19 research outputs found

    On the Reliability of LTE Random Access: Performance Bounds for Machine-to-Machine Burst Resolution Time

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    Random Access Channel (RACH) has been identified as one of the major bottlenecks for accommodating massive number of machine-to-machine (M2M) users in LTE networks, especially for the case of burst arrival of connection requests. As a consequence, the burst resolution problem has sparked a large number of works in the area, analyzing and optimizing the average performance of RACH. However, the understanding of what are the probabilistic performance limits of RACH is still missing. To address this limitation, in the paper, we investigate the reliability of RACH with access class barring (ACB). We model RACH as a queuing system, and apply stochastic network calculus to derive probabilistic performance bounds for burst resolution time, i.e., the worst case time it takes to connect a burst of M2M devices to the base station. We illustrate the accuracy of the proposed methodology and its potential applications in performance assessment and system dimensioning.Comment: Presented at IEEE International Conference on Communications (ICC), 201

    Serial intravital 2-photon microscopy and analysis of the kidney using upright microscopes

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    Serial intravital 2-photon microscopy of the kidney and other abdominal organs is a powerful technique to assess tissue function and structure simultaneously and over time. Thus, serial intravital microscopy can capture dynamic tissue changes during health and disease and holds great potential to characterize (patho-) physiological processes with subcellular resolution. However, successful image acquisition and analysis require significant expertise and impose multiple potential challenges. Abdominal organs are rhythmically displaced by breathing movements which hamper high-resolution imaging. Traditionally, kidney intravital imaging is performed on inverted microscopes where breathing movements are partly compensated by the weight of the animal pressing down. Here, we present a custom and easy-to-implement setup for intravital imaging of the kidney and other abdominal organs on upright microscopes. Furthermore, we provide image processing protocols and a new plugin for the free image analysis software FIJI to process multichannel fluorescence microscopy data. The proposed image processing pipelines cover multiple image denoising algorithms, sample drift correction using 2D registration, and alignment of serial imaging data collected over several weeks using landmark-based 3D registration. The provided tools aim to lower the barrier of entry to intravital microscopy of the kidney and are readily applicable by biomedical practitioners

    Nodule inception recruits the lateral root developmental program for symbiotic nodule organogenesis in Medicago truncatula

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    To overcome nitrogen deficiencies in the soil, legumes enter symbioses with rhizobial bacteria that convert atmospheric nitrogen into ammonium. Rhizobia are accommodated as endosymbionts within lateral root organs called nodules that initiate from the inner layers of Medicago truncatula roots in response to rhizobial perception. In contrast, lateral roots emerge from predefined founder cells as an adaptive response to environmental stimuli, including water and nutrient availability. CYTOKININ RESPONSE 1 (CRE1)-mediated signaling in the pericycle and in the cortex is necessary and sufficient for nodulation, whereas cytokinin is antagonistic to lateral root development, with cre1 showing increased lateral root emergence and decreased nodulation. To better understand the relatedness between nodule and lateral root development, we undertook a comparative analysis of these two root developmental programs. Here, we demonstrate that despite differential induction, lateral roots and nodules share overlapping developmental programs, with mutants in LOB-DOMAIN PROTEIN 16 (LBD16) showing equivalent defects in nodule and lateral root initiation. The cytokinin-inducible transcription factor NODULE INCEPTION (NIN) allows induction of this program during nodulation through activation of LBD16 that promotes auxin biosynthesis via transcriptional induction of STYLISH (STY) and YUCCAs (YUC). We conclude that cytokinin facilitates local auxin accumulation through NIN promotion of LBD16, which activates a nodule developmental program overlapping with that induced during lateral root initiation

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

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    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.I den hĂ€r avhandlingen betraktar vi trĂ„dlösa system för ultra-pĂ„litlig lĂ„g-latens kommunikation (``ultra-reliable low-latency communication'', URLLC). URLLC-system erfordras exempelvis i industriella slutna reglersystem, dĂ€r data mĂ„ste överföras med en fördröjning av högst nĂ„gra millisekunder. ÖvertrĂ€delse av denna tidsfrist kan leda till kostsamma fel och bör dĂ€rför endast ske med mycket lĂ„g sannolikhet -- t.ex. högst 10-8. Detta presenterar ett antal nya utmaningar ur forskningsperspektiv. Först och frĂ€mst Ă€ndras den trĂ„dlösa kanalen över tiden pĂ„ grund av ``fading''. NĂ€r systemet inte kan utnyttja mĂ„ngfald för att mildra effekterna av fading vid varje överföringsförsök, kan sĂ€ndaren behöva anpassa kanalkodens grad till det nuvarande kanaltillstĂ„ndet för att minska sannolikheten för överföringsfel. Tidsberoende datahastigheter och överföringsfel leder emellertid till en slumpmĂ€ssig köningsfördröjning av data, vilket kan överskrida den maximala fördröjningen som tolereras av applikationen. För att sĂ€kerstĂ€lla att övertrĂ€delser av tidsfristen endast sker med mycket liten sannolikhet, mĂ„ste utvĂ€rderingen av systemprestandan dĂ€rför ta hĂ€nsyn till denna köningsfördröjning. För det andra Ă€r mĂ„nga traditionella prestandamodeller för det fysiska lagret av trĂ„dlösa kommunikationssystem inte giltiga nĂ€r kommunikationsfördröjningen Ă€r kort. Till exempel antar mĂ„nga tidigare verk i trĂ„dlös kommunikation att felfri kommunikation vid kanalkapaciteten kan uppnĂ„s med hjĂ€lp av kanalkodning. Denna modell Ă€r inte lĂ€ngre giltig nĂ€r blocklĂ€ngden för kanalkoden Ă€r mycket kort, vilket Ă€r fallet i URLLC-system. Ett annat antagande som blir ogiltigt vid mycket korta latenser Ă€r att sĂ€ndaren kan mĂ€ta kanalens nuvarande tillstĂ„nd pĂ„ perfekt vis. Med endast fĂ„ resurser tillgĂ€ngliga för kanaluppskattning Ă€r det inte möjligt att fĂ„ exakt kanalinformation (``channel state information'', CSI). SĂ€ndaren kan sĂ„lunda inte perfekt anpassa kodningsgraden till det nuvarande kanaltillstĂ„ndet, vilket resulterar i överföringsfel. I den hĂ€r avhandlingen tillĂ€mpar vi stokastisk nĂ€tverkskalkyl för att analysera systemets köningsfördröjning med realistiska modeller av dataöverföring pĂ„ det fysiska lagret som tar hĂ€nsyn till ofullkomlig CSI och effekterna av Ă€ndliga blocklĂ€ngder. Vi undersöker sedan tre olika typer av system.Först betraktar vi ett enkelantennsystem och övervĂ€ger effekterna av kanalkodning vid Ă€ndlig blocklĂ€ngd, sĂ„vĂ€l som ofullkomlig CSI. En av huvudutmaningarna i detta sammanhang Ă€r att inget uttryck med sluten form finns för den gemensamma avkodningsfelsannolikheten pĂ„ grund av kanalkodning vid Ă€ndlig blocklĂ€ngd och ofullkomlig CSI, sĂ„ prestationsanalys pĂ„ högre lager Ă€r fortfarande omöjligt. Vi löser denna utmaning genom att kombinera en aktuell resultat frĂ„n informationsteori om kodning med Ă€ndlig lĂ€ngd med en approximation för estimeringsosĂ€kerheten pĂ„ grund av ofullkomlig CSI, vilket tillĂ„ter oss att hĂ€rleda en approximation med sluten form för den resulterande gemensamma avkodningsfelssannolikheten. Detta uttryck kan sedan anvĂ€ndas för att hitta det optimala kodningsgradanpassningsschemat med avseende pĂ„ fördröjningsprestandan, dvs den optimala avvĂ€gningen mellan den valda kodningsgraden och den resulterande felsannolikheten. Vi anvĂ€nder Ă€ven dessa resultat för att bestĂ€mma den optimala trĂ€ningssekvenslĂ€ngden, dvs den optimala avvĂ€gningen mellan tiden som spenderas vid kanaluppskattning och tiden som Ă„terstĂ„r för den faktiska dataöverföringen. För det andra anser vi nedlĂ€nkstransmissioner i ett flerantennsystem med flera anvĂ€ndare.Specifikt betraktar vi MISO-system (``multiple-input single-output'', dvs flera ingĂ„ngssignaler och en enda utgĂ„ngssignal), vilket innebĂ€r att en sĂ€ndare med flera antenner kan överföra data till flera anvĂ€ndare som var och en har en enda antenn. Om sĂ€ndaren har perfekt CSI kan strĂ„lformning appliceras och data kan skickas samtidigt till flera anvĂ€ndare, utan att signalen som skickas mot en mottagare skapar störningar hos andra. Men med ofullkomlig CSI Ă€r strĂ„lformningen ocksĂ„ ofullkomlig, vilket medför stor interferens mellan signalerna för de olika anvĂ€ndarna, vilket igen kan leda till avkodningsfel. Vi erhĂ„ller approximationer med sluten form för felsannolikheten pĂ„ grund av denna interferens, och tillĂ€mpar vĂ„ra tidigare resultat för att Ă€ven ta hĂ€nsyn till effekterna pĂ„ grund av Ă€ndliga blocklĂ€ngder. Intressant Ă€r att det kvalitativa beteendet och det optimala antalet samtidiga planerade anvĂ€ndare förblir mycket snarlika, Ă€ven om vi observerar en vĂ€sentlig kvantitativ prestandaförlust pĂ„ grund av ofullkomlig CSI. För det tredje betraktar vi ett system med ``non-othogonal multiple-access'' (NOMA) i upplĂ€nken. I NOMA-upplĂ€nken kan tvĂ„ enheter komma Ă„t kanalen samtidigt, vilket skapar ömsesidig interferens. Lyckligtvis kan interferensen av en av anvĂ€ndarna mildras genom att tillĂ€mpa successiv interferensavskrivning (``successive interference cancellation'', SIC). Men nĂ€r de valda kodningsgraderna för sĂ€ndning vĂ€ljs utifrĂ„n ofullkomlig CSI, kan avkodningen för en eller bĂ„da anvĂ€ndare misslyckas. Vi försörjer approximationer med sluten form för avkodningsfelssannolikheter för bĂ„de SIC och ett mer generellt gemensamt avkodningsschema. Vidare tar vi ocksĂ„ hĂ€nsyn till effekterna av kodning med Ă€ndliga blocklĂ€ngder. Felsannolikheten för varje anvĂ€ndare beror pĂ„ de kodningsgrader som valts för bĂ„da anvĂ€ndarna, och vi bestĂ€mmer den optimala avvĂ€gningen mellan bĂ„da graderna sĂ„ att bĂ„da anvĂ€ndarnas fördröjningsprestanda optimeras. ÄndĂ„ finner vi att NOMA i fördröjningsbegrĂ€nsade system med realistiska systemantaganden kan resultera i lĂ€gre prestanda Ă€n ortogonal Ă„tkomst, Ă€ven med optimerade systemparametrar.QC 20190520</p

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

    No full text
    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.I den hĂ€r avhandlingen betraktar vi trĂ„dlösa system för ultra-pĂ„litlig lĂ„g-latens kommunikation (``ultra-reliable low-latency communication'', URLLC). URLLC-system erfordras exempelvis i industriella slutna reglersystem, dĂ€r data mĂ„ste överföras med en fördröjning av högst nĂ„gra millisekunder. ÖvertrĂ€delse av denna tidsfrist kan leda till kostsamma fel och bör dĂ€rför endast ske med mycket lĂ„g sannolikhet -- t.ex. högst 10-8. Detta presenterar ett antal nya utmaningar ur forskningsperspektiv. Först och frĂ€mst Ă€ndras den trĂ„dlösa kanalen över tiden pĂ„ grund av ``fading''. NĂ€r systemet inte kan utnyttja mĂ„ngfald för att mildra effekterna av fading vid varje överföringsförsök, kan sĂ€ndaren behöva anpassa kanalkodens grad till det nuvarande kanaltillstĂ„ndet för att minska sannolikheten för överföringsfel. Tidsberoende datahastigheter och överföringsfel leder emellertid till en slumpmĂ€ssig köningsfördröjning av data, vilket kan överskrida den maximala fördröjningen som tolereras av applikationen. För att sĂ€kerstĂ€lla att övertrĂ€delser av tidsfristen endast sker med mycket liten sannolikhet, mĂ„ste utvĂ€rderingen av systemprestandan dĂ€rför ta hĂ€nsyn till denna köningsfördröjning. För det andra Ă€r mĂ„nga traditionella prestandamodeller för det fysiska lagret av trĂ„dlösa kommunikationssystem inte giltiga nĂ€r kommunikationsfördröjningen Ă€r kort. Till exempel antar mĂ„nga tidigare verk i trĂ„dlös kommunikation att felfri kommunikation vid kanalkapaciteten kan uppnĂ„s med hjĂ€lp av kanalkodning. Denna modell Ă€r inte lĂ€ngre giltig nĂ€r blocklĂ€ngden för kanalkoden Ă€r mycket kort, vilket Ă€r fallet i URLLC-system. Ett annat antagande som blir ogiltigt vid mycket korta latenser Ă€r att sĂ€ndaren kan mĂ€ta kanalens nuvarande tillstĂ„nd pĂ„ perfekt vis. Med endast fĂ„ resurser tillgĂ€ngliga för kanaluppskattning Ă€r det inte möjligt att fĂ„ exakt kanalinformation (``channel state information'', CSI). SĂ€ndaren kan sĂ„lunda inte perfekt anpassa kodningsgraden till det nuvarande kanaltillstĂ„ndet, vilket resulterar i överföringsfel. I den hĂ€r avhandlingen tillĂ€mpar vi stokastisk nĂ€tverkskalkyl för att analysera systemets köningsfördröjning med realistiska modeller av dataöverföring pĂ„ det fysiska lagret som tar hĂ€nsyn till ofullkomlig CSI och effekterna av Ă€ndliga blocklĂ€ngder. Vi undersöker sedan tre olika typer av system.Först betraktar vi ett enkelantennsystem och övervĂ€ger effekterna av kanalkodning vid Ă€ndlig blocklĂ€ngd, sĂ„vĂ€l som ofullkomlig CSI. En av huvudutmaningarna i detta sammanhang Ă€r att inget uttryck med sluten form finns för den gemensamma avkodningsfelsannolikheten pĂ„ grund av kanalkodning vid Ă€ndlig blocklĂ€ngd och ofullkomlig CSI, sĂ„ prestationsanalys pĂ„ högre lager Ă€r fortfarande omöjligt. Vi löser denna utmaning genom att kombinera en aktuell resultat frĂ„n informationsteori om kodning med Ă€ndlig lĂ€ngd med en approximation för estimeringsosĂ€kerheten pĂ„ grund av ofullkomlig CSI, vilket tillĂ„ter oss att hĂ€rleda en approximation med sluten form för den resulterande gemensamma avkodningsfelssannolikheten. Detta uttryck kan sedan anvĂ€ndas för att hitta det optimala kodningsgradanpassningsschemat med avseende pĂ„ fördröjningsprestandan, dvs den optimala avvĂ€gningen mellan den valda kodningsgraden och den resulterande felsannolikheten. Vi anvĂ€nder Ă€ven dessa resultat för att bestĂ€mma den optimala trĂ€ningssekvenslĂ€ngden, dvs den optimala avvĂ€gningen mellan tiden som spenderas vid kanaluppskattning och tiden som Ă„terstĂ„r för den faktiska dataöverföringen. För det andra anser vi nedlĂ€nkstransmissioner i ett flerantennsystem med flera anvĂ€ndare.Specifikt betraktar vi MISO-system (``multiple-input single-output'', dvs flera ingĂ„ngssignaler och en enda utgĂ„ngssignal), vilket innebĂ€r att en sĂ€ndare med flera antenner kan överföra data till flera anvĂ€ndare som var och en har en enda antenn. Om sĂ€ndaren har perfekt CSI kan strĂ„lformning appliceras och data kan skickas samtidigt till flera anvĂ€ndare, utan att signalen som skickas mot en mottagare skapar störningar hos andra. Men med ofullkomlig CSI Ă€r strĂ„lformningen ocksĂ„ ofullkomlig, vilket medför stor interferens mellan signalerna för de olika anvĂ€ndarna, vilket igen kan leda till avkodningsfel. Vi erhĂ„ller approximationer med sluten form för felsannolikheten pĂ„ grund av denna interferens, och tillĂ€mpar vĂ„ra tidigare resultat för att Ă€ven ta hĂ€nsyn till effekterna pĂ„ grund av Ă€ndliga blocklĂ€ngder. Intressant Ă€r att det kvalitativa beteendet och det optimala antalet samtidiga planerade anvĂ€ndare förblir mycket snarlika, Ă€ven om vi observerar en vĂ€sentlig kvantitativ prestandaförlust pĂ„ grund av ofullkomlig CSI. För det tredje betraktar vi ett system med ``non-othogonal multiple-access'' (NOMA) i upplĂ€nken. I NOMA-upplĂ€nken kan tvĂ„ enheter komma Ă„t kanalen samtidigt, vilket skapar ömsesidig interferens. Lyckligtvis kan interferensen av en av anvĂ€ndarna mildras genom att tillĂ€mpa successiv interferensavskrivning (``successive interference cancellation'', SIC). Men nĂ€r de valda kodningsgraderna för sĂ€ndning vĂ€ljs utifrĂ„n ofullkomlig CSI, kan avkodningen för en eller bĂ„da anvĂ€ndare misslyckas. Vi försörjer approximationer med sluten form för avkodningsfelssannolikheter för bĂ„de SIC och ett mer generellt gemensamt avkodningsschema. Vidare tar vi ocksĂ„ hĂ€nsyn till effekterna av kodning med Ă€ndliga blocklĂ€ngder. Felsannolikheten för varje anvĂ€ndare beror pĂ„ de kodningsgrader som valts för bĂ„da anvĂ€ndarna, och vi bestĂ€mmer den optimala avvĂ€gningen mellan bĂ„da graderna sĂ„ att bĂ„da anvĂ€ndarnas fördröjningsprestanda optimeras. ÄndĂ„ finner vi att NOMA i fördröjningsbegrĂ€nsade system med realistiska systemantaganden kan resultera i lĂ€gre prestanda Ă€n ortogonal Ă„tkomst, Ă€ven med optimerade systemparametrar.QC 20190520</p
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