Rate Analysis of Two-Receiver MISO Broadcast Channel with Finite Rate Feedback: A Rate-Splitting Approach

To enhance the multiplexing gain of two-receiver Multiple-Input-Single-Output Broadcast Channel with imperfect channel state information at the transmitter (CSIT), a class of Rate-Splitting (RS) approaches has been proposed recently, which divides one receiver's message into a common and a private part, and superposes the common message on top of Zero-Forcing precoded private messages. In this paper, with quantized CSIT, we study the ergodic sum rate of two schemes, namely RS-S and RS-ST, where the common message(s) are transmitted via a space and space-time design, respectively. Firstly, we upper-bound the sum rate loss incurred by each scheme relative to Zero-Forcing Beamforming (ZFBF) with perfect CSIT. Secondly, we show that, to maintain a constant sum rate loss, RS-S scheme enables a feedback overhead reduction over ZFBF with quantized CSIT. Such reduction scales logarithmically with the constant rate loss at high Signal-to-Noise-Ratio (SNR). We also find that, compared to RS-S scheme, RS-ST scheme offers a further feedback overhead reduction that scales with the discrepancy between the feedback overhead employed by the two receivers when there are alternating receiver-specific feedback qualities. Finally, simulation results show that both schemes offer a significant SNR gain over conventional single-user/multiuser mode switching when the feedback overhead is fixed.Comment: accepted to IEEE Transactions on Communication

The effects of emergence timing and herbicide resistance on the ecological fitness and adaptation of common waterhemp (Amaranthus tuberculatus (Moq) Sauer) to agricultural systems

Common waterhemp (Amaranthus tuberculatus (Moq) Sauer) is a problematic weed in the Midwest United States. One of the weediness characteristics of this species is its prolonged emergence pattern, which typically calls for follow-up herbicide treatment later in the growing season. Another weediness characteristic that causes control problems in common waterhemp is its propensity to evolve resistance to herbicides. Common waterhemp populations have evolved resistance to six herbicide modes of action. This thesis addresses these two facets of this notorious weed, beginning with a general introduction in chapter 1 describing the biology of the species and the effects of emergence timing on life history traits of natural common waterhemp populations (e.g. flowering phenology, seed development, seed production, seed after-ripening). The second part of chapter 1 provides background information on plant fitness and the fitness costs associated with the evolution of resistance to protoporphyrinogen oxidase (PPO) and glyphosate herbicides. Chapter 2 addresses a study that described the effect of emergence timing on the reproductive biology of natural common waterhemp populations. The study focused on the flowering phenology and seed production of different common waterhemp cohorts. It was found that common waterhemp emergence timing was closely correlated with rain events, and growth degree day (GDD), soil degree day (SDD) and precipitation are important factors that are influencing the extent of weed emergence. Common waterhemp exhibited flowering phenology plasticity, with later common waterhemp cohorts having a relatively earlier reproduction time and shorter reproductive duration period compared with the early cohorts. Common waterhemp cohorts exhibited a pulsed flowering pattern with multiple flowering peaks in both years. The flowering pattern of common waterhemp was influenced by temporal distribution of rain events, suggesting that common waterhemp populations are plastic enough to tailor their flowering to variable environmental conditions for pollination. Common waterhemp maintained high seed production throughout the growing season regardless of decreased plant size in later cohorts. Seed production for common waterhemp populations was more influenced by plant emergence timing, while individual plant seed production was more affected by common waterhemp population densities. In Chapter 3, we continued to determine the effect of emergence timing on the fate of the next generation of common waterhemp cohorts and research was conducted to evaluate variations in seed mass, seed maturation time and the seed after-ripening pattern among cohorts. Results differed among years and thus were presented separately. We were able to find that: 1) cohorts needed the same amount of time to generate viable seeds in 2009, while the earliest cohort took significantly longer time (30 days) to generate viable seeds than later cohorts (21 to 25 days) in 2010; 2) In 2009, later cohorts produced significantly heavier seeds (P\u3c0.0001), while no significant differences in seed mass among cohorts were detected in 2010 (P=0.1182); 3) In 2009, seeds from different cohorts had similar after-ripening pattern. Newly harvested seeds have strong primary dormancy (\u3c10% germination), which was gradually released during dry storage and reached maximum germination (\u3e80%) rate at 4 months after harvest (MAH). However, germination dropped to 40% at 6 and 8 MAH, indicating induction of secondary seed dormancy. In 2010, strong primary dormancy at harvest could not be released by dry after-ripening, which was probably due to strong interspecific competition and less favorable parental environments. However, in 2010 there was a difference in seed dormancy among common waterhemp cohorts. In Chapter 4, we tested the effect of herbicide selection on the ecological fitness of common waterhemp by comparing two protoporphyrinogen oxidase -(PPOB, PPOW) and three glyphosate (Gly) resistant (R) (Gly IA, Gly IL, Gly MO) common waterhemp populations with a herbicide susceptible (S) common waterhemp population (CUTS) throughout different life stages. The greenhouse studies were repeated but at different times during the year, which likely contributed to the inconsistent results. The experiment was first conducted (designated Experiment 1) on May 22 and ended on August 28 in 2009 and was repeated (designated Experiment 2) on November 2, 2009 and ended on March 1, 2010. We found that all PPO and Gly R populations had higher germination percentages but only some also germinated much faster than the S population in both experiments. Also environmental conditions and plant growth stages had significant influence on the manifestation and magnitude of fitness cost on vegetative growth. Fitness cost on vegetative growth associating with PPO resistance existed at least in certain growth stages in common waterhemp. Fitness cost on vegetative growth with glyphosate resistance varied with the growing conditions of the plants. Under favorable growing conditions (i.e. Experiment 1), S plants have faster growth rate during vegetative growth stage but the advantages disappeared when plants flowered. However in less favorable growing conditions (i.e. Experiment 2), no fitness cost were detected which was indicated by similar plant heights and stem diameters between Gly R and S populations. Similar results were found in fitness cost with reproductive biology. Flowering time, reproductive effort, and seed mass were not different between PPO-R and S plants in both experiments. However, a significant fitness cost in seed production was seen in PPO R population in Experiment 2. Fitness cost in reproductive biology of glyphosate resistance was evidenced only on some common waterhemp populations. Flowering time and seed production were significantly different between CUTS population and only Gly IA population. Seed production of Gly IA population was much higher than CUTS population in Experiment 1, while much lower seed production of Gly IA population than CUTS population was observed in Experiment 2. In Chapter 5, we summarized the research based on our two projects and provided insights on the how these data could be used to help us get a better idea of controlling common waterhemp in the United States. Understanding the biology and ecology of common waterhemp cohorts will likely help make effective weed management decisions by targeting the most vulnerable stages of common waterhemp development. Information from fitness studies may be valuable in modeling herbicide resistance evolution