Spectral analysis of non-linear systems involving square-law operations

This paper contains a number of useful theoretical formulas to analyze the frequency domain properties of Gaussian input data passing through non-linear square-law systems. Special bispectral density functions are defined and applied that are functions of a single variable. From measurements of input data and output data only, results are obtained to identify the separate frequency response functions for two models of linear systems in parallel with non-linear square-law systems. Non-linear coherence functions are defined from these models which determine the proportion of the output spectrum due to the non-linear operations. Together with ordinary coherence functions, a measured output spectrum for these models can be decomposed into three components representing the linear operations, the non-linear operations, and the remaining uncorrelated noise effects. This material indicates also how to analyze other types of non-linear models by employing similar techniques.     

Spectral and energy efficiency for uplink massive MIMO systems with mixed-ADC architecture

In this paper, we introduce a mixed- analog-to-digital converter (ADC) architecture for massive multiple-input multiple-output (MIMO) systems and study the system’s performance mainly includes the achievable spectral efficiency and energy efficiency. In principle, the mixed-ADC architecture permits the one part of antennas at the base station (BS) are connected to speed and expensive full-resolution ADCs and the remaining part of the antennas are connected to the cheap low-resolution ADCs. By applying the general maximum-ratio combining detector, a tractable approximate expression for the achievable SE is obtained. Leveraging on the derived results, the effects of the number of BS antennas and the percent of the full-resolution ADCs on the achievable SE are investigated. Results show that the achievable SE increases with the percent of the full-resolution ADCs and the number of BS antennas. Based on a realistic power consumption model, we evaluate the energy efficiency for the considered mixed-ADC architecture. Moreover, under the certain achievable SE constraint, we maximize the energy efficiency by adjusting the number of low-resolution ADCs and the resolution bits of the corresponding ADC device. Numerical results showcase that the energy efficiency can be improved by enhancing the average transmitted power, and there exists an optimal number of resolution bits and the number of antennas to maximize the energy efficiency, which indicates that the application of mixed-ADC architecture has a great potential in future mobile communication system.     

Spectral efficiency for IRS-assisted uplink mmWave massive MISO systems with low-resolution ADCs

In this paper, we investigate the uplink achievable spectral efficiency (SE) for an intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) multiple-input single-output (MISO) system, where all antennas at the BS are equipped with cheaper low-resolution analog-to-digital converters (ADCs) and an IRS adjusts its reflecting phase shifts to facilitate information transfer. To maximize the uplink achievable SE, we design the phase shift of each reflecting element and obtained the optimal phase shift matrix in the terms of the statistical channel state information (CSI). An theoretical expression of the uplink achievable SE of massive MISO system is obtained with the zero forcing (ZF) detector is derived. Based on this derived theoretical result, the behaviors of the achievable SE with respect to several physical parameters are revealed that includes the number of antennas, the transmit power, the number of reflecting elements, and the quantization bits of the low-resolution ADCs. Finally, we provide the numerical results by Monte Carlo simulation to verify that our theoretical analysis is accurate. Results show that the achievable SE increases with the number of antennas, the number of quantization bits of the ADC and the reflecting elements of the IRS, but tends to a saturation rate. In addition, we find that the SE inevitably suffers a certain loss due to the phase shift noise is unavoidable and the quantization accuracy of IRS, which can be compensated by increasing the transmit power and the number of reflecting elements.     

Design of double-weight code for synchronous OCDMA systems with power control

Double-weight optical code division multiple access(OCDMA) systems are proposed for studying differentiated quality-of-service transmission. Based on quadratic congruence code(QCC), we construct a one-dimensional double-weight code family, which can be well utilized in incoherent synchronous double-weight OCDMA networks. By introducing algebraic transformation to code sequences of QCC in level 1, we obtain multiple double-weight codes with cross-correlation 1. Under the same-bit-power assumption, the performance of low-weight codes can be significantly improved and is always superior to that of high-weight codes in double-weight OCDMA systems with power control. This property is contrary to previous conclusions under the same-chip-power assumption.     

A novel encoder/decoder design scheme utilizing differential detection in OCDMA systems

In this paper, we report the use of differential detection in optical code-division multiple access (OCDMA) systems which use encoders and decoders based on unbalanced codes and utilize bipolar modulation/differential detection to demonstrate a significant improvement in system performance. Differential detection has been reported earlier also requiring a large number of one-chips in the code for (balanced codes) or with unbalanced codes with very long temporal dimensions requiring a large number of delay elements (either the delay lines in the ladder-type structures or the gratings in the multiple fiber gratings) making the encoder/decoder structures. We use single pulse per row codes to design our system and carry out the simulations for showing the results. The improved BER performance is achieved that can be traded for increasing the number of codes. Using optical simulation tool, the OCDMA system has been simulated for four users. The results of this system utilizing differential detection and another system that uses the same coding scheme but employing direct detection, for the same number of interfering users, are shown for comparison. The BER and the power penalty plots are shown for the two systems. Also, it is shown that performance degradation occurs due to the linear and non-linear effects of the fiber medium. The BER worsens more rapidly with link length for direct detection case, whereas for differential detection with an initial improvement of 8 dB, the increase in BER is insignificantly small for a link length of 500 km.     

Performance analysis and improvement of spectrally amplitude encoded/decoded OCDMA system

This paper describes a performance analysis of an incoherent optical code-division multiple-access scheme based on wavelength/time (W/T) codes. The system supports 16 users operating at 2.5Gb/s/user while maintaining bit-error rate (BER) < 10⁻¹¹ for the correctly decoded signal. It has been observed that there are two major problems giving rise to performance degradation of the system in terms of number of users and type of code.In this paper we have studied the optical simulator Encoding/Decoding for different lengths & gain in terms of Quality factor (Q) and Bit Error Rate (BER) performance. The system supports 16 users while maintaining bit-error rate (BER) < 10⁻¹¹ for the correctly decoded signal. Our aim is to design and simulate a Tree Network Topology Optical Code Division Multiple Access System for large number of users using wavelength–time code and to analyze the performance of the system based on BER and Eye Diagram under the influence of number of simultaneous users with different received powers.     

A divided spectrum balanced detection technique for intensity noise reduction in SAC OCDMA systems

In this paper we propose a simple divided spectrum balanced detection (DSBD) for spectral amplitude coding (SAC) optical code division multiple access (OCDMA) systems. SAC OCDMA systems are limited by phase induced intensity noise (PIIN), which is a signal dependent source of noise. Our proposed technique reduces the PIIN by dividing the spectrum of the signal into two or more, and detecting each spectrum by a different photodiode. The DSBD scheme reduces the detected optical power at photodetection, thus resulting in a higher mitigation of the PIIN. Theoretical results show that DSBD demonstrate noticeable improvement over traditional balanced detection technique, for example an up to 33% increase in the number of active users can be achieved, and at least 1 × 10⁻³ b/s Hz increase in the spectral efficiency is obtained. However, the SDBD is more complex and append more constrains on system components.     

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T _c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional “eggbox type” charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments. Received 14 June 1999     

Spectral decomposition of expanding probabilistic dynamical systems

We study probabilistic combinations of expanding dynamical systems, which we call expanding probabilistic dynamical systems, in one dimension. If the system is composed by exact endomorphisms we prove that the probabilistic dynamical system is an exact Markov semigroup, and we determine a generalized spectral decomposition of the associated Markov operator on densities for an example of the tent map coupled with the 2-Renyi map.     

A high efficiency construction method of multilength optical orthogonal codes with correlation constraint two for OCDMA multimedia network

In order to construct multilength optical orthogonal codes (ML OOCs) with correlation constraint 2 for multi-rate OCDMA passive optical networks, a high efficiency construction method is presented. The main idea is to construct high efficiency mapping sequences to map optimal short length OOCs with cross correlation 2 into long length OOCs with cross correlation 2. Fundamental of constructing high efficiency mapping sequence is derived, and the mapping sequences based on multiplication table of integer domain is examined. Simulations based on the method show that the cardinality of long length OOCs is just slightly lower than Johnson bound. Therefore, it has very high variable length efficiency.     

Spectral analysis of uranium glasses

A Taylor-series expansion of the intermediate coupling energy levels for the U⁴⁺(5f²) has been developed for the first time by using the mathematical procedures of Racah. The partial derivatives, eigenvalues and eigenfunctions reported in this paper will be of great use in analysing the optical spectral properties of the tetravalent uranium doped crystalline or non-crystalline materials. The usefulness of the Taylor serier expansion has been verified by examining the optical absorption results of the U⁴⁺ doped fluoride glasses. The physical properties, namely the refractive index and density, were also determined.Our thanks are due to Prof. S. V. J. Lakshman for his kind cooperation and support in the present work. We are also thankful to the technical staff of the Hull University, Physics Department, UK in the preparation and measurement of various physical properties of the U⁴⁺ doped alkali mixed heavy metal based fluoride glass systems.     

Spectral stochastic uncertainty quantification in chemical systems

Uncertainty quantification (UQ) in the computational modelling of physical systems is important for scientific investigation, engineering design, and model validation. We have implemented an ‘intrusive’ UQ technique in which (1) model parameters and field variables are modelled as stochastic quantities, and are represented using polynomial chaos (PC) expansions in terms of Hermite polynomial functions of Gaussian random variables, and (2) the deterministic model equations are reformulated using Galerkin projection into a set of equations for the time evolution of the field variable PC mode strengths. The mode strengths relate specific parametric uncertainties to their effects on model outputs. In this work, the intrusive reformulation is applied to homogeneous ignition using a detailed chemistry model through the development of a reformulated pseudospectral chemical source term. We present results analysing the growth of uncertainty during the ignition process. We also discuss numerical issues pertaining to the accurate representation of uncertainty with truncated PC expansions, and ensuing stability of the time integration of the chemical system.