Reliability-Optimal Pilot-Assisted Transmission for URLLC over Non-Reciprocal MISO Channels: TDD or FDD?

Yuncong Xie,Pinyi Ren,*

1 School of Information and Communications Engineering,Xi’an Jiaotong University,Xi’an 710049,China

2 Shaanxi Smart Networks and Ubiquitous Access Research Center,Xi’an 710049,China

Abstract:In this paper,we focus on the pilot-assisted transmission design for downlink URLLC over nonreciprocal channels,in which the multi-antenna controller sends mission-critical data signals to a singleantenna actuator.In this system,the prior knowledge of downlink channel state information(CSI)is a prerequisite for reliable data transmission.Generally,the acquisition of downlink CSI is completed either via the uplink pilot measurement exploiting channel reciprocity and time-division duplex(TDD)operation,or via the downlink pilot measurement with quantized feedback and frequency division duplex(FDD)operation.Inspired by this,we aim to investigate how the degree of channel non-reciprocity impacts the transmission reliability of our URLLC system,and the superiority between the TDD mode and FDD mode in terms of transmission reliability maximization.To describe the degree of reliability loss,we derive the closed-form approximations on the transmission error probability of URLLC in TDD and FDD modes,via leveraging the Gauss-Hermite and Gauss-Chebyshev quadrature rules.Following by the theoretical approximations,we demonstrate how to determine the optimal training pilot length and quantized feedback duration that maximize the transmission reliability under given latency constraint.Through numerical results,we validate the accuracy of theoretical approximations derived in this paper,and obtain some meaningful conclusions.

Keywords:URLLC;channel non-reciprocity;channel training;quantized feedback;Gaussian quadrature

I.INTRODUCTION

With the standardization and deployment of 5G wireless networks,the concept of ultra-reliable and lowlatency communications(URLLC)is regarded as a promising paradigm for supporting various emerging mission-critical Internet-of-Things(IoT)and tactile Internet applications,e.g.,self-driving cars,target tacking,industrial automation and telesurgery[1].Different from the human-to-human(H2H)communication services such as video streaming and web browsing,the payload size in typical URLLC applications is relatively small(e.g.,hundreds of bits),and the data arrival traffic is sporadic.More importantly,each URLLC packet must be delivered within an ultra-low user-plane latency(e.g.,1ms),and while meeting the strict constraint in terms of transmission error probability(e.g.,no more than 10-5)[2].Considering the propagation loss in wireless communication environment,it is very challenging to simultaneously ensure the latency and reliability constraints of URLLC.To overcome this bottleneck,some advanced technologies and network protocols were developed for supporting URLLC in wireless environment,e.g.,short frame structure[3],grant-free access[4],cooperative relaying[5],massive MIMO[6]and resource allocation optimization[7].

In practical wireless communication systems,the pilot-assisted transmission manner is widely utilized to ensure the reliable data transmission[8].Accordingly,the total transmission delay of URLLC contains the delay components caused by channel estimation and information-bearing data signals.Also,the ultralow transmission delay of URLLC(e.g.,less than 1ms)implies that the codeword blocklength of training pilot and data signals are both very limited,and then causes two fundamental challenges as follows: On the one hand,the limited training pilot length will lead to an inaccurate channel estimation,which implies that the channel estimation error is always non-zero[9].On the other hand,the short codeword blocklength of data signals also implies that the data decoding error is inevitable,even when the signal-to-noise ratio(SNR)at the receiver is arbitrarily high[10].Therefore,the conventional performance metrics such as shannon capacity and outage probability are no longer applicable to characterize the maximal achievable rate and transmission reliability of URLLC,since these metrics are established under the ideal assumption of infinite codeword blocklength.Against this background,there have been some related works[11–15]focused on the pilot-assisted transmission design for supporting URLLC in a cost-efficient manner.Considered the uplink URLLC system with randomly deployed users and shadow fading,the authors in[11]investigated the transmission reliability performance of accessing users,which is described by the transmission error probability with given E2E latency bound.Then,an iterative algorithm was developed to minimize the transmission error probability,via designing an optimal symbol duration for channel training.The authors in[12]aimed to maximize the coverage range of URLLC in industrial IoT networks under given E2E latency constraint,where the number of channel uses assigned for channel training pilot and data signals were jointly optimized to achieve this goal.The authors in[13]focused on the effective throughput maximization problem in a massive MIMO-enabled URLLC system,where the transmit power allocated to training pilot and data signals were jointly optimized.Then,an iterative power allocation algorithm was developed to solve this optimization problem.Considered the mismatch between the arrival process and service process in event-driven URLLC applications,the authors in[14]studied the statistical queuing behavior of URLLC data flows with finite-length coding and imperfect CSI,and designed the optimal training pilot length and rate adaptation strategy to minimize the delay-bound violation probability that describes the degree of transmission reliability loss.The authors in[15]focused on the optimal transmission design fordownlink URLLC system with limited training pilot length and quantized feedback bits,and attempted to maximize the average data rate through rational allocation of restricted resources.

In this research work,we are interested in the downlink URLLC transmission scenario(e.g.,industrial automation)in a multiple-input-single-output(MISO)system,where the controller equipped with multiple antennas sends mission-critical information(e.g.,remote control signals)to a single-antenna actuator.In this case,the controller needs to generate a beamforming vector for data transmission,which requires the knowledge of instantaneous downlink CSI.Generally,the acquisition of downlink CSI is deployed in time division duplex(TDD)mode or frequency division duplex(FDD)mode[16],which are respectively described as follows:In the TDD mode,the actuator first sends a predefined training pilot to measure the uplink CSI,and the controller can accordingly generates a beamforming vector based on the estimated uplink CSI and perfect channel reciprocity.In the FDD mode,the controller first sends a known training sequence to the actuator,and the actuator detects the training sequence and quantizes one particular channel vector from a predefined codebook as the estimated downlink CSI[17].Afterwards,the actuator feedbacks a beamforming vector based on the estimated downlink CSI to the controller for data transmission.Taking advantage of channel reciprocity,the channel training overhead in TDD system is much lower than FDD system,especially when the controller is equipped with a large number of transmit antennas.However,due to the mismatch of amplitude scaling and phase shift between the uplink and downlink channels,it is impractical to ensure prefect channel reciprocity in wireless communication systems[18].Meanwhile,the degree of channel reciprocity is one of decisive factors that affect the channel estimation accuracy of TDD systems.Based on the descriptions above,the transmission delay and reliability loss components for URLLC in TDD and FDD modes are summarized in Table 1,and it is essential to revisit the superiority between the TDD mode and FDD mode when designing the pilotassisted transmission scheme for downlink URLLC over non-reciprocal channels.However,this fundamental question is still unsolved in the existing literatures.

Table 1.The transmission delay and reliability loss components for URLLC in TDD and FDD modes.

Motivated by this open issue,we attempt to investigate the transmission reliability of URLLC over downlink non-reciprocal MISO channels,and illustrate how the degree of channel non-reciprocity impacts the superiority between TDD mode and FDD mode in terms of transmission reliability maximization.Specifically,the main contributions of this research work are enumerated as follows:

1.In the TDD mode,the total transmission delay of URLLC contains the symbol durations of training pilot and information-bearing data signals.Therefore,the reliability loss of URLLC in TDD mode is caused by the channel reciprocity error,channel estimation error and data decoding error.To describe the degree of reliability loss,we first derive the expression of transmission error probability of URLLC in TDD mode.Since the above expression has an intractable form,we also derive a closed-form approximation to simplify the calculation,via leveraging the Gauss-Hermite and Gauss-Chebyshev quadrature rules.Following by this approximation,we also demonstrate how to determine the optimal training pilot length that maximizes the transmission reliability of URLLC system in TDD mode.

2.Different from TDD mode,the FDD mode removes the impact of channel non-reciprocity,at the expense of additional quantized feedback error.Therefore,the reliability loss of URLLC in FDD mode is caused by the channel estimation error,quantized feedback error and data decoding error.Similar to the previous section,we first derive the closed-form approximations of transmission error probability of URLLC in FDD mode.Then,we analyze how to maximize the transmission reliability of URLLC system in FDD mode,via jointly optimizing the codeword blocklength of training pilot and quantized feedback bits.

3.Through extensive numerical evaluations,we validate the accuracy of theoretical derivations presented in this paper,and illustrate how the degree of channel non-reciprocity impacts the superiority between the TDD mode and FDD mode in terms of transmission reliability maximization.Meanwhile,we also illustrate how the particular system parameters impact the transmission performance of our URLLC system.

The remainder of this paper is organized as follows:In Section II,we introduce the system model considered in this paper and the transmission procedures of TDD and FDD modes.Meanwhile,we also provide the general expression of transmission error probability of URLLC with short blocklength coding.In Section III,we provide theoretical derivations to describe the transmission reliability of our URLLC system in TDD mode.Moreover,the reliability analysis and optimization for URLLC in FDD mode is presented in Section IV.Numerical results are implemented in Section V and the paper is concluded in Section VI.

II.SYSTEM MODEL DESCRIPTION

2.1 TDD Mo de

2.2 FDD Mode

2.3 Finite-Blocklength Performance Metric

III.RELIABILITY ANALYSIS AND OPTIMIZATION IN TDD MODE

IV.RELIABILITY ANALYSIS AND OPTIMIZATION IN FDD MODE

V.NUMERICAL RESULTS

In this section,we provide extensive numerical results to validate the accuracy of theoretical approximations derived in this paper,and illustrate how the particular system parameters impact the transmission reliability of our URLLC system.The simulation parameters are listed as follows,unless otherwise specified:The communication distance from controller to actuator is set tod=250m,and the path-loss coefficient is given by-10 log10β=35.3+37.6 log10d.Each URLLC message with size ofL=256 information bits is transmitted over a dedicated bandwidth ofW=360kHz[25].For the reader’s convenience,we remind that the total available number of channel uses within one millisecond is 360.The single-side noise spectral density isN0=-174 dBm/Hz,and the variance of AWGN is expressed as Ω0=N0W.The transmit power of channel training pilot and information-bearing data signals are respectively set toρt=5dBm andρs=10dBm.As depicted in Figure 3,we illustrate how the transmission error probabilityϵof our URLLC system changes as the transmission latencymvaries,and validate the accuracy of closed-form approximations presented in this paper.Specifically,the Gauss-Hermite quadrature parametersandused in our derived approximations are shown in Table 2,and the Gauss-Chebyshev quadrature parameters are respectively given byN= 50 andϱ= 30.Firstly,we can clearly observe that the approximations derived in(23)and(33)almost perfectly coincide the integral values in(13)and(28),which validates the accuracy of theoretical derivations in this paper.Secondly,the transmission error probability of URLLC in TDD mode significantly rises as the channel reciprocity coefficientφdeclines,due to the negative impact of channel non-reciprocity error on the channel estimation accuracy in TDD mode.More importantly,the transmission error probability of URLLC always declines as the transmission latency increases.In other words,there exists a fundamental tradeoff between the latency and reliability when designing the pilot-assisted transmission scheme for URLLC,i.e.,the transmission error probability can be suppressed via relaxing the latency constraint,and vice versa.

Figure 1.The transmission procedure of URLLC in TDD mode,including the uplink channel training and downlink data transmission.

Figure 2.The transmission procedure of URLLC in FDD mode,including the downlink channel training,uplink quantized feedback and downlink data transmission.

Figure 4.The transmission error probability ϵ vs.the channel reciprocity coefficient φ,where AT = {2,4,8,12}and m=180(channel uses).

Table 2.The Gauss-Hermite quadrature parameters when M =3[22].

Table 2.The Gauss-Hermite quadrature parameters when M =3[22].

Index iaibi 14.46029770466658e-1 1.90554149798192e-1 23.96468266998335e-1 8.48251867544577e-1 34.37288879877644e-2 1.79977657841573e0

Figure 3.The transmission error probability ϵ vs.the total transmission latency m(channel uses),where AT = 4 and φ={0.7,0.8,0.9,1}.

In Figure 4,we illustrate how the degree of channel non-reciprocity impacts the superiority between TDD mode and FDD mode in terms of transmission reliability maximization.On the one hand,the transmission reliability of URLLC in TDD mode is superior to the FDD mode as long as the channel reciprocity coefficientφis not less than a certain thresholdφth.This phenomenon is explained as follows: whenφ ≥φth,the quantized feedback error in FDD mode causes a higher degree of transmission reliability degradation compared to the additional non-reciprocity error in TDD mode.On the other hand,the thresholdφthgradually declines as the number of transmit antennas at the controller increases,i.e.,the performance advantage of TDD mode will gradually obvious.For instance,the value ofφthdeclines from 0.95 to 0.7 as the number of transmit antennasATincreases from 2 to 8.This is because the channel training power at each antennaρt/ATand the quantized feedback errorin FDD mode is inversely proportional to the value ofAT,and the constraintmt ≥ATmust be guaranteed in FDD mode.Therefore,more channel training and quantized feedback overheads are required to ensure the reliable data transmission in FDD mode whenATincreases,while the channel training overhead required in TDD mode does not change.As a supplementary to Figure 4,we also provide Figure 5 to depict how the latency constraint impacts the superiority between TDD mode and FDD mode in terms of transmission reliability maximization.It is not hard to observe thatφthgradually rises as the transmission latencymincreases,and this phenomenon is explained as follows: Compared to the TDD mode,a longer training pilot and additional quantized feedback overhead are required in FDD mode to ensure the reliable data transmission,and this performance disadvantage will be gradually marginalized via loosing the latency constraint.Meanwhile,the FDD mode removes the negative impact of channel non-reciprocity.Based on the discussions above,we can obtain that the performance advantage of FDD mode will gradually obvious as the transmission latency increases.

Figure 5.The transmission error probability ϵ vs.the channel reciprocity coefficient φ,where AT = 8 and m ={180,270,360}(channel uses).

Figure 6.The transmission error probability ϵ under different resource allocation strategies vs.the number of transmit antennas at controller AT,where φ=0.8.

Figure 7.The transmission error probability ϵ in the short blocklength regime and the conventional outage probability ϵout with asymptotically infinite blocklength assumption vs.the training pilot length mt(channel uses),where AT = 8,m=180(channel uses)and φ={0.8,1}.

In Figure 6,we demonstrate that optimizing resource allocation strategies for URLLC,i.e.,determine the optimal training pilot length and quantized feedback duration,are efficient to improve the transmission reliability under given latency constraint.To confirm this viewpoint,we introduce a benchmark strategy called asfixed-ratio overheads allocation(FROA)to provide comparable results,in which both the training pilot lengthmt= 0.25mand the quantized feedback durationmf= max{0.1m,AT-1}(is equal to zero in TDD mode)are fixed.To gain a comprehensive insight,we also provide the following two resource configurations for comparison: 1)m= 180(channel uses),ρt= 5dBm,ρs= 10dBm,and 2)m= 200(channel uses),ρt= 7dBm,ρs=14dBm.It can be clearly seen from Figure 6 that the transmission reliability performance of our proposed strategy is always superior to the FROA-based transmission strategy.From this phenomenon,we can validate the effectiveness of resource allocation optimization in terms of improving the transmission reliability of our URLLC system.In addition,the transmission reliability performance of our URLLC system with resource configuration 1 andAT=16 is superior to the case with resource configuration 2 andAT= 4.Seen from a different perspective,we can conclude that the multi-antenna transmission has significant advantages in terms of reducing the latency consumption required to support URLLC,as well as improving the energy efficiency of our considered URLLC system.

As depicted in Figure 7,we illustrate how the optimization variables(i.e.,the training pilot lengthmtand the quantized feedback durationmf)impact the transmission reliability of our URLLC system in TDD and FDD modes.Meanwhile,we also demonstrate how the short-blocklength characteristic of URLLC impacts the evaluation of transmission reliability,via comparing the finite-blocklength(FBL)transmission error probability derived in this paper and the conventional outage probability with asymptotically infinite blocklength assumption.Specifically,the outage probability is expressed aswhereR=L/msdenotes the data rate andFγ(z)is the CDF of instantaneous received SNRγ.It can be clearly seen that the FBL transmission error probabilityϵderived in this paper is always higher than the outage probabilityϵout.Therefore,the outage probability derived from conventional shannon theory is not applicable to evaluate the transmission performance of URLLC,since it significantly underestimates the degree of reliability loss in URLLC systems.Meanwhile,the transmission error probability declines at first and then rises as the training pilot lengthmtincreases,and there exists a unique optimal training pilot lengththat minimizes the transmission error probability.This phenomenon is explained as follows: As the training pilot lengthmtincreases,the transmission error probabilityϵfirst declines thanks to the improvement of channel estimation accuracy.However,whenmtis too largethe remaining duration for data transmission is too short and the improvement of channel estimation accuracy is gradually marginalized,which leads to the degradation of transmission reliability.Additionally,the transmission error probabilityϵalso declines at first and then rises as the quantized feedback durationmfincreases.For example,ϵdeclines whenmfincreasing from 6 to 18,and rises whenmfincreasing from 18 to 29.This is due to the fact that a longer quantized feedback durationmfimplies a lower quantized feedback error,and the channel estimation accuracy is improved indirectly.However,whenmtis too large,the remaining durations for channel training and data transmission are insufficient and then leads to the degradation of transmission reliability.Based on the descriptions above,we can conclude that designing an appropriate tradeoff between the training pilot lengthmt,quantized feedback durationmfand codeword blocklength of data signalsmsunder given latency constraint is indispensable for the transmission reliability maximization in URLLC systems.

VI.CONCLUSIONS

In this research work,we focused on the pilot-assisted transmission design for URLLC over downlink nonreciprocal MISO channels,and investigated the transmission reliability of our considered URLLC system.Specifically,we derived the closed-form approximations on the transmission error probability of URLLC in TDD and FDD modes,via using the Gauss-Hermite and Gauss-Chebyshev quadrature rules.Following by the derived theoretical approximations,we also developed efficient algorithms to determine the optimal system parameters that maximize the transmission reliability under given latency constraint.Through numerical results,we validated the accuracy of theoretical approximations presented in this paper,and obtained the following conclusions that offers some design guidelines for pilot-assisted URLLC transmission over nonreciprocal channels:

1.There exists a fundamental tradeoff between the latency and reliability when designing the transmission scheme for URLLC,i.e.,the transmission error probability can be suppressed via loosening the latency constraint,and vice versa.

2.If and only if the number of transmit antennas is relatively small and the channel reciprocity coefficient is lower than a certain threshold,the transmission reliability performance of URLLC in FDD mode is superior to the TDD mode.Additionally,the performance advantage of TDD mode will gradually obvious as the number of transmit antennas increases,especially when the latency constraint is stringent.

3.The transmission reliability of URLLC can be significantly improved via increasing the number of transmit antennas,as well as designing an appropriate tradeoff between the training pilot length,quantized feedback duration and codeword blocklength of data signals.Seen from a different perspective,the multi-antenna transmission also has significant advantages in terms of reducing the latency consumption required to support URLLC,as well as improving the energy efficiency of our URLLC system.

ACKNOWLEDGEMENT

This research work was supported in part by the National Natural Science Foundation of China(NSFC)under Grant No.62071373,in part by the Innovation Talents Promotion Program of Shaanxi Province under Grant No.2021TD-08,in part by Fundamental Research Funds for the Central Universities under Grant No.xzy022020055,and also in part by the Zhejiang Lab’s International Talent Fund for Young Professionals.