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A Random Access Protocol for Pilot Allocation in Crowded Massive MIMO Systems

Emil Björnson, Elisabeth de Carvalho, Jesper H. Sørensen, Erik G. Larsson, Petar Popovski

arXiv:1604.04248v2cs.ITcs.NImath.IT

TL;DR

Massive MIMO must share a limited pilot pool among many intermittently active UEs seeking network access. SUCRe uses channel properties to detect and resolve pilot collisions at the UEs, and simulations report high collision resolution and access success in crowded, overloaded scenarios.

Abstract

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The Massive MIMO (multiple-input multiple-output) technology has great potential to manage the rapid growth of wireless data traffic. Massive MIMO achieves tremendous spectral efficiency by spatial multiplexing of many tens of user equipments (UEs). These gains are only achieved in practice if many more UEs can connect efficiently to the network than today. As the number of UEs increases, while each UE intermittently accesses the network, the random access functionality becomes essential to share the limited number of pilots among the UEs. In this paper, we revisit the random access problem in the Massive MIMO context and develop a reengineered protocol, termed strongest-user collision resolution (SUCRe). An accessing UE asks for a dedicated pilot by sending an uncoordinated random access pilot, with a risk that other UEs send the same pilot. The favorable propagation of Massive MIMO channels is utilized to enable distributed collision detection at each UE, thereby determining the strength of the contenders' signals and deciding to repeat the pilot if the UE judges that its signal at the receiver is the strongest. The SUCRe protocol resolves the vast majority of all pilot collisions in crowded urban scenarios and continues to admit UEs efficiently in overloaded networks.

I. INTRODUCTION

Massive MIMO’s limited pilot pool must serve many intermittently active UEs, making scalable random access important in crowded deployments. SUCRe uses Massive MIMO channel properties to resolve pilot contention at the UEs and allocate dedicated pilots before payload transmission.

A. Random Access Functionality in LTE

  • LTE’s four-step PRACH can leave colliding UEs sharing the Step 3 resource, after which centralized contention resolution may require a new access attempt.The BS responds to detected preambles, and Step 4 resolves collisions.Source: A. Random Access Functionality in LTE · p. 2

B. Prior Work on Random Access in Massive MIMO

  • Crowded urban cells have far more active and inactive UEs than available pilots, so pilots must be allocated opportunistically to match intermittent traffic.The proposed protocol targets urban deployments with small initial timing variations and seeks distributed, scalable collision resolution.Source: §I · p. 1, B. Prior Work on Random Access in… · p. 2
  • Prior Massive MIMO random-access proposals include random-pool payload transmission, which avoids access delays but incurs pilot collisions and intra-cell pilot contamination.This paper instead assigns each UE a pilot before payload transmission.Source: B. Prior Work on Random Access in… · p. 2

II. PROPOSED RANDOM ACCESS PROTOCOL

  • Massive MIMO temporarily assigns mutually orthogonal pilots to active UEs, while separate random-access blocks let inactive UEs request admission to payload blocks.Adjacent cells use different random-access block locations to protect the procedure from the strongest forms of inter-cell interference.Source: §II · p. 3

A. Strongest-user collision resolution (SUCRe)—Overview

  • SUCRe lets UEs detect contention from downlink pilots and has only the UE with the strongest uplink signal gain repeat the random-access pilot.Step 4 assigns a payload pilot or starts further contention resolution if a collision remains.Source: A. Strongest-user collision resolution… · p. 3

B. Detailed Description of the SUCRe Protocol

The protocol models inactive UEs selecting random-access pilots and transmitting with a scenario-dependent access probability. The BS correlates the received signal with each pilot, while Massive MIMO channel properties support pilot detection and distributed collision resolution.

B. Detailed Description of the SUCRe Protocol

  • Each of K0 inactive UEs independently attempts access with probability Pa and selects one of τp orthogonal pilots uniformly, so multiple UEs may select the same pilot.The set St contains the UEs transmitting pilot t; the model treats each RA block independently, although retries correlate blocks in practice.Source: B. Detailed Description of the SUCRe… · p. 4
  • The channel assumptions include channel hardening and asymptotic favorable propagation, properties satisfied by several stochastic models and some deterministic line-of-sight channels.The analysis particularizes the protocol to uncorrelated Rayleigh fading for a more detailed performance characterization.Source: B. Detailed Description of the SUCRe… · p. 5

1) Random Pilot Sequence:

  • In Step 1, the BS receives pilot transmissions with noise and inter-cell interference, then correlates the received signal with a pilot to obtain its observation.Interference includes neighboring-cell data and random-access transmissions.Source: 1) Random Pilot Sequence · p. 5
  • The BS can determine whether a pilot is active, while SUCRe does not require it to know which pilots were used in Step 1.Massive MIMO channel hardening and favorable propagation make detecting an active pilot particularly easy.Source: 1) Random Pilot Sequence · p. 5

2) Precoded Random Access Response:

The base station sends precoded downlink pilots toward UEs that used each random-access pilot. Each UE uses its received pilot signal to estimate the aggregate signal and interference gain, which supports its later contention decision.

2) Precoded Random Access Response:

  • The base station precodes each downlink pilot toward the UEs that used the corresponding uplink pilot, using multicast maximum-ratio transmission.The response uses a predefined downlink transmit power, and pilot length is independent of the number of antennas.Source: 2) Precoded Random Access Response · pp. 5–6
  • A UE correlates its received signal with the normalized downlink pilot to obtain z_k, then discards its imaginary part to estimate α_t.The imaginary component contains only noise, interference, and estimation errors.Source: 2) Precoded Random Access Response · p. 6
  • Different downlink pilot assignments across nearby cells are used to avoid coherent pilot-contaminated interference.The assumption that inter-cell interference is unaffected by M is motivated by assigning downlink pilots differently in the closest interfering cells.Source: 2) Precoded Random Access Response · p. 6
  • As M grows, the estimator based on the real part of z_k is asymptotically error-free.The estimate takes the maximum of its computed value and the UE's known lower bound, ρ_kβ_kτ_p.Source: 2) Precoded Random Access Response · p. 6

3) Contention Resolution & Pilot Repetition:

SUCRe makes contention resolution distributed: each contender compares its own average signal gain with an estimate of the aggregate contender gain and decides whether to repeat the pilot. A collision is resolved only when exactly one UE appoints itself the winner.

3) Contention Resolution & Pilot Repetition:

  • A UE treats itself as strongest when its average signal gain exceeds the estimated aggregate contender gain by the decision rule's margin, then repeats; otherwise it withdraws.The estimate includes inter-cell interference, and the bias parameter can tune the trade-off between resolved collisions and false positives or negatives.Source: 3) Contention Resolution & Pilot… · pp. 6–7
  • The contention winner is the UE with the largest average signal gain, and a collision is resolved if and only if exactly one UE appoints itself winner.With exact knowledge of α_t, a UE is certain to be strongest when its gain exceeds α_t/2, regardless of contender count.Source: 3) Contention Resolution & Pilot… · p. 6
  • In practice, estimates, three or more contenders, and inter-cell interference can leave multiple UEs or none identifying themselves as winner.The latter is a false negative; multiple self-appointed winners constitute a false positive.Source: 3) Contention Resolution & Pilot… · p. 6
  • With two contenders, resolution occurs when exactly one repeats; both withdrawing is a false negative, while both repeating is a false positive.The resolution probability depends on channel realizations, inter-cell interference, noise, and possibly random UE locations.Source: 3) Contention Resolution & Pilot… · p. 7
  • Probabilistic bias terms could make a UE's winner decision probabilistic, but their design is left as an engineering problem because it depends on difficult-to-model propagation and UE distributions.The probability may depend on the ratio of the UE's own signal gain to the estimated aggregate gain; it could also prioritize weaker UEs.Source: 3) Contention Resolution & Pilot… · p. 7

4) Allocation of Dedicated Payload Pilots:

The protocol's final access step admits a UE after the base station decodes its repeated pilot and message; the paper also analyzes channel and estimator behavior under uncorrelated Rayleigh fading. In that analysis, the three estimators become asymptotically unbiased, with NMSE below 10^-1 for M ≥ 50.

4) Allocation of Dedicated Payload Pilots:

  • The base station estimates the channel from repeated pilot transmissions and tries to decode the accompanying UE identity; successful decoding leads to a dedicated payload pilot allocation.If decoding fails, SUCRe has failed to resolve the collision; unused pilots also result in decoding failure.Source: 4) Allocation of Dedicated Payload… · p. 7
  • UAs not admitted can retry after a random wait or use an additional conventional contention-resolution step, such as randomly selecting new uplink pilots.The paper says few remaining collisions make the risk of new collisions vastly reduced in that example.Source: 4) Allocation of Dedicated Payload… · p. 7
  • With constant transmit power, SUCRe favors strong-channel UEs, typically nearer the cell center, while cell-edge UEs are more likely to lose contention.This short-term fairness cost accompanies the reported admission of around 0.9τ_p UEs out of the maximum τ_p per random-access block, even under high load; the weakest UEs are expected to succeed after a few attempts.Source: 4) Allocation of Dedicated Payload… · p. 7

III. PERFORMANCE WITH UNCORRELATED RAYLEIGH FADING CHANNELS

  • For uncorrelated Rayleigh fading, the received-signal mean approaches its asymptotic limit and its variance goes to zero, confirming asymptotic favorable propagation.The analysis is presented as tractable for any M, unlike the earlier analysis focused on antenna counts where channel hardening and asymptotic favorable propagation apply, typically M > 50.Source: §III · pp. 7–8

A. Different Estimators of αt

  • The maximum-likelihood estimate of α_t can be computed numerically, while an approximate closed-form estimate is obtained by solving for α_t using the received signal's real-part mean.The approximate estimator is asymptotically equivalent to the estimator from the earlier channel-hardening approximation and both are asymptotically error-free.Source: A. Different Estimators of αt · p. 8
  • All three estimators perform badly for M < 25, become asymptotically unbiased as M increases, and achieve NMSEs below 10^-1 for M ≥ 50.The maximum-likelihood estimator has the smallest NMSE, but the differences are tiny; the paper prefers the approximate second estimator because ML is computationally involved.Source: A. Different Estimators of αt · p. 8

B. Probability of Pilot Repetition

The paper derives the probability that a UE repeats its pilot under the proposed decision rule, then gives its large-antenna limit. The limiting rule makes repetition certain above a signal-gain threshold, while finite antenna counts retain collision risk.

B. Probability of Pilot Repetition

  • For large M, a UE repeats with probability 0 below the threshold, 1/2 at it, and 1 above it: ρ_kβ_kτ_p compared with α_t/2 + ϵ_k.This limit applies for ϵ_k < ρ_kβ_kτ_p/2.Source: B. Probability of Pilot Repetition · p. 9
  • When one UE's signal gain exceeds the sum of all others' plus inter-cell interference, it repeats with probability one as M grows.A positive bias for all UEs ensures that at most one UE transmits the pilot in Step 3.Source: B. Probability of Pilot Repetition · p. 9
  • At finite M, collisions remain possible and UE repetition decisions are correlated, so the exact collision-resolution probability is studied numerically.The exact repeat probability follows from the CDF of the received signal's real part; implementing the conditional PDF requires care for numerical stability.Source: B. Probability of Pilot Repetition · pp. 8–9

C. Example: Resolving a Two-UE Collision

In two-UE collisions, SUCRe favors pilot repetition by the UE with the stronger SNR, and added antennas sharpen that distinction. The protocol resolves most collisions when the UEs' SNRs differ, while equal-SNR collisions remain more difficult.

C. Example: Resolving a Two-UE Collision

IV. NUMERICAL RESULTS

Numerical results test SUCRe under high load across several channel models and interference conditions. Collision resolution improves with antenna count, and SUCRe admits roughly four times as many UEs per pilot as the baseline.

A. Channel Propagation Models

  • The tested propagation models are uncorrelated Rayleigh, correlated Rayleigh with adjacent-antenna correlation r = 0.7, and deterministic ULA line-of-sight.The models use different urban pathloss and shadow-fading settings.Source: A. Channel Propagation Models · pp. 10–11

B. Probability to Resolve Collisions

  • P_resolved rises from 20–40% at M = 1 to 75–90% at M = 50; SUCRe admits roughly four times as many UEs per RA pilot as the baseline.The evaluated network is highly loaded, and Fig. 8 compares cases with and without inter-cell interference.Source: Figure 8 · p. 11, B. Probability to Resolve Collisions · p. 12

IV. NUMERICAL RESULTS

  • Simulations use 5,000 inactive UEs, 10 pilots, and a 0.5% access probability, averaging 2.5 UEs per pilot and collisions on more than 75% of pilots.The hexagonal cell radius is 250 m, and UEs are placed more than 25 m from the BS.Source: §IV · p. 10, B. Probability to Resolve Collisions · p. 11

B. Probability to Resolve Collisions

  • Uncorrelated Rayleigh performs better than correlated Rayleigh, with a small difference at large M; LoS is slightly worse, while randomized LoS pilot power gives the highest performance.The paper attributes the LoS disadvantage to smaller pathloss differences and finds SUCRe suited to both LoS and non-LoS channels.Source: B. Probability to Resolve Collisions · p. 12
  • Inter-cell interference causes only minor performance degradation overall, and performance in the LoS case is almost unaffected.The comparison includes adjacent cells with regular data transmission and cases where they are silent during random access.Source: B. Probability to Resolve Collisions · pp. 11–12, A. Channel Propagation Models · p. 11

C. Tuning Probabilities using Bias Term

SUCRe's bias term trades collision resolution against false positives and false negatives, while the protocol continues admitting users at loads where the retransmission-only baseline breaks down. The conclusion reports around 90% collision resolution and robustness to inter-cell interference and channel distribution.

C. Tuning Probabilities using Bias Term

  • The bias term is set to ϵk = δβk/√M − ω̄/2, making δ a control for shifting the decision threshold by standard deviations of ∥hk∥2/M around βk.The probabilities are plotted against δ for M = 100, with and without inter-cell interference.Source: C. Tuning Probabilities using Bias Term · p. 12, Figure 9 · p. 12
  • Subtracting one or two standard deviations from the decision threshold increases collision resolution but raises false positives; adding them suppresses false positives but increases false negatives.The latter setting also resolves fewer collisions and can leave no UEs repeating their pilots.Source: C. Tuning Probabilities using Bias Term · p. 12
  • SUCRe with δ = −1 resolves 92% of two-UE collisions, 82% of five-UE collisions, and 71% of ten-UE collisions.Resolution probability decreases as the number of colliding users grows; more than a handful per pilot is unlikely except under extreme overload.Source: C. Tuning Probabilities using Bias Term · p. 12

D. Average Number of RA Attempts in Crowded Scenarios

V. CONCLUSION

  • The conclusion reports that SUCRe resolves around 90% of collisions, is robust to inter-cell interference and channel distribution, and continues admitting a subset of users under overload.The protocol uses channel hardening and favorable propagation for distributed collision detection and resolution at the UEs.Source: §V · p. 13

APPENDIX A SOME USEFUL RESULTS

The appendix states useful Gamma-function results and applies incomplete-gamma identities to evaluate integrals, with separate cases for the sign of B.

APPENDIX A SOME USEFUL RESULTS

  • For non-negative integer m and real A and B, Lemma 3 supplies an integral result used in the appendix calculations.The supplied passage does not include the lemma's full expression.Source: Appendix A · p. 13
  • For B ≥ 0, the remaining integral is evaluated by substituting y = x̃² and identifying incomplete gamma functions.The binomial formula is applied to (x̃ + B)^m in the preceding step.Source: Appendix A · p. 14
  • For B < 0, the appendix gives a separate integral evaluation, and substituting either sign-case result into (47) yields the final result.The sign-specific expressions are referenced as (48) and (49).Source: Appendix A · p. 14

APPENDIX B COLLECTION OF PROOFS

The proof appendix develops channel-estimation and decision-probability results used in the analysis. It derives a Gaussian limit for a channel-related quantity and uses it to obtain a CDF.

APPENDIX B COLLECTION OF PROOFS

  • Assuming the contender set St is known, the proof uses the MMSE estimator of hk and decomposes the true channel into its estimate and estimation error.The error is stated to be independent of the channel estimate.Source: Appendix B · p. 14
  • The proof identifies gk as a scaled chi-distributed quantity with 2M degrees of freedom, based on a sum of squares of 2M independent Gaussian variables.The variables are described as zero-mean with unit variance.Source: Appendix B · p. 14
  • For the ML estimator, the proof factors the joint density into independent real and imaginary components, then computes the real-part density by convolution.The imaginary component is the PDF of ℑ(νk); the convolution combines the PDFs of gk and ℜ(νk).Source: Appendix B · p. 14
  • The pilot-repeat probability is derived from the decision rule, with the CDF of ℜ(zk) computed by convolving the CDF of gk with the PDF of ℜ(νk).The proof uses Lemma 3 to evaluate the remaining integral.Source: Appendix B · pp. 14–15
  • As M grows, gk converges to a Gaussian distribution, and the proof uses the resulting limit to obtain the CDF for ℜ(zk) and asymptotic probabilities.The real part of zk is the sum of gk and ℜ(νk), which are treated as independent Gaussian variables in the limit.Source: Appendix B · p. 15
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