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Coordinated and Uncoordinated Channel Tracking for High-Rate IoT in Distributed Massive MIMO With Low-Resolution ADCs

Hediyeh Soltanizadeh, Ardavan Rahimian

arXiv:2610.37508v1eess.SPcs.SYeess.SY

TL;DR

Pilot reuse, mobility, and low-resolution ADCs complicate CSI tracking in distributed mMIMO, especially when pilot activity is uncertain and decoupled from data activity. The paper develops coordinated and uncoordinated quantization-aware trackers and reports simulations that corroborate the analyses and runtime gains.

  • Problem

    In distributed mMIMO, pilot reuse, mobility, low-resolution quantization, and independent pilot and data activity complicate CSI acquisition and recursive tracking.

    Source: §I · p. 1

  • Method

    The paper develops Q-JCKF for known pilot activity and Q-DPDAF for unknown activity, incorporating AP-dependent quantization into recursive channel tracking.

    Source: §I · p. 2

  • Results

    Simulations corroborate the UatF analyses, cross-AP association bound, large-N pilot-reuse behavior, and complexity trends, and report runtime gains over legacy implementations.

    Source: §I · p. 2

  • Takeaways & Limitations

    The reported results quantify how distributed reception, ADC resolution, mobility, and pilot-access probability relate to spectral efficiency, tracking, and activity inference.

    Source: §I · p. 2

Abstract

from arXiv · show

This paper investigates dynamic channel tracking for high-rate Internet of things (IoT) in distributed massive multiple-input multiple-output (mMIMO) with low-resolution analog-to-digital converters (ADCs), where pilot and data activities are decoupled, pilots are reused, and mobile channels evolve across access slots. We hereby develop a quantization-aware joint coordinated Kalman filter (Q-JCKF) for known pilot activity and a quantization-aware distributed probabilistic data association filter (Q-DPDAF) for uncoordinated access. For uplink analysis, we derive a closed-form statistical use-and-then-forget (UatF) expression for Q-JCKF and mixture-aware, pilot-conditioned, and long-term statistical UatF formulations for Q-DPDAF, together with the large-N pilot-reuse ceiling and a cross-access point (AP) association term with an O(epsilon) posterior-concentration bound. The proposed framework recovers JC-KF/PDAF in the ideal-ADC co-located limit, and quantifies the conditional loss of Kalman measurement information caused by finite-resolution quantization. We further characterize computational, memory, and fronthaul scaling: Kronecker-structured Q-JCKF reduces covariance-processing complexity, while groupwise Q-DPDAF limits hypothesis enumeration from 2^K to 2^{K_r} and enables parallel AP-local processing. Simulations corroborate the analytical and complexity outcomes, quantify ADC-resolution and pilot-access effects, and demonstrate improved lower-tail spectral efficiency, robust mobility tracking, near-ideal 4-bit performance, reliable Q-DPDAF activity inference, and substantial runtime reductions over legacy implementations and processing frameworks.

I. INTRODUCTION

Distributed mMIMO can improve lower-tail spectral efficiency, but pilot reuse, mobility, low-resolution quantization, and unknown pilot activity complicate CSI tracking. The paper develops coordinated and uncoordinated quantization-aware trackers and analyzes their performance and implementation scaling.

I. INTRODUCTION

  • Distributed APs provide macro-diversity and improve lower-tail spectral efficiency, but AP-dependent channel statistics complicate CSI acquisition and increase cooperative processing and fronthaul demands.Low-resolution ADCs reduce hardware and power costs but introduce signal-dependent quantization distortion that varies with AP resolution and received power.Source: §I · p. 1
  • Prior methods address activity detection, channel estimation, or quantization, but do not maintain recursive temporally correlated CSI while modeling activity-dependent quantization in distributed reception.Independent pilot and data activity makes tracking relevant even in slots when data-active users do not transmit pilots.Source: §I · pp. 1–2
  • Q-JCKF handles known pilot activity, while Q-DPDAF jointly tracks channels and uncertain activity in distributed mMIMO with pilot reuse, mobility, and low-resolution ADCs.The coordinated tracker preserves pilot-induced inter-user error cross-covariances; the uncoordinated tracker fuses AP-local conditional updates using activity probabilities.Source: §I · p. 2
  • The framework derives UatF analyses, characterizes quantization-related information loss, and reduces computation through Kronecker-structured covariance processing and groupwise hypothesis evaluation.Groupwise Q-DPDAF reduces enumeration from 2^K to 2^{K_r}, while simulations validate analytical and complexity trends and report runtime gains.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The system uses TDD access slots with pilot and data phases, and channel estimates are maintained across slots because channel states evolve while pilot and data activities are independent.The model assumes known large-scale fading at each tracking update and a first-order Gauss–Markov channel evolution.Source: §II · pp. 2–3

A. Pilot Observation Before and After Quantization

The pilot observation model accounts for quantization before despreading, so each AP’s effective distortion depends on aggregate received pilot power. This model supplies the observations used by the channel trackers.

A. Pilot Observation Before and After Quantization

  • The AQNM represents quantized pilot observations with a gain-scaled signal and Gaussian distortion modeled as uncorrelated with the ADC input, white across pilot samples, and independent across APs.The model is a Gaussian second-order surrogate for the nonlinear quantizer.Source: A. Pilot Observation Before and After… · p. 3
  • Despreading preserves the distortion covariance, and received power from other pilot groups still contributes to quantization noise despite removal of their signals.For unknown activity, the outside-group contribution is approximated by its prior mean.Source: A. Pilot Observation Before and After… · p. 3
  • Equations (6) and (7) define the quantization-aware state-space model used for tracking at all APs, with known pilot activity in coordinated access and joint activity-and-channel inference in uncoordinated access.The covariance averages over small-scale fading and receiver noise conditioned on large-scale coefficients and pilot activity.Source: A. Pilot Observation Before and After… · p. 3

III. QUANTIZATION-AWARE CHANNEL TRACKING

The coordinated Q-JCKF uses known pilot activity to perform conditional MMSE tracking under the linear-Gaussian AQNM model. Its Kronecker structure reduces covariance recursion to the pilot-group user domain while retaining pilot-induced cross-covariances.

A. Coordinated Q-JCKF

  • With known pilot activity, Q-JCKF uses the linear-Gaussian AQNM state-space model to produce the conditional MMSE estimate.This optimality is limited to the adopted surrogate, not the underlying nonlinear quantizer.Source: A. Coordinated Q-JCKF · p. 4
  • Although the channel state has dimension N K_r, the Q-JCKF covariance recursion operates in the K_r-dimensional user domain.The exact Kronecker reduction lowers covariance-processing complexity.Source: §III · p. 3, A. Coordinated Q-JCKF · p. 4
  • Pilot reuse can generate off-diagonal estimation-error covariances between users sharing a pilot, and later predictions propagate those terms.These cross-covariances determine coherent same-pilot interference in the Q-JCKF UatF analysis.Source: A. Coordinated Q-JCKF · p. 4

B. Uncoordinated Q-DPDAF

Q-DPDAF handles unknown pilot activity by evaluating hypotheses within each pilot-sharing group, fusing AP likelihoods, and retaining activity uncertainty through posterior-weighted moment matching. Its approximations limit complexity but preclude a global MMSE claim for the original nonlinear quantized system.

B. Uncoordinated Q-DPDAF

  • Q-DPDAF evaluates 2^{K_r} activity patterns within each pilot-sharing group instead of enumerating all 2^K network patterns.For unknown activity, it approximates outside-group pilot power by its prior mean while retaining candidate-dependent in-group power.Source: B. Uncoordinated Q-DPDAF · p. 4
  • APs compute hypothesis-conditioned Kalman likelihoods, send one log-likelihood per hypothesis to the CPU, and receive shared posterior weights without forwarding raw pilot observations or conditional covariances.Hard activity decisions are not used by the channel tracker.Source: B. Uncoordinated Q-DPDAF · p. 4
  • Posterior-weighted Gaussian moment matching retains both conditional estimation uncertainty and uncertainty across activity hypotheses.The between-hypothesis term can destroy the Kronecker covariance structure, so Q-DPDAF propagates a full AP-local covariance.Source: B. Uncoordinated Q-DPDAF · p. 5
  • Q-DPDAF uses AQNM, prior-mean outside-group power, factorized AP-local prediction, and Gaussian moment matching, so it does not claim global MMSE optimality for the original nonlinear quantized system.Cross-AP dependence from earlier mixture updates is not propagated, although current-slot association is retained for rate evaluation.Source: B. Uncoordinated Q-DPDAF · p. 5

C. Reduction to JC-KF/PDAF and Quantization Penalty

The trackers recover the earlier JCKF/PDAF framework in the ideal-ADC, co-located limit. Under the Gaussian AQNM surrogate, finite-resolution quantization reduces conditional Kalman measurement information, with limits on extending covariance ordering to final Q-DPDAF rates.

C. Reduction to JC-KF/PDAF and Quantization Penalty

IV. UPLINK SPECTRAL-EFFICIENCY ANALYSIS

The analysis derives UatF spectral-efficiency bounds for local MRC and coherent CPU combining under a Gaussian-AQNM rate model. For Q-JCKF, the statistical bound captures tracking uncertainty and coherent same-pilot interference tied to the tracker’s cross-covariances and activity history.

IV. UPLINK SPECTRAL-EFFICIENCY ANALYSIS

  • The rate analysis uses a Gaussian-AQNM second-order surrogate for quantization distortion, rather than an exact sample-wise nonlinear-quantizer model.Source: §IV · p. 5

A. Q-JCKF Statistical UatF Analysis

2. For G(k)

The large-N behavior depends on whether coherent same-pilot interference persists: when that term vanishes, SINR grows linearly with antenna count; when it remains nonzero, a finite ceiling applies.

2. For G(k)

  • When the coherent same-pilot interference term vanishes, SINR grows linearly with N.Source: §2 · p. 7
  • A finite SINR ceiling requires persistent coherent interference, and increasing N cannot remove that interference.Source: §2 · p. 7
  • A nonzero local cross-covariance alone is insufficient for a ceiling because weighted AP contributions may cancel during coherent CPU combining.Source: §2 · p. 7

B. Q-DPDAF Mixture-Aware UatF Analysis

Q-DPDAF evaluates current-slot rates using a Gaussian-mixture posterior that retains pilot-activity uncertainty. Its UatF formulations preserve shared-hypothesis cross-AP association, while statistical averaging generally requires numerical evaluation.

B. Q-DPDAF Mixture-Aware UatF Analysis

C. Cross-AP Association Analysis

The shared activity hypothesis induces current-slot dependence across APs, which contributes an association correction to the mixture-aware UatF second moment. Its effect depends on posterior ambiguity and hypothesis-dependent mean separation, so the AP-local approximation has no universal rate ordering.

C. Cross-AP Association Analysis

  • Marginalizing the shared activity hypothesis induces cross-AP dependence and adds an association term to the mixture-aware UatF second moment.The AP states are conditionally independent under a fixed hypothesis in the adopted factorized model; the dependence arises when that hypothesis is marginalized.Source: C. Cross-AP Association Analysis · p. 8
  • The association correction can be positive or negative, so independent AP-local moment matching gives neither a universal upper nor lower bound on the mixture-aware UatF rate.An approximation preserving the complete posterior mean and covariance yields the same fixed-combiner UatF first and second moments.Source: C. Cross-AP Association Analysis · p. 8
  • The association magnitude is controlled jointly by posterior ambiguity and hypothesis-dependent mean separation; under bounded quantities, the omitted contribution is O(ε).A diffuse posterior need not produce large association when the conditional means remain close.Source: C. Cross-AP Association Analysis · pp. 8–9
  • For bounded conditional-mean diameters, posterior concentration makes the mixture-aware and AP-local second moments coincide, and the rate gap vanishes when this holds for all active users.This O(ε) result concerns only current-slot cross-AP dependence, not total tracking, AQNM, or outside-group mean-field errors; concentration alone does not make Q-DPDAF equivalent to Q-JCKF.Source: C. Cross-AP Association Analysis · p. 9

D. Long-Term Statistical UatF Estimation

The long-term statistical UatF estimate pools effective-channel moments and effective receiver-noise power across retained post-burn-in slots and independent replicas. A cross-replica estimator avoids self-product bias when estimating the squared coherent desired gain.

D. Long-Term Statistical UatF Estimation

  • Long-term UatF moments are pooled over post-burn-in slots and independent replicas sharing the layout and slow-time fading trajectory, then used to form the SINR and rate.The outer Monte Carlo average retains realized pilot-activity sequences, while the Q-DPDAF recursion still uses the outside-group mean-field variance.Source: D. Long-Term Statistical UatF Estimation · p. 9
  • A cross-replica estimator of the squared coherent desired gain is unbiased before clipping, conditioned on the common layout and slow-time trajectory.Replica independence gives the stated expectation for the estimator.Source: D. Long-Term Statistical UatF Estimation · p. 9
  • Negative finite-sample estimates of the squared desired gain are clipped to zero, and a small positive floor is applied only to estimated disturbance power.The floor is used for numerical stability.Source: D. Long-Term Statistical UatF Estimation · p. 9

V. COMPLEXITY ANALYSIS

The complexity analysis contrasts Q-JCKF's Kronecker-reduced covariance processing with Q-DPDAF's hypothesis-conditioned full-covariance processing. It also describes parallel AP-local updates and distinguishes idealized parallel scaling from the reported single-process MATLAB runtime.

A. Q-JCKF

  • Q-JCKF reduces the N K_r-dimensional covariance recursion to the K_r-dimensional user domain, with O(K_r^2) covariance-update and O(N K_r) state-mean costs per AP and pilot group.Without the reduction, the dense covariance correction scales as O(N^3 K_r^2) per AP and pilot group.Source: A. Q-JCKF · p. 9

B. Q-DPDAF

  • Q-DPDAF evaluates 2^K_r in-group activity hypotheses and propagates a full N K_r × N K_r AP-local covariance after moment matching generally destroys the Kronecker structure.The dominant full-covariance correction for one hypothesis, AP, and pilot group scales as O(N^3 K_r^2).Source: B. Q-DPDAF · p. 9
  • Under the factorized AP-local model, Q-DPDAF hypothesis-conditioned AP updates are separable and can run in parallel, with CPU likelihood fusion on the critical path.The paper distinguishes this idealized parallel scaling from its single-process MATLAB runtime, which executes AP-local updates serially.Source: B. Q-DPDAF · p. 9

VI. NUMERICAL RESULTS

The numerical results validate the proposed UatF analyses and complexity trends, and show how antenna distribution, ADC resolution, mobility, and pilot access affect performance. The conclusion highlights scalability through user-domain covariance processing and pilot-group-wise activity inference.

VI. NUMERICAL RESULTS

  • With pilot reuse, Q-JCKF SINR reaches a finite large-N ceiling; without reuse, it grows approximately linearly with N, while payload prelog falls from 0.95 to 0.70.The closed-form SINR and SE expressions agree with conditional Monte Carlo to maximum relative discrepancies of approximately 1.25% and 0.604%, respectively.Source: Figure 2 · p. 10, §VI · p. 10
  • Direct posterior Monte Carlo matches the mixture-aware Q-DPDAF rate, while the AP-local approximation has 3.0×10−6 median relative error and remains below 5% rate error in all tested samples.The association decomposition agrees with direct evaluation to within 1.3×10−15, and the maximum actual-to-bound ratio remains below unity across 2160 posterior samples.Source: §VI · p. 10
  • At 2 bits, distributed reception yields 0.0171 bit/s/Hz 5th-percentile SE versus an essentially zero co-located lower tail; distributed 4-bit and ideal-ADC results are not distinguishable within bootstrap uncertainty.The comparison uses equal total antenna counts; distribution mainly benefits the lower tail through AP–user proximity and macro-diversity.Source: Figure 3 · p. 11, §VI · p. 11
  • At 30 m/s, distributed Q-JCKF/Q-DPDAF achieve NMSEs of 0.2525/0.2558 versus 0.3053/0.3129 for JC-KF/PDAF, but the ideal-ADC co-located architecture is more accurate at low mobility.The crossover is specific to the evaluated configurations; recursive schemes remain well below the one-shot estimator in the instantaneous-mobility comparison.Source: Figure 4 · p. 11, §VI · p. 11
  • Across tested pilot-access probabilities, distributed trackers have higher mean UatF SE point estimates, while activity-detection rankings reverse: PDAF leads at low λ and Q-DPDAF at λ = 0.7 and 0.9.The activity accuracies are prior-aware, so comparisons across λ are not prior-independent detector metrics.Source: Figure 5 · p. 11, §VI · p. 12
  • At Kr = 6, Q-JCKF takes 0.541 ms versus 10.476 ms for JC-KF, while Q-DPDAF takes 178.821 ms versus 1097.120 ms for PDAF in the reported serial implementation.Q-JCKF's structured and dense implementations agree to relative mean and covariance discrepancies on the order of 10−16; the measured speed ratios are implementation-dependent.Source: Figure 6 · p. 12, §VI · p. 12
  • Simulations corroborate the UatF analyses, association bound, large-N pilot-reuse behavior, and complexity trends, while showing lower-tail rate benefits and robust tracking under mobility and intermittent pilots.Together, the results indicate that distributed low-resolution reception can preserve favorable rate and tracking behavior while shifting processing burden toward the pilot-group dimension.Source: §VI · p. 12

VII. CONCLUSION

  • The conclusion identifies exact Kronecker reduction and groupwise hypothesis enumeration as scalability mechanisms, with Q-DPDAF limiting enumeration from 2^K to 2^Kr and supporting parallel AP-local processing.The paper also recovers the ideal-ADC co-located JC-KF/PDAF model as a limiting case and quantifies finite-resolution loss of Kalman measurement information.Source: §VII · pp. 12–13
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