An Improved Deterministic SoS Channel Simulator for Multiple Uncorrelated Rayleigh Fading Channels

The generation of multiple uncorrelated Rayleigh fading waveforms is often demanded for simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels. In this letter, an improved deterministic sum-of-sinusoids (SoS) channel simulator with a new parameter computation method is proposed to simulate a large number of uncorrelated Rayleigh fading processes. Compared with the existing SoS channel simulators, the proposed deterministic SoS model yields a much better simulation efficiency while still preserving satisfactory approximations to the desired statistical properties of the reference model.     

无线信道中一种新的瑞利波形仿真模型

该文提出了一种新的简单的产生满足任意自相关特性的瑞利波形的仿真模型,在此基础上得出无线信道中瑞利衰落波形的产生方法。该方法可以容易地产生多个相互独立的瑞利衰落波形,从而为研究各种频率分集无线通信系统提供了可能。仿真结果表明该模型能够有效地产生符合小尺度无线信道特征的瑞利衰落波形,满足自相关特性及平稳性的要求。     

Jakes fading model revisited

The Jakes fading model is a deterministic method for simulating time-correlated Rayleigh fading waveforms and is still widely used today. However, since it is difficult to create multiple uncorrelated fading waveforms with this model, the authors propose modifications to the model which solve this problem.<>     

The simulation of independent Rayleigh faders

Multiple independent Rayleigh fading waveforms are often required for the simulation of wireless communications channels. Jakes (1974) Rayleigh fading model and its derivatives based on the sum-of-sinusoids provide simple simulators, but they have major shortcomings in their simulated correlation functions. A novel sum-of-sinusoids fading model is proposed and verified, which generates Rayleigh fading processes satisfying the theoretical independence requirements and providing desired power spectral densities with ideal second-order moment. The effects of replacing sinusoids in the proposed model by their approximate waveforms are also analyzed and tested. Performance evaluation and comparison are provided, using the quality measures of the mean-square-error of autocorrelation function and the second-order moment of the power spectral density.     

STBC-Based (Turbo) STTC Codes Built by Set Partitioning for Three Transmit Antennas: Construction and Performances

Simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels often demands the generation of multiple uncorrelated Rayleigh fading waveforms. In this letter, two appropriate parameter computation methods, namely the method of exact Doppler spread (MEDS) and L_p -norm method (LPNM), for deterministic sum-of-sinusoids (SoS) channel simulators are investigated to guarantee the uncorrelatedness between different simulated Rayleigh fading processes. Numerical and simulation results show that the resulting deterministic SoS channel simulator can accurately and efficiently reproduce all the desired statistical properties of the reference model     

The diversity gain of transmit diversity in wireless systems withRayleigh fading

In this paper, we study the ability of transmit diversity to provide diversity benefit to a receiver in a Rayleigh fading environment. With transmit diversity, multiple antennas transmit delayed versions of a signal to create frequency-selective fading at a single antenna at the receiver, which uses equalization to obtain diversity gain against fading. We use Monte Carlo simulation to study transmit diversity for the case of independent Rayleigh fading from each transmit antenna to the receive antenna and maximum likelihood sequence estimation for equalization at the receiver. Our results show that transmit diversity with M transmit antennas provides a diversity gain within 0.1 dB of that with M receive antennas for any number of antennas. Thus, we can obtain the same diversity benefit at the remotes and base stations using multiple base-station antennas only     

Efficient simulation of digital transmission over WSSUS channels

This paper proposes an efficient Monte Carlo method which reduces computation for digital communication simulations over a multipath Rayleigh fading, wide-sense-stationary uncorrelated-scattering (WSSUS) channel. An equivalent discrete-time channel representation, which can be realized by a FIR filter with time-variant tap gains, is employed. In the proposed method, the tap gains are generated from a linear transformation of a set of orthogonal zero-mean complex Gaussian random processes. By the central limit theorem, each random process is approximated by summing a finite number of randomly generated phasors (Monte Carlo approximation). When compared with the tap gain generation method, which approximates the physical channel by the Monte Carlo approximation first and then generates the tap gain values, the proposed method demonstrates a considerable reduction in the required simulation time as well as improved accuracy under similar conditions     

Analysis and Simulation of Second-Order Statistics with Modified Characteristic Function Parameters in a Multipath Fading Environment

In this paper, we analyse and implement a modified low pass filtering based characteristic function for a multipath Rayleigh fading channel. A new class of this modified filtering sequence based statistical simulation model is proposed for a Rayleigh fading environment. Comparing with the sum-of-sinusoids (SOS) deterministic model and its modifications as a new SOS model, the proposed model reintroduces the randomness to Doppler frequency and initial phase of the sinusoids to have non-deterministic simulators with desired statistical properties. The expressions and simulation results of level crossing rate (LCR) and average fade duration are derived and shown in this paper. Comparison of power spectra reveals that the spectrum spread is much less for our proposed method. Therefore, we would expect reduction in the rapidity of fading which is observed in LCR calculations.     

Data-Aided Fading Estimation Technique for Shadowed Mobile Satellite Fading Channels

A novel data-aided fading estimation technique that employs both pilot anddata symbols is proposed to significantly reduce the bandwidth redundancy ofthe pilot-symbol-aided (PSA) systems using receivers with low complexity andlatency in the shadowed mobile satellite fading channels. The shadowed mobilesatellite fading channels are modeled as the sum of a lognormally distributeddirect component and a Rayleigh distributed multipath component, and the PSAsystem employs 16-ary quadrature-amplitude-modulation (16QAM) fortransmission. Monte Carlo computer simulation has been used to assess thetechnique on the bit-error-rate (BER) performances of the system in the lightshadowed, the average shadowed and the heavy shadowed Rician fadingenvironments. The results have shown that the proposed technique requires avery low bandwidth redundancy to provide satisfactory BER performances, andcan substantially lower the error floors of the PSA systems.     

An Exact Close-form PEP and a new PEP for Space-Time Codes in Rayleigh Fading Channels

A close-form expression for the exact Pair-wise Error Probability (PEP) of Space-Time (S-T) codes in Rayleigh fading channel is derived using the general and close-form solution for the probability-density function (PDF) of a sum of independent exponential distributed random variables. The expression requires evaluating the coefficients for partial fraction expansion, so an easy analytical way is proposed for doing this. The exact PEP is subsequently used to develop a simple PEP using the upper bound. Both PEPs are used in the Union bound for error rate evaluation. Numerical calculations and Monte Carlo computer simulation are used to study the accuracies of these Union bounds for error rate evaluation of a rotation-based diagonal S-T code (D code) in Rayleigh fading channels. Four other PEPs based on different bounds, i.e., the Chernoff bound, the asymptotic bound, the tight asymptotic bound, and the Eigen-Geometric-Mean (EGM) bound, are also studied for comparison. Results show that our derived close-form PEP is an exact PEP and our proposed PEP is a very tight bound to the exact PEP.     

BER Performance of Bandlimited DS-CDMA Systems in Nakagami Fading

Accurate average bit-error rate analysis of asynchronous bandlimited binary direct-sequence code-division multiple-access (DS-CDMA) systems in Nakagami-m fading is studied. The fading is assumed to be flat and slow. The spectrum raised-cosine (SRC) and Beaulieu-Tan-Damen (BTD) pulse-shapes are employed. A new method which combines the characteristic function (CF) method with the improved Gaussian approximation (GA) is proposed for evaluating the BER of bandlimited DS-CDMA. A substantial computational complexity reduction is achieved. The well-known standard GA, Holtzman's simplified improved GA, and improved Holtzman's GA methods are also considered. The accuracies of the approximation methods are assessed using Monte Carlo simulation. For a system employing a deterministic sequence for the desired user and random sequences for the active interfering users, a CF method is employed to derive precise BER results. The new BTD pulse outperforms the SRC pulse in all situations     

Linear dispersion codes for MIMO systems based on frame theory

Multiple-input multiple-output (MIMO) wireless communication systems provide high capacity due to the plurality of modes available in the channel. Existing signaling techniques for MIMO systems have focused primarily on multiplexing for high data rate or diversity for high link reliability. In this paper, we present a new linear dispersion code design for MIMO Rayleigh fading channels. The proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability. This is important because, as we show, designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view. Various techniques are presented for finding codes with good error probability performance. Monte Carlo simulations illustrate performance of some example code designs in terms of ergodic capacity, codeword error probability, and bit error probability.     

Precoding of space-time block coded signals for joint transmit-receive correlated MIMO channels

A memoryless linear precoder is designed for orthogonal space-time block codes (OSTBC) for improved performance over block-fading flat correlated Rayleigh fading multiple-input multiple-output (MIMO) channels. Original features of the proposed technique include 1) the precoder can handle both transmit and receive correlation, and 2) the precoder handles any arbitrary joint correlation structure, including the so-called Kronecker (non-Kronecker) correlation models. The precoder is designed to minimize a symbol error-based metric as function of the joint slowly-varying channel correlation coefficients, which are supposed to be known to the transmitter. Several useful properties of the optimal precoder are given, evidencing the impact of receive correlation on transmitter optimization in certain situations. An iterative fast-converging numerical optimization algorithm is proposed. Monte Carlo simulations over fading channels are used to validate our claims.     

Fast convergent monte carlo receiver for OFDM systems

The paper investigates the problem of the design of an optimal Orthogonal Frequency Division Multiplexing (OFDM) receiver against unknown frequency selective fading. A fast convergent Monte Carlo receiver is proposed. In the proposed method, the Markov Chain Monte Carlo (MCMC) methods are employed for the blind Bayesian detection without channel estimation. Meanwhile, with the exploitation of the characteristics of OFDM systems, two methods are employed to improve the convergence rate and enhance the efficiency of MCMC algorithms.One is the integration of the posterior distribution function with respect to the associated channel parameters, which is involved in the derivation of the objective distribution function; the other is the intra-symbol differential coding for the elimination of the bimodality problem resulting from the presence of unknown fading channels. Moreover, no matrix inversion is needed with the use of the orthogonality property of OFDM modulation and hence the computational load is significantly reduced. Computer simulation results show the effectiveness of the fast convergent Monte Carlo receiver.     

Multidimensional M-PSK trellis codes for fading channels

This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation     

Wavelet-based sequential Monte Carlo blind receivers in fading channels with unknown channel statistics

Recently, an adaptive Bayesian receiver for blind detection in flat-fading channels was developed by the present authors, based on the sequential Monte Carlo methodology. That work is built on a parametric modeling of the fading process in the form of a state-space model and assumes the knowledge of the second-order statistics of the fading channel. In this paper, we develop a nonparametric approach to the problem of blind detection in fading channels, without assuming any knowledge of the channel statistics. The basic idea is to decompose the fading process using a wavelet basis and to use the sequential Monte Carlo technique to track both the wavelet coefficients and the transmitted symbols. A novel resampling-based wavelet shrinkage technique is proposed to dynamically choose the number of wavelet coefficients to best fit the fading process. Under such a framework, blind detectors for both flat-fading channels and frequency-selective fading channels are developed. Simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers.     

Results for Infinite Integrals Involving Higher-Order Powers of the Gaussian Q-Function with Application to Average SEP Analysis of DE-QPSK

Exact results are presented for infinite integrals that consist of higher-order powers of the one dimensional Gaussian Q-function averaged over Rayleigh fading envelopes in multi-branch diversity reception with maximal ratio combining (MRC). Some known results for the average of the 1st and 2nd powers are shown as special cases. The results obtained in this paper are utilized to study the average symbol error probability (SEP) performance of differentially encoded quadri-phase shift-keying (DE-QPSK) in Rayleigh fading channels employing MRC, and new exact expressions are presented for different fading scenarios. The derived mathematical expressions are verified using Monte Carlo simulations.     

Outage Probability and Average Channel Capacity of Amplify-and-Forward in Conventional Cooperative Communication Networks over Rayleigh Fading Channels

Performance of conventional cooperative communication networks using amplify-and-forward relay over independent and identically distributed Rayleigh fading channels is investigated in this paper. An expression for probability density function by using moment generating function is obtained. Further closed-form expressions of the outage probability and the average channel capacity are derived. The derived analytical results are compared with Monte Carlo simulations to confirm correctness of the derived expressions.     

Fast simulation of DS/CDMA with and without coding in multipathfading channels

Code-division multiple access (CDMA) has found widespread applications in various applications such as advanced wireless technologies and digital cellular communications. We consider the error-rate performance of asynchronous direct-sequence CDMA in a wireless radio communications environment that is characterized by Rayleigh multipath fading channels. Because of the system complexity, the performance of CDMA systems in such an environment is difficult to assess analytically. Monte Carlo simulations can offer an alternative performance evaluation tool. Unfortunately, in practice, such an alternative is often limited by an excessive computational burden. Importance sampling is a variance reduction technique which can significantly reduce the computational cost required by Monte Carlo simulations. This paper describes the basic principles behind this powerful technique. In particular, it illustrates its use as a computationally efficient and accurate tool for computer-aided design and analysis of uncoded as well as coded CDMA in wireless communications     

Simplified eIRA code design and performance analysis for correlated Rayleigh fading channels

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for Rayleigh fading channels, instead of implementing the complex design procedures targeted, specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also show that eIRA codes designed for the BuEC enjoy the advantage of efficient encodability and a lower error-rate floor. Finally, we demonstrate that it is the distribution of the number of faded bits per codeword which determines the difference between correlated and uncorrelated fading channel performance. Perfect channel state information is assumed in this paper.