User Activity Detection and Channel Estimation for Grant-Free Random Access in LEO Satellite-Enabled Internet-of-Things

I. INTRODUCTION

• Remote IoT deployments are costly to serve with terrestrial cellular infrastructure, while LEO networks are presented as a route to global coverage with lower propagation delay and path loss than GEO.The introduction also notes their reduced reliance on terrestrial infrastructure and lower transmission-power requirements relative to GEO.Source: §I · p. 1

A. Related Works

• Conventional satellite RA assumes sufficient access resources and static TSL, infeasible for massive IoT connectivity and mobile LEO; GF-RA shares resources without grants, reducing signaling overhead and improving short-packet efficiency.The cited space-diversity GF-RA work [18] bypassed joint UAD and CE by roughly modeling the TSL as an erasure-collision channel. Other approaches formulate joint UAD and CE as compressed sensing – or use variational Bayesian inference –.Source: A. Related Works · p. 2

B. Motivations

• Existing GF-RA UAD and CE algorithms are designed for Rayleigh channels, whereas terrestrial-satellite links require both line-of-sight and scattering components; the paper identifies little work tailored to LEO GF-RA.The authors connect this gap to the rapidly changing links and possible access-resource shortages in LEO IoT.Source: B. Motivations · p. 2

C. Contributions

• The paper proposes terrestrial-satellite GF-RA and BR-MP-EM, combining inner Bernoulli-Rician updates for UAD and CE with outer EM updates of channel-impairment hyper-parameters.Active devices share an access resource and transmit directly; the EM update is described as independent of the hyper-parameter distributions and robust to unknown impairments.Source: C. Contributions · pp. 2–3

D. Potential Applications

• The proposed scheme is presented as potentially applicable to remotely deployed IoT, including smart grids, emergency management, windmills, and land or ocean monitoring.The text particularly motivates these cases when LEO satellite assistance is essential.Source: D. Potential Applications · p. 3

E. Section Organization

• The paper organizes the system model and joint UAD-CE formulation in Section II, presents BR-MP-EM in Section III, and evaluates performance and robustness in Section IV.Section V concludes the paper.Source: E. Section Organization · p. 3

A. System Model

• Each device is modeled as a physical access point, and K potential devices are randomly activated with probability pa to send packets and unique pilots on a shared access resource.The model assumes stationary devices, receiver synchronization with aligned packet timing, and GF-RA at a fixed satellite orbital position in each round.Source: A. System Model · p. 3

B. Problem Formulation

• The terrestrial-satellite link includes line-of-sight and scattering components plus propagation-fading and phase-shift impairments, while the receiver must detect αk and estimate hk for active devices.Non-orthogonal Gaussian pilots of length L<K are used to reduce access delay and improve transmission efficiency for short packets.Source: A. System Model · p. 3, B. Problem Formulation · p. 4

III. BR-MP-EM ALGORITHM FOR JOINT UAD AND CE

• The factor graph represents the joint UAD and CE problem, with inner message-passing iterations followed by outer EM updates of propagation-fading and phase-shift hyper-parameters.The outer estimates feed the next round of inner iterations.Source: §III · pp. 4–5

A. Bernoulli-Rician Message Passing

• The method represents channel estimates with Rician-message means and variances and device activity with Bernoulli probabilities, assuming fixed impairment hyper-parameters during inner iterations.The Rician channel includes a deterministic line-of-sight component and a complex Gaussian scattering component.Source: A. Bernoulli-Rician Message Passing · p. 5

1) Message Update at Sum Nodes:

• At sum nodes, incoming Bernoulli and Rician messages are used to update outgoing channel and activity messages; Bernoulli messages use log-likelihood ratios to avoid probability-product overflow.The passage describes separate sum-node updates for Rician channel estimates and Bernoulli activity probabilities.Source: 1) Message Update at Sum Nodes · pp. 5–6

2) Message Update at Variable Nodes:

• Variable nodes combine incoming Bernoulli and Rician messages to produce updated outgoing messages for the next inner iteration.The update follows the message-combination rule described in the passage.Source: 2) Message Update at Variable Nodes · p. 6
• The Rician variable-node update uses the prior channel mean and variance together with messages from other sum nodes to update the channel estimate.The prior is specified after the τ-th outer iteration.Source: 2) Message Update at Variable Nodes · p. 6
• The Bernoulli variable-node update incorporates incoming activity messages and the prior activity log-likelihood ratio to determine the next activity probability.The updated probability is expressed through the logistic relationship with the Bernoulli log-likelihood ratio.Source: 2) Message Update at Variable Nodes · p. 6

• After Nin inner iterations, each variable node combines incoming messages to produce its final channel-estimation output and user-activity decision.Source: 3) CE Output and UAD Decision at… · p. 6
• The channel estimate and its deviation are obtained by combining all incoming Rician messages about the device channel.Source: 3) CE Output and UAD Decision at… · p. 6
• An LLR greater than zero marks a device active, and its channel estimate is then retained; otherwise, it is marked inactive.Source: 3) CE Output and UAD Decision at… · p. 6
• The activity decision uses an LLR that includes an additional channel-estimation term to improve user-activity detection.Source: 3) CE Output and UAD Decision at… · p. 6
• The channel-estimation result is used to improve activity detection, with estimation error approximated as a complex Gaussian variable.Source: 3) CE Output and UAD Decision at… · p. 6

• Rician messages characterize each device channel's posterior complex Gaussian distribution, which is used in the outer EM update.Source: B. Expectation-Maximization Update of… · p. 7
• The EM step seeks hyper-parameters that maximize an expectation over the posterior channel distribution, given the current hyper-parameters.Source: B. Expectation-Maximization Update of… · p. 7
• The multi-user update extends the single-user EM equation by pooling channel estimates from active devices that share hyper-parameters.Source: B. Expectation-Maximization Update of… · p. 7

• Each outer iteration follows inner message updates, channel estimation and activity decisions, then EM updating; estimates enter EM only for active devices with relative variation below ηth.The threshold ηth is chosen empirically; ηth = 0.2 achieved a better trade-off between convergence speed and robustness against error propagation in the reported experiments.Source: C. Summary of BR-MP-EM Algorithm · p. 8
• The EM update treats random phase shift and propagation fading as hyper-parameters and does not rely on their specific distributions, needing only average measured propagation fading.Source: C. Summary of BR-MP-EM Algorithm · p. 8
• If channel impairments affect only the line-of-sight component, the algorithm requires only minor modifications, without loss of generality.Source: C. Summary of BR-MP-EM Algorithm · p. 8
• For devices with different impairments, the algorithm can perform separate EM updates for geographical groups sharing an impairment.The paper assumes stationary devices, allowing the satellite to acquire group membership.Source: C. Summary of BR-MP-EM Algorithm · p. 8

D. Computational Complexity

• Local computations at different sum nodes and variable nodes can run in parallel, yielding low computational complexity favorable for reducing satellite-receiver processing delay.Source: D. Computational Complexity · p. 8
• Without that approximation, each inner iteration costs about 35KL multiplications or divisions and 2KL exponential or logarithm operations; Bernoulli-Rician message passing dominates the cost.EM update operations are described as almost negligible.Source: D. Computational Complexity · p. 8
• With full-message approximation, each inner iteration costs 31KL multiplications and KL exponential operations, giving overall complexity O(KL Nit) for both operation types.Nit = NinNout is the total number of iterations.Source: D. Computational Complexity · p. 8

IV. SIMULATION RESULTS

• The simulations assume log-normal propagation fading and Gaussian phase shifts for convenience, then examine activity-detection and channel-estimation performance under different system configurations.The EM update does not rely on those specific distributions.Source: §IV · p. 9

A. Impacts of Signal-to-Noise Ratio

• Both UAD and CE accuracy improve linearly with SNR in logarithmic scale, and convergence takes fewer than 20 iterations under the Fig. 4 configurations.The algorithm is reported to work over a wide SNR range.Source: A. Impacts of Signal-to-Noise Ratio · p. 9, Figure 4 · p. 10

B. Impacts of Activation Probability

• When pa rises from 0.1 to 0.19, final UAD/CE performance does not degrade seriously; at pa=0.22 and 0.25, performance is undermined and more iterations are required.The passage suggests longer pilot sequences may potentially address this congestion.Source: B. Impacts of Activation Probability · p. 9, Figure 5 · p. 10

C. Impacts of Pilot Length

• When L is below the critical value of 225, joint UAD/CE performance deteriorates severely; above it, convergence improves, but further lengthening does not significantly improve accuracy.The authors note that accuracy is also limited by parameters such as SNR.Source: C. Impacts of Pilot Length · p. 9

D. Robustness Against Channel Impairments

• At σ_r=1, raising σ_δ from π/8 to π preserves converged UAD/CE accuracy; as σ_r rises from 1 to 7, impairment variance rises from 2.05 × 10−1 to 2.64 and Δhp from 7.5×10−3 to 2.58×10−2.The reported result also states that greater fading uncertainty gradually degrades UAD/CE accuracy.Source: D. Robustness Against Channel… · p. 9

E. Phase Transition for Sparse Recovery

• Below the phase-transition curve, successful recovery is guaranteed; sampling ratio grows almost linearly with sparsity, so longer pilots support more simultaneously active devices.Successful recovery is defined as average UAD error below 1/K.Source: E. Phase Transition for Sparse Recovery · pp. 9–10

V. CONCLUSIONS

• The conclusion describes BR-MP-EM as inner Bernoulli-Rician message passing for joint UAD and CE, followed by outer EM updates of channel-impairment hyper-parameters.The hyper-parameters concern propagation fading and phase shift.Source: §V · pp. 11–12

F. Performance Comparison

• With only Nit = 20 iterations, BR-MP-EM closely approaches the NMSE lower bound across a wide SNR range; OMP diverges from it as SNR increases, while LS and LMMSE fail on the joint problem.The lower bound is the GA-MMSE estimator, which assumes known device activity and channel hyper-parameters.Source: F. Performance Comparison · pp. 10–11, Figure 9 · p. 12
• Fig. 9 compares BR-MP-EM with LS, LMMSE, OMP, and GA-MMSE, whose NMSE serves as the lower bound.The OMP comparison assumes a known number of active devices; GA-MMSE assumes known activity and hyper-parameters.Source: F. Performance Comparison · pp. 10–11, Figure 9 · p. 12

V. CONCLUSIONS

• Simulations are reported to show joint UAD and CE accuracy and robustness to unknown channel impairments.The stated impairment-related quantities are propagation fading and phase shift.Source: §V · pp. 11–12

APPENDIX A DERIVATION OF EM UPDATE FOR HYPER-PARAMETERS

• The derivation obtains updated estimates of φδ and hr by solving an equation set after mathematical manipulation of the preceding equations.The appendix differentiates with respect to hr and uses substitutions and expectations to form the update equations.Source: Appendix A · pp. 12–13
• The appendix rules out one of two mathematical solutions by interpreting M as a weighted mean of device messages, with the line-of-sight channel serving as the weight.Under the stated ideal estimate assumption, the expected angle of M equals φδ.Source: Appendix A · p. 13

APPENDIX B MODIFICATIONS WHEN CHANNEL IMPAIRMENTS ONLY

• For impairments confined to the line-of-sight component, the scattering component in hk has constant variance.Source: AFFECT LOS COMPONENT · p. 13
• The outer EM update is also modified for the line-of-sight-only impairment model.The appendix changes the prior function and substitutes it into the EM equations to obtain a modified solution.Source: AFFECT LOS COMPONENT · p. 13
• The inner Bernoulli-Rician message-passing updates are modified to reflect that constant scattering variance.The passage identifies changes to vpri in equations (13), (17), and (19).Source: AFFECT LOS COMPONENT · p. 13