Rayleigh Fading Channel Simulators Research Articles

Hierarchical Circular θ-QAM

Hierarchical modulation provides unequal error protection to transmitted data according to their relative importance. In this article, hierarchical modulation constellation based on circular θ-quadrature amplitude modulation (CTQAM), 4/M-CTQAM, M = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> , k ≥ 4, is proposed. We provide a construction method and bit-to-symbol mapping for the proposed hierarchical modulation constellation. We then examine the bit error rate performance of 4/M-CTQAM and validate the theoretical results through computer simulations in additive white Gaussian noise (AWGN) and Rayleigh fading channels.

Hardware Implementation of Overlap-Save-Based Fading Channel Emulator

An efficient hardware implementation of correlated Rayleigh fading channel simulator is presented in this brief. It emulates Doppler effects based on the use of Overlap-Save (OLS) method. OLS is used for both, the fading variates generator and the time domain interpolator, leading to a scalable complete solution. Moreover, additional simplifications were introduced to reduce even further algorithmic complexity when compared with the original OLS-based proposal. An efficient hardware implementation is achieved through maximizing the utilization rate of allocated hardware resources. When added to its scalability, this makes the proposal appealing to emulate channels with multipath effects for MIMO systems. Indeed, the proposed parallel architecture enables a throughput of 34 Mega Samples per Second per path at a clock frequency of 275 MHz on Xilinx Virtex-7 FPGA. The achieved throughput allows the support of the most demanding LTE configuration with 20 MHz channel bandwidth. To the best of our knowledge, this is the first ever real-time hardware implementation of OLS-based channel emulator.

Design and Performance Analysis of MISO-SRMR-DCSK System over Rayleigh Fading Channels

The major drawback of the differential chaos shift keying (DCSK) system is that equal time and energy are spent on the reference and data signal. This paper presents the design and performance analysis of a short reference multifold rate DCSK (SRMR-DCSK) system to overcome the major drawback. The SRMR-DCSK system is proposed to enhance the data rate of the short reference differential chaos shift keying (SR-DCSK) system. By recycling each reference signal in SR-DCSK, the data slot carries N bits of data and by P times. As a result, compared with SR-DCSK, the proposed system has a higher data transmission rate and evaluates the energy efficiency with respect to the conventional DCSK system. To further improve the bit-error-rate (BER) performance over Rayleigh fading channels, the multiple-input single-output SRMR-DCSK (MISO-SRMR-DCSK) is also studied. The BER expression of the proposed system is derived based on Gaussian approximation (GA), and simulations in Rayleigh fading channels are performed. Simulation results show a perfect match with the analytical expression.

Design of Fading Channel Simulator Based on IIR Filter Using Genetic Algorithm

This article designs a Rayleigh fading channel simulator using IIR filter (called Doppler filter), which is used to approximate the Jakes Doppler spectrum. We mainly focus on the design of Doppler filter and model it as an optimization problem. Non-convexity of the problem is proved in this paper and genetic algorithm (GA) is used to optimize it, which has never been used before in this area. Simulation result shows that GA converges at the solution corresponding to very accurate approximation of Jakes PSD. Finally, several statistical characteristics of the simulator are verified, including correlation functions and level-crossing rate (LCR), all of which match the theoretical predictions pretty well.

Improving Energy Efficiency of OFDM Using Adaptive Precision Reconfigurable FFT

Being an essential issue in digital systems, especially battery-powered devices, energy efficiency has been the subject of intensive research. In this research, a multi-precision FFT module with dynamic run-time reconfigurability is proposed to trade off accuracy with the energy efficiency of OFDM in an SDR-based architecture. To support variable-size FFT, a reconfigurable memory-based architecture is investigated. It is revealed that the radix-4 FFT has the minimum computational complexity in this architecture. Regarding implementation constraints such as fixed-width memory, a noise model is exploited to statistically analyze the proposed architecture. The required FFT word-lengths for different criteria--namely BER, modulation scheme, FFT size, and SNR--are computed analytically and confirmed by simulations in AWGN and Rayleigh fading channels. At run-time, the most energy-efficient word-length is chosen and the FFT is reconfigured until the required application-specific BER is met. Evaluations show that the implementation area and the number of memory accesses are reduced. The results obtained from synthesizing basic operators of the proposed design on an FPGA show energy consumption experienced a saving of over 80 %.

FPGA Implementation of a Nakagami-m fading channel Simulator using Random Number Generator

&lt;p class="abstract"&gt;By realizing the concept of implementation of the radio propagation channels on simulators is the eminent intention of this work. Even though prototyping software simulators are effortless to design we prefer hardware simulators as they endeavors distinguishable quickness, compared to earlier. Prior to this work fading channels like Gaussian, Rayleigh and Rician fading channel simulators were executed on hard ware.(i.e. FPGA) The significant target of this attempt is to implement Nakagami-m fading channel on hardware as they preserved for unsubstantial consideration. While differentiating with other fading channels Nakagami-m fading channel acquires wide spread applications, as its capability of providing appropriate fit for practical fading data, as this is flexible through its size parameter ‘m’, over which representation of signal fading conditions that vary from serious to modest, to normal fading or no fading is accomplished . The proposed hardware simulator can hatches complex Nakagami variates after it was implemented on XilinxSpartan-xc3s500e-4fg320 FPGA. This is operated at 50MHz.&lt;/p&gt;

A pilot aided channel estimator using DFT based time interpolator for massive MIMO-OFDM systems

Massive multi input multi output orthogonal frequency division multiplexing (MIMO-OFDM) systems are progressively improving the current wireless communication standards towards 5G, due to their high data rates. The channel estimator (CE) employed in these systems is based on 2D-grid type pilot arrangement, which offers better spectral efficiency. The 2D arrangement requires the CE to incorporate a time interpolator (TI) in addition to the usual frequency interpolator (FI). The prime concerns for a TI in massive systems are minimal storage, low computational complexity, and system reliability. The existing low-pass FI or a linear FI can serve as TI; however, each of them does not address all the prime concerns in totality. In this paper, a discrete Fourier transform (DFT) based TI is introduced with three distinguished features; minimum storage space similar to a linear TI, computational complexity at par with linear TI, and improved system reliability compared to low-pass TI. Using system bit error rate (BER) simulations in various Rayleigh fading channels characterized by U-shaped Doppler spectrum, it is verified that the proposed CE incorporating the DFT-based TI indeed provides better system reliability with minimal storage and low computational complexity.

A reconfigurable hardware architecture for the simulation of Rayleigh fading channels under arbitrary scattering conditions

Owing to the constant evolution of modern communication systems, it is necessary to have channel simulators able of reproducing the channel characteristics with a high level of accuracy. Currently, hardware simulators are able to reproduce only scenarios with isotropic scattering conditions. In this paper, a novel reconfigurable hardware architecture for the efficient generation of Rayleigh fading waveforms with predefined autocorrelation properties is presented. The proposed architecture is based on the sum-of-sinusoids (SoS) method, and was devised to allow the simulation of mobile fading channels under isotropic and non-isotropic scattering conditions. Additionally, the sinusoids’ parameters of the hardware fading channel simulator can be configured for any stochastic or deterministic parameter computation method (PCM). Likewise, the proper performance of the designed hardware channel simulator is verified via simulation, where it is shown that the first and the second order statistics of the fixed-point Rayleigh fading waveforms match those of the waveforms generated in floating-point on a software platform. Hardware implementation results show an area reduction and an improvement in the sinusoid frequency resolution of the SOS based method (as precise as 1.9μHz in this work), when compared with previous approaches.

A multi-criteria comparative analysis of different Rayleigh fading channel simulators

In this paper, an in-depth comparative analysis of the most accepted and approved Rayleigh fading channel simulators is presented. Our study addresses the three common methods for generating time-correlated Rayleigh fading processes: the inverse discrete Fourier transform (IDFT) method, the filtering white Gaussian noise (FWGN) method and the sum-of-sinusoids (SOS) method. Totally seven models, including the recently proposed models, are analyzed and compared with Clarke's reference model. We use four quantitative measures for judicious assessment of the quality of generated processes in terms of both first-order and second-order statistics. Additionally, these measures cover analysis in time domain as well as in frequency domain. An evaluation of the computational effort is also depicted. The simulation results suggest that the recently published Wang's model is very attractive and it outperforms all SOS-based models. We conclude that Zheng and Xiao's first model remains the best choice among Zheng and Xiao's family models. Several other important remarks and conclusions about the accuracy and the capability of the different Rayleigh fading simulators are driven from this study.

Classes of sum-of-cisoids processes and their statistics for the modeling and simulation of mobile fading channels

In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel’s statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble average. We investigate the wide-sense stationarity, first-order stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of the underlying random processes characterizing the different classes of stochastic SOC simulators. The obtained results demonstrate that only the class of SOC models comprising cisoids with constant gains, constant frequencies, and random phases is defined by a set of stationary and ergodic random processes. The analysis presented here can easily be extended with respect to the modeling and simulation of frequency-selective single-input single-output (SISO) and multiple-input multiple-output channels. For the case of frequency-selective SISO channels, we investigate the stationarity and ergodicity in both time and frequency of 16 different classes of SOC simulation models. The findings presented in this paper can be used in the laboratory as guidelines to design efficient simulation platforms for the performance evaluation of modern mobile communication systems.

On the Correlation and Ergodic Properties of the Squared Envelope of SOC Rayleigh Fading Channel Simulators

In this paper, we investigate the correlation and ergodic properties of the squared envelope of a class of autocorrelation-ergodic (AE) sum-of-cisoids (SOC) simulation models for mobile Rayleigh fading channels. Novel closed-form expressions are presented for both the ensemble and the time autocorrelation functions (ACFs) of the SOC simulation model's squared envelope. These expressions have been derived by assuming that the SOC model's inphase and quadrature (IQ) components have arbitrary autocorrelation and cross-correlation properties. This consideration makes the results herein presented more general than those given previously in other papers, where it is assumed that the IQ components of the simulation model are strictly uncorrelated. We show that under certain conditions, the squared envelope of the SOC model is an AE random process. In addition, we evaluate the performance of three fundamental methods for the computation of the model parameters--namely the generalized method of equal areas, the L p -norm method, and the Riemann sum method--regarding their accuracy for emulating the squared envelope ACF of a reference narrowband Rayleigh fading channel model. The obtained results are important to design efficient simulators for the performance analysis of systems and algorithms sensitive to the correlation properties of the channel's squared envelope, such as speed estimators and handover mechanisms.

An Ergodic Sum-of-Cisoids Simulator for Multiple Uncorrelated Rayleigh Fading Channels Under Generalized Scattering Conditions

In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulators for multiple uncorrelated narrowband Rayleigh fading channels. The method, which is intended for a special class of SOS models known as sum-of-cisoids (SOC) models, enables the generation of an unlimited number of mutually uncorrelated Rayleigh fading waveforms with specified autocorrelation properties. This is in contrast to all known methods proposed for SOS simulators, which are restricted to the simulation of multiple uncorrelated Rayleigh fading channels characterized by autocorrelation functions (ACFs) derived under the isotropic scattering assumption. The excellent performance of this new method is exemplarily demonstrated by comparing the correlation properties and the envelope distribution of a set of waveforms generated by the simulator with the corresponding quantities of a reference set of multiple uncorrelated Rayleigh fading channels. The method's performance is evaluated in not only theoretical simulation scenarios, where the lengths of the generated waveforms approach infinity, but also practical scenarios, where the waveform lengths are limited. The simulation approach described in this paper is important to the performance analysis of mobile broadband communication systems using diversity, multicarrier, or multiple-input-multiple-output (MIMO) techniques under generalized scattering conditions.

The design of sum-of-cisoids rayleigh fading channel simulators assuming non-isotropic scattering conditions

In this letter, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to emulate the channel's autocorrelation function (ACF), whereas the latter two methods are more precise regarding the approximation of the envelope distribution. The results also show that the benefits of increasing the number of cisoids are more significant in the case of the RSM than in the case of the GMEA and LPNM. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the laboratory analysis of mobile communication systems operating in non-isotropic scattering environments.

Rayleigh fading channel simulator based on inner–outer factorization

The paper deals with the design of Rayleigh fading channel simulators based on the inner–outer factorization. The core of the approach is to approximate the outer spectral factor of the channel power spectral density (PSD) by either finite-order polynomials or rational functions. This, respectively, leads to MA or AR/ARMA models. The parameter estimation operates in two steps: the outer factor, which leads to a minimum-phase filter, is first evaluated inside the unit disk of the z-plane. Then, we propose to compute the Taylor expansion coefficients of the outer factor because they coincide with the model parameters. Unlike other simulation techniques, this has the advantage that the first p parameters remain unchanged when one increases the model order from p to p+1. A comparative study with existing channel simulation approaches points out the relevance of our ARMA model-based method. Moreover, the ARMA model weakens the oscillatory deviations from the theoretical PSD in the case of AR models, or low peaks at the Doppler frequencies for MA models.

A Comparative Study of Different Rayleigh Fading Channel Simulators

In this paper, we have presented a comparative study of four different Rayleigh fading channel simulation methods with respect to computational complexity and accuracy. Fidelity of the various simulators is examined in terms of confidence interval also. The sum-of-sinusoids (SOS)-based simulation method can accurately generate a very long sequence without any impact on computer memory usage. The inverse discrete Fourier transform (IDFT)-based simulator is relatively fast and able to generate a sequence corresponding to a given autocorrelation function (ACF). However, its applicability is limited due to large memory space requirement. For small sequences, algorithm based on covariance matrix is most efficient but its time complexity grows many folds as the sequence length is increased. Autoregressive modelling (AR) of fading process is needed when time evolution of fading process is exploited for channel tracking. The accuracy of the generated sequence ACF using the above four methods is also compared through an example.

Compact Rayleigh and Rician fading simulator based on random walk processes

This article describes a significantly improved sum-of-sinusoids-based model for the accurate simulation of time-correlated Rayleigh and Rician fading channels. The proposed model utilises random walk processes instead of random variables for some of the sinusoid parameters to more accurately reproduce the behaviour of wireless radio propagation. Every fading block generated using our model has accurate statistical properties on its own and hence, unlike previously proposed models, there is no need for time-consuming ensemble-averaging over multiple blocks. Using numerical simulation it is shown that the important statistical properties of the generated fading samples have excellent agreement with the theoretical reference functions. A fixed-point hardware implementation of the corresponding Rayleigh and Rician fading channel simulator on a field-programmable gate array (FPGA) is presented. By efficiently scheduling the operations, the reconfigurable fading channel simulator is compact enough that it can be efficiently used to simulate multipath scenarios and multiple-antenna systems (e.g. a 4×4 MIMO channel) using a single FPGA.

Computer simulation of Rayleigh fading channels in MC-CDMA systems

For Multi-Carrier-Code Division Multiple Access (MC-CDMA) systems, it is usually assumed that the fading of the subcarriers is frequency non-selective and independent of each other. This paper shows that the two assumptions are incompatible. In fact, the MC-CDMA signals at each subcarrier undergo fading that are highly correlated. Based on this observation, this paper develops a simulation algorithm for Rayleigh fading channels via frequency-domain correlation function, which incorporates the Doppler effect simultaneously. Numerical examples are presented to demonstrate the effectiveness of the new algorithm, with the conclusion that the independence assumption of subcarrier fading overrates the system performance.

Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician Fading Channels

The statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency

A New Design Concept for High-Performance Fading Channel Simulators Using Set Partitioning

In this paper, we introduce a new technique for the design of high-performance Rayleigh fading channel simulators. The proposed design method uses set partitioning --- a technique, which plays a key role in the design of trellis-coded modulation schemes. We show how set partitioning can be used to design multiple uncorrelated fading waveforms enabling the simulation of Rayleigh fading channels. For the important case of isotropic scattering, we show that the sample average of the generated waveforms results in a deterministic process, the autocorrelation function (ACF) of which tends to the zeroth-order Bessel function of the first kind as the number of sample functions increases. The proposed procedure is completely deterministic. The comparison with a stochastic procedure using Monte Carlo techniques will be made. A study of the performance shows clearly that the new technique using set partitioning outperforms by far existing Monte Carlo methods.

Comparative Analysis of Statistical Models for the Simulation of Rayleigh Faded Cellular Channels

Several new sum-of-sinusoids models have recently been introduced for the simulation of Rayleigh fading channels. These models are statistical in nature implying that their simulation parameters such as the Doppler frequencies are random. They have been shown to accurately reproduce some of the desired statistical properties of the faded envelope such as the time autocorrelation and the level crossing rate. However, a comparative analysis of these models, hitherto scattered throughout the literature, is not available. This paper compares these models in terms of their complexity and performance. The performance assessment is based upon the variance of the time average statistical properties from their ideal ensemble averages.