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Multi-Domain Iterative Detection for Massive Connectivity in LEO Satellite Networks
Xinhua Liu, Yueqing Wang, Keke Ying, Peihu Duan, Dapeng Li, Ziwei Wan, Zhongliang Zhao, Chabalala S. Chabalala, Andrey Ivanov, Zhen Gao
TL;DR
Massive LEO satellite connectivity exposes GF-RA to overloaded, rank-deficient detection and weak performance from existing schemes. The paper proposes IRF-MAMP with alternating SF/AD-domain processing and joint spatial-frequency spreading, achieving superior AUD, CE, and BER performance, including under low pilot overhead.
Problem
Existing GF-RA methods perform poorly in massive connectivity, while overloaded or spatially close terminals make conventional data detection rank-deficient or underdetermined.
Method
IRF-MAMP alternates SF-domain AUD and AD-domain CE with residual feedback, while joint spatial-frequency spreading expands observations for multi-domain data detection.
Results
Simulations show significant superiority over existing GF methods in AUD accuracy, CE precision, and BER, especially with low effective pilot lengths and practical SNRs.
Takeaways & Limitations
The framework maintains robust access performance under low pilot overhead and improves BER over non-spreading detection by exploiting expanded spatial-frequency observations.
Abstract
from arXiv · showhide
Grant-Free (GF) random access is promising for low Earth orbit satellite Internet due to its reduced access latency. However, existing schemes suffer from poor performance in massive connectivity scenarios. To address this challenge, we firstly propose an iterative residual feedback multi-measurement vector approximate message passing algorithm. This algorithm leverages multi-domain synergistic sparsity in the spatial-frequency and angular-delay domains to alternately perform active user terminal detection (AUD) and channel estimation (CE). Additionally, a residual feedback mechanism is incorporated to suppress error accumulation, thereby enhancing AUD performance. Furthermore, conventional data detection (DD) methods significantly degrade when active user terminals are spatially close or outnumber the satellite's receive antennas, making the demodulation problem rank-deficient or underdetermined. To mitigate this, we design a data modulation scheme via joint spatial-frequency multi-domain spreading, which utilizes observations from both spatial and frequency domains to facilitate multi-domain DD. Simulation results demonstrate that the proposed scheme significantly outperforms existing GF methods in terms of AUD accuracy, CE precision, and bit error rate, especially under conditions of low effective pilot length and practical signal-to-noise ratios.
I. INTRODUCTION
LEO satellite IoT requires low-latency massive connectivity, motivating GF-RA, but overloaded and correlated channels challenge detection. The paper addresses these issues with multi-domain iterative detection and spreading-based observation expansion.
- GF-RA reduces signaling overhead and latency by bypassing grant-based handshakes for bursty satellite IoT traffic.
- Existing massive-access systems become severely underdetermined when active terminals exceed onboard antennas, limiting traditional zero-forcing data detection.
- The proposed framework alternates AUD in the SF-domain with CE in the AD-domain to exploit structured and cluster sparsity.
- Joint spatial-frequency spreading expands effective observations and improves detection robustness under highly correlated angles of arrival.
- IRF-MAMP adds residual feedback to cancel interference from highly active terminals and suppress error accumulation before LMMSE-based data detection.
- Simulation results confirm the proposed approach’s effectiveness and superiority in practical LEO massive-access scenarios.
II. SYSTEM MODEL
The system models OFDM uplink random access from sporadically active terminals through Rician multipath channels and satellite and terminal planar arrays. It incorporates matched-filter analog beamforming and postsynchronization processing assumptions.
- The uplink uses OFDM with K user terminals, M subcarriers, and a satellite equipped with a uniform planar receive array.
- Only Ka ≪ K terminals are active, represented by binary activity indicators and an active-user set.
- Limited scattering and long satellite-terminal distances motivate a common AoA across multipath components with distinct propagation delays.
- The channel follows a Rician Lp-path model with Q delay taps and frequency-dependent path gains across the M subcarriers.
- Terminal analog beamforming is approximated by matched filtering, producing an effective Nr-dimensional channel vector at each subcarrier.
III. PROPOSED TRANSMIT SIGNAL DESIGN AND UPLINK TRANSMISSION PROBLEM FORMULATION
The transmit design spreads user signals across selected subcarriers to expand observations and address rank deficiency under overloaded, correlated channels. The resulting tensor formulation exposes structured sparsity across users, frequency, and angular-delay domains.
- Highly correlated angles and active-user overload create rank-deficient demodulation, especially when active terminals exceed satellite antennas.
- SF-domain spreading partitions subcarriers into G resource blocks and forms groups by uniformly selecting corresponding subcarriers.
- Subcarrier selection extracts an SG-specific frequency-domain channel tensor using V, whose entries select ξ + (g − 1)∆.
- The frame contains Tp pilot slots followed by Td data slots, with T denoting the slots used in the current phase.
- Each user spreads one signal over G subcarriers using a non-orthogonal spreading code, while pilot and data symbols share the tensorized uplink model.
- The equivalent channel exhibits traffic-induced spatial-frequency sparsity and common activity patterns across subcarriers and receive antennas.
- Transforming the channel into the virtual AD-domain leverages narrow angular spread, few scatterers, and resulting cluster sparsity.
IV. PROPOSED RECEIVER DETECTION SCHEME AT THE LEO SATELLITE
The proposed receiver uses an alternating AUD and CE module, followed by data detection, to process pilot and data transmissions at the LEO satellite.
- The receiver comprises an Alt-ADCE module for alternating AUD and CE and a DD module for data transmission.
- During the pilot phase, AUD is performed in the SF-domain while CE is performed in the AD-domain.
- After Alt-ADCE estimates the channel matrix, the receiver uses received data signals at the satellite for data detection.
A. Residual Feedback-Based Alternating AUD and CE
The residual feedback-based alternating scheme iteratively detects active terminals and estimates channels, feeding selected reconstructed signals back to refine subsequent iterations.
- IRF-MAMP alternates detection and estimation stages to exploit multi-domain synergistic sparsity.
- The detection stage identifies coarse and high-reliability active user sets from posterior active probabilities, while estimation recovers channels for the coarse set.
- Residual feedback reconstructs signals from a selected reliable-terminal subset and subtracts them from the received signal for the next iteration.
- The detection and estimation stages repeat on the remaining received signals until convergence.
B. MAMP Algorithm
The MAMP component uses sparse Bayesian modeling and approximate inference to estimate channels and detect active terminals from posterior activity probabilities.
- The algorithm adopts AMP to solve the sparse signal recovery problem.
- A spike-and-slab prior models each channel coefficient, with ψ_k,g representing its probability of being non-zero.
- AMP approximates the high-dimensional posterior as scalar posteriors, avoiding high-dimensional integrals in MMSE estimation.
- The detector uses posterior active probabilities η_n,k,g and a threshold condition to identify active terminals.
C. Data Detection Stage
The data detection stage estimates transmitted symbols from stacked received signals and estimated channels across all satellite antennas, with performance evaluated against pilot length and SNR.
- The data model relates received signals to transmitted symbols through the estimated SF-domain channel matrix plus noise.
- Figure 2 compares ADEP, NMSE, and BER versus effective pilot length at SNR = 16 dB.
- Figure 3 compares NMSE and BER versus SNR at T = 80.
- Signals from all satellite antennas are stacked before estimating the data symbols with an LMMSE estimator.
D. Computational Complexity Analysis
The proposed IRF-MAMP approach adds residual feedback to iterative detection and estimation, requiring moderate extra receiver-side computation and memory while improving robustness in overloaded massive access.
- Complexity structure: IRF-MAMP performs detection across all K potential users, while estimation operates only on the coarse active-user set Σ.The detection complexity is given over K users; estimation reduces the corresponding terms by using |Σ|c.
- Complexity structure: The proposed Alt-ADCE complexity scales with the number of outer residual-feedback iterations Liter multiplying the detection and estimation complexities.The estimation stage is repeated over Lamp inner MAMP iterations within each outer iteration.
- Data detection: The DD stage has complexity O(|K̂a|^3c + 2|K̂a|^2cGNr + |K̂a|cGNrTd).This expression accounts for the detected active-user count, spreading-resource count, receive-antenna dimension, and data duration terms shown in the analysis.
- Comparison: Compared with OAMP-MMV and SOMP schemes, IRF-MAMP requires moderate additional receiver-side computation and memory due to residual feedback.The paper attributes this overhead specifically to the residual-feedback mechanism.
- Comparison: The added receiver-side cost is accompanied by improved robustness in overloaded massive access scenarios.The paper states that this robustness is verified in the performance evaluation.
V. PERFORMANCE EVALUATION
Simulations evaluate AUD, CE, and DD using ADEP, NMSE, and BER across effective pilot lengths, SNRs, active-user loads, and spreading configurations. The proposed scheme consistently performs best, including under low pilot overhead and practically relevant SNR conditions.
- Evaluation setup: The evaluation uses ADEP, NMSE, and BER to measure AUD, CE, and DD, respectively, against six GF-RA baselines.The main scenario uses K = 500 potential UTs and Ka = 50 active UTs.
- Evaluation setup: Effective pilot length equalizes the JADCE measurement dimension but does not imply identical waveform durations or physical pilot overheads across frame structures.For padded training-sequence baselines, it counts the interference-free non-inter-symbol-interference region rather than total training-sequence length.
- Pilot-length results: Across varying effective pilot lengths, the proposed scheme achieves superior ADEP, NMSE, and BER performance and remains robust under low pilot overhead.The angular-delay clustered sparsity used by Baseline 4 explains its advantage over the SF-only Baseline 3, but both remain below the proposed scheme.
- SNR results: Across the plotted SNR range at T = 80, the proposed scheme achieves the lowest estimation error and BER among all baselines.The comparison covers NMSE for channel estimation and BER for data detection; practical LEO links commonly operate at low-to-medium SNR because of severe path loss.
- Spreading and scaling: At SNR = 16 dB, joint spatial-frequency spreading with G > 1 outperforms the non-spreading G = 1 scheme, while G = 32 gives the best fixed-Nr performance.For fixed G = 16, increasing Nr decreases BER, although the gain narrows at longer pilot lengths and remains superior for Nr = 6 × 6.
- Active-user load: As Ka increases from 40 to 60 at T = 60 and SNR = 20 dB, all BERs increase, but Baselines 1 and 2 degrade fastest while Baseline 4 exceeds Baselines 3 and 5.The reported differences are associated with correlated channels, zero-forcing error amplification, limited spatial-sparsity use, and greedy sensitivity to proximate AoAs.
VI. CONCLUSIONS
The paper combines multi-domain iterative detection with joint spatial-frequency spreading to improve massive-access detection under overloaded satellite conditions. It reports performance evaluations for varying subcarriers, antennas, and active-user counts, while noting implementation costs from spreading.
- The IRF-MAMP framework alternately exploits SF-domain sparsity for AUD and AD-domain cluster sparsity for CE, with residual feedback suppressing error accumulation.
- Fig. 4 evaluates proposed-scheme DD performance across subcarrier and satellite-antenna counts at SNR = 16 dB.
- Fig. 5 evaluates different schemes as active UTs vary, using T = 60 and SNR = 20 dB.
- Joint spatial-frequency spreading expands the effective observation dimension to address rank-deficient demodulation in overloaded LEO connectivity.
- Spatial-frequency spreading improves BER performance but introduces additional synchronization, computational, and memory costs, making moderate spreading more practical under payload constraints.