In this work we propose a communication and

control joint design strategy using packetized predictive control

and halted Chase combining hybrid automatic repeat request

to minimize the bandwidth required to provide ultra-reliable

low latency communications towards wireless networked control

systems. The joint design nature comes from tunning at the

same time both the length of the control horizon, a control

parameter, and the maximum number of transmission attempts,

a communication variable. Numerical results show that by using

this strategy and correctly choosing the parameters, significant

savings in bandwidth can be achieved

Imran, Muhammad

Nadas, João P.B.

Souza, Richard D.

Zhao, Guodong

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Leveraging Retransmissions in Wireless Networked Control Systems with Packetized Predictive Control

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       Nadas, J. P.B., Zhao, G., Souza, R. D. and Imran, M. (2018) Leveraging Retransmissions in Wireless Networked Control Systems with Packetized Predictive Control. 2018 IEEE Wireless Communications and Networking Conference (WCNC), Barcelona, Spain, 15-18 Apr 2018.     There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it.    http://eprints.gla.ac.uk/157534/               Deposited on: 19 February 2018                       Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk    Leveraging Retransmissions in Wireless NetworkedControl Systems with Packetized Predictive ControlJoão P. B. Nadas⇤ ,Guodong Zhao⇤†, Richard D. Souza‡ and Muhammad A. Imran⇤⇤School of Engineering, Univesrity of Glasgow, Scotland, United Kingdom†National Key Lab. on Communications, UESTC, Chengdu, China‡Federal University of Santa Catarina, Florianópolis, BrazilAbstract—In this work we propose a communication andcontrol joint design strategy using packetized predictive controland halted Chase combining hybrid automatic repeat requestto minimize the bandwidth required to provide ultra-reliablelow latency communications towards wireless networked controlsystems. The joint design nature comes from tunning at thesame time both the length of the control horizon, a controlparameter, and the maximum number of transmission attempts,a communication variable. Numerical results show that by usingthis strategy and correctly choosing the parameters, significantsavings in bandwidth can be achieved.I. INTRODUCTIONFactory automation constitutes one of the most relevantapplications of ultra-reliable low latency communications(URLLC) [1]. Using a wireless network in networked controlsystems (NCS) provides great flexibility, quick deploymentand increased modularity to a wide range of factory au-tomation applications [2], however, wireless communicationsintroduce random probabilities of packet dropouts, which posea significant challenge to the stability and performance of theNCS [3]. Since the target error rates and latencies can be verystringent in NCS applications (i.e. 10 9 and 1 ms) [4], jointdesign techniques—wherein both communication and controlparameters are considered at the same time—are crucial toprovide URLLC performance whilst minimizing wireless re-source consumption [5].One way of dealing with random packet dropouts in thecontroller to actuator link is to use a model predictive con-troller (MPC) to generate K control signals and send themin one packet to the actuators, such that if the next packetfails, the following instruction is available for execution. Thisis known as packetized predictive control (PPC) [3]. In thiswork we propose a joint design strategy using PPC andhalted Chase combining hybrid automatic repeat request (CC-HARQ), wherein any failed packet is retransmitted up toz times and the message is combined at the receiver withall previous failed attempts using maximum ratio combiningbefore decoding.II. SYSTEM MODELA. Control ArchitectureConsider a networked control architecture with a wirelesslink connecting the controller to the actuator—which is po-Corresponding author: JPB Nadas (j.battistella-nadas.1@research.gla.ac.uk)sitioned at the plant—, as illustrated in Figure 1. PPC isperformed such that a buffer stores the vector u(t), whichcontains K control signals to be used if a packet is dropped.Controller Channel Buffer Plant✏s(t) r(t) u(t)Fig. 1: Control architecture with a wireless link connectingcontroller and actuator considering ✏ packet drop probability.In PPC, sending longer packets to include the additionalcontrol signals creates a trade-off, as it increases the messagelength (which imposes higher transmit rates for the samelatency) resulting in a higher probability of a communicationerror, while at the same time it making the system more faulttolerant. The stability and performance of the NCS depend onthe packet drop rate ✏c and on the communication latency  .B. Communication ModelAt every instant t a packet containing K control signalsis sent to the buffer, such that the received signal, r(t), isexpressed by r(t) = h(t)s(t)+w(t). Here s(t) is the generatedsignal at the controller, w(t) is the additive white Gaussiannoise (AWGN) and h(t) is the wireless channel gain, whichis random and follows a Nakagami-m distribution. Since inNCS the mobility is very low, the channel does not varybetween symbols. Also, slow frequency hopping is considered,so subsequent transmissions are performed in an uncorrelatedfrequency channel and thus the channel model is block-fading.The probability of dropping a packet ✏ depends on thecondition of the wireless channel. As there is a strict max-imum deadline, the capacity at finite block length should beconsidered in order to obtain achievable rates. However, sincethe channel is block-fading and the rates are relatively high,as is the SNR, the average error probability can be tightlyapproximated by the outage probability [6].Considering the header length LH and the control signallength LU, both in bits, the total length of the forward packetLT is equal to LH +KLU. Lastly, the minimum bit rate Rb tomeet the target latency isRb =LT . (1)We use the minimum bit rate because using a larger one wouldresult in a higher error probability for the same bandwidth B.III. PROPOSED SOLUTIONThe proposed solution works by the controller attempting tosend a packet containing K control signals every   seconds. Ifthe packet fails, a retransmission is attempted using the CC-HARQ strategy and this is repeated up to z times. This isenabled by the fact that in PPC at any sampling instant t, Kcontrol signals are transmitted and thus if a message is decodedon instant t + j, the controller can obtain K   j relevantcontrol signals. The maximum value of z which guaranteesthe availability of every control signals is dK/2e1.By carefully choosing the value for z and K, it is possibleto optimize communication resources while still meeting thecontrol design target. Since energy is not critical at thecontroller or the actuator, the focus of this work is to minimizethe required bandwidth B for each transmission2.The outage probability Pout,z after z rounds in CC-HARQis approximated at high signal to noise ratio (SNR) by [7]Pout,z ⇡⇣m 0 ̄⌘mz (mz + 1), (2)where m is the Nakagami-m parameter which relates to line ofsight (LOS) conditions,  0 = 2Rb/B 1 is the outage thresholdfrom the channel capacity,  (.) is the gamma function and theaverage SNR  ̄ is obtained via ̄ =PtBN0MlA0d↵. (3)In (3), Pt is the transmit power, N0 is the noise spectralpower density, A0 is the loss at a reference distance, d isthe distance between transmitter and receiver, ↵ is the pathloss exponent and Ml is a link margin which accounts for anyunforeseen losses, including the noise figure. Since a minimumerror probability must be guaranteed, Pout,z  ✏c must hold.Thus, using (2) and (3) we arrive atB⇣2RbB   1⌘  , (4)where   = (✏c (mz+1))1/mzPtmN0MlA0d↵. Using W 1, the lower part ofthe main Lambert-W function, (4) becomesB    Rb ln(2)W 1( Rb ln(2)  ). (5)Since W 1 can only yield real values for inputs greater thanor equal to  1/e (where e is Euler’s constant), using (1) andanalyzing the argument of W 1 in (5) provides the boundK  1LU✓  e ln(2)  LH◆. (6)1Using z > dK/2e violates the target error probability because when amessage is decoded after having failed j > dK/2e times, only K j controlsignals are not outdated and the next packet would have to succeed in K  jattempts, which is less than dK/2e by definition.2The excess bandwidth consumed due to slow frequency hopping betweendifferent transmission attempts is not an issue since in CC-HARQ the averagenumber of retransmissions is typically close to one, even for large values ofz, when the target error probability is very low, as in URLLC.2 3 4 5 6 7 8 9 101015202530354045z = 2, 3, 4, 5Optimal K and zLength of Prediction Horizon KRequiredBandwidthB(KHz)Fig. 2: Required bandwidth for different values of K and z.Finally, we write the optimization problem asminimizeK 2 N⇤, z 2 N⇤B = Rb ln(2)W 1( Rb ln(2)  )(7a)subject to z ⌃K/2⌥, (7b)which can be tackled numerically.IV. NUMERICAL RESULTSTo illustrate the effect of K and z in the required bandwidth,we have performed numerical simulations computing B from(7) using ✏c = 10 9,   = 1 ms, Pt =  30 dB, d = 10 m,LH = 40 bits, LU = 16 bits, Ml = 10 dB, N0 =  204dB, A0 = 30 dB, m = 1 and ↵ = 3. Figure 2 shows theminimum required bandwidth for different values of K. Eachcurve represents a value of z, ranging from 2 to 5. Using theinequality in (6), we can observe that K would have to assumea negative value for z = 1, which is not possible. Here thebest choice of parameters is K = 5 and z = 3.REFERENCES[1] B. Holfeld, D. Wieruch, T. Wirth, L. Thiele, S. A. Ashraf, J. Huschke,I. Aktas, and J. Ansari, “Wireless communication for factory automation:An opportunity for LTE and 5G systems,” IEEE Commun. Mag., vol. 54,no. 6, pp. 36–43, 2016.[2] P. Park, “Traffic generation rate control of wireless sensor and actuatornetworks,” IEEE Commun. Lett., vol. 19, no. 5, pp. 827–830, May 2015.[3] D. E. Quevedo, J. Ostergaard, and D. Nesic, “Packetized predictive controlof stochastic systems over bit-rate limited channels with packet loss,”IEEE Trans. Autom. Control, vol. 56, no. 12, pp. 2854–2868, Dec. 2011.[4] S. Ashraf, Y. P. E. Wang, S. Eldessoki, B. Holfeld, D. Parruca, M. Serror,and J. Gross, “From radio design to system evaluations for ultra-reliableand low-latency communication,” in Proc. European Wireless 2017; 23thEuropean Wireless Conf, May 2017, pp. 1–8.[5] P. Park, S. C. Ergen, C. Fischione, C. Lu, and K. H. Johansson, “Wirelessnetwork design for control systems: A survey,” IEEE Commun. SurveysTuts., vol. PP, no. 99, p. 1, 2017.[6] P. Mary, J. M. Gorce, A. Unsal, and H. V. Poor, “Finite blocklengthinformation theory: What is the practical impact on wireless communi-cations?” in IEEE Globecom Workshops, Dec. 2016, pp. 1–6.[7] V. A. Aalo, “Performance of maximal-ratio diversity systems in a cor-related Nakagami-fading environment,” IEEE Trans. Commun., vol. 43,no. 8, pp. 2360–2369, 1995.

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Leveraging Retransmissions in Wireless Networked Control Systems with Packetized Predictive Control

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