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Can Terahertz Provide High-Rate Reliable Low Latency Communications for Wireless VR?

Christina Chaccour, Mehdi Naderi Soorki, Walid Saad, Mehdi Bennis, Petar Popovski

arXiv:2005.00536v2cs.IT

TL;DR

The paper investigates whether THz communications can support transmission requiring high reliability and high rates. It analyzes E2E-delay tails and TVaR, derives delay and reliability expressions, and finds that guaranteeing LoS is primary for improving tail performance and system reliability.

  • Problem

    High-rate and high-reliability transmission must be supported simultaneously for wireless VR communications.

  • Method

    The paper derives E2E-delay and reliability expressions, analyzes the E2E-delay tail through lower-order moments and TVaR, and conducts asymptotic analysis.

  • Results

    Guaranteeing LoS is of primary importance for improving tail performance, while artificial THz links significantly improve system reliability.

  • Takeaways & Limitations

    Tail-based E2E-delay performance analysis is fundamental for characterizing worst-case reliability in THz wireless systems.

Abstract

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Wireless virtual reality (VR) imposes new visual and haptic requirements that are directly linked to the quality-of-experience (QoE) of VR users. These QoE requirements can only be met by wireless connectivity that offers high-rate and high-reliability low latency communications (HRLLC), unlike the low rates usually considered in vanilla ultra-reliable low latency communication scenarios. The high rates for VR over short distances can only be supported by an enormous bandwidth, which is available in terahertz (THz) frequency bands. Guaranteeing HRLLC requires dealing with the uncertainty that is specific to the THz channel. To explore the potential of THz for meeting HRLLC requirements, a quantification of the risk for an unreliable VR performance is conducted through a novel and rigorous characterization of the tail of the end-to-end (E2E) delay. Then, a thorough analysis of the tail-value-atrisk (TVaR) is performed to concretely characterize the behavior of extreme wireless events crucial to the real-time VR experience. System reliability for scenarios with guaranteed line-of-sight (LoS) is then derived as a function of THz network parameters after deriving a novel expression for the probability distribution function of the THz transmission delay. Numerical results show that abundant bandwidth and low molecular absorption are necessary to improve the reliability. However, their effect remains secondary compared to the availability of LoS, which significantly affects the THz HRLLC performance. In particular, for scenarios with guaranteed LoS, a reliability of 99.999% (with an E2E delay threshold of 20 ms) for a bandwidth of 15 GHz along with data rates of 18.3 Gbps can be achieved by the THz network (operating at a frequency of 1 THz), compared to a reliability of 96% for twice the bandwidth, when blockages are considered.

I. INTRODUCTION

Wireless VR requires high-rate and high-reliability low-latency communication, motivating THz networks while making blockage and channel uncertainty central concerns. The paper studies whether THz can provide HRLLC by analyzing E2E-delay tails, TVaR, and reliability.

  • VR requires high rates and high reliability simultaneously to transmit large content packets within a low latency constraint.
  • 1911.03 Gbps is the stated uncompressed bit rate for ultimate VR, motivating investigation beyond mmWave toward THz bands.
  • THz propagation is short-range and susceptible to blockages and molecular absorption, producing an on-off wireless link.
  • Prior wireless-VR studies mainly examine average delays and data rates, providing limited information about reliability and extreme E2E behavior.
  • The paper introduces an MHCPP-based VR model and analyzes E2E-delay tails, TVaR, and THz reliability for HRLLC.
  • The work presents itself as the first analysis of reliability and latency achieved by VR services over a THz cellular network.

C. Main Findings

The paper’s findings emphasize that tail delays, LoS availability, and blockage behavior determine wireless-VR reliability in THz networks. Bandwidth and molecular absorption help, but LoS is the primary reliability factor.

  • Tail delays capture extreme events such as deep fades and blockages, whereas average delay can give overly optimistic THz-VR performance predictions.
  • THz HRLLC requires mechanisms that guarantee LoS and alleviate harsh propagation conditions.
  • Increasing bandwidth and reducing molecular absorption lower the risk of worst-case extreme events but are insufficient to sustain reliable experience alone.
  • TVaR reliability above 90% is possible only at tail delays of 100 ms even with 30 GHz bandwidth.
  • With continuously available LoS, 99.999% reliability at a 20 ms E2E threshold and 18.3 Gbps is achievable.

B. Wireless Model and Data Rate

The wireless model represents THz links primarily through LoS propagation, molecular absorption, interference, noise, and bandwidth-dependent achievable rate. LoS probability is treated as a key determinant of rate and VR QoE.

  • The model considers short user-to-SBS distances and therefore uses only the LoS link for total path loss.
  • THz propagation is modeled with molecular absorption transmittance τ(f,r) ≈ exp(−K(f)r), where K(f) is the medium’s absorption coefficient.
  • Total receiver noise combines molecular absorption noise with Johnson-Nyquist noise, while interference comes from other SBSs.
  • The instantaneous LoS rate depends on frequency, received signal, interference, noise, and bandwidth W.
  • The total rate combines LoS and NLoS rates, with NLoS contribution treated as negligible because of the significant LoS–NLoS power gap.
  • LoS probability is derived from static and dynamic blockage probabilities and can degrade rate and affect VR QoE.

C. Interference Analysis

The interference analysis approximates dense-network interference as normally distributed and uses the resulting delay distribution to study THz HRLLC under extreme events. Tail analysis is needed because rate alone does not determine reliability.

  • Dense MHCPP-distributed SBS interference converges asymptotically to a normal distribution, making the analysis tractable.
  • THz networks require dense deployments to address range limitations and reduce blockage likelihood, while minimum node spacing prevents arbitrarily close SBSs.
  • Large THz bandwidth can meet rate requirements, but reliability remains uncertain because of THz propagation conditions.
  • The paper characterizes the E2E-delay tail to describe worst-case performance and derives its associated TVaR.

III. RELIABILITY ANALYSIS

The analysis derives the probability of an available LoS link and uses it to study tail reliability and unreliable VR experience risks at THz frequencies. Blockage availability is central: larger self-blockage sectors reduce LoS availability, while network parameters affect it exponentially.

  • The section evaluates blockage probability and tail E2E-delay risks for unreliable VR experience at THz frequencies.
  • A LoS path is necessary for the promised high THz rate, motivating a probability model for available LoS links.
  • The derived LoS probability captures blockage susceptibility as an exponential function of network parameters.
  • Larger VR-blocker regions and larger self-blockage sectors reduce LoS availability.

1) Queuing Analysis:

The queuing model represents VR processing and THz transmission as two sequential queues, then analyzes their combined delay to assess dual high-rate and low-latency reliability requirements. The model emphasizes that extreme delay events, not averages alone, matter for VR QoE.

  • The VR service model uses Q1 for 360° VR-content processing and Q2 for wireless transmission.
  • The total delay combines waiting and processing at Q1 with waiting and transmission at Q2.
  • Q1 is modeled as an M/M/1 queue with Poisson arrivals, FCFS service, infinite buffering, and service rate µ1 > λ1.
  • Q2 is modeled as an M/G/1 queue because its transmission service time depends on VR-content size, LoS rate, and the random THz channel.
  • The framework targets dual HRLLC QoS: high data rate for visual perception and low latency for haptic perception.
  • Reliability analysis must account for the full delay distribution because sudden movements or blockages can create extreme events that averages miss.

2) Tail Reliability Analysis:

The tail-reliability analysis models extreme E2E delays rather than relying on averages, using moments and extreme-value methods to quantify unreliable-experience risk. It then derives TVaR as a risk measure for HRLLC.

  • The analysis uses tail behavior because average or median E2E delay does not guarantee continuous reliability under dynamic wireless conditions.
  • Reliability is defined as the probability that E2E delay remains below a stringent threshold δ.
  • Extreme-value theory models the maximum E2E delay using block maxima and a generalized extreme-value distribution.
  • The E2E-delay moments are matched to the GEV model, producing a tractable tail distribution not characterized in prior cited work.
  • The GEV location equals the average E2E delay, its scale equals the E2E-delay variance, and its shape depends on the number of VR requests per session.
  • TVaR quantifies E2E-delay values at specified confidence levels, characterizing worst-case delay and risk of unreliable experience.

IV. RELIABILITY FOR SCENARIOS WITH GUARANTEED LOS

For guaranteed-LoS scenarios, the paper derives the transmission-delay PDF and the resulting E2E-delay CDF to obtain tractable reliability as a function of THz channel parameters. The analysis highlights communication distance and molecular absorption as important constraints.

  • Assuming continuous LoS, the model derives the transmission-delay PDF and combines it with queueing distributions to obtain the E2E-delay CDF.
  • The resulting reliability is the probability that E2E delay stays below threshold δ and is characterized as a function of THz channel parameters.
  • The E2E delay is often dominated by THz transmission delay when MEC processing is sufficiently fast.
  • Increasing user-to-SBS distance sharply deteriorates reliability because molecular absorption increases and limits THz communication range.
  • The full E2E-delay PDF provides reliability information without relying only on averages or tail distributions.
  • In guaranteed-LoS scenarios, robust reliability is constrained by short communication range from molecular absorption and interference from high network density.
  • Figure 3 compares fitted and simulated PDFs for tail E2E delay and transmission delay under guaranteed LoS.

V. SIMULATION RESULTS AND ANALYSIS

Simulations show that average delay can make THz VR appear reliable while extreme blockage events create substantially worse tail delays. Reliability improves with bandwidth and lower molecular absorption, but LoS availability is the dominant factor.

  • Tail-delay behavior: At 1 THz, average E2E delay stays below 20 ms, but a single blockage can impose a minimum tail delay of 30 ms and disrupt the VR experience.Average-delay behavior therefore gives a more favorable reliability impression than tail-delay behavior.
  • Bandwidth and blockage effects: At 20 GHz bandwidth, blockages increase Q2 delay from 0.3 ms to 4 ms at THz frequencies and from 0.23 ms to 3.5 ms at sub-THz frequencies.Increasing bandwidth improves performance, but in blockage scenarios bandwidth up to 30 GHz is not sufficient to guarantee high reliability.

VI. CONCLUSION

The paper develops a tail-focused reliability analysis for THz wireless VR and identifies line-of-sight availability as the primary determinant of reliable performance. Bandwidth and molecular absorption matter, but continuous LoS remains challenging and other impairments persist even after LoS is guaranteed.

  • Contributions: The study derives the E2E delay distribution, its tail and TVaR, and a reliability expression for THz VR networks.The model uses a two-tandem-queue formulation and derives the transmission-delay PDF before obtaining E2E delay and reliability expressions.
  • Scope: Blockage-related LoS unavailability disrupts user QoE and increases E2E delay, motivating reliability analysis beyond average delay.The conclusion links extreme events and unavailable LoS paths to unreliable VR experience.
  • Contributions: Tail-based E2E-delay analysis characterizes extreme events that average-delay metrics can miss.The tail analysis is used to represent worst-case behavior under high uncertainty and extreme network conditions.
  • Key observations: Guaranteeing LoS is of primary importance for improving tail performance, while outdoor settings and highly mobile users make this guarantee more difficult.The paper suggests increasing LoS availability through user micro-mobility and micro-orientation prediction, with RIS and multi-band control as possible directions.
  • Future directions: AI-based prediction is identified as a promising future direction for mitigating the intermittent nature of THz links and improving system reliability.The proposed extension concerns predicting user micro-mobility and micro-orientation at every time step.
  • Key observations: After LoS is guaranteed, molecular absorption, short communication range, and interference from high network density still impede THz reliability.The conclusion calls for predictive mechanisms that can handle the large-scale nature of wireless networks.

APPENDIX A. Proof of Proposition 1

The appendix derives the LoS probability and the first two moments of transmission delay from the network model. It uses conditional path distributions, independence, Taylor approximation, and Jensen’s inequality to obtain the required quantities.

  • LoS probability: The proof derives the conditional and marginal probability of LoS by integrating over independently distributed SBS distances.The independent-distance assumption yields a powered conditional density and an expression for P(Λ|q).
  • Transmission delay: The transmission delay is expressed using VR content size and the LoS rate, then transformed from the interference distribution to obtain its PDF.The derivation treats interference as the random term in the rate expression and applies a change of variables.
  • Moments: The first two moments of transmission delay are computed using independence between P(Λ) and C_L, together with first-order Taylor approximation.The VR image size is treated as constant, and the mean is factored into expectations involving LoS probability and rate.
  • Moment bounds: Jensen’s inequality is applied to the rate and delay functions because their curvature with respect to interference bounds the corresponding expectations.The derivation uses convexity of the rate and concavity of transmission delay to obtain the required inequalities.
  • Role in reliability analysis: The resulting moments support the paper’s characterization of E2E-delay statistics and system reliability under uncertainty.The appendix connects the transmission-delay moments to the broader reliability analysis.

C. Proof of Lemma 1

This appendix derives the second moment of E2E delay for the tandem queues and identifies parameters for modeling its tail with a generalized extreme-value distribution. It also derives the transmission-delay PDF from the interference distribution.

  • Queueing derivation: The first queue’s second waiting-time moment is obtained from its M/M/1 formulation, while the second queue requires a Laplace-Stieltjes transform.Higher-order derivatives of the transform are evaluated using L’Hopital’s rule to resolve indeterminate limits.
  • Queueing derivation: The second-moment derivation separates numerator and denominator derivatives before substituting the resulting expression into the E2E-delay formula.This manipulation is used to handle the challenging limits arising in the transform calculation.
  • E2E-delay moments: The E2E delay is formed from the waiting times of two queues, whose independence follows from Burke’s Theorem.The second moment combines the queue-specific second moments with twice the product of their means.
  • Tail model: The positive support of delay imposes a positive-support condition on the generalized extreme-value model used for the delay tail.The appendix identifies the GEV parameters by matching its moments with the derived E2E-delay moments.
  • Transmission-delay PDF: The transmission rate is rewritten in terms of content size and a delay-related variable, with interference assumed to follow a normal distribution.Transforming the interference PDF through the transmission-delay relation yields the transmission-delay PDF.
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