Source-linked AI summary
Random Access and Localization in Cell-Free User-Centric Networks with Multipath Channels
Simon Tarboush, Eleni Gkiouzepi, Giuseppe Caire
TL;DR
Random access users in cell-free networks need to be detected and localized so they can be assigned user-centric RU clusters. The paper compares geographically partitioned codebooks with ZC/GLRT and multisource AMP receivers, alongside localization from RACH preambles. AMP performs better for detection, while the frequency-domain scheme has lower localization errors than the time-domain scheme in the reported comparison.
Problem
Random-access users in cell-free networks must be detected and accurately localized to assign each user a user-centric cluster of radio units.
Source: §I · p. 1, A. System Model · p. 2Method
The paper compares location-partitioned access codebooks using a time-domain ZC/GLRT receiver and a frequency-domain multisource AMP receiver.
Source: §I · p. 1, A. System Model · p. 2Results
AMP outperforms the legacy time-domain scheme in detection, while frequency-domain localization error is below 12 m with 90% probability versus approximately 16 m for time-domain localization.
Source: §IV · pp. 6–7Takeaways & Limitations
Accurate localization of detected random-access users is desirable because cell-free networks must assign each user a serving radio-unit cluster.
Source: §I · p. 1
Abstract
from arXiv · showhide
In a wireless network, the initial/random access mechanism (RACH) allows idle/new users to join the network and (possibly) request allocated transmission resources for subsequent traffic. Building on our own previous work, for cell-free user-centric networks, we consider location-dependent random access codebooks such that users in a certain geographic area (location) make use of the corresponding set of random access preambles (codewords). We expand our previous work in two ways: (1) we consider multipath channels with line-of-sight (LoS) propagation within a given radius; (2) we consider two different approaches. The first makes use of Zadoff-Chu (ZC) sequences and GLRT detection to cope with the unknown delay, and it is conceptually similar to the 3GPP 2-step RACH specification (here extended to the cell-free case). The second builds on our previous work on multisource approximate message passing (AMP). For both schemes, we also consider a novel near Maximum-Likelihood approach for localization of the random access users directly from the detected RACH preambles, implicitly using angle of arrival and time difference of arrival information embedded into the LoS components. Simulation results show that the AMP approach achieves generally better performance for random access user detection, while both approaches have similar localization capability with a slight superiority for the frequency-domain scheme.
I. INTRODUCTION
The paper compares location-partitioned random-access codebooks and two receiver pipelines for detecting and localizing users in cell-free networks. The system model assigns users to geographic access zones and requires the network to identify active preambles and refine user positions.
I. INTRODUCTION
- Random access lets idle or new users signal their presence with shared preambles, and localized access users need accurate positions to receive user-centric RU clusters.Unsourced random access assumes a virtually infinite user population with only a finite number transmitting in a slot.Source: §I · p. 1
- Location-based codebook partitioning aims to resolve ambiguity between transmitted codewords and propagation large-scale fading coefficients.The time-domain pipeline uses Zadoff–Chu sequences and GLRT; the frequency-domain pipeline uses multisource AMP and combines observations across RUs.Source: §I · p. 1
- AMP outperforms the ZC scheme in random-access detection and provides better localization accuracy in a unified comparison at the same channel load.The comparison uses frequency-selective, spatially consistent propagation.Source: §I · p. 1
A. System Model
- The coverage area is divided into disjoint locations, each with its own codebook, and the network must detect transmitted codewords and refine active-user positions.The numerical layout uses 36 RUs across seven hexagonal locations; results assume no preamble collisions.Source: A. System Model · p. 2
B. Channel Model
The channel model combines geometry-dependent LoS and reflected NLoS paths, with delays, large-scale fading, and arrival angles tied to user and scatterer positions. This gives spatial consistency across the network.
B. Channel Model
- A LoS path exists only when a user is within the RU truncation radius and its angle of arrival falls within that RU’s angular sector.The LoS component includes a distance-dependent large-scale fading coefficient, propagation delay, array response, and uniformly random phase.Source: B. Channel Model · p. 2
- Delays, large-scale fading, and angles of arrival depend on user and scatterer positions relative to each RU, ensuring spatial consistency across the network.NLoS paths are modeled as single-bounce reflections from randomly distributed scatterers.Source: B. Channel Model · pp. 2–3
- The model samples continuous-time channels into finite-duration discrete-time impulse responses, with each path contributing at most two nonzero taps.The channel taps are assembled into a zero-padded time-space matrix; a cyclic downshift matrix represents shifted codewords.Source: B. Channel Model · p. 3
C. Received Signal Models
The received RACH block is modeled for frequency-selective channels using a cyclic prefix, enabling circular convolution after prefix removal.
C. Received Signal Models
- A cyclic prefix lets the receiver discard the prefix samples and obtain a length-L RACH block with circular convolution by the delay-domain channel.The model assumes signal bandwidth exceeds channel coherence bandwidth.Source: Time-domain ZC signaling with CP · p. 3
Time-domain ZC signaling with CP:
The received-signal model includes activity, quantized shortest-path delay, and noise plus residual multiuser interference.
Time-domain ZC signaling with CP:
- The received-signal model includes an activity indicator, the quantized delay of the shortest path, and noise plus residual multiuser interference.The delay is indexed by RU and user; the residual term accounts for non-ideal cyclic cross-correlations.Source: Time-domain ZC signaling with CP · p. 3
Frequency-domain CP-OFDM signaling:
The frequency-domain CP-OFDM scheme forms received subcarrier samples from the transformed channel and pilot signals. It uses consecutive blocks while preserving the schemes’ overall transmission length in chips.
Frequency-domain CP-OFDM signaling:
- At each subcarrier, the received frequency-domain sample at an RU is formed from the transmitted CP-OFDM pilot and the frequency-domain channel.The channel components are obtained by a discrete Fourier transform of the sampled time-domain channel.Source: Frequency-domain CP-OFDM signaling · p. 3
- Q consecutive blocks of Lf chips plus cyclic prefixes replace one long time-domain block while keeping the same overall transmission length in chips.Pilot observations are stacked across the RU’s M antennas.Source: Frequency-domain CP-OFDM signaling · p. 3
- The frequency-domain channel matrix spans subcarriers, with integer propagation delays represented by linear phase shifts and fractional delays represented in the frequency domain.The fractional-delay representation accounts for pulse shaping and sampling.Source: Frequency-domain CP-OFDM signaling · p. 4
III. ACTIVE CODEWORDS DETECTION AND USER POSITIONING
This section covers active-codeword detection for the time-domain and frequency-domain schemes, along with the proposed user-localization approaches.
III. ACTIVE CODEWORDS DETECTION AND USER POSITIONING
- The section treats active-codeword detection in both signaling schemes and the proposed approaches to localizing users.Source: §III · p. 4
A. Time-domain scheme
The time-domain detector exploits Zadoff–Chu sequence correlations and tests codewords using nearby radio units selected from the codeword’s associated location. It uses a GLRT-style delay search based on received signal energy.
A. Time-domain scheme
- Zadoff–Chu sequences provide quasi-perfect cyclic autocorrelation and low cyclic cross-correlation for the receiver.Source: A. Time-domain scheme · p. 4
- Each codeword is associated with a location, and detection uses observations from a subset of nearby radio units selected around that location.For the illustrated layout, the selected units are the three radio units at the location hexagon’s vertices whose sectors face the hexagon.Source: A. Time-domain scheme · p. 4
- The GLRT searches candidate delays for a cyclic-prefix-length window with maximum signal energy, sums the maxima across selected radio units, and compares the total with a threshold.The threshold controls the trade-off between false alarms and misdetections.Source: A. Time-domain scheme · p. 4
B. Frequency-Domain Approach
The frequency-domain approach applies multisource AMP to each subcarrier and pools its outputs for detection. It uses a location- and radio-unit-dependent mismatched denoiser and disregards unknown frequency correlation in its likelihood test.
B. Frequency-Domain Approach
- The method applies multisource AMP to each subcarrier’s parallel-channel model and pools the outputs before detection.Source: B. Frequency-Domain Approach · p. 4
- Because the channel statistics are not fully known, the mismatched AMP denoiser treats channels as zero-mean Gaussian vectors with diagonal covariance indexed by location and radio unit.The covariance can be learned from network topology and large-scale fading coefficients.Source: B. Frequency-Domain Approach · p. 4
- The likelihood test disregards frequency correlation because that correlation is a priori unknown for random-access users.The AMP outputs are conditionally independent across radio units but dependent across subcarriers under the frequency-correlated channel model.Source: B. Frequency-Domain Approach · p. 5
- For active codewords, the model exploits the known line-of-sight radio-unit associations and represents the line-of-sight contribution as a Rician term with random phase.Source: B. Frequency-Domain Approach · p. 5
C. Active User Position Estimation
Both schemes estimate position from the detected user’s RACH observation, exploiting the position dependence of LoS delay and angle of arrival. The frequency-domain method evaluates a mismatched likelihood over a fine grid; the time-domain method uses the matched-filter observation.
C. Active User Position Estimation
- LoS delay and angle of arrival depend on user position, providing the basis for positioning from detected RACH observations in both schemes.Each codeword is associated with a location, and the RUs in LoS conditions provide position-dependent channel parameters.Source: C. Active User Position Estimation · p. 5
- The frequency-domain method forms a positioning likelihood from the output of multisource AMP, while the time-domain method uses the matched-filter receiver output.The likelihood models the channel vector as Rician with random phase and treats the scattered component as zero-mean Gaussian with a nominal diagonal covariance estimated from the environment.Source: C. Active User Position Estimation · p. 5
- The MMLE selects the candidate position with the highest likelihood over a fine discretization grid within the user’s location.The frequency-domain method uses a mismatched covariance formed from AMP state evolution and offline-estimated diagonal covariance matrices.Source: C. Active User Position Estimation · p. 6
IV. SIMULATION RESULTS
The simulations compare time-domain ZC and frequency-domain AMP schemes under matched channel load and transmission resources. AMP has lower missed-detection probability, while frequency-domain localization errors are lower than time-domain errors in the reported comparison.
IV. SIMULATION RESULTS
- The frequency-domain receiver uses 144 CP-OFDM pilot symbols over 16 subcarriers, while the time-domain receiver uses length-2297 ZC sequences with cyclic prefixes for equal resource allocation.The frequency-domain location subcodes contain 288 codewords; time-domain subcodes contain 164 and use a reuse factor of two.Source: §IV · p. 6
- Performance is evaluated without preamble collisions using missed-detection and false-alarm probabilities, while localization error is measured only for true-positive users.The channel realizations include LoS and specular paths, and the reference SNR is defined for a user at a hexagon center received by its nearest RU.Source: §IV · p. 6
- At fixed PFA = 10^-1 and SNR = -30 dB, Fig. 2 shows the AMP-based frequency-domain scheme's missed-detection probability is superior to the legacy time-domain scheme as total active users increase.Source: §IV · p. 6, Figure 2 · p. 6
- The localization heatmap evaluates the log-likelihood on a 121-point fine hexagonal grid, with time-domain results on the left and frequency-domain results on the right.Each small grid hexagon has a radius of 8.2 m.Source: §IV · p. 6, Figure 3 · p. 7
- At SNR = 10 dB with 300 active users, 90% of frequency-domain localization errors are below 12 m, versus approximately 16 m for the time-domain scheme.Both error CDFs rise steeply at first and are compared with an oracle representing the grid-quantization lower bound.Source: §IV · p. 7, Figure 4 · p. 7
V. CONCLUSION
The paper compares ZC-based time-domain detection with frequency-domain multisource AMP for unsourced random access in a geometrically consistent cell-free channel model. AMP offers greater codebook flexibility and better detection performance, with higher computational complexity; both schemes use approximate maximum-likelihood localization.
V. CONCLUSION
- The frequency-domain AMP scheme outperforms the legacy-like time-domain ZC scheme in detection and provides better localization accuracy.The comparison uses the same average active-user load per unit area in frequency-selective, spatially consistent propagation.Source: §V · p. 7
- Frequency-domain codebooks offer more flexibility and better control of preamble collision probability, but generally require longer sequences and AMP has substantially higher computational complexity.AMP jointly processes codewords, RUs, antennas, and subcarriers at every iteration, unlike the time-domain scheme’s bank of matched filters and GLRT.Source: §V · p. 7
- Both schemes localize detected active users with an approximate maximum-likelihood method that uses position-dependent delay and angle information to fuse observations from multiple RUs.The authors identify collision-aware models and more refined channel priors for AMP inference as future work.Source: §V · p. 7