# Performance Trade-offs for Ultra-Reliable Low-Latency Communication Systems

Abstract: In this dissertation, we consider wireless systems for ultra-reliable low-latency communication (URLLC). URLLC systems are required for example in industrial closed loop control systems, where data must be transmitted within a short target delay of at most a few milliseconds. Violations of this deadline could result in costly failures, and should therefore occur only with very low probability, with target violation probabilities of 10-8 and below.This presents a number of novel challenges from a research perspective. First of all, the wireless channel is changing over time due to fading. When the system cannot exploit diversity to mitigate the effects of fading in each transmission attempt, then the transmitter may need to adapt the rate of the channel code to the current channel state in order to reduce the probability of transmission errors. However, time-varying data rates and transmission errors lead to a random queueing delay of the data, which may exceed the maximum delay that is tolerated by the application. In order to ensure that violations of the deadline occur only with very small probability, the evaluation of the system performance must therefore take this queueing delay into account. Second, many traditional performance models for the physical layer of wireless communication systems do not hold when the communication latency is short. For example, many previous works in wireless communications assume that by using channel coding, one can achieve error-free communication at the channel capacity. This model is no longer accurate when the blocklength of the channel code is very short, as it is the case in URLLC systems. Another assumption that becomes invalid at very short latency is that the transmitter can perfectly estimate the current state of the channel. With only few resources available for channel estimation, it will not be possible to obtain accurate channel state information (CSI). Thus, the transmitter cannot perfectly adapt the coding rate to the current channel state, which will result in transmission errors. In this dissertation, we apply stochastic network calculus to analyze the queueing delay of the system, while using realistic models of the physical layer transmissions that take imperfect CSI and finite blocklength effects into account. We then investigate three different types of systems. First, we consider a single-antenna system and consider the effects of channel coding at finite blocklength, as well as imperfect CSI. One of the main challenges in this context is that no closed-form expression for the joint decoding error probability due to channel coding at finite blocklength and due to imperfect CSI exists, so that higher-layer performance analysis remains infeasible. We solve this challenge by combining recent results from information theory on finite-length coding with an approximation for the estimation uncertainty due to imperfect CSI, which allows us to derive a closed-form approximation for the resulting joint decoding error probability. This expression can then be used to find the optimal rate adaptation scheme with respect to the delay performance, i.e., the optimal trade-off between the selected coding rate and the resulting error probability. We use these results also to determine the optimal training sequence length, i.e., the optimal trade-off between the time spent on channel estimation and the time remaining for the actual data transmission. Second, we consider downlink transmissions in a multi-antenna systems with multiple users. Specifically, we consider MISO (multiple-input single-output) systems, which means that a transmitter with multiple antennas can transmit data to several users that have a single antenna each. If the transmitter has perfect CSI, it can apply beamforming and send data simultaneously to multiple users, without the signal sent towards one receiver creating any interference at the other receivers. However, with imperfect CSI, the beamforming is imperfect, resulting in substantial interference between the signals for the different users, which can again lead to decoding errors. We derive closed-form approximations for the error probability due to this interference, and apply our previous results to take also the finite blocklength effects into account. Interestingly, although we observe a substantial quantitative performance loss due to imperfect CSI, the qualitative behavior and the optimal number of simultaneously scheduled users remains very similar.Third, we consider a system that uses non-orthogonal multiple access (NOMA) in the uplink. In the NOMA uplink, two devices may access the channel at the same time, mutually interfering with each other. Fortunately, the interference of one of the users can be mitigated by applying successive interference cancellation (SIC). However, when the chosen transmission rates are selected based on imperfect CSI, the decoding of one or both users can fail. We provide closed-form approximations for the decoding error probabilities for both SIC and a more general joint decoding scheme. Furthermore, we also take the effects of finite blocklength coding into account. The error probability for each user depends on the rates chosen for both users, and we determine the optimal trade-off between both rates such that the delay performance of both users is optimized. Nevertheless, we find that in delay-limited systems with realistic system assumptions, NOMA may result in lower performance than orthogonal access, even with optimized system parameters.

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