Error probabilities for Rician fading multichannel reception of binary andn-ary signals

Performance characteristics are derived for two different forms of multireceivers (the coherent and noncoherent) which are used with binary andN-ary signaling through the Rician fading multichannel. The coherent multireceiver is capable of perfectly measuring the channel amplitudes and phases whereas, at the other extreme, the noncoherent multireceiver implies a receiver which requires no channel measurement whatsoever. The multichannel model presumes that each transmission mode supports a specular or fixed component and a random or scatter component which fades according to the Rayleigh distribution. Heretofore, performance analyses of multichannel links have assumed that the fading obeys the Rayleigh law. This multichannel model is sufficiently general to include four practical types: the Rician and the Rayleigh fading multichannels, multichannels whose propagation modes do not fade, and those which simultaneously contain Rician and Rayleigh fading propagation paths or the so called mixed-mode multichannel. Error probabilities are graphically illustrated and compared for various multichannel models. It is found that the effectiveness of multichannel reception is highly dependent on the strength of the specular channel component relative to the mean squared value of the random channel component. In particular, multichannel reception is more effective when applied to the completely random multichannel. For special cases the error-rate expressions reduce to well-known results.     

Statistical Analysis of a Mobile-to-Mobile Rician Fading Channel Model

Mobile-to-mobile communication is an important application for intelligent transport systems and mobile ad hoc networks. In these systems, both the transmitter and receiver are in motion, subjecting the signals to Rician fading and different scattering effects. In this paper, we present a double-ring with a line-of-sight (LOS) component scattering model and a sum-of-sinusoids simulation method to characterize the mobile-to-mobile Rician fading channel. The developed model can facilitate the physical-layer simulation for mobile ad hoc communication systems. We also derive the autocorrelation function, level crossing rate (LCR), and average fade duration (AFD) of the mobile-to-mobile Rician fading channel and verify the accuracy by simulations.     

Generating rice processes with given spectral properties

The autocorrelation function (acf) of a stochastic Rician fading process is numerically evaluated, and useful approximations are given. The spectral properties of the fading are related to the component processes constituting the fading process. The result is that for Rayleigh fading and first-order Butterworth characteristic of the component processes the fading bandwidth is double the component bandwidth. The fading bandwidth decreases to the component bandwidth, however, when the Gaussian channel is approached or when high-order faltered components are assumed.     

An iterative algorithm for Doppler spread estimation in LOS environments

An iterative algorithm is proposed to estimate the maximum Doppler frequency in a line-of-sight (LOS) environment. While the autocorrelation function of a Rayleigh fading signal depends only on the maximum Doppler frequency, that of a Rician fading signal is also related to the K factor and the angle of arrival (AOA) of the LOS component. The performance of conventional Doppler spread estimators based on the Rayleigh fading assumption degrades in LOS environments due to the autocorrelation function mismatch. The proposed estimator estimates the Rician K factor first, then iteratively estimates the Doppler spread and the AOA of the LOS component. The performance degradation due to channel parameter variations is investigated by means of matching the autocorrelation functions. The simulation results indicate that the proposed estimator is not only superior to the conventional autocorrelation-based Doppler spread estimator but also robust to the channel parameter variation in both LOS and non-LOS environments.     

一种新的Jakes模型参数计算方法

本文分析了小尺度无线衰落信道的理论参考模型—Clark模型,比较了两种较为重要的确定性仿真模型的参数计算方法—精确多普勒扩展法（MEDS）和随机精确多普勒扩展法（R_MEDS）,提出了一种新的用于仿真平坦衰落信道Jakes模型的参数计算方法,即在MEDS的基础上对离散多普勒频率引入随机抖动。仿真数据和图形表明,在模型复杂度较低的情况下,新的信道模型的自相关和互相关特性较R_MEDS有很大改善,而且与原始MEDS相比,新模型多普勒频率为随机变量,可以有效仿真瑞利衰落、多个不相关的瑞利衰落和频率选择性衰落信道等,并且可以结合工程需要设定随机抖动幅度,保证了衰落信道的不相关性和遍历性的有机统一。      

A Model for Correlated Rician Fading Channels Based on a Finite Queue

We study the problem of approximating the family of hard-decision frequency-shift keying demodulated correlated flat Rician fading channels via a recently introduced queue-based channel (QBC) model for binary communication channels with memory. For a given ldquodiscretizedrdquo fading channel, we construct a QBC whose noise process is statistically ldquocloserdquo in the Kullback-Leibler sense to the error or noise process that is generated by the fading channel, and the modeling accuracy is evaluated in terms of noise autocorrelation function (ACF) and channel capacity. Numerical results indicate that the QBC provides a good approximation of the fading channels for a wide range of channel conditions. Furthermore, it estimates the noise ACF more accurately than the finite-state Markov models that have been recently studied by Pimentel , while, at the same time, remaining mathematically tractable.     

On the generation of correlated Rayleigh fading envelopes for accurate simulation of diversity channels

The generation of correlated Rayleigh fading envelopes based on mobile radio channel characteristics for realistic simulation of diversity systems was documented in 1974 by Jakes. In this letter, a survey of recent algorithms which draw upon Jakes' work will be given, as well as an illustration of their shortcomings. Subsequently, a procedure is presented for the generation of multiple equal-power correlated Rayleigh fading envelopes, with desired cross-correlations and autocorrelation functions specified so as to model channel conditions under the general assumption of isotropic scattering. The algorithm presented will enable accurate simulation and investigation of the effect of correlated fading on diversity schemes.     

Two-Dimensional DPCM Image Transmission Over Fading Channels

A combined source-channel coding approach is described for the encoding, transmission, and remote reconstruction of image data. The transmission medium considered is that of a fading dispersive communications channel. Both the Rician fading and Rayleigh fading channel models are considered. The image source encoder employs two-dimensional (2-D) differential pulse code modulation (DPCM). This is a relatively efficient encoding scheme in the absence of channel errors. In the presence of fading, however, the performance degrades rapidly. By providing error control protection to those encoded bits which contribute most significantly to image reconstruction, it is possible to minimize this degradation without sacrificing transmission bandwidth. Several modulation techniques are employed in evaluation of system performance including noncoherent multiple frequency shift-keyed (MFSK) modulation. Analytical results are provided for assumed 2-D autoregressive image models, while simulation results are described for real-world images.     

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.     

Achievable performance over the correlated Rician channel

The correlated Rician channel is a useful model for a slowly fading channel, in which the complex fading process is composed of two quadrature Gaussian processes with a given autocorrelation function. For slow fading the correlation between adjacent symbols is relatively high. The authors investigate the achievable error probabilities over the channel, employing coherent detection and ideal side information on the realization of the fading processes at the receiver. An underlying decoding delay constraint which precludes the use of (ideal) interleaving is assumed. Coded BPSK performance is addressed both with and without the piecewise constant approximation (according to which the fading value remains constant during the symbol duration). For the latter case, that is no piecewise constant approximation, the analysis relies on the Fredholm determinant associated with the fading process autocorrelation function. The authors focus on the exponentially correlated channel. The “worst case” pairs of codewords are identified. The exponential behavior of the error probability with random coding (and i.i.d. Gaussian inputs) is analyzed, and the behavior of the cut-off rate and capacity is addressed. The results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block-fading channel model     

Error Performance of Direct Sequence Spread Spectrum Systems on Non-Selective Fading Channels

The effects of fading on the performance of a spread spectrum multiple-access communication system using direct sequence modulation are investigated. General series expansions are developed for the average probability of error and specific results are given for the irreducible error rate associated with propagation over independent Rician fading channels or correlated Rayleigh fading channels. Simple single-term approximations for the irreducible error rate, which are proportional to the second moment of the cross-correlation between the spreading codes employed by the users, are derived for these cases.     

Enhanced correlated shadowing generation in channel simulation

An enhanced method of generating a shadow fading for mobile radio channel simulation is proposed. It is verified that simulated samples satisfy the properties of variance, autocorrelation and cross-correlation. The proposed channel simulation method can be utilized for evaluating the performances in mobile communication systems where the exchange of interactive information between uplink and downlink channels is required     

On the Analysis of Envelope Correlation and Spectra for Rician Fading Channel

Physical fading radio channels encountered in wireless mobile communication are often modeled as a complex Gaussian process whose envelope is statistically described by Rayleigh or Rician probability distribution function (PDF). In most of the literature, the accuracy of the simulation model is estimated by comparing the simulated autocorrelation function (ACF) of inphase (or quadrature phase) component of the fading process and ACF of squared envelope with the analytical ones. In this paper, we examine the performance of a sum of sinusoid (SOS) based Rician fading channel simulator on the basis of the ACF and power spectral density (PSD) of the fading envelope. We obtained simplified approximate expressions for the autocorrelation and mean value of the fading envelope which become more accurate as the value of Rice factor increases. In the simulation, the line-of-sight (LOS) component is modeled as a zero-mean random variable with pre-chosen angle of arrival (AOA) and random initial phase. We showed that the AOA of the LOS component significantly affects the level crossing rate (LCR) and average fade duration (AFD) of the fading envelope. All simulation results are compared with the analytical results and a very good agreement between them is found.

Optimum Pilot Symbol Assisted Modulation

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.     

Cutoff rates of multichannel MFSK and DPSK signals in mobilesatellite communications

This paper studies the coded performance of multichannel MFSK and DPSK signalings in mobile satellite environments characterized by various kinds of multipath fading. Rician, Rician/lognormal, and a convex combination of Rician and Rician/lognormal or Rayleigh/lognormal distributions are used to model these communication channels. We investigate the minimum average signal-energy-to-noise ratio required to yield a cutoff rate that is greater than or equal to a given code rate. Also examined are system design issues such as the effect of quantization and metric conversion, the choice between binary codes and M-ary symbol codes, the optimization of the diversity order and the signal size, and the order of deinterleaving and diversity combining. Numerical examples are given to answer concerns raised by these issues     

Fading Margin Analysis for Asynchronous CDMA Systems

In this paper, a detailed theoretical analysis of fading margin in an asynchronous code division multiple access (A-CDMA) system is discussed. Rayleigh and Rician frequency-selective slowly fading channels are considered. Probability distribution and density functions of the probability of error are derived for Rayleigh and Rician fading channels. The fluctuations in the channel capacity are proved to be directly proportional to the signal-to-noise ratio (SNR) variations. Fading margin is calculated for both Rayleigh and Rician fading channels as a function of the probability of error specification and the probability of unsatisfactory operation.     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

Rician K-Factor Distribution in Broadband Fixed Wireless Access Channels under Rain Fades

The performance of broadband fixed wireless access (BFWA) systems operating at frequencies above 10 GHz is adversely influenced by rainfall, which introduces severe attenuation and a short-term variation to the received signal. In this letter, the fading channel of a BFWA link is modeled as Rician with a strong Rician K-factor. A novel analytical model relating the Rician K-factor with the rain fading effects is presented based on which, an analytical prediction model for the cumulative distribution of the Rician K-factor is derived. Experimental data is necessary to validate the proposed models. The presented methodology provides an efficient way to incorporate the mathematically intractable physical input of rain fading into the "easy-to-simulate" Rician channel model. The proposed models can be applied on a global scale and incorporate the impact of various crucial operational and geometrical parameters of a BFWA system on the wideband multipath behavior of the channel. Useful numerical results regarding the validity of the presented models are also provided     

Capacity of an FH-SSMA system in different fading environments

The capacity of a previously proposed frequency-hopped spread-spectrum multiple-access system (FHSSMA) is evaluated under three types of fading, namely, Rician, shadowed Rician, and Nakagami fading. The results of experiments have indicated that these fading phenomena occur in various environments, where the FH-SSMA system may be implemented. This paper presents the derivation of the deletion probability for each type of fading and analyzes the system capacity in terms of the maximum number of users versus the average bit-error rate (BER). The effect of a change in the signal-to-noise ratio (SNR) level on the system capacity is also demonstrated. For Rician fading, we find that the capacity of the system with a Rician factor of 2 dB is reduced by 13% as compared to the capacity for the nonfading case. For shadowed Rician fading, three shadowing scenarios are considered: light, average, and heavy. It is shown that the light and average shadowing scenarios provide only a slight decrease in the capacity, while the heavy shadowing scenario renders a capacity identical to that for the Rayleigh fading case. Finally, for Nakagami fading, the capacity is found to decrease by 50% as the fading parameter is reduced to 0.5     

Error probabilities of an FFH/BFSK self-normalizing receiver in aRician fading channel with multitone jamming

We derive the analytical bit-error rate (BER) expressions for a fast frequency-hopped binary frequency-shift keying self-normalizing receiver over a fading channel with the worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The desired signal and MTJ are assumed to undergo independent Rician fading and our analyses, validated with simulation results, show that the system performance is not sensitive to different types of MTJ fading conditions. The self-normalizing receiver is found to be superior to the linear-combining receiver when the signal amplitude does not experience severe fading, while the converse is true under Rayleigh fading signal conditions. Under a Rician fading channel and AWGN conditions, the worst-case MTJ and the worst-case partial-band noise jamming are shown to have similar effects on the BER performance of the self-normalizing receiver with diversity