Source-linked AI summary
Joint User Association and Pilot Assignment via Phase-Shifted Pilots for Scalable Cell-Free mMIMO
Mumtaz Ozlen, Ahmet Sacid Sumer, Ahmed Naeem, Huseyin Arslan
TL;DR
CF-mMIMO scalability is limited because coherence-bounded orthogonal pilots must be reused at high UE density, causing pilot contamination. The paper jointly assigns users and pilots with APS phase shifts and a 0/1 knapsack, more than doubling scheduled UEs while preserving or improving MSE and fairness metrics.
Problem
Coherence-bounded orthogonal pilot pools become insufficient as UE density rises, forcing pilot reuse and limiting scalable, contamination-free service.
Method
The framework combines APS pilots, which separate CIRs in contiguous delay-domain intervals, with a 0/1 knapsack whose item weights are UE tap counts.
Results
More than twice as many UEs are scheduled as with the CI benchmark, with equal MSE under equal total pilot power and lower MSE under equal per-subcarrier power.
Takeaways & Limitations
Penalizing existing UE connections improves 5th-percentile connectivity and Jain’s fairness index while retaining the framework’s scalability gains.
Abstract
from arXiv · showhide
Cell-free massive multiple-input multiple-output (CF-mMIMO) promises uniform service across the coverage area, and this service relies on accurate channel estimation for every user equipment (UE). These estimates are obtained from orthogonal pilot sequences, whose number is bounded by the channel coherence block. As a result, the sequences are reused as the UE density increases and the resulting pilot contamination limits the scalability. This paper proposes a joint user association (UA) and pilot assignment (PA) framework built on the adaptive phase-shifted (APS) pilot design, in which all UEs share a single full-band pilot and a per-UE phase shift applied in the frequency domain places their channel impulse responses (CIRs) in contiguous, non-overlapping intervals of the time domain at the access point (AP). The number of UEs that an AP can separate is thus set by the number of subcarriers rather than by the number of orthogonal sequences, and the UA is formulated as a $\mathbf{0/1}$ knapsack problem whose item weights are the numbers of taps and whose capacity is the number of subcarriers. Analysis and simulations show that the proposed design more than doubles the number of UEs scheduled by the conventional interleaved (CI) benchmark. It attains the same mean-squared error (MSE) as the CI benchmark under an equal total pilot power, and a lower MSE under an equal per-subcarrier power. It further improves the 5th-percentile connectivity and Jain's fairness index by penalizing the number of existing connections of a UE in the value assigned to each candidate link.
I. INTRODUCTION
CF-mMIMO improves coverage uniformity through user-centric AP clusters, but limited orthogonal pilots still constrain scalability as UE density rises. This paper jointly designs UA and PA using APS pilots and a capacity-aware fairness mechanism.
- User-centric CF-mMIMO reduces fronthaul and processing burdens while preserving coverage without cell-edge effects.
- Pilot reuse becomes unavoidable when UE density exceeds the coherence-limited pool of orthogonal sequences, causing pilot contamination.
- Joint UA and PA determine serving-AP overlap, pilot sharing, channel-estimation accuracy, and scalability.
- The proposed APS framework places served UEs’ CIRs in contiguous, non-overlapping delay-domain intervals, substantially increasing AP capacity.
- The 0/1 knapsack profit favors strong, low-tap links and penalizes existing UE connections to direct capacity toward less-connected UEs.
- Simulations evaluate varying AP and UE densities, cyclic-prefix lengths, and fairness exponents, with MSE, overhead, and complexity quantified.
C. Notation
The paper models a single-antenna, TDD CF-mMIMO system with distributed APs and frequency-selective multipath channels. Channel gains, delays, fading, path loss, and tap counts define the channel and large-scale coefficients.
- The system has L distributed APs and K uniformly distributed UEs, with single antennas, TDD operation, and CPU-connected fronthaul links.
- Large-scale fading uses a log-distance path-loss model with Friis-based free-space reference and independent shadow fading across UE–AP links.
- Each UE–AP channel is frequency-selective, time-invariant, and modeled with Gk,l resolvable multipath taps.
- The channel gains are independent across paths, have unit small-scale power, and place large-scale attenuation in the LSFC.
- The number of resolvable taps is determined by multipath delay spread, which varies slowly and can be estimated in advance.
B. Large-Scale Fading Coefficient-Based Masking Process
The masking stage converts LSFC-based received-power conditions into candidate UE–AP links. These candidates form the binary association structure that the subsequent knapsack optimization selects under AP capacity constraints.
- The masking process determines each AP’s candidate links from LSFC-based received power.
- Links exceeding the predefined threshold γdBm_th are collected in the binary matrix S.
- S_k,l indicates whether UE k is eligible for AP l, while M_k and D_l collect candidate APs and UEs.
- The proposed knapsack algorithm converts the candidate matrix S into the selected UA matrix S′ and corresponding serving clusters.
C. Adaptive Phase-Shifted Pilot Design for UL Training
APS pilots give UEs a shared full-band base sequence plus UE–AP-specific phase shifts, translating frequency-domain shifts into separated time-domain CIR intervals. UA determines the offsets, subject to the total tap capacity N.
- The APS design uses N subcarriers and a unit-modulus base pilot sequence shared by all UEs.
- Each served UE multiplies the base sequence by its own phase shift, with separate offsets possible for different serving APs.
- Intra-AP pilot contamination is eliminated by construction, while inter-AP separation uses AP-orthogonal training symbols.
- A UE’s phase offset follows its position in the AP-specific ordering and is obtained by summing the tap counts of preceding UEs.
- CIRs remain contiguous and non-overlapping when the total assigned taps do not exceed the N time-domain samples.
- A cyclic prefix of Ncp samples is appended before transmission, and the receiver processes the propagated pilots with an FFT.
2) Receiver Side Process:
The receiver separates served UEs by transforming the received pilot signal into time-domain CIR intervals determined by phase shifts, while UA selects an AP-specific serving subset through a knapsack constraint.
- Receiver-side channel estimation: The received pilot signal is divided by the base pilot sequence, but the channel estimate initially contains a superposition of the served UEs’ CFRs.
- Receiver-side channel estimation: An N-point IFFT converts the frequency-domain channel estimate into a time-domain estimate at each AP, where the UEs are separated.
- Receiver-side channel estimation: The served UEs’ CIRs occupy contiguous, non-overlapping time-domain intervals determined by their phase shifts.
- Joint user association and pilot assignment: Each AP serves only a subset of candidate UEs, called its serving cluster D′l, obtained from a 0/1 knapsack problem.
- Joint user association and pilot assignment: Each candidate UE is an item weighted by its number of resolvable taps Gk,l, while the knapsack capacity is N.
- Joint user association and pilot assignment: Candidate links are retained when their received power exceeds the predefined threshold γdBmth before the knapsack selects among them.
A. Fairness-Aware Profit Formulation
The fairness-aware formulation assigns link profits using received power, tap occupancy, and existing UE connections, then solves one capacity-constrained knapsack per AP.
- Per-AP optimization: The knapsack is solved separately for each AP, after which UE connection counts are updated.
- Fairness-aware candidate selection: Each AP’s candidate set is restricted to UEs with item weights between one and the capacity C.
- Profit formulation: Link profit increases with received power and decreases with the number of taps and the UE’s existing connections.
- Fairness-aware allocation: A UE with no preceding connection enters at full profit, directing remaining capacity toward the least-connected UEs.
- Profit formulation: The fairness penalty exponent β governs the trade-off between average connectivity and UE fairness.
- Profit formulation: Because profit is inversely proportional to Gk,l, links with strong received power and fewer taps attain higher profit and consume less AP capacity.
B. Dynamic Programming Solution
The NP-hard per-AP knapsack is solved exactly with dynamic programming, whose value and decision tables support optimal selection and backtracking.
- Dynamic programming formulation: Dynamic programming solves the knapsack because its capacity is bounded by N, using a Bellman recursion.
- Dynamic programming formulation: The value table V(i,c) stores the maximum total profit obtainable from the first i candidates within capacity c.
- Value recursion: The recursion processes candidates sequentially by carrying forward the best value from preceding candidate states.
- Value recursion: Each candidate is selected at most once, consistent with the 0/1 knapsack formulation.
- Decision tracking: The binary table B(i,c) records when selecting candidate i improves the value over rejecting it.
- Decision tracking: Backtracking from state (vl,C) recovers the selected candidates and updates remaining capacity by each selected candidate’s weight.
C. Computational Complexity Analysis
The proposed algorithm adds a capacity-dependent dynamic-programming cost to candidate processing, yielding complexity that is bilinear in AP and UE counts for fixed N.
- Complexity model: The complexity comparison counts arithmetic and comparison operations used when serving clusters are updated, excluding common LSFC and tap acquisition.
- CI benchmark: The CI benchmark sorts each AP’s candidates by received power, requiring O(|Dl| log |Dl|) operations per AP.
- Proposed algorithm: The proposed algorithm computes candidate profits in O(|Dl|) operations per AP and solves its knapsack in O(|˜Dl| N) operations per AP.
- Complexity comparison: The proposed algorithm’s additional cost is the knapsack factor N rather than the CI benchmark’s log |Dl| factor.
- Complexity comparison: For fixed N, the proposed complexity is bilinear in the numbers of APs L and UEs K.
D. Control Signaling Analysis
The proposed scheme adds per-UE phase-shift signaling to separate CIRs, while its larger number of serving links increases signaling relative to the CI benchmark; updates occur only when serving clusters change.
- Control signaling mechanism: Each UE receives an AP-specific phase-shift offset computed by the CPU and forwarded over fronthaul for downlink control signaling.The offset is applied separately at every serving AP and is selected from N possible values.
- Control signaling overhead: The proposed scheme requires log2 N control bits per link, whereas the CI benchmark requires log2(1/ρp) bits.The number of possible index values determines the per-link signaling requirement.
- Update frequency: Control signaling is repeated once per cluster update and remains negligible relative to payload transmitted between consecutive updates.Offsets change only when serving clusters are updated.
- Evaluation metrics: The proposed evaluation uses average connectivity, 5th-percentile connectivity, Jain’s fairness index, and MSE over served links.The 5th-percentile metric characterizes the least-connected UEs, while Jain’s index measures connection uniformity.
- Evaluation assumptions: MSE comparison is made on equal terms because both schemes use the same estimated resolvable taps and time-domain noise suppression.Tap acquisition and common masking operations are excluded from the comparison.
A. MSE Performance
The APS design gives every UE all subcarriers and separates CIRs in non-overlapping delay-domain intervals, while CI assigns interleaved subcarrier sets constrained by cyclic-prefix length. Under equal total pilot power, both designs attain the same MSE; under equal per-subcarrier power, APS performs better.
- Pilot allocation: The CI benchmark schedules U CI = N/Ncp = 1/ρp UEs per AP, while APS allocates all N subcarriers to every UE.Reliable CI channel estimation requires at least Ncp pilot subcarriers per UE.
- MSE conditions: APS and CI are interference-free in the MSE comparison, so estimation error results only from AWGN.APS separates each UE’s CIR by transforming samples from its assigned delay-domain interval.
- MSE results: Under equal total pilot power, APS and CI attain the same MSE.CI compensates for its lower per-subcarrier power in the per-subcarrier-power comparison by boosting that power under the total-power constraint.
B. Joint User Association and Pilot Assignment Performance
The joint UA and PA evaluation shows that APS schedules substantially more UEs than CI, with gains increasing under larger cyclic prefixes and denser deployments. A tunable fairness penalty trades average connectivity for improved least-connected-UE connectivity and fairness.
- Effect of UE density: For 100 UEs, APS-to-CI average-connectivity ratios are 2.13, 2.72, and 3.48 for Ncp = 8, 16, and 32, respectively.The ratio increases with Ncp because APS capacity depends on selected UEs’ resolvable taps rather than CI’s fixed pilot allocation.
- Effect of UE density: For 160 UEs, the corresponding APS-to-CI ratios reach 2.50, 3.15, and 4.12 for Ncp = 8, 16, and 32.The larger candidate set contains more UEs with few taps and strong received power, increasing APS selection priority.
- Fairness penalty: Increasing β decreases average connectivity but substantially increases the connectivity of the least-connected UEs relative to β = 0.The fairness penalty lowers the priority of UEs already holding many connections.
- Fairness penalty: For β ≥10, Jain’s fairness index remains nearly constant up to 300 UEs, while β = 0 causes the index to decrease as UE load grows.The fairness penalty preserves connection distribution under heavy load.
2) Effect of AP Density:
As AP density increases, the proposed method preserves its connectivity advantage and improves fairness, with negligible average-connectivity loss under dense deployments. This comes at the cost of higher signaling overhead and computational complexity.
- Connectivity: 2.29, 2.92, and 3.69 are the proposed-to-CI average-connectivity ratios for 60 APs at Ncp = 8, 16, and 32, respectively.Because both methods scale linearly with AP count, these ratios remain nearly constant across the examined AP range.
- Connectivity: As AP density increases, different fairness-penalty settings produce nearly coincident average-connectivity curves because greater knapsack capacity rejects fewer candidates.The remaining rejections mainly affect which UEs receive connections and therefore influence the lower tail rather than average connectivity.
- Fairness: The fairness index approaches 1 with increasing AP density, while the CI benchmark remains below the proposed method across the examined AP range.The average-connectivity loss from the fairness penalty becomes negligible, while gains in 5th-percentile connectivity and fairness are preserved.
- Trade-off: The proposed method requires more than ten times the CI benchmark’s measured complexity and higher control signaling overhead, while scheduling more than twice as many UEs at the same MSE.The measured complexity remains 0.111 × 10^4 per UE, verifying linearity in the number of UEs stated in (26).