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Dynamic Connectivity for Robust Applications in Rayleigh-Fading Channels Tom Hößler, Lucas Scheuvens, Philipp Schulz, André Noll Barreto, Meryem Simsek, and Gerhard P

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Dynamic Connectivity for Robust Applications in Rayleigh-Fading Channels Tom Hößler, Lucas Scheuvens, Philipp Schulz, André Noll Barreto, Meryem Simsek, and Gerhard P 1 Dynamic Connectivity for Robust Applications in Rayleigh-Fading Channels Tom Hößler, Lucas Scheuvens, Philipp Schulz, André Noll Barreto, Meryem Simsek, and Gerhard P. Fettweis Abstract—The fifth generation (5G) of mobile networks envi- the duration of failures into account is gaining interest in the sions ultra-reliability in wireless communications. One common area of wireless communications systems: Related concepts approach to guarantee that is diversity, e.g., by sending data comprise "survivability", "minimum duration outage", and redundantly over several channels to prevent the interruption of the combined signal. However, many applications, which we "mission availability" [5]–[7]. However, existing static diver- refer to as robust, are able to tolerate short communication sity schemes are not able to dynamically react to instantaneous outages. Thus, we propose a dynamic connectivity scheme named failures and therefore waste resources that are not needed for "reaction diversity", which only switches the channel in case of a smooth operation [4]. bad conditions, instead of providing multiple channels throughout In this letter, we propose a novel dynamic connectivity the transmission. As a result, time-correlated failures, e.g., caused by fading, are shortened. Through simulations with Rayleigh concept, namely reaction diversity (RD), which reacts to fades fading channels, we show that if short outages are acceptable, by selecting a different channel. We study the outage proba- the application outage probability can be reduced by several bility of robust applications, which can compensate for short orders of magnitude over selection combining of two channels, communication outages. By means of numerical simulations while only consuming half the resources. with Rayleigh fading as the cause of failure, we evaluate the Index Terms—5G, Application outage probability, Reaction performance in comparison with state-of-the-art approaches diversity, URLLC such as single-connectivity (SC), multi-connectivity, and chan- nel hopping (CH). We demonstrate the potential of dynamic I. INTRODUCTION connectivity approaches (in particular RD and CH), which can improve the application outage probability by several orders of Achieving wireless ultra reliable low latency communica- magnitude, while utilizing significantly fewer resources than tions (URLLC) is one of the main challenges in the fifth static diversity schemes. generation (5G) of wireless communication systems and be- yond. A latency in the (sub-)millisecond range together with ultra-high reliability is expected to enable wireless factory II. SYSTEM MODEL automation and self-driving cars, among other services; and We assume a set of N channels which are separated in real-time remote control, which will pave the way to the Tactile frequency at least by the coherence bandwidth resulting in Internet [1]. In URLLC, packet delivery success probabilities independent small-scale fading. We consider a single user of 1 − 10−5 up to 1 − 10−9 are targeted [2], [3]. Although connected simultaneously to L ≤ N channels. Without loss any wireless communications system suffers from signal fluc- of generality, path loss and shadowing are not considered in tuations over time, referred to as fading, the analysis of time- this letter, because compensation by transmit power control or based dependability attributes is still lacking in the context automatic gain control is assumed, as in [7]. Furthermore, the of URLLC. Fortunately, many modern applications, such as time scale of shadowing and path loss is large and, thus, not robotics, can tolerate short communication outage times due relevant for the analysis in the context of this work. to appropriate mechanisms in the application domain, e.g., fault-tolerant controllers [4]. We name these wireless systems A signal can be successfully received if the instantaneous with applications that are not sensitive to short outages robust. power p(t) is above a certain threshold pmin, which may be This potential can be leveraged for the design of the wireless determined by the receiver’s hardware sensitivity. The consid- communications system, since the importance of a packet ered wireless channel can be interpreted as a repairable item for the application depends on the success or failure of based on the Gilbert-Elliot model [8]. Thus, we distinguish immediately preceding packet transmissions. Hence, taking between two states by introducing the following notation, which originates from dependability theory: Manuscript received September 13, 2019; revised October 25, 2019. "down", if p(t) < p This research was co-financed by public funding of the state of Sax- A channel is min : (1) ony/Germany. "up", if p(t) ≥ pmin T. Hößler, P. Schulz, and A. Noll Barreto are with the Barkhausen Institut, Dresden, Germany, Emails: {tom.hoessler, philipp.schulz, an- We consider a Rayleigh-faded channel following Clarke’s dre.nollbarreto}@barkhauseninstitut.org L. Scheuvens and G. P. Fettweis are with the Vodafone Chair Mobile Com- model, whose time correlation properties are characterized by munications Systems, Technische Universität Dresden, Dresden, Germany, the temporal auto-correlation function Emails: {lucas.scheuvens, gerhard.fettweis}@tu-dresden.de. M. Simsek is with the International Computer Science Institute, Berkeley, USA, Email: [email protected]. θ(∆t) = J0(2πfD∆t) : (2) 2 J0(:) denotes the zero-order Bessel function of the first kind Level crossing analysis yields the mean downtime for a and the maximum Doppler frequency is given by Rayleigh-fading channel with Clarke’s model, according to [5] p f = vf=c (3) F (exp(1=F ) − 1) D τ¯d = p ; (8) f 2π with the carrier frequency of the signal f and the speed of D light c. The relative velocity between transmitter, receiver, and which depends on the maximum Doppler shift fD and, thus, scatterers is denoted as v. The coherence time Tcoh is the time on the mobility properties. interval for which the correlation decreases from its maximum Analogously, the uptime τ u specifies the duration from a 1 to 0.5, transition to an up state until the first transition back to a down state. For the considered system model, the mean uptime jθ(Tcoh)j = 0:5jθ(0)j: (4) is given by [5] Since the time correlation function can be calculated by the 1 τ¯u = p : (9) inverse Fourier transform of the Doppler power spectrum, fD 2π there are reciprocal relations between the coherence time and Consequently, the introduced performance metrics are linked the Doppler spread. In order to estimate the coherence time, according to the basic relation [7] the maximum Doppler frequency fD is often used according to [9] τ¯d Po = : (10) 9 τ¯d +τ ¯u Tcoh ≈ : (5) 16πfD In order to further characterize the performance of the It should be noted that the contributions of this work system, we take the downtime and uptime distributions into can be directly adopted to other channel models, which also account. Unfortunately, general closed-form solutions of the incorporate temporal auto-correlation, e.g., Rician fading: In downtime and uptime distributions for Rayleigh-fading are not available. Thus, we will evaluate them by means of addition to the maximum Doppler frequency fD, the temporal auto-correlation function of a Rician-faded signal simulations. K exp (j2πfD cos φ∆t) + J0(2πfD∆t) θRic(∆t) = (6) C. Application Outage Probability K + 1 Some applications can bridge short communication outages also depends on the K factor and the angle of arrival φ of the with appropriate design, e.g., fault-tolerant controllers. Thus, line-of-sight component [10]. an application outage event occurs only when the communica- tions system exhibits a down state which lasts for more than III. PERFORMANCE METRICS a tolerable threshold. Hence, we define the application outage A d In this section, we introduce and compare performance probability Po (τmax) as the probability of experiencing fades d metrics to evaluate robust wireless systems. The definitions which are longer than the maximum tolerated downtime τmax, are applied to Rayleigh-fading channels. i.e., A d d d Po (τmax) = Pr p < pmin ^ τ > τmax : (11) A. Outage Probability For a sufficiently long observation duration T , the appli- An outage occurs when the received power level falls below cation outage probability can be expressed by the fraction of a threshold p . We denote the outage probability of the min time the system experiences outages that are longer than the wireless communications system as P . The outage probability o threshold τ d , i.e., of one Rayleigh-faded channel is max P τ d 1 A τ d2C(T ) P = Pr[p < p ] = 1 − exp − ; (7) Po = ; (12) o;1 min F T where the set of downtimes that cause application outages is where F = p =p represents the fading margin with the avg min denoted by average received power pavg. Since we assume that all packets d d d d are lost during an outage, the outage probability corresponds C(T ) = τ j τ 2 F(T ); τ > τmax (13) to the packet loss rate. and the set F(T ) contains every individual downtime τ d during the time interval [0;T ]. The metric application outage B. Downtime and Uptime probability translates to the concept of minimum duration The downtime τ d is defined as the time interval from a outage, published in [6], where the focus is on shadow transition of the instantaneous receive power level p(t) to the fading. However, in this letter we propose a more precise down state p(t) < pmin until the first transition back to the up mathematical definition. Furthermore, by utilizing the term state p(t) ≥ pmin. The term downtime is common in classical application outage probability, we emphasize the application’s dependability theory and corresponds to the fade duration in ability to tolerate short outage times. It should be noted that the context of this work. outage probability is a special case of the application outage 3 probability, where the maximum tolerated downtime is zero, 1 % i.e., A 0.8 % Po = Po (0): (14) 0.6 % IV.
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