Dual-Purpose SSB Design for Joint Time-Frequency Synchronization Using Relocated DMRS

I. INTRODUCTION

• NB-IoT introduced dedicated synchronization signals and cell-search procedures for bandwidth-constrained receivers, but its synchronization architecture remains distinct from the conventional UE framework.Other proposed NB synchronization improvements likewise continue to rely on dedicated NB signaling.Source: §I · p. 1
• Existing cellular IoT synchronization uses dedicated NB signals, while low-power signaling approaches require an additional waveform instead of reusing the periodically transmitted SSB.The paper identifies this as a mismatch between legacy cellular IoT synchronization, conventional NR synchronization, and low-power receiver operation.Source: §I · p. 2
• The proposed DP-SSB uses contiguous, LS-optimized DMRS to support low-complexity IoT synchronization while preserving classical SSB-based synchronization for UEs.The design targets a time-domain correlation structure after receiver filtering and decimation.Source: §I · p. 2

II. DP-SSB SIGNAL SHAPING AND FRAME DESIGN

• A shared base station serves UEs and IoT devices through a unified synchronization infrastructure, rather than separate IoT gateways or base stations.The proposed scheme uses the same BS for both device types.Source: §II · pp. 2–3

A. Conventional SSB

• The conventional SSB has four contiguous OFDM symbols, with PSS in the first, PBCH and DMRS in the second, and SSS alongside PBCH and DMRS in the third and fourth.The first symbol carries PSS; the second and fourth carry PBCH and DMRS, while the third carries SSS with PBCH and DMRS.Source: A. Conventional SSB · p. 3

B. Proposed Dual Purpose SSB

• Selected DMRS from the second and fourth OFDM symbols are moved into one or more contiguous PRBs, and displaced PBCH symbols fill the vacated resource elements.The original PSS and SSS allocations and overall SSB structure are preserved.Source: B. Proposed Dual Purpose SSB · p. 3

C. LS-Based DMRS Signal Shaping

• The LS design uses the receiver’s narrowband filtering and decimation, with fixed PBCH and unmodified SSB resources treated as known contributions rather than design variables.Finite filter attenuation, convolution edge transients, and decimation can leak this known energy into the observation window.Source: C. LS-Based DMRS Signal Shaping · p. 4
• The target LP-SS is a complex, time-localized waveform whose phase must be preserved because the IoT receiver performs correlation against a stored replica.The design expands the relocated DMRS symbols to the OFDM sample grid and weights the reference waveform with a Gaussian window.Source: C. LS-Based DMRS Signal Shaping · p. 5
• The target waveform’s magnitude profile sets the autocorrelation shape, while its phase profile determines the time location of the correlation peak.The Gaussian weighting trades a sharper peak against increased sidelobes and energy outside the designable bins when its temporal spread is small.Source: C. LS-Based DMRS Signal Shaping · p. 5
• The LS formulation absorbs deterministic PBCH and residual-SSB leakage within the designable subspace, reducing waveform-approximation error by the observable leakage energy.The remaining error is irreducible with K degrees of freedom and decreases as K grows.Source: C. LS-Based DMRS Signal Shaping · pp. 5–6
• The optimized DMRS coefficients are rescaled to retain the original relocated-DMRS energy without changing normalized autocorrelation or peak-to-sidelobe ratio.The coefficients are then inserted into the remapped OFDM symbols to form the DP-SSB.Source: C. LS-Based DMRS Signal Shaping · p. 6

III. PROPOSED SYNCHRONIZATION FRAMEWORK

• The IoT receiver uses the K-dependent DMRS PRB to obtain a narrowband LP-SS observation, then applies hierarchical coarse and fine time-frequency synchronization after DP-SSB detection.This contrasts with conventional UE receivers that process the complete SSB bandwidth.Source: §III · p. 7

A. DP-SSB Reception

• Multipath preserves the original LP-SS correlation for equal path indices, while unequal path indices add shifted components around its main peak.The narrowband filter further shapes the correlation by convolution with the filter autocorrelation.Source: A. DP-SSB Reception · p. 7
• The LP-SS autocorrelation after narrowband filtering is the convolution of the LP-SS autocorrelation and the filter autocorrelation.The filter modifies the signal according to the relative separation of its taps.Source: A. DP-SSB Reception · p. 7
• After decimation, a lag of one reduced-rate sample corresponds to DK samples on the original sampling grid.The reduced-rate mainlobe occupies the same number of samples across K-PRB configurations; temporal correlation resolution improves as K increases.Source: A. DP-SSB Reception · p. 8
• When channel paths are separated by less than DK original-rate samples, decimation makes them less temporally resolvable and they are absorbed in the correlation metric.The reduced-rate path separation is less than one sample in this case.Source: A. DP-SSB Reception · p. 8

B. Narrowband DP-SSB Detection

• The IoT receiver tests DP-SSB presence noncoherently from received energy over a candidate observation window before symbol-boundary knowledge is available.The detector’s noise statistics reflect correlation introduced by front-end filtering.Source: B. Narrowband DP-SSB Detection · p. 8
• When DK > Lf − 1, decimated filtered-noise samples are uncorrelated and therefore independent, yielding covariance Cv,K = cKσ2_wIM.The front-end filter colors the noise before decimation.Source: B. Narrowband DP-SSB Detection · p. 8
• The energy-detection threshold γd is set for the considered K configuration and desired probability of false alarm.The detection statistic is used to decide whether DP-SSB is present.Source: B. Narrowband DP-SSB Detection · p. 8

C. Coarse Timing and CFO Acquisition

• Decimation leaves CFO unchanged but increases its phase progression between retained samples because the output sampling rate is lower.Coherent correlation therefore requires estimating and compensating that progression.Source: C. Coarse Timing and CFO Acquisition · p. 9
• The receiver correlates the narrowband observation with a shifted reference across candidate timing and coarse CFO hypotheses to form an acquisition metric.Timing and CFO candidates are drawn from predefined search grids.Source: C. Coarse Timing and CFO Acquisition · p. 9
• The estimated timing shift positions the narrowband observation window, while coarse CFO compensation leaves a residual offset for later refinement.The residual frequency offset must lie within the fine estimator’s unambiguous range.Source: C. Coarse Timing and CFO Acquisition · p. 9
• The remaining timing error is bounded by |ǫτ,K| ≤ DK/2, and the design does not require a separate fine timing estimator.The bound is on the decimated sampling-grid resolution.Source: C. Coarse Timing and CFO Acquisition · p. 9

D. Fine CFO Refinement

• The receiver forms a frequency-domain inner product from two DP-SSB symbols under the assumption that the channel is approximately constant across them.A reference cross-product calibrates deterministic phase differences between the symbols.Source: D. Fine CFO Refinement · p. 9
• The calibrated two-symbol cross-product removes deterministic phase differences, so its phase measures the residual CFO rotation ∆φK.The channel-independent phase relation is ∠ζK = ∆φK = 2πfr,K∆N/Fs (mod 2π).Source: D. Fine CFO Refinement · p. 9
• The fine estimator’s unambiguous range follows from −π < ∠ζK ≤ π, and the coarse estimate must leave residual CFO within that range.The maximum fine CFO range is specified as ffine,max in the passages.Source: D. Fine CFO Refinement · p. 9

• The analysis covers detection probability and synchronization error for the proposed DP-SSB framework.Source: §IV · p. 9
• It also examines the framework’s computational complexity.Source: §IV · p. 9
• Bit error rate is another performance metric considered in the analysis.Source: §IV · p. 9

• Under H0, the normalized energy statistic follows a central chi-square distribution for an M-sample observation.Source: A. DP-SSB Detection Performance · p. 9
• For a desired false-alarm probability, the required detection threshold is determined using the central chi-square CDF.Source: A. DP-SSB Detection Performance · p. 10
• Under H1, the added DP-SSB signal component yields a non-central chi-square energy statistic, from which detection probability is expressed using the generalized Marcum-Q function.The derivation also gives the statistic’s PDF using a modified Bessel function.Source: A. DP-SSB Detection Performance · p. 10

B. Synchronization Estimation Performance

• The section frames the IoT receiver’s synchronization performance in terms of errors for narrowband timing acquisition, coarse CFO estimation, and phase-based fine CFO refinement.Source: B. Synchronization Estimation… · p. 10

1) Timing Error Metric

• Timing acquisition is evaluated by RMSE because its error is affected by noise, multipath, and uncompensated CFO.After decimation, the estimate lies on the narrowband timing grid, whose resolution is set by the reduced sampling interval.Source: 1) Timing Error Metric · p. 10

2) CFO Error Metrics

• The coarse CFO error includes grid-limited error and error from noise, multipath, and timing; residual CFO must also fall within the fine estimator’s unambiguous range.The final CFO-estimator error is characterized by RMSE.Source: 2) CFO Error Metrics · p. 10

C. Computational Complexity Analysis

• Synchronization complexity is counted in complex multiplications, excluding filtering, decimation, and energy detection, with timing and coarse-frequency searches depending on their candidate-set sizes.The proposed scheme also incurs FFT and residual-CFO refinement costs.Source: C. Computational Complexity Analysis · p. 10

D. NR UE Communication Performance

• With perfect TF synchronization and known modified-DMRS locations and coefficients assumed, perfect CSI isolates PBCH detection from channel-estimation errors, while LS and LMMSE assess communication penalty.Source: D. NR UE Communication Performance · pp. 10–11
• Although the total number of DMRS symbols is preserved, relocation and LS optimization alter the channel-estimation matrix and can affect estimation accuracy.The DP-SSB uses both remaining distributed DMRS and the modified DMRS block, so estimation depends on DMRS locations and transmitted coefficients.Source: D. NR UE Communication Performance · p. 11

V. SIMULATION RESULTS

• Detection probability rises with SNR, and K = 48 gives the best detection performance, followed by K = 24 and K = 12.Analytical results closely follow Monte Carlo simulations; reducing PFA from 10−2 to 10−4 requires higher SNR for equal detection performance.Source: Figure 5 · p. 11, §V · p. 11
• At high SNR, K = 24 and K = 48 achieve lower TO RMSE than ML and LoRa, while K = 12 encounters a decimation-related error floor.Increasing decimation raises TO variance; K = 48 has the lowest variance and highest timing resolution among the tested K values.Source: Figure 6 · p. 11, §V · pp. 11–12
• Fine CFO estimates improve with SNR, with K = 48 reaching Hz-level final RMSE; increasing filter order reduces CFO variance until performance saturates after order 33.SC is competitive at higher SNR but uses full-rate sampling, while LoRa achieves the lowest RMSE through repetitive preambles.Source: Figure 7 · p. 12, §V · p. 12
• K = 48 yields the lowest effective frame-alignment error, whereas K = 2 has the lowest computational complexity among the proposed and baseline schemes.Conventional SC and ML incur higher complexity in the full-rate regime, and LoRa has the highest cost under the adopted repeated-observation implementation.Source: Figure 8 · p. 12, §V · p. 12
• DMRS-aware LS and LMMSE channel estimation approach the perfect-CSI PBCH BER reference, while DMRS-unaware estimators exhibit pronounced BER floors.As K increases, the DMRS-aware LS error floor grows relative to LMMSE; mismatch also degrades BER as channel taps increase.Source: Figure 9 · p. 12, §V · pp. 12–13

VI. CONCLUSION

• The proposed DP-SSB combines low-power IoT synchronization with conventional UE operation in one IA signaling block.Selected DMRS are relocated and LS-optimized for a sharp time-domain signal after filtering and decimation; simulations show reliable IoT synchronization and assess UE-side PBCH performance.Source: §VI · p. 13