detection and channel estimation for grant-free NOMA systems. IEEE Trans Veh Technol, 67(10):9631-9640.

[44]Zhang ZJ, Li Y, Huang CW, et al., 2019. DNN-aided block sparse Bayesian learning for user activity detection and channel estimation in grant-free non-orthogonal random access. IEEE Trans Veh Technol, 68(12):12000-12012.

[45]Zhang ZJ, Guo QH, Li Y, et al., 2023. Variational Bayesian inference clustering-based joint user activity and data detection for grant-free random access in mMTC. IEEE Int Things J, 10(11):9906-9916.

[46]Zheng ST, Wu S, Jia HG, et al., 2024. Hybrid driven learning for joint activity detection and channel estimation in IRS-assisted massive connectivity. IEEE Trans Wirel Commun, 23(9):10834-10849.

[47]Zhu LJ, Liu KH, Wan LT, et al., 2023. Active user detection and channel estimation via fast ADMM. Proc IEEE Wireless Communications and Networking Conf, p.1-6.