On the symbol error probability of general order rectangular qam in nakagami-m fading

Recently, Beaulieu, following an ingenious concept, presented a closed-form expression for a useful integral, which was used for the evaluation of the symbol error probability (SEP) of general order rectangular quadrature amplitude modulation (QAM) in slow Rayleigh fading. In this letter, these results are extended to Nakagami-m fading channels, deriving a novel closed-form formula for the average over Nakagami-m fading of the product of two Gaussian Q-functions, which can be efficiently used to study the impact of fading severity on the error performance of general rectangular QAM constellations     

Symbol Error Rate Performance Analysis for Generalized Coordinate Interleaved Orthogonal Designs over Nakagami-m Fading Channels

Space-time block codes (STBC) using generalized coordinate interleaved orthogonal designs (GCIOD) proposed by Khan and Rajan (IEEE Trans Inf Theory 52(5):2062–2091, 2006) allow single-complex symbol decoding and offer higher data rates than orthogonal STBC. In this paper, we present an exact closed-form formula (i.e., not in integral form) for the average symbol pair-wise error probability of GCIODs derived in quasi-static frequency-nonselective independent identically distributed Nakagami- \(m\) fading channels. By using the formula, a tight union bound (UB) on symbol error rate (SER) is presented. Extensive simulation results show that the curves for the UB are asymptotically tight with the simulated SER curves for various antenna configurations and different modulations. The UB thus can be used to accurately predict and optimize the performance of GCIODs without the need of time-consuming simulations.     

Estimating parameters of multiple wideband polynomial-phase sourcesin sensor arrays

We consider the problem of estimating the parameters of multiple wideband polynomial-phase signal (PPS) sources in sensor arrays. A new maximum likelihood (ML) direction-of-arrival (DOA) estimator is introduced, and the exact Cramer-Rao bound (CRB) is derived for the general case of multiple constant-amplitude polynomial-phase sources. Since the proposed exact ML estimator is computationally intensive, an approximate solution is proposed, originating from the analysis of the log-likelihood (LL) function in the single chirp signal case. As a result, a new form of spatio-temporal matched filter (referred to as the chirp beamformer) is derived, which is applicable to "well-separated" sources that have distinct time-frequency or/and spatial signatures. This beamforming approach requires solving a three-dimensional (3-D) optimization problem and, therefore, enjoys essentially simpler implementation than that entailed by the exact ML. Simulation results are presented, illustrating the performance of the estimators and validating our theoretical CRB analysis     

A simplified exact expression of SEP for cross QAM in AWGN channel from M × N rectangular QAM and its usefulness in Nakagami-m fading channel

This paper derives a simple exact expression of symbol error probability (SEP) for general order cross QAM constellation in the presence of additive white Gaussian noise (AWGN) channel. The key idea is to obtain this novel expression from a simple analysis of the corresponding rectangular QAM. The analysis of the expression involves simple one dimensional Gaussian Q functions unlike other complex SEP expressions. A simple tight bound approximation of the proposed exact SEP is also given, which provides performance improvement over the existing SEP approximations, particularly for low signal to noise ratios (SNRs). Also, with the help of simulation results, we show that the proposed approximation is in excellent agreement with the exact SEP curve. Moreover, the proposed expressions prove to be useful for accurate estimation of the SEP in Nakagami-m fading channel, including the special case of Rayleigh fading (m = 1).     

A simplified 2-D analytic model for the threshold-voltage of fullydepleted short gate-length Si-SOI MESFET's

We present a simplified form of the exact solution of the 2-D Poisson equation of fully depleted Si-SOI MESFET's by Hou and Wu (1995). The major improvement is that the Fourier coefficient of the electric displacement at the Si-SiO₂ interface is given in (finite) closed form, rather than infinite series. Their 2-D analytic model for the threshold-voltage can be simplified accordingly     

SEP Performance of Cross QAM Signaling with MRC over Fading Channels and its Arbitrarily Tight Approximation

The exact average symbol error probability (SEP) of the cross quadrature amplitude modulation signal in a single-input multiple-output system over independent but not necessarily identical fading channels is derived. The maximal-ratio combining (MRC) is considered as the diversity technique, and the average SEP is obtained by using the moment generating function (MGF) method. The obtained closed-form SEP expression is presented in terms of a finite sum of single integrals with finite limits and an integrand composed of a finite product of elementary functions. In addition, the arbitrarily tight approximations with the form of a sum of constant coefficient exponential functions for Gaussian Q-function and the generalization of its Craig’s form are proposed by applying the composite rectangle and Simpson numerical integration rules, respectively. The proposed approximations are simple and accurate enough even with only a few terms of exponential functions, and they are particularly suitable for applications of averaging Q-function and the generalized Q-function over the fading distributions. As a result, the closed-form approximations of the SEP over the AWGN channel and fading multichannels are expressed as a finite sum of exponential functions and a finite sum of MGFs, respectively, such that it is convenient and rapid to evaluate the SEP performances. Both the simulation results and the approximations show excellent agreement with the exact analytical expressions.     

一种基于格理论构造高维星座图的方法

星座图的增益指数是格理论中的一个术语,它可以分解成格的编码增益和星座图边界的成形增益.本文将最大化星座图增益指数的过程构造为一系列优化问题,并将星座图的几何特性作为优化问题的约束条件.由于可通过求解优化问题来得到所需的星座图,因此本文的方法可以作为一种构造高维星座图的通用方法.相比现有算法均只适用于星座点个数较少的情况,本文方法可以简便地构造星座点数目较大的高维星座图.仿真结果显示出：在星座点数目较少时,由本文方法所构造的星座图的误符号率性能与最优值十分接近;而当星座点数目较多时,本文构造的星座图较传统基于整数格的星座图具有更低的误符号率.     

Shadow boundary incremental length diffraction coefficients appliedto scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone     

Rigid-motion-invariant classification of 3-D textures

This paper studies the problem of 3-D rigid-motion-invariant texture discrimination for discrete 3-D textures that are spatially homogeneous by modeling them as stationary Gaussian random fields. The latter property and our formulation of a 3-D rigid motion of a texture reduce the problem to the study of 3-D rotations of discrete textures. We formally develop the concept of 3-D texture rotations in the 3-D digital domain. We use this novel concept to define a "distance" between 3-D textures that remains invariant under all 3-D rigid motions of the texture. This concept of "distance" can be used for a monoscale or a multiscale 3-D rigid-motion-invariant testing of the statistical similarity of the 3-D textures. To compute the "distance" between any two rotations R(1) and R(2) of two given 3-D textures, we use the Kullback-Leibler divergence between 3-D Gaussian Markov random fields fitted to the rotated texture data. Then, the 3-D rigid-motion-invariant texture distance is the integral average, with respect to the Haar measure of the group SO(3), of all of these divergences when rotations R(1) and R(2) vary throughout SO(3). We also present an algorithm enabling the computation of the proposed 3-D rigid-motion-invariant texture distance as well as rules for 3-D rigid-motion-invariant texture discrimination/classification and experimental results demonstrating the capabilities of the proposed 3-D rigid-motion texture discrimination rules when applied in a multiscale setting, even on very general 3-D texture models.     

Some new results on stability robustness of two-dimensional discrete systems

In this paper, we study the problem of stability robustness of two-dimensional discrete systems in a local state-space setting. Two methods are proposed for efficient numerical evaluation of the exact complex perturbation bound . The first method combines Byers' bisection method with a three-point-pattern optimization technique to compute . The second method utilizes a direct optimization technique to find the bound. In addition, a 2-D Lyapunov approach is proposed to obtain two lower bounds of , and numerical techniques for solving the constant 2-D Lyapunov equation involved are presented. The paper is concluded with an example illustrating the main results obtained.     

On the Average of the Product of Two Gaussian Q-Functions over Nakagami-q (Hoyt) Fading and Its Application

In this letter, the average of the product of two Gaussian Q-functions over the Nakagami-q (Hoyt) distribution with arbitrary parameters is presented in terms of the Lauricella hypergeometric function, which can be evaluated numerically using its integral or converging series representation. The result obtained is then applied to evaluate the symbol error probability (SEP) of general rectangular quadrature amplitude modulation (QAM) constellations over Nakagami-q fading channels. The impact of fading severity (parameter q) on the error performance of the general rectangular QAM system is also investigated.     

A new simplified two-dimensional model for the threshold voltage ofMOSFET's with nonuniformly doped substrate

A new simplified two-dimensional model for the threshold voltage of MOSFETs is derived in terms of simple characteristic functions. These characteristic functions are transformed from the exact series solution of the two-dimensional Poisson's equation, in which the effects of a nonuniformly doped substrate and a finite graded source-drain junction depth are included. In this model, charge-screening effects are proposed to account for the weak dependence of the threshold voltage on the substrate bias for short-channel MOSFETs, and exact source and drain boundary potentials can be approximated by their equivalent power functions. The accuracy of the simplified 2-D model is verified by 2-D numerical analysis. Moreover, comparisons between the simplified 2-D model and the experimental results are made, and good agreement is obtained for wide ranges of channel lengths, applied substrate, and drain biases     

Transient response of an infinite cylindrical antenna in a dissipative medium

The transient solution of an infinite cylindrical antenna in a dissipative medium caused by an impulse excitation at a delta gap is obtained via an exact solution in the form of definite integrals and a simple asymptotic formula. This formula is used to obtain an integral for calculating the antenna current caused by a double exponential input voltage at the gap; furthermore, the resulting integral reduces to Sunde's classic result under the diffusion limit. These results are applied to the transient response of a buried wire subject to an electromagnetic pulse (EMP) or nearby lightning incident wave.     

Exact calculation of the union bound on performance oftrellis-coded modulation in fading channels

This paper presents a method for the exact calculation of the union bound on the error performance of trellis-coded modulation (TCM) in fading channels. Previous analyses have approximated the error expression to allow the use of the transfer function, or restricted their attention to the most common error events, or both. In contrast, we combine the transfer function, which counts all error events, with exact calculation of event probabilities, and produce an exact expression for the union bound. Although computationally intensive, the technique produces the tightest bound yet published. In addition, it is very general and is applicable to coherent, differential, and pilot-based detection, and to phase-shift keying (PSK)- and quadrature amplitude modulation (QAM)-types of constellations     

Generalized solution to symbol error probability integral containing over different fading models

This paper presents a generalized solution to the symbol error probability (SEP) integral containing the product of two Gaussian Q‐functions . Numerical integration technique is first used to approximate the polar form of as a sum of exponentials. This approximation is then used to derive a closed‐form solution to the related SEP integral. Due to the exponential nature of the approximation, solution to the integral is expressed in terms of moment generating function (MGF) of a fading distribution. Therefore, the solution to integral exists for all fading distributions which have well‐defined MGF. The mathematical complexity of the proposed solution is directly proportional to the complexity of MGF expression. For most of the fading models, the corresponding MGF involves power or exponential functions, which guarantees algebraic simplicity of the proposed solution. Further, this generalized solution is used to evaluate the SEP of various modulation schemes over different fading channels. Various computer simulations run in MATLAB for wide range of scenarios confirm the accuracy of the proposed approximation and solution.     

Closed-form expressions for the symbol error probability of 3-D OFDM

In this letter, closed-form expressions for the symbol error probability of 3-D orthogonal frequency division multiplexing in additive white Gaussian noise channel are derived. When a 3-D 4-ary constellation is used as signal mapper, we calculate the upper and the lower bound for the error probability, and also provide its approximation. Since decision boundaries of 8- ary constellation form an extended regular hexahedron, an exact symbol error probability can be computed. It is verified that the theoretical error probabilities are very close to or almost the same as simulation results.     

Performance of high-diversity multidimensional constellations

Following the approach introduced by Cavers and Ho (1992), the performance of component-interleaved multidimensional constellations over the Rayleigh fading channel is evaluated analytically. The error probabilities are approximated by the union bound using an exact expression of the pairwise error probability. Simulation results show that this bound can be used effectively as a design criterion for the selection of high-diversity multidimensional constellation over the Rayleigh fading channel     

An efficient TCS formula for rainfall microwave attenuation:T-matrix approach and 3-D fitting for oblate spheroidal raindrops

The T-matrix approach to the computation of total cross sections of spheroidal raindrops due to electromagnetic scattering is considered numerically exact, and has therefore been used in this paper for the analysis of the total cross section (TCS) of the spheroidal raindrops. A more accurate computer programme based on the T-matrix method has been developed in MATHEMATICA^TM so as to evaluate the TCSs of the spheroidal raindrop scatterers. With the checked programme after comparison, a large amount of TCS data has been obtained and plotted in a three-dimensional (3-D) graphic in this paper. Utilizing these exact data points, a 3-D (or two-step) nonlinear least squares fitting procedure has been proposed and implemented successfully. As a result, an efficient formula of the TCS as a function of both raindrop mean radius and operating frequency has been obtained. In the analysis, four cases (both parallel and perpendicular polarizations, and outdoor temperatures of 10 and 20°C) are considered. Covering a very large validity range for practical useful problems, this formula is very compact, easy to use, and very much faster (by about two orders of magnitude) than the conventional algorithm     

Analysis of 3-D integral imaging displays using the Wigner distribution

Integral imaging is a promising technology for 3-D TV and 3-D display. In this paper, a theoretical analysis of 3-D integral imaging systems is performed in the frame of the Wigner distribution formalism. It is shown that the entire intensity distribution in the pick-up image plane of these systems can be obtained from a single 2-D Wigner distribution function of a single lenslet pupil. This result reveals the Wigner distribution function as a powerful tool for analysis of 3-D integral imaging systems with different pupil functions. As an example, the extension of the depth of field of an integral imaging system with lenslets having amplitude modulation (central obscuration) is proposed.     

Performance evaluation of HDAF relaying systems for pilot and data symbol burst transmission over quasi‐static Rayleigh fading channels

This paper analyzes averaged symbol error probabilities of burst transmission consisting of pilot and data symbols for hybrid adaptive decode‐or‐amplify‐forward (HDAF) relaying systems. Under the assumption of quasi‐static Rayleigh fading channels with independent and non‐identically distribution, we consider a channel estimation scheme based on pilot symbols and show how channel estimation error affects received signal‐to‐noise ratio (SNR) and symbol error probability (SEP). Firstly, all the possible detection error‐events are presented for all the relay nodes, and their probabilities are derived as forms related with data symbol burst transmission. For the given error event, we analyze the conditional SEP as an exact form and then, the averaged SEP (ASEP) is approximately derived as a closed‐form. The simulation results verify that our derived ASEP expression is accurate over all the regions of SNR. Utilizing the proposed expressions, we can evaluate ASEP performance of HDAF relay systems easily and fast. Copyright © 2015 John Wiley & Sons, Ltd.