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Massive Access in Cell-Free Massive MIMO-Based Internet of Things: Cloud Computing and Edge Computing Paradigms

Malong Ke, Zhen Gao, Yongpeng Wu, Xiqi Gao, Kat-Kit Wong

arXiv:2007.09617v2cs.ITcs.NIeess.SPmath.IT

TL;DR

Grant-free massive access in cell-free MIMO IoT requires reliable active-user detection and channel estimation despite limited radio resources. The paper proposes a frame design and quantization-aware SS-GAMP and SIC processing across cloud or edge AP cooperation. Its simulations report that edge computing approaches cloud-computing performance, with almost the same performance at Nco = 4 cooperating APs.

Abstract

from arXiv · show

This paper studies massive access in cell-free massive multi-input multi-output (MIMO) based Internet of Things and solves the challenging active user detection (AUD) and channel estimation (CE) problems. For the uplink transmission, we propose an advanced frame structure design to reduce the access latency. Moreover, by considering the cooperation of all access points (APs), we investigate two processing paradigms at the receiver for massive access: cloud computing and edge computing. For cloud computing, all APs are connected to a centralized processing unit (CPU), and the signals received at all APs are centrally processed at the CPU. While for edge computing, the central processing is offloaded to part of APs equipped with distributed processing units, so that the AUD and CE can be performed in a distributed processing strategy. Furthermore, by leveraging the structured sparsity of the channel matrix, we develop a structured sparsity-based generalized approximated message passing (SS-GAMP) algorithm for reliable joint AUD and CE, where the quantization accuracy of the processed signals is taken into account. Based on the SS-GAMP algorithm, a successive interference cancellation-based AUD and CE scheme is further developed under two paradigms for reduced access latency. Simulation results validate the superiority of the proposed approach over the state-of-the-art baseline schemes. Besides, the results reveal that the edge computing can achieve the similar massive access performance as the cloud computing, and the edge computing is capable of alleviating the burden on CPU, having a faster access response, and supporting more flexible AP cooperation.

I. INTRODUCTION

Massive access in cell-free MIMO IoT must address active-user detection and channel estimation amid limited radio resources and wide-area, power-limited deployments. The paper proposes grant-free processing across cooperating APs, including cloud and edge architectures, structured-sparsity algorithms, and a frame design.

A. Related Work

  • Prior work addresses AUD and data detection – or joint AUD and CE, –, while some Bayesian schemes assume known noise and channel-prior parameters,.Source: A. Related Work · p. 2

B. Main Contributions

  • The paper studies massive access across a wide area where multiple APs cooperate, contrasting with single-cell and non-cooperative multi-cell architectures.The authors describe cell-free MIMO as better at combating inter-cell interference and offering flexible AP cooperation.Source: B. Main Contributions · p. 2
  • The proposed OFDM frame structure uses an advanced resource-division strategy and reduces access latency relative to the conventional frame structure in.Source: B. Main Contributions · pp. 2–3
  • Edge computing can approach cloud-computing AUD and CE performance while offloading CPU work and reducing cooperation cost, but requires DPUs at some APs.Source: B. Main Contributions · p. 3
  • SS-GAMP uses channel-matrix structured sparsity to jointly perform AUD and CE while accounting for quantized processed signals.A weighted message-refining strategy further leverages channel-matrix sparsity.Source: B. Main Contributions · p. 3
  • The SIC-based algorithm alternates spatial-domain AUD, angular-domain CE, and identified-UE cancellation to reduce access latency relative to solutions without SIC.The approach incurs higher computational complexity from repeated SS-GAMP calls and cancellation matrix multiplication.Source: B. Main Contributions · p. 3

A. Proposed Cell-Free Massive MIMO-Based IoT

  • The system model assumes co-located massive-antenna APs and contrasts centralized CPU processing with selected DPU-APs that process signals from adjacent APs.Edge processing can ease CPU and backhaul burdens but requires additional DPUs.Source: A. Proposed Cell-Free Massive… · pp. 3–4

B. Massive Access in Cell-Free Massive MIMO Systems

  • In the grant-free procedure, active UEs send pilots and payload data, APs forward collected signals for joint processing, and resulting activity and channel estimates support data detection.Source: B. Massive Access in Cell-Free Massive… · p. 4

1) The Proposed Frame Structure Design:

The proposed frame separates pilot and payload transmission, using shorter OFDM symbols in the pilot phase to reduce access latency. The section also models received uplink signals and describes spatial-domain channel sparsity associated with sparse UE activity.

1) The Proposed Frame Structure Design:

  • Approximately 94% lower access latency is reported for the proposed frame than for the traditional frame when P = N_CP = 64 and N = 2048.The pilot phase uses G symbols of duration (N_CP + P)/B_s, versus (N_CP + N)/B_s for the traditional frame, with P ≪ N.Source: 1) The Proposed Frame Structure Design · p. 4
  • The frame assigns the first G time slots to access pilots for AUD and CE, and reserves the remaining T − G slots for payload data.Pilot-phase OFDM uses DFT length P; the data phase uses length N ≫ P.Source: 1) The Proposed Frame Structure Design · p. 4

2) Received Signal Model at APs:

  • At each AP, the received pilot-subcarrier signal combines active UEs’ uplink pilots and channels with additive white Gaussian noise.The channel includes large-scale fading from path loss and small-scale fading.Source: 2) Received Signal Model at APs · pp. 4–5

1) Spatial-Domain Structured Sparsity:

  • Only a small subset of UEs is active, so their channel matrix has sparse rows and shared support across AP antennas and pilot subcarriers.The channel model includes large-scale fading and small-scale fading; path loss can make some active UE links to distant APs approximately zero.Source: 1) Spatial-Domain Structured Sparsity · p. 5

2) Angular-Domain Structured Sparsity:

The virtual angular-domain channel is sparse and clustered because the one-ring model yields limited angular spread. Its support is shared across subchannels, and the paper uses angular-domain sparsity for channel estimation.

2) Angular-Domain Structured Sparsity:

  • The one-ring model gives limited angular spread when the UE is far from the AP relative to its scattering radius, making angular-channel sparsity level proportional to that spread and far below M_c.The AP-side array transform is unitary and depends on array geometry; for a ULA with half-wavelength antenna spacing, it becomes the DFT matrix.Source: 2) Angular-Domain Structured Sparsity · pp. 5–6
  • Angular-domain channel sparsity is clustered, and subchannels share a common sparsity pattern when their scattering environment remains unchanged across the bandwidth.The common support is stated across pilot subcarriers.Source: 2) Angular-Domain Structured Sparsity · p. 6
  • This angular-domain sparsity is stated to hold even below 6 GHz, while the paper considers co-located rather than distributed massive MIMO.The passage distinguishes this setting from distributed massive MIMO, where angular-domain sparsity does not exist.Source: 2) Angular-Domain Structured Sparsity · p. 6
  • The paper uses approximate common spatial sparsity to improve AUD and angular-domain enhanced sparsity to improve CE for identified UEs.AUD uses the spatial-domain channel model; CE uses the angular-domain channel model.Source: 2) Angular-Domain Structured Sparsity · p. 6

III. CLOUD COMPUTING-BASED AND EDGE COMPUTING-BASED MASSIVE ACCESS

The receiver jointly acquires active-user identities and channel information from grant-free pilot transmissions. In the cloud paradigm, APs quantize their received signals for centralized CPU processing, where AUD and CE exploit channel sparsity.

III. CLOUD COMPUTING-BASED AND EDGE COMPUTING-BASED MASSIVE ACCESS

  • The receiver estimates the active-user indicators and corresponding channel coefficients from pilot observations collected across successive time slots.The grant-free setup assumes frame length is far shorter than channel coherence time and UE activity remains unchanged during that time.Source: §III · p. 6

A. Cloud Computing-Based Massive Access

  • In cloud computing, APs send quantized received signals over backhaul links to a CPU, which centrally processes them for AUD and CE.The quantization accounts for limited wireless-backhaul capacity.Source: A. Cloud Computing-Based Massive Access · p. 6
  • Quantized measurements make the cloud AUD problem a generalized linear-model compressed-sensing problem, with spatial-domain structured sparsity used to exploit sparse UE activity.The quantization error is included in the received-signal model.Source: A. Cloud Computing-Based Massive Access · pp. 6–7
  • After AUD, cloud CE is formulated in the angular domain as a compressed-sensing problem, with angular structured sparsity refining channel estimates for identified UEs.The effective noise includes AWGN, quantization error, and AUD estimation error.Source: A. Cloud Computing-Based Massive Access · p. 7

B. Edge Computing-Based Massive Access

Edge computing offloads central processing to selected APs equipped with distributed processing units. Each such unit cooperates with nearby APs to process received signals for AUD and CE.

B. Edge Computing-Based Massive Access

IV. PROPOSED ACTIVE USER DETECTION AND CHANNEL ESTIMATION ALGORITHM

The section develops SS-GAMP for quantized compressed-sensing formulations of grant-free active-user detection and channel estimation, then proposes a successive-interference-cancellation scheme. SS-GAMP alternates nonlinear and linear-estimation modules, using quantized observations to estimate channels.

IV. PROPOSED ACTIVE USER DETECTION AND CHANNEL ESTIMATION ALGORITHM

  • The section proposes a successive-interference-cancellation-based scheme for active-user detection and channel estimation, building on SS-GAMP.The algorithm discussion uses cloud computing as its example and says it can be extended to edge computing.Source: §IV · p. 7

A. SS-GAMP Algorithm

  • SS-GAMP applies a unified Bayesian inference framework to quantized compressed-sensing measurements and uses message-passing heuristics for recovery.The paper characterizes it as more performant than greedy methods and lower-complexity than conventional message-passing algorithms [33].Source: A. SS-GAMP Algorithm · p. 7

1) Nonlinear Module:

  • The nonlinear module uses quantized received signals and noise variance to estimate the linear received signal, then sends equivalent measurements and noise variance to the SLM module.These extrinsic quantities represent the equivalent measurement of SH + N and its noise variance.Source: A. SS-GAMP Algorithm · p. 7, 1) Nonlinear Module · p. 8

A. SS-GAMP Algorithm

  • The SLM module applies AMP to estimate the channel matrix and returns extrinsic messages that the nonlinear module uses as a priori information.The two modules execute alternately in a turbo manner until convergence.Source: A. SS-GAMP Algorithm · pp. 7–8

1) Nonlinear Module:

  • The nonlinear module processes real and imaginary parts separately and handles signals from different APs separately when their quantization codebooks differ.The posterior mean and variance are derived for the real part, with the imaginary part computed analogously.Source: 1) Nonlinear Module · p. 8

2) SLM Module:

The SLM module uses AMP to estimate channels after transforming the quantized compressed-sensing problem into a conventional linear-measurement problem. The broader SS-GAMP procedure learns unknown hyperparameters and refines sparsity estimates using channel structure across subcarriers, APs, or angular-domain neighborhoods.

2) SLM Module:

  • The SLM module applies a conventional AMP algorithm to the transformed linear-measurement problem to estimate the channel matrix.In the large-system limit, AMP decouples matrix estimation into scalar estimation problems.Source: 2) SLM Module · p. 8
  • Because the sparsity ratio and effective noise variance may be unknown in practice, the algorithm uses expectation maximization to learn these hyperparameters.The number of active UEs varies, and the effective noise variance is hard to compute for angular-domain channel estimation when AUD error is unknown.Source: 2) SLM Module · p. 9
  • SS-GAMP extends message updates across multiple subcarriers and jointly refines sparsity ratios using spatial- or angular-domain channel structure.It uses damping parameter ρ = 0.3 to prevent divergence; except for the structured sparsity refinement, variables are updated independently.Source: 2) SLM Module · p. 9
  • For spatial-domain detection, nearby APs receive greater weight than remote APs when refining a UE’s sparsity ratio.The weighting reflects that activity observed at adjacent APs can be more reliable than activity observed at remote APs.Source: 2) SLM Module · p. 10
  • For angular-domain channel estimation, the method applies the SLM module directly, treats quantization error as noise, and uses clustered sparsity because the angular transform disrupts shared antenna sparsity.The passage identifies mismatch between transformed signals and the quantization codebook as making the nonlinear module’s estimate unreliable.Source: 2) SLM Module · p. 10
  • SS-GAMP’s superiority over conventional SLM compressed-sensing algorithms is mainly in low-resolution quantization cases.With sufficiently many quantization bits, the quantization error can be negligible, so the SLM module can be applied directly with negligible performance loss and reduced computational complexity.Source: 2) SLM Module · p. 10

B. SIC-Based AUD and CE Algorithm

The SIC-based scheme alternates active-user detection, channel estimation, and cancellation to refine activity and channel estimates. It improves reliability and significantly reduces access latency, with higher computational complexity.

B. SIC-Based AUD and CE Algorithm

  • Each iteration detects active UEs in the spatial domain, estimates channels in the angular domain, then cancels selected UE signals and returns residuals to detection.These three modules run alternately until convergence.Source: B. SIC-Based AUD and CE Algorithm · p. 10
  • The BI-AUE detector forms rough and more reliable activity estimates using thresholds pdet = 0.1 and prel = 0.9, respectively.The reliable set is a subset of the rough estimate.Source: B. SIC-Based AUD and CE Algorithm · p. 11
  • Module B estimates angular-domain channels for the rough activity set, with effective noise that includes AWGN, quantization error, and AUD-estimation error.A low missed-detection probability is desirable to reduce this effective noise.Source: B. SIC-Based AUD and CE Algorithm · p. 11
  • Module C cancels signals from only a subset of reliably detected UEs, with λaus < 1 used to support robustness.The selected subset Γ is drawn from the reliable activity estimate.Source: B. SIC-Based AUD and CE Algorithm · p. 11
  • SIC iterations refine active-user and CSI estimates, improving AUD and CE reliability and significantly reducing access latency at the cost of higher computational complexity.The SS-GAMP algorithm is called twice per iteration, and cancellation adds matrix multiplication.Source: B. SIC-Based AUD and CE Algorithm · p. 12

V. DIFFERENCES BETWEEN CLOUD COMPUTING AND EDGE COMPUTING PARADIGMS

The comparison identifies edge computing's operational benefits and its deployment-cost trade-off relative to cloud computing.

V. DIFFERENCES BETWEEN CLOUD COMPUTING AND EDGE COMPUTING PARADIGMS

  • Edge computing alleviates backhaul and CPU burden, responds faster, and supports more flexible AP cooperation, while increasing large-scale AP deployment cost.Source: §V · p. 12

A. Algorithm Implementation

Cloud computing centrally processes signals from all APs, whereas edge computing distributes AUD and CE across local processing units.

A. Algorithm Implementation

  • Cloud computing processes signals from all APs in parallel and centrally refines the sparsity ratio, although distant AP signals may contribute negligibly for a given UE.The paper notes that central refinement using all AP signals may therefore be inefficient.Source: A. Algorithm Implementation · p. 12
  • Edge computing groups APs at distributed processing units, each detecting part of the UEs using signals from a nearby unit and cooperating APs.The approach allows different numbers of cooperative APs and reduces backhaul transmission burden.Source: A. Algorithm Implementation · p. 12

B. Computational Complexity

The complexity comparison attributes a lower processing burden to edge computing's partitioned workload.

B. Computational Complexity

  • Ccloud > Cedge because each DPU-AP detects fewer UEs and uses fewer cooperating APs, allowing edge processing to alleviate the CPU burden.Source: B. Computational Complexity · p. 12

C. Access Latency

Edge computing can provide faster access response than cloud computing, while requiring DPU-equipped APs and additional inter-AP links. The simulations evaluate AUD and channel-estimation performance in a cell-free massive-access setting.

C. Access Latency

  • Edge computing can have a faster access response than cloud computing because it reduces propagation delay and avoids cloud network-management delays.The paper says computation latencies can be similar: CPU capacity is larger, but CPU sharing and processing complexity offset that advantage.Source: C. Access Latency · p. 12

D. Cost of AP Deployment

VI. SIMULATION RESULTS

  • The simulations use 2,800 uniformly distributed UEs and 7 geographically distributed APs, with AUD pilots drawn from eP of P subcarriers.Performance is evaluated using AUD detection error probability and channel-estimation NMSE.Source: §VI · p. 13
  • The benchmarks include non-cooperative multi-cell processing, spatial-domain SS-GAMP joint AUD and CE, and SS-GAMP using SLM on quantized signals.Source: §VI · p. 13

A. Superiority of Cell-Free Massive MIMO

The simulations compare cell-free massive access schemes and cloud and edge processing, including performance under limited backhaul capacity. They report advantages over selected baselines, near-cloud edge performance with cooperation, and improved performance when quantization is accounted for.

A. Superiority of Cell-Free Massive MIMO

  • Cell-free cloud processing outperforms non-cooperative multi-cell processing in AUD; SIC-based detection beats spatial-domain joint AUD and CE for G ≥ 20, but not at very low pilot overhead.The paper attributes the cell-free advantage to avoiding inter-cell interference through AP cooperation, and the low-overhead reversal to inaccurate AUS and CSI estimates causing SIC error propagation.Source: A. Superiority of Cell-Free Massive MIMO · p. 13
  • The proposed schemes improve channel-estimation performance, and SIC-based massive access improves AUD and CE as AP antenna counts increase.More antennas strengthen spatial-domain structured sparsity for AUD and angular-domain sparsity for CE; the paper notes degradation when APs have relatively few antennas, such as Mc = 16.Source: A. Superiority of Cell-Free Massive MIMO · p. 14, Figure 8 · p. 14, Figure 10 · p. 14
  • Increasing eP improves the proposed cloud scheme’s AUD and CE performance by enhancing spatial-domain structured sparsity.Source: A. Superiority of Cell-Free Massive MIMO · p. 14, Figure 9 · p. 14, Figure 11 · p. 14

B. Comparison of Cloud Computing and Edge Computing Paradigms

C. Massive Access Under Limited Backhaul Capacity

  • With Q = 3, 4, and 5 quantization bits, SS-GAMP outperforms the SLM baseline for both joint AUD and CE and SIC-based schemes.The paper attributes this advantage to accounting for quantization through SS-GAMP’s nonlinear module.Source: C. Massive Access Under Limited… · p. 15

VII. CONCLUSION

  • The paper develops quantization-aware SS-GAMP for structured-sparse channel recovery and builds a SIC-based AUD and CE scheme on it.Its conclusion reports that edge performance can approach cloud performance, with CPU and backhaul relief alongside potentially higher deployment cost.Source: §VII · p. 15
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