Over the past few years there has been an extensive growth in data traffic consumption devices. Billions of mobile data devices are connected to the global wireless network. Customers demand revived services and up-to-date developed applications, like real-time video and games. These applications require reliable and high data rate wireless communication with high throughput network. One way to meet these requirements is by increasing the number of transmit and/or receive antennas of the wireless communication systems. Massive multiple-input multiple-output (MIMO) has emerged as a promising candidate technology for the next generation (5G) wireless communication. Massive MIMO increases the spatial multiplexing gain and the data rate by adding an excessive number of antennas to the base station (BS) terminals of wireless communication systems. However, building efficient algorithms able to decode a coherently or non-coherently large flow of transmitted signal with low complexity is a big challenge in massive MIMO. In this dissertation, we propose novel approaches to achieve optimal performance for joint channel estimation and signal detection for massive MIMO systems. The dissertation consists of three parts depending on the number of users at the receiver side. In the first part, we introduce a probabilistic approach to solve the problem of coherent signal detection using the optimized Markov Chain Monte Carlo (MCMC) technique. Two factors contribute to the speed of finding the optimal solution by the MCMC detector: The probability of encountering the optimal solution when the Markov chain converges to the stationary distribution, and the mixing time of the MCMC detector. First, we compute the optimal value of the “temperature'' parameter such that the MC encounters the optimal solution in a polynomially small probability. Second, we study the mixing time of the underlying Markov chain of the proposed MCMC detector. We assume the channel state information is known in the first part of the dissertation; in the second part we consider non-coherent signal detection. We develop and design an optimal joint channel estimation and signal detection algorithms for massive (single-input multiple-output) SIMO wireless systems. We propose exact non-coherent data detection algorithms in the sense of generalized likelihood ratio test (GLRT). In addition to their optimality, these proposed tree based algorithms perform low expected complexity and for general modulus constellations. More specifically, despite the large number of the unknown channel coefficients for massive SIMO systems, we show that the expected computational complexity of these algorithms is linear in the number of receive antennas (N) and polynomial in channel coherence time (T). We prove that as $N \rightarrow \infty$, the number of tested hypotheses for each coherent block equals $T$ times the cardinality of the modulus constellation. Simulation results show that the optimal non-coherent data detection algorithms achieve significant performance gains (up to 5 dB improvement in energy efficiency) with low computational complexity. In the part three, we consider massive MIMO uplink wireless systems with time-division duplex (TDD) operation. We propose an optimal algorithm in terms of GLRT to solve the problem of joint channel estimation and data detection for massive MIMO systems. We show that the expected complexity of our algorithm grows polynomially in the channel coherence time (T). The proposed algorithm is novel in two terms: First, the transmitted signal can be chosen from any modulus constellation, constant and non-constant. Second, the algorithm decodes the received noisy signal, which is transmitted a from multiple-antenna array, offering exact solution with polynomial complexity in the coherent block interval. Simulation results demonstrate significant performance gains of our approach compared with suboptimal non-coherent detection schemes. To the best of our knowledge, this is the first algorithm which efficiently achieves GLRT-optimal non-coherent detections for massive MIMO systems with general constellations.

The theme of this thesis relates to solving the optimal portfolio selection problems using linear programming. There are two key contributions in this thesis. The first contribution is to generalize the well-known linear optimization framework of Conditional Value-at-Risk (CVaR)-based portfolio selection problems (see Rockafellar and Uryasev (2000, 2002)) to more general risk measure portfolio selection problems. In particular, the class of risk measure under consideration is called the Coherent Distortion Risk Measure (CDRM) and is the intersection of two well-known classes of risk measures in the literature: the Coherent Risk Measure (CRM) and the Distortion Risk Measure (DRM). In addition to CVaR, other risk measures which belong to CDRM include the Wang Transform (WT) measure, Proportional Hazard (PH) transform measure, and lookback (LB) distortion measure. Our generalization implies that the portfolio selection problems can be solved very efficiently using the linear programming approach and over a much wider class of risk measures. The second contribution of the thesis is to establish the equivalences among four formulations of CDRM optimization problems: the return maximization subject to CDRM constraint, the CDRM minimization subject to return constraint, the return-CDRM utility maximization, the CDRM-based Sharpe Ratio maximization. Equivalences among these four formulations are established in a sense that they produce the same efficient frontier when varying the parameters in their corresponding problems. We point out that the first three formulations have already been investigated in Krokhmal et al. (2002) with milder assumptions on risk measures (convex functional of portfolio weights). Here we apply their results to CDRM and establish the fourth equivalence. For every one of these formulations, the relationship between its given parameter and the implied parameters for the other three formulations is explored. Such equivalences and relationships can help verifying consistencies (or inconsistencies) for risk management with different objectives and constraints. They are also helpful for uncovering the implied information of a decision making process or of a given investment market. We conclude the thesis by conducting two case studies to illustrate the methodologies and implementations of our linear optimization approach, to verify the equivalences among four different problem formulations, and to investigate the properties of different members of CDRM. In addition, the efficiency (or inefficiency) of the so-called 1/n portfolio strategy in terms of the trade off between portfolio return and portfolio CDRM. The properties of optimal portfolios and their returns with respect to different CDRM minimization problems are compared through their numerical results.

Technological progress in commercializing ultrafast lasers and detectors has allowed realization of cooperative processes on an ultrashort time scale, which demand a re-evaluation of the conventional cooperative phenomena with a new insight. Ultrafast cooperative phenomena in coherently prepared media and various applications of superfluorescence and coherent Raman scattering are studied in this dissertation. In particular, a simple theoretical testimony on analogy between a cooperative emission and coherent Raman scattering is presented by offering an opportunity to perform parallel research on these two processes from a unified point of view. On one hand, the superfluorescent pulse with a time duration of a few tens of picoseconds (ps) from alkali metal vapor is observed for the first time, even though cooperative phenomena in atomic vapor have been extensively studied for more than five decades. A dense rubidium vapor pumped by ultrashort (100 femtosecond, fs) pulses allows a realization of the ultrafast superfluorescence while a time-resolved study of superfluorescence is accomplished by using a streak camera with 2 ps time resolution. Experimental research on quantum nature of cooperative emissions has been “frozen” over the years (three decades) possibly because of the technical difficulties. Quantum fluctuations of superfluorescence development are explored experimentally by taking advantage of the ultra fast streak camera. Presumable applications of the superfluorescent pulse in e.g., a remote sensing, and an ultraviolet upconversion of the input infrared laser pulse are presented. The quantum interference due to different excitation pathways is revealed by the temporal coherent control technique while observing interferometric signals from alkali metal vapors. On the other hand, a new spectroscopic technique based on ultrafast coherent Raman scattering is developed. The key advantage of the presented technique is to suppress the non-resonant background noise which usually obscures possible applications of the other conventional coherent Raman techniques in practice. A reduction of the background noise is achieved by shaping and delaying the third pulse which probes the coherence of the medium (i.e., an enhancement of specific vibrations of the target molecules in unison) firstly prepared by two broadband pulses. We demonstrate a robustness and superiority of signal-to-noise ratio of the developed technique by identifying as few as 10000 bacterial spores at a single laser shot level. Finally, several comparative studies between cooperative and uncooperative processes are presented. A picosecond cooperative phenomenon in a three-photon resonant medium induced by a single as well as two-color ultrashort pulses is investigated. A time-resolved study shows that a picosecond cooperative effect is crucial in the well-established fields of resonant-enhanced multiphoton ionizations and harmonic generations. We also present a quantitative analysis for spontaneous versus broadband coherent Raman scattering on pyridine molecules. The spontaneous Raman signal is enhanced by 5 orders as a result of cooperative phenomena.

The theme of this thesis relates to solving the optimal portfolio selection problems using linear programming. There are two key contributions in this thesis. The first contribution is to generalize the well-known linear optimization framework of Conditional Value-at-Risk (CVaR)-based portfolio selection problems (see Rockafellar and Uryasev (2000, 2002)) to more general risk measure portfolio selection problems. In particular, the class of risk measure under consideration is called the Coherent Distortion Risk Measure (CDRM) and is the intersection of two well-known classes of risk measures in the literature: the Coherent Risk Measure (CRM) and the Distortion Risk Measure (DRM). In addition to CVaR, other risk measures which belong to CDRM include the Wang Transform (WT) measure, Proportional Hazard (PH) transform measure, and lookback (LB) distortion measure. Our generalization implies that the portfolio selection problems can be solved very efficiently using the linear programming approach and over a much wider class of risk measures. The second contribution of the thesis is to establish the equivalences among four formulations of CDRM optimization problems: the return maximization subject to CDRM constraint, the CDRM minimization subject to return constraint, the return-CDRM utility maximization, the CDRM-based Sharpe Ratio maximization. Equivalences among these four formulations are established in a sense that they produce the same efficient frontier when varying the parameters in their corresponding problems. We point out that the first three formulations have already been investigated in Krokhmal et al. (2002) with milder assumptions on risk measures (convex functional of portfolio weights). Here we apply their results to CDRM and establish the fourth equivalence. For every one of these formulations, the relationship between its given parameter and the implied parameters for the other three formulations is explored. Such equivalences and relationships can help verifying consistencies (or inconsistencies) for risk management with different objectives and constraints. They are also helpful for uncovering the implied information of a decision making process or of a given investment market. We conclude the thesis by conducting two case studies to illustrate the methodologies and implementations of our linear optimization approach, to verify the equivalences among four different problem formulations, and to investigate the properties of different members of CDRM. In addition, the efficiency (or inefficiency) of the so-called 1/n portfolio strategy in terms of the trade off between portfolio return and portfolio CDRM. The properties of optimal portfolios and their returns with respect to different CDRM minimization problems are compared through their numerical results.

We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on the entropy is proved via a sharp norm bound. The norm bound is deduced by using an interesting identity for Fisher information of SU(1,1) coherent state transforms on the hyperbolic plane and a new family of sharp Sobolev inequalities on the hyperbolic plane. To prove the sharpness of our Sobolev inequality, we need to first prove a uniqueness theorem for solutions of a semi-linear Poisson equation (which is actually the Euler-Lagrange equation for the variational problem associated with our sharp Sobolev inequality) on the hyperbolic plane. Uniqueness theorems proved for similar semi-linear equations in the past do not apply here and the new features of our proof are of independent interest, as are some of the consequences we derive from the new family of Sobolev inequalities. We also prove Fisher information identities for the groups SU(n,1) and SU(n,n).

Turbulent flow is widespread in many applications, such as airplanes or cars. Such flow is characterized by being highly chaotic and impossible to predict far into the future. In turbulent flow, there exist regions that have different properties compared to neighboring flow; these regions are called coherent turbulent structures. These structures are connected to Reynolds stress which is essential for modeling turbulent flow. Machine learning techniques have recently had very impressive results for modeling turbulence. In this thesis, we investigate their capabilities of modeling coherent structures. We use data from a highly accurate simulation to create two different artifical neural networks. These networks are tuned by hand, trained, and then we evaluate their performance. We investigate the loss of the networks and the statistical properties of their predictions and compare them to the simulated data. / Turbulent flöde är utbrett i många applikationer, såsom flygplan eller bilar. Sådant flöde kännetecknas av att det är mycket kaotiskt och omöjligt att förutse långt in i framtiden. I turbulent flöde finns det regioner som har olika egenskaper jämfört med närliggande flöde; dessa regioner kallas coherent turbulent structures. Dessa strukturer är kopplade till Reynolds stress, som är avgörande för att modellera turbulent flöde. Maskininlärningstekniker har nyligen haft mycket imponerande resultat för modellering av turbulens. I denna avhandling undersöker vi deras förmåga att modelelera coherent turbulent structures. Vi använder data från en mycket exakt simulering för att skapa två olika artificiella neurala nätverk. Dessa nätverks hyperparameterar väljs manuellt, tränas och sedan utvärderar vi deras resultat. Vi undersöker förlusten av nätverken och de statistiska egenskaperna hos deras förutsägelser och jämför dem med simulerade data.

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PN code tracking plays a very important role in CDMA communication systems. In literature, the influences of multipath fading and of multiuser interference on PN code tracking are studied separately. The multipath fading influence is mitigated by combining a rake receiver and a channel estimator in the Delay-Locked Loop (DLL). The multiuser interference is overcome by incorporating a data estimator into the DLL. In the downlink, PN code tracking may suffer from the multipath fading influence. However, the multipath fading and the multiuser interference influences exist in the uplink. Unfortunately, sole use of the aforementioned methods cannot solve out both influences simultaneously. In this thesis, two new Coherent Decision-Directed Delay-Locked Loop (CDD-DLL) PN-Code tracking schemes are developed and either can overcome both influences. First, a channel and a data estimators are incorporated into the DLL inherent with a rake receiver. This new scheme works properly in an environment with multipath fading and multiuser interference. Second, the original CDD-DLL is combined with a multipath interference canceller (MPI) to reduce both influences. Analytical results are derived for the two schemes proposed and are validated with numerical simulations. Simulation results show that the conventional DLLs working in a multipath fading and multiuser interference environment can be significantly improved using the new schemes. Moreover, the latter outperforms the former because the multipath interference is cancelled completely.

The objective of this research is to present a low power modem technology for a high speed millimeter wave wireless system. The first part of the research focuses on a robust ASIC design methodology. There are several aspects of the ASIC flow that require special attention such as logical synthesis, timing driven physical placement, Clock Tree Synthesis, Static Timing Analysis, estimation and reduction of power consumption and LVS and DRC closure. The latter part is dedicated to high speed baseband circuits such as Coherent and Non coherent demodulator which are critical components of a multi-gigabit wireless communication system. The demodulator operates at input data rates of multiple gigabits per second, which presents the challenge of designing the building blocks to operate at speeds of multiple GHz. The high speed complex multiplier is a major component of the non coherent demodulator. As part of the coherent demodulator the complex multiplier derotates the input sequence by multiplying with cosine and sine functions, Costas error calculator computes the phase error in the derotated input signal. The NCO (Numerically controlled Oscillator) is a look up table based system used to generate the cosine and sine functions, used by the derotator.The CIC filter is used to decimate the costas error signal as the loop bandwidth is significantly smaller compared to the sampling frequency. All these modules put together form the coherent demodulator which is an integral part of the wireless communication system. An implementation of Serdes is also presented which acts as an interface between the baseband modules and the RF front end.