Tractable Expressions Research Articles

Cell-Free Massive MIMO Systems With Oscillator Phase Noise: Performance Analysis and Power Control

Cell-free massive multiple-input multiple-output (MIMO) is considered as a promising technology for satisfying higher rate requirement of users in beyond-5G networks. This paper investigates the impact of phase noise on the performance of cell-free MIMO systems which employ a large number of multi-antenna access points (APs). For both downlink and uplink transmissions, we derive the tractable closed-form achievable rate expressions when signal detection with channel state information (CSI) and channel distribution information (CDI), respectively, by utilizing the extended deterministic equivalence method in random matrix theory. The closed-form achievable rate expressions provide efficient evaluation for the impact of phase noise on system performance. The analytical results indicate that the phase noise influences the power of the desired signal, the beamforming uncertainty gain, and the inter-user interference increment caused by the pilot contamination. In addition, the special cases that only APs have phase noise and only users have phase noise are discussed. It is found that the impact of phase noise at users is more severe than that at APs. Besides, we discuss the system performance at low and high SNR regimes. It demonstrates that the phase noise is the major limitation of the system performance in high SNR regime while it can be neglected in low SNR regime. Furthermore, we formulate the max-min power control problem for both downlink and uplink transmissions to guarantee the users’ fairness and prove that the downlink max-min problem is a quasi-concave problem while the uplink max-min problem is a geometric programming (GP) problem. Then, the phase noise-aware max-min power control schemes for both downlink and uplink transmissions are proposed to ensure the users’ fairness. Finally, numerical results are provided to validate the analytical results and the proposed phase noise-aware power control scheme.

Hovering UAV-Based FSO Communications: Channel Modelling, Performance Analysis, and Parameter Optimization

Relay-assisted free-space optical (FSO) communication systems are exploited as a means to mitigate the limiting effects of the turbulence induced atmospheric scintillation. However, conventional ground relays are stationary, and their optimal placement is not always feasible. Due to their mobility and flexibility, unmanned aerial vehicles (UAVs) provide new opportunities for FSO relaying systems. In this paper, a hovering UAV-based serial FSO decode-and-forward relaying system is investigated. In the channel modelling for such a system, four types of impairments (i.e., atmospheric loss, atmospheric turbulence, pointing error, and link interruption due to angle-of-arrival fluctuation) are considered. Based on the proposed channel model, a tractable expression for the probability density function of the total channel gain is obtained. Closed-form expressions of the link outage probability and end-to-end outage probability are derived. Asymptotic outage performance bounds for each link and the overall system are also presented to reveal insights into the impacts of different impairments. To improve system performance, we optimize the beam width, field-of-view and UAVs' locations. Numerical results show that the derived theoretical expressions are accurate to evaluate the outage performance of the system. Moreover, the proposed optimization schemes are efficient and can improve performance significantly.

Static Replication of European Multi-Asset Options with Homogeneous Payoff

ABSTRACT The replication of any European contingent claim by a static continuous portfolio of calls and puts, formally proven by [Carr, Peter, and Dilip Madan. 1998. “Towards a Theory of Volatility Trading.” In Volatility: New Estimation Techniques for Pricing Derivatives, Vol. 29, edited by Robert A. Jarrow, 417–427. Risk books.] extends to multi-asset claims with absolutely homogeneous payoff. Using sophisticated tools from integral geometry, we show how such claims may be replicated with a continuum of vanilla basket calls and derive closed-form solutions to replicate two-asset best-of and worst-of options. We also derive a novel mathematical formula to invert the Radon transform which we apply to obtain a tractable expression of the joint implied distribution. Consequently, a large class of multi-asset options admit a model-free price enforced by arbitrage, just as single-asset European claims do.

Secure Transmission in Cell-Free Massive MIMO With RF Impairments and Low-Resolution ADCs/DACs

This paper considers the secure transmission in a cell-free massive MIMO system with imperfect radio frequency (RF) chains and low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) at both access points (APs) and legitimate users, where an active eavesdropper attempts to wiretap the confidential data. The Gaussian RF impairment model (GRFIM) and additive quantization noise model (AQNM) are used to evaluate the impacts of the RF impairments and low resolution ADCs/DACs, respectively. The analytical results of the linear minimum mean square error (MMSE) channel estimation show that there is nonzero floor on the estimation error with respect to the RF impairments, ADC/DAC precision and the pilot power of the eavesdropper which is different from the conventional case with perfect transceiver. Then, a tractable closed-form expression for the ergodic secrecy rate is obtained with respect to key system parameters, such as the antenna number per AP, the AP number, user number, quality factors of the ADC/DAC and the RF chain, pilot signal power of the eavesdropper, etc. Moreover, a compensation algorithm between the imperfect RF components and the inexpensive coarse ADCs/DACs is also presented. Finally, numerical results are provided to illustrate the efficiency of the achieved expressions and the devised algorithm, and show the effects of RF impairments and low resolution ADC/DAC on the secrecy performance.

The Risk-Adjusted Carbon Price

The social cost of carbon is the expected present value of damages from emitting one ton of carbon today. We use perturbation theory to derive an approximate tractable expression for this cost adjusted for climatic and economic risk. We allow for different aversion to risk and intertemporal fluctuations, skewness and dynamics in the risk distributions of climate sensitivity and the damage ratio, and correlated shocks. We identify prudence, insurance, and exposure effects, reproduce earlier analytical results, and offer analytical insights into numerical results on the effects of economic and damage ratio uncertainty and convex damages on the optimal carbon price. (JEL E12, G22, H23, O44, Q35, Q51, Q54)

Performance Analysis of mmWave Communications With Selection Combining Over Fluctuating-Two Ray Fading Model

In this letter, the performance of millimeter-wave (mmWave) communications with selection combining (SC) over non-identical fluctuating two-ray (FTR) fading channels is analyzed. Consequently, the exact expressions and asymptotic approximations at high signal-to-noise ratio (SNR) regime of the moment generating function (MGF) and probability density function (PDF) of the maximum of non-identical FTR variates are provided. To this effect, mathematically tractable expressions of the outage probability (OP), outage capacity (OC), average bit error probability (ABEP), and average channel capacity (ACC) are derived. The truncation of the infinite series of the cumulative distribution function (CDF) for a specific number of terms is also given. A comparison between the numerical and simulated results is performed to verify the validation of our analysis.

Information-Theoretic Security of MIMO Networks Under $\kappa$-$\mu$ Shadowed Fading Channels

This paper investigates the impact of realistic propagation conditions on the achievable secrecy performance of multiple-input multiple-output systems in the presence of an eavesdropper (Eve). Specifically, we concentrate on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> shadowed fading model because its physical underpinnings capture a wide range of propagation conditions, while, at the same time, it allows for a much better tractability than other state-of-the-art fading models. By considering transmit antenna selection and maximal ratio combining reception at the legitimate (Bob) and Eve's receiver sides, we study two relevant scenarios: 1) the transmitter knows Bob's channel state information (CSI) but not Eve's CSI, and 2) the transmitter is aware of the CSI of both Bob and Eve channels. For this purpose, we first obtain novel and tractable expressions for the statistics of the maximum of independent and identically distributed (i.i.d.) variates related to the legitimate channel. Based on these results, we derive novel closed-form expressions of the two aforementioned scenarios to assess the secrecy performance of the underlying system. Specifically, for cases: 1) the secrecy outage probability (SOP), the probability of strictly positive secrecy capacity (SPSC), and 2) the average secrecy capacity (ASC). Moreover, we develop analytical asymptotic expressions of the SOP and ASC in the high signal-to-noise ratio regime. In all instances, secrecy performance metrics are characterized in closed-form, without requiring the evaluation of Meijer-G or Fox-H functions. Some useful insights on how the different propagation conditions and the number of antennas impact the secrecy performance are also provided.

Spectral efficiency of superimposed pilots in cell-free massive MIMO systems with hardware impairments

In this paper, the spectral efficiency (SE) of an uplink hardware-constrained cell-free massive multi-input multi-output (MIMO) system with maximal ratio combining (MRC) receiver filters in the context of superimposed pilots (SPs) is investigated. Tractable closed-form SE expressions for the considered system are derived, which share us with opportunities to explore the impacts of the hardware quality coefficient, the length of coherence interval, and the power balance factor between pilot and data signals. Numerical results indicate that the achievable SE deteriorates as the hardware quality decreases and is more susceptible to the hardware impairments at the user equipments (UEs). Besides, we observe that SPs outperform regular pilots (RPs) in terms of SE and this performance gain is heavily dependent on the values of power balance factor and coherence interval. However, the superiorities of SPs over RPs have vanished when severe hardware imperfections are considered.

Optimizing Information Freshness in Wireless Networks: A Stochastic Geometry Approach

Optimization of information freshness in wireless networks has usually been performed based on queueing analysis that captures only the temporal traffic dynamics associated with the transmitters and receivers. However, the effect of interference, which is mainly dominated by the interferers' geographic locations, is not well understood. In this paper, we leverage a spatiotemporal model, which allows one to characterize the age of information (AoI) from a joint queueing-geometry perspective, for the design of a decentralized scheduling policy that exploits local observation to make transmission decisions that minimize the AoI. To quantify the performance, we also derive accurate and tractable expressions for the peak AoI. Numerical results reveal that: i) the packet arrival rate directly affects the service process due to queueing interactions, ii) the proposed scheme can adapt to traffic variations and largely reduce the peak AoI, and iii) the proposed scheme scales well as the network grows in size. This is done by adaptively adjusting the radio access probability at each transmitter to the change of the ambient environment.

Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling

Improving and optimizing oceanographic sampling is a crucial task for marine science and maritime resource management. Faced with limited resources in understanding processes in the water column, the combination of statistics and autonomous systems provides new opportunities for experimental design. In this work we develop efficient spatial sampling methods for characterizing regions, defined by simultaneous exceedances above prescribed thresholds of several responses, with an application focus on mapping coastal ocean phenomena based on temperature and salinity measurements. Specifically, we define a design criterion based on uncertainty in the excursions of vector-valued Gaussian random fields and derive tractable expressions for the expected integrated Bernoulli variance reduction in such a framework. We demonstrate how this criterion can be used to prioritize sampling efforts at locations that are ambiguous, making exploration more effective. We use simulations to study and compare properties of the considered approaches, followed by results from field deployments with an autonomous underwater vehicle as part of a study mapping the boundary of a river plume. The results demonstrate the potential of combining statistical methods and robotic platforms to effectively inform and execute data-driven environmental sampling.

Optimization of Culture Conditions for Oxygen-Tolerant Regulatory [NiFe]-Hydrogenase Production from Ralstonia eutropha H16 in Escherichia coli.

Hydrogenases are abundant metalloenzymes that catalyze the reversible conversion of molecular H2 into protons and electrons. Important achievements have been made over the past two decades in the understanding of these highly complex enzymes. However, most hydrogenases have low production yields requiring many efforts and high costs for cultivation limiting their investigation. Heterologous production of these hydrogenases in a robust and genetically tractable expression host is an attractive strategy to make these enzymes more accessible. In the present study, we chose the oxygen-tolerant H2-sensing regulatory [NiFe]-hydrogenase (RH) from Ralstonia eutropha H16 owing to its relatively simple architecture compared to other [NiFe]-hydrogenases as a model to develop a heterologous hydrogenase production system in Escherichia coli. Using screening experiments in 24 deep-well plates with 3 mL working volume, we investigated relevant cultivation parameters, including inducer concentration, expression temperature, and expression time. The RH yield could be increased from 14 mg/L up to >250 mg/L by switching from a batch to an EnPresso B-based fed-batch like cultivation in shake flasks. This yield exceeds the amount of RH purified from the homologous host R. eutropha by several 100-fold. Additionally, we report the successful overproduction of the RH single subunits HoxB and HoxC, suitable for biochemical and spectroscopic investigations. Even though both RH and HoxC proteins were isolated in an inactive, cofactor free apo-form, the proposed strategy may powerfully accelerate bioprocess development and structural studies for both basic research and applied studies. These results are discussed in the context of the regulation mechanisms governing the assembly of large and small hydrogenase subunits.

Underlay Radar-Massive MIMO Spectrum Sharing: Modeling Fundamentals and Performance Analysis

In this work, we study underlay radar-massive MIMO cellular coexistence in LoS/near-LoS channels, where both systems have 3D beamforming capabilities. Using mathematical tools from stochastic geometry, we derive an upper bound on the average interference power at the radar due to the 3D massive MIMO cellular downlink under the worst-case `cell-edge beamforming' conditions. To overcome the technical challenges imposed by asymmetric and arbitrarily large cells, we devise a novel construction in which each Poisson Voronoi (PV) cell is bounded by its circumcircle to bound the effect of the random cell shapes on average interference. Since this model is intractable for further analysis due to the correlation between adjacent PV cells' shapes and sizes, we propose a tractable nominal interference model, where we model each PV cell as a circular disk with an area equal to the average area of the typical cell. We quantify the gap in the average interference power between these two models and show that the upper bound is tight for realistic deployment parameters. We also compare them with a more practical but intractable MU-MIMO scheduling model to show that our worst-case interference models show the same trends and do not deviate significantly from realistic scheduler models. Under the nominal interference model, we characterize the interference distribution using the dominant interferer approximation by deriving the equi-interference contour expression when the typical receiver uses 3D beamforming. Finally, we use tractable expressions for the interference distribution to characterize radar's spatial probability of false alarm/detection in a quasi-static target tracking scenario. Our results reveal useful trends in the average interference as a function of the deployment parameters (BS density, exclusion zone radius, antenna height, transmit power of each BS, etc.).

Generalized Transform Analysis for Asset Pricing and Parameter Estimation

In this paper, we extend the existing generalized transform analysis in a way that allows us to propose a novel GMM approach for estimating asset pricing models. Our methodology is capable of incorporating a broad class of assets within both reduced-form and structural models, while avoiding the drawbacks of competing approaches. To formulate moment conditions, we derive expressions for moments involving transform-based asset prices. Our theory yields analytically tractable expressions for exact moments and an additionally computationally efficient strategy to obtain approximate moments, whose convergence we establish under standard conditions. Exact and approximate moments induce exact and approximate GMM estimators, respectively, for which we discuss asymptotic properties. Finally, we exemplify our methodology with a worked-out estimation problem involving equity options.

GMM Estimation of Stochastic Volatility Models Using Transform-Based Moments of Derivatives Prices

Derivatives, especially equity and volatility options, contain valuable and oftentimes essential information for estimating stochastic volatility models. Absent strong assumptions, their typically highly nonlinear pricing dependence on the state vector prevents or at least severely impedes their inclusion into standard estimation approaches. This paper develops a novel and unified methodology to incorporate moments involving derivatives prices into a GMM-type estimation procedure. Invoking new results from generalized transform analysis, we derive analytically tractable expressions for exact moments and devise a computationally efficient approximation procedure. We exemplify our methodology with an estimation problem that jointly accounts for stock returns as well as prices of equity and volatility options.

Reputation-Based Federated Learning for Secure Wireless Networks

The dilemma between the ever-increasing demands for data processing, and the limited capabilities of mobile devices in a wireless communication system calls for the appearance of federated learning (FL). As a distributed machine learning (ML) method, FL executes in an iterative manner by distributing the global model parameters and aggregating the local model parameters, which avoids the transmission of huge raw data and preserves data privacy during the training process. However, since FL cannot control the local training and transmission process, this gives malicious users the opportunity to deteriorate the global aggregation. We adopt a reputation model based on beta distribution function to measure the credibility of local users, and propose a reputation-based scheduling policy with user fairness constraint. By taking into account the impact of wireless channel conditions and malicious attack features, we derive tractable expressions for the convergence rate of FL in a wireless setting. Moreover, we validate the superiority of the proposed reputation-based scheduling policy via numerical analysis and empirical simulations. The results show that the proposed secure wireless FL framework can not only distinguish malicious users from normal users but also effectively defend against several typical attack types featured in attack intensity and attack frequency. The analysis also reveals that the effect of average attack intensity on the convergence performance of FL is dominated by the percentage of malicious user equipments (UEs), and imposes even greater negative effect on the convergence performance of FL as the percentage of malicious UEs increases.

Analysis of a Cooperative Caching-Multicast Strategy in D2D-Aided Networks

Due to characteristics of video request, i.e., request-repeatability and group-orientation, we propose a cooperative caching-multicast strategy in typical Device-to-Device (D2D)-aided networks to improve the timeliness and space coverage of video services. First, based on the request cumulative time window (RCTW), a multicast-scale based caching resource allocation scheme is presented and videos whose corresponding multicast groups have larger probabilities to be non-empty are allocated more caching spaces. Second, a collaborative transmission scheme is presented, where base station opportunistically multicasts blocks of the requested video to group while failed receivers can obtain the missing blocks from successful receivers with the aid of D2D joint transmission. Finally, the tractable expressions for the average transmission coverage rate and the system average transmission delay are derived. The effectiveness of the proposed strategy when the video popularity distribution is in the general dip range is verified by numerical examples. Simulation results demonstrate that a reasonable RCTW can balance the relationship between the service probability of more users through one multicast transmission and the system transmission delay.

Static Replication of European Multi-Asset Options with Homogeneous Payoff

The replication of any European contingent claim by a static continuous portfolio of calls and puts, formally proven by Carr and Madan (1998), extends to multi-asset claims with absolutely homogeneous payoff. Using sophisticated tools from integral geometry, we show how such claims may be replicated with a continuum of vanilla basket calls and derive closed-form solutions to replicate two-asset best-of and worst-of options. We also derive a novel mathematical formula to invert the Radon transform which we apply to obtain a tractable expression of the joint implied distribution. Consequently, a large class of multi-asset options admit a model-free price enforced by arbitrage, just as single-asset European claims do.

Intelligent Reflecting Surfaces Assisted UAV Communications for IoT Networks: Performance Analysis

The increasing demand for wireless connectivity and the emergence of the notion of the Internet of Everything require new communication paradigms that will ultimately enable a plethora of new applications and new disruptive technologies. In this context, the present contribution investigates the use of the recently introduced intelligent reflecting surface (IRS) concept in unmanned aerial vehicles (UAV) enabled communications aiming to extend the network coverage and improve the communication reliability as well as spectral efficiency of Internet of Things (IoT) networks. In particular, we first derive tractable analytic expressions for the achievable symbol error rate (SER), ergodic capacity, and outage probability of the considered set up. Following this, we also derive tight upper and lower bounds on the average signal-to-noise ratio (SNR). Our derivations are then compared with the corresponding asymptotic performance, based on the central limit theorem (CLT) assumption, which reveals that the asymptotic SNR falls within the area between derived bounds, and approaches either bound depending on the number of reflective elements (REs). We further show that the asymptotic SER becomes in a tight agreement with the corresponding exact simulation SER for N ≥ 16. In addition, the offered results demonstrate that the use of the IRS is significantly effective as they assist in improving the achievable SER by five orders of magnitude. We further demonstrate that, in terms of achievable ergodic capacity, IRS-assisted UAV communication systems can exhibit ten times higher capacity compared to conventional UAV communications. Based on the above, these results and related insights are anticipated to be useful in the design and deployment of IRS-assisted UAV systems in the context of beyond 5G communications, such as 6G communications.

Cooperative Hybrid VLC/RF Systems With SLIPT

A hybrid downlink system that simultaneously uses visible light communication (VLC) and radio frequency (RF) is investigated, assuming that only one of the two considered users is capable of receiving information over the optical band. In order to facilitate information transmissions from the VLC access point to the RF user, mixed VLC/RF relaying and simultaneous lightwave information and power transfer (SLIPT) are utilized. Moreover, a cognitive-based resource allocation policy and tractable bounds for the harvested energy are introduced. Furthermore, by taking into account the random location of the VLC and RF user terminals, the closed-form outage probability for the VLC user is given, while for the RF user, the outage probability is derived in terms of infinite-series, which is also approximated by a tractable closed-form expression. In addition, the outage probability of the RF user is minimized by optimizing the direct current (DC) component. Finally, simulations are provided to verify the accuracy of the theoretical analysis and demonstrate the effectiveness of the proposed optimization framework.

Imitation Learning of Neural Spatio-Temporal Point Processes

We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete event data, the study of spatial-temporal aspects of such data is relatively scarce. Our model captures complex spatio-temporal dependence between discrete events by carefully design a mixture of heterogeneous Gaussian diffusion kernels, whose parameters are parameterized by neural networks. This new kernel is the key that our model can capture intricate spatial dependence patterns and yet still lead to interpretable results as we examine maps of Gaussian diffusion kernel parameters. The imitation learning model fitting for the NEST is more robust than the maximum likelihood estimate. It directly measures the divergence between the empirical distributions between the training data and the model-generated data. Moreover, our imitation learning-based approach enjoys computational efficiency due to the explicit characterization of the reward function related to the likelihood function; furthermore, the likelihood function under our model enjoys tractable expression due to Gaussian kernel parameterization. Experiments based on real data show our method’s good performance relative to the state-of-the-art and the good interpretability of NEST’s result.