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Impact of Synchronization Offsets and CSI Feedback Delays on Coherent Joint Transmission in Distributed MIMO-OFDM

Kumar Sai Bondada, Daniel J. Jakubisin, R. Michael Buehrer

arXiv:2610.33181v1eess.SP

TL;DR

Distributed CJT depends on synchronization and CSI accuracy, yet prior work has often treated synchronization errors individually and used BER/SER rather than multicarrier SE. This paper derives received-signal and SE models for timing, frequency, phase-noise, and CSI-aging effects, then evaluates synchronization targets. Its results identify bounded timing, frequency, phase-tracking, and feedback-delay conditions associated with limited SE degradation.

  • Problem

    Prior studies often examined synchronization errors individually using BER/SER, leaving their joint effects and CSI aging on multicarrier DMIMO spectral efficiency insufficiently characterized.

    Source: A. Related Work and Motivation · p. 2

  • Method

    The paper derives received-signal and spectral-efficiency models for residual timing, CFO, SCO, phase noise, and Doppler-induced CSI aging, then numerically evaluates their effects.

    Source: §V · p. 10

  • Results

    A start-time jitter standard deviation below 10% of the sampling period and normalized CFO standard deviation around 0.001 yield negligible SE degradation; Doppler-delay products below 0.1 limit SE loss.

    Source: §V · pp. 10–11

  • Takeaways & Limitations

    Maintaining CJT coherent-combining gains requires propagation-delay compensation, bounded residual timing and frequency errors, reliable phase tracking, and timely CSI feedback.

    Source: §V · p. 11

    The analysis does not explicitly model path loss or network-level interference.

    Source: §V · p. 11

Abstract

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This paper studies the impact of synchronization offsets and CSI feedback delay on coherent joint transmission (CJT) in distributed MIMO-OFDM systems. Unlike conventional co-located MIMO, distributed CJT is highly sensitive to transmitter-dependent synchronization impairments because coherent combining requires phase, frequency, and timing alignment across geographically separated transmitters. Received signal models are derived for residual timing offsets, carrier frequency offsets (CFOs), sampling clock offsets (SCOs), phase noise, and channel variations accumulated during channel state information (CSI) feedback delay. The corresponding spectral efficiency (SE) expressions quantify the degradation in capacity due to loss in coherent-combining gain caused by residual phase rotations, inter-carrier interference (ICI), and precoder misalignment. The SE expressions are numerically evaluated to determine synchronization requirements for maintaining negligible SE degradation, yielding the following findings: a Gaussian-distributed start-time jitter with a standard deviation below 10\% of the sampling period results in negligible SE degradation, with the SE loss decreasing from 0.68\% at an SNR of 0 dB to 0.17\% at 40 dB. A normalized CFO standard deviation of 0.001 also results in negligible ICI-induced degradation, with the SE loss increasing from 0.05\% at an SNR of 0 dB to 2\% at 40 dB. At an SNR of 26 dB, limiting the SE loss to 5\% yields feasible operating points with clock-error standard deviations up to 50 ppb, Doppler-delay products up to 0.1, and phase-tracking error standard deviations up to $40^{\circ}$ at carrier frequency of 3.5 GHz with 30 kHz sub-carrier spacing with 15.36 MHz sampling rate.

I. INTRODUCTION

The introduction motivates coherent joint transmission (CJT) in distributed MIMO as a promising route to spectral-efficiency gains, while emphasizing practical synchronization and CSI challenges. The paper develops a wideband distributed SU MIMO-OFDM analysis and evaluates synchronization requirements for preserving coherent gain.

I. INTRODUCTION

  • CJT in LTE CoMP and 5G multi-TRP uses UE-assisted inter-TRP calibration to estimate relative delay, frequency, and phase offsets for network reporting.Distributed MIMO also faces synchronization, CSI acquisition, and fronthaul constraints; wired and GPS-based approaches have mobility, scalability, coverage, or interference limitations.Source: §I · p. 1

A. Related Work and Motivation

  • Prior work often studied timing or frequency errors in isolation with BER/SER measures; multicarrier SE effects and CSI aging remain insufficiently characterized.The paper frames this gap as relevant to synchronization requirements and synchronization-aware precoder design.Source: A. Related Work and Motivation · p. 2

B. Contribution

  • The paper extends prior narrowband, single-carrier analysis to wideband SU MIMO-OFDM over multipath Rayleigh fading and derives models and SE expressions for synchronization impairments and CSI delay.Its contributions include analyzing timing, CFO, SCO, phase noise, and CSI aging, then numerically evaluating synchronization requirements; path loss and shadowing are not explicitly modeled.Source: B. Contribution · p. 2

II. DISTRIBUTED SINGLE-USER MIMO-OFDM

  • The system model uses distributed transmitters jointly serving one receiver over OFDM, with a cyclic prefix and per-transmitter power allocation.The ideal-synchronization baseline assumes time-invariant channels between pilot-based precoder design and CJT; the analysis later relaxes the channel assumption to examine Doppler-induced CSI aging.Source: §II · p. 3

III. SPECTRAL EFFICIENCY IN PRESENCE OF IMPAIRMENTS

The impairment analysis models oscillator imperfections and residual transmitter offsets after synchronization correction. The resulting received-signal model represents how those residuals enter the distributed CJT link.

III. SPECTRAL EFFICIENCY IN PRESENCE OF IMPAIRMENTS

  • The oscillator model separates long-term frequency offset from short-term phase noise, which is modeled as a zero-mean Wiener process with independent Gaussian increments.The frequency offset can arise from oscillator tolerance, temperature, aging, and supply or load fluctuations.Source: §III · p. 4
  • A shared reference oscillator’s frequency offset appears as both CFO and SCO, while oscillator and PLL phase noise contribute carrier phase noise and sampling-clock jitter.Residual transmitter time offsets also reflect clock-reference differences and propagation-delay estimation or compensation errors.Source: §III · p. 4
  • The analysis treats residual offsets separately to isolate their effects; their levels depend on synchronization-link quality and estimation and correction accuracy.The received-signal model incorporates residual time and frequency offsets, with the transmitter’s constant phase factor absorbed into its channel response.Source: §III · p. 4

A. Time Synchronization Offsets

Residual transmitter timing offsets shrink the receiver’s valid processing interval, which is further reduced by NLOS channel delay spread. Timing jitter between channel estimation and CJT can also change the effective channel used for precoding.

A. Time Synchronization Offsets

  • Residual time offsets reduce the receiver’s valid processing-start interval within the cyclic prefix; in NLOS, channel delay spread shrinks it further.A valid interval is necessary, and minimizing transmitter time-offset spread limits required CP overhead.Source: A. Time Synchronization Offsets · p. 4
  • Fig. 1 illustrates three transmitter arrivals with zero, positive, and negative time offsets at the receiver in the NLOS case.The processing start time must be selected within the available timing margin.Source: A. Time Synchronization Offsets · p. 4, Figure 1 · p. 5
  • When start-time offsets remain fixed between channel estimation and CJT and processing lies within the timing margin, their phase rotations are absorbed into the effective channel and SE matches ideal synchronization.CE-to-CJT start-time jitter changes the effective channel; the resulting precoder misalignment reduces coherent-combining gain.Source: A. Time Synchronization Offsets · p. 5

B. Frequency Synchronization Offsets

Residual CFO adds transmitter-dependent phase rotation and ICI to the received subcarrier signal. Its useful-signal attenuation and ICI reduce SE, with additional precoder misalignment possible if CFO-induced channel variation is not tracked.

B. Frequency Synchronization Offsets

  • Residual CFO adds transmitter-dependent phasor terms and ICI; its normalized value is the CFO divided by subcarrier spacing.The CFO also creates symbol-dependent phase rotation, while ICI attenuates useful signal power through a sinc factor.Source: B. Frequency Synchronization Offsets · p. 5
  • The achievable SE decreases through useful-signal attenuation and ICI, with further degradation when untracked CFO-induced channel variation misaligns the precoder.The received-signal expression combines residual timing and frequency offsets, and the precoder should include a CFO phase-compensation term.Source: B. Frequency Synchronization Offsets · p. 5

C. Sampling Clock Offsets

Sampling clock errors tied to the carrier reference create subcarrier- and symbol-dependent phase evolution and accumulating timing drift. The analysis characterizes their effects on the received signal and precoder alignment, including phase tracking over the CSI feedback delay.

C. Sampling Clock Offsets

  • A shared sampling-clock and carrier reference makes the same fractional error apply to both SCO and CFO, while symbol durations differ across transmitters.The resulting relative timing offset accumulates over successive OFDM symbols; periodic correction resets that drift before it exceeds the allowable timing margin.Source: C. Sampling Clock Offsets · pp. 5–6
  • At 1 ppb error and 15.36 MHz sampling, timing drift reaches about one sampling interval after 10^9 samples, or 65.10 s.The passage gives a maximum two-transmitter relative error of 2 ppb, corresponding to about two samples after 10^9 samples.Source: C. Sampling Clock Offsets · p. 6
  • SCO changes useful-signal attenuation and ICI, with subcarriers farther from the center more sensitive to its effects.It also adds subcarrier dependence to phase rotation, which otherwise varies by symbol under CFO alone.Source: C. Sampling Clock Offsets · p. 6
  • With quasi-static physical channels, phase rotation accumulated during the CSI feedback delay is attributed primarily to residual CFO and SCO.The precoder uses estimated tracked phase; imperfect phase tracking reduces coherent-combining gain, while start-time jitter is excluded because it is random between CE and CJT and may bias compensation.Source: C. Sampling Clock Offsets · pp. 6–7
  • A processing-start-time difference between CE and CJT causes small precoder misalignment, but its impact is negligible for offsets of tens to hundreds of nanoseconds.The receiver model assumes separate detection per subcarrier, treats ICI as colored Gaussian noise, and does not jointly decode across subcarriers.Source: C. Sampling Clock Offsets · pp. 6–7

D. CSI Feedback Delay

CSI feedback delay leaves the precoder based on an earlier channel realization. The resulting loss of coherent-combining gain worsens as Doppler or feedback delay increases.

D. CSI Feedback Delay

  • For a feedback delay of L OFDM symbols, the channel realizations at channel estimation and CJT are modeled as jointly Gaussian and correlated by ρ(L).The correlation uses J0, the zeroth-order Bessel function, and the maximum Doppler frequency fd.Source: D. CSI Feedback Delay · p. 7
  • The precoder for CJT is designed using the outdated effective channel from the earlier channel-estimation time.The channel can vary between channel estimation and CJT due to motion of the receiver and scatterers.Source: D. CSI Feedback Delay · p. 7
  • CSI aging leaves the precoder misaligned with the effective channel’s dominant right-singular subspace, reducing coherent-combining gain.The effect worsens with faster aging, caused by higher Doppler or larger feedback delay.Source: D. CSI Feedback Delay · p. 7

E. Phase Noise

Phase noise makes the common coefficient used for coherent joint transmission vary between channel estimation and transmission. Its effects include reduced effective channel gain, precoder misalignment, and inter-carrier interference.

E. Phase Noise

  • The received signal model for phase noise is derived in Appendix D.The passage introduces its matrix-form expression for received data across the receive antennas.Source: E. Phase Noise · p. 7
  • Phase noise creates a transmitter-dependent complex common coefficient with magnitude at most one that evolves randomly between channel estimation and CJT.The coefficient is a sum of complex exponential phasors; its variation can misalign the precoder with the effective channel and reduce effective channel gain, SNR, and SE.Source: E. Phase Noise · p. 7
  • Phase noise introduces inter-carrier interference in addition to reducing coherent-combining gain through precoder misalignment.The degradation is stronger for poorer phase-noise profiles.Source: E. Phase Noise · p. 7

IV. SIMULATION RESULTS AND ANALYSIS

Simulations quantify how timing, frequency, clock, phase-tracking, and CSI-aging impairments reduce coherent-joint-transmission spectral efficiency, with impacts depending on impairment type and operating conditions.

IV. SIMULATION RESULTS AND ANALYSIS

  • A start-time jitter standard deviation below 10% of the sampling period yields minimal SE degradation, with SE loss decreasing from 0.68% at SNR = 0 dB to 0.17% at SNR = 40 dB.At 15.36 MHz sampling rate, 10% of the sampling period is approximately 6.5 ns; transmitter-dependent phase variation misaligns the effective channel and precoder.Source: §IV · p. 8, Figure 3 · p. 8
  • A normalized CFO standard deviation of 0.001 causes negligible ICI-induced degradation, with SE loss increasing from 0.05% at SNR = 0 dB to 2% at SNR = 40 dB.At high SNR, phase drift between channel estimation and joint transmission must also be tracked or incorporated into the precoder.Source: §IV · pp. 8–9, Figure 4 · p. 8
  • At 15.36 MHz sampling and 3.5 GHz carrier frequency, SCO alone has negligible impact up to 1000 ppb, while combined SCO and CFO degradation remains small up to 10 ppb.For fixed sampling rate, reduced subcarrier spacing increases sensitivity to synchronization errors; for a given clock error, higher carrier frequency increases residual CFO and ICI.Source: §IV · p. 9, Figure 5 · p. 9
  • With 10 ppb clock error, phase-tracking error up to 20° results in SE degradation around 2.5%.The coherent-combining loss initially decreases as SNR rises, then grows again at high SNR due to ICI.Source: §IV · p. 9, Figure 6 · p. 9
  • At SNR = 30 dB, keeping SE degradation below approximately 2% requires a Doppler-delay product below 0.1; below 9% requires it below 0.2.At maximum Doppler frequency 5 Hz, these limits correspond to feedback delays below 20 ms and 40 ms, respectively; larger products can show slight SE recovery from oscillatory Bessel correlation.Source: §IV · p. 9, Figure 7 · p. 10
  • At SNR = 26 dB, SE loss stays within 5% at numerous operating points combining clock error up to 50 ppb, Doppler-delay product up to 0.1, and phase-tracking error up to 40°.The zero-offset baseline is approximately 26.3 bit/s/Hz.Source: §IV · p. 10, Figure 8 · p. 10
  • Increasing transmitter phase-noise level increases precoder-to-effective-channel mismatch and reduces coherent-combining gain during a 25 ms feedback delay.Phase noise is modeled as filtered Gaussian noise using a baseline profile and uniform offsets of 0, 10, 20, and 30 dB.Source: §IV · p. 10, Figure 9 · p. 10
  • Residual CFO, SCO, and phase noise impose an ICI-related performance ceiling that transmit-power increases alone cannot overcome, while jitter, phase-tracking error, and CSI delay degrade SE across SNR through precoder misalignment.The simulations use a static multipath Rayleigh channel with perfect CSI and phase tracking unless otherwise stated, and assume timing offsets remain within the timing margin to avoid ISI.Source: §IV · pp. 8, 10

V. CONCLUSION AND FUTURE WORK

The conclusion synthesizes how synchronization errors and CSI delay degrade coherent joint transmission, then states operating targets and future extensions. It emphasizes that preserving coherent-combining gain requires managing these impairments together.

V. CONCLUSION AND FUTURE WORK

  • The analysis models residual timing, CFO, SCO, Doppler-induced CSI aging, and phase noise, which degrade CJT through precoder misalignment, ICI, and effective channel-gain reduction.It considers wideband multipath propagation and analyzes oscillator-induced impairments alongside channel time variation.Source: §V · p. 10
  • Start-time jitter below 10% of the sampling period causes negligible SE degradation, while residual CFO near 0.001 times subcarrier spacing also causes negligible degradation.Residual timing differences must remain within the CP; periodic correction is needed to limit SCO-driven timing drift, and larger subcarrier spacing improves frequency-error robustness.Source: §V · pp. 10–11
  • A phase-tracking error standard deviation up to 20° causes SE degradation around 2.5%.Phase tracking becomes critical for precoder alignment once residual timing, CFO, and SCO errors are sufficiently bounded.Source: §V · p. 11
  • A Doppler-delay product below 0.1 yields SE loss declining from 6% at an SNR of 0 dB to 1.7% at 40 dB.CSI delay leaves the precoder based on outdated channel information, misaligning it with beamforming directions associated with the strongest singular modes.Source: §V · p. 11
  • The study does not explicitly model path loss from spatially distributed transmitters or interferers; future work will examine those effects and compare CJT with non-coherent joint transmission.The conclusion also calls for considering impairments jointly because each can reduce coherent-combining gain and limit achievable SE improvement.Source: §V · p. 11

APPENDIX A DERIVATION WITH IDEAL SYNCHRONIZATION

The appendix derives received-data expressions by applying matched filtering to the OFDM signal. It then extends the derivation to residual timing and frequency offsets, separating desired-subcarrier and ICI components.

APPENDIX A DERIVATION WITH IDEAL SYNCHRONIZATION

  • Matched filtering extracts the kth-subcarrier data for the lth OFDM symbol and leads to a received-data expression for the receiver antenna.The ideal-synchronization derivation refers to the channel frequency response on the ith subcarrier and defines nominal per-transmitter SNR from allocated transmit power and noise variance.Source: Appendix A · p. 11

DERIVATION WITH TIME AND FREQUENCY OFFSETS

  • The offset derivation separates the desired subcarrier component from ICI terms after matched filtering.The processing start time within the CP is denoted by Δ.Source: DERIVATION WITH TIME AND FREQUENCY… · p. 11
  • Residual time offsets introduce a transmitter-dependent phasor that produces linear phase variation across subcarriers.The received signal expression is considered with only residual time offsets.Source: DERIVATION WITH TIME AND FREQUENCY… · pp. 11–12
  • Residual frequency offsets introduce transmitter-dependent phasors producing constant and symbol-dependent phase rotations.The frequency-offset expression is derived with the processing start time set to the CP duration.Source: DERIVATION WITH TIME AND FREQUENCY… · p. 12

APPENDIX C DERIVATION WITH SAMPLING CLOCK OFFSET

The derivation constructs a sampled received-signal model and applies matched filtering to obtain the received data under residual CFO and SCO. It then incorporates processing start time and timing offsets.

APPENDIX C DERIVATION WITH SAMPLING CLOCK OFFSET

  • The derivation defines the channel frequency response after substituting the transmitted-signal expression into the received-signal model.The expression is developed for the mth antenna of the qth transmitter.Source: Appendix C · p. 12
  • Sampling the received signal at interval Ts and applying the matched filter yields a received-data expression for the lth OFDM symbol.The derivation selects the lth symbol and changes the summation index to u = 0, . . . , K −1.Source: Appendix C · p. 12
  • The received-signal model includes residual CFO and SCO, then adds processing start time and the time-offset term to form the combined-offset expression.The derivation identifies q = i − k + δqTeff before using a finite-sum approximation.Source: Appendix C · p. 12

APPENDIX D DERIVATION WITH PHASE NOISE

The phase-noise derivation isolates phase noise by setting residual CFO and SCO to zero, then uses the resulting finite-sum term to express the received signal.

APPENDIX D DERIVATION WITH PHASE NOISE

  • The received signal is sampled at interval Ts before the matched filter extracts data on subcarrier k of OFDM symbol l.The sampled-signal model includes the received signal and noise.Source: Appendix D · p. 12
  • To isolate phase noise, the derivation sets residual CFO and SCO terms to zero before simplifying the finite-sum term.It then considers the lth OFDM symbol, applies matched filtering, and changes the summation index to u = 0, . . . , K −1.Source: Appendix D · p. 12
  • The resulting received-signal expression includes a phase-noise term and an ICI coefficient from subcarrier i to subcarrier k.The passage also identifies the phase-noise magnitude as bounded by 1 across subcarriers of the lth OFDM symbol from transmitter q.Source: Appendix D · pp. 12–13
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