Diversity improvement of voice signal transmission using postdetection selection combining in land mobile radio

This paper describes the effect of postdetection selection combining diversity on voice signal transmission for wide-band PM and narrow-band PM in a Rayleigh fading environment. First, the baseband average SNR versus the average CNR for a two-branch selection diversity with the syllabic compandor is derived in a closed form including the effect of the envelope correlation coefficient. Then, the dual selection diversity receiver, which shares an envelope detector with two branches in time division, and its performance are described. Finally, laboratory tests using a Rayleigh fading simulator are carried out with the result that an effective diversity improvement is obtained for a cross correlation coefficient in the range from 0 to 0.5.     

Diversity Improvement of Voice Signal Transmission Using Postdetection Selection Combining in Land Mobile Radio

This paper describes the effect of postdetection selection combining diversity on voice signal transmission for wide-band PM and narrow-band PM in a Rayleigh fading environment. First, the baseband average SNR versus the average CNR for a twobranch selection diversity with the syllabic Compandor is derived in a closed form including the effect of the envelope Correlation coefficient. Then, the dual selection diversity receiver, which shares an envelope detector with two branches in time division, and its performance are described. Finally, laboratory tests using a Rayleigh fading simulator are carried out with the result that an effective diversity improvement is obtained for a cross correlation coefficient in the range from 0 to 0.5.     

Bit-error-probability for noncoherent orthogonal signals in fadingwith optimum combining for correlated branch diversity

Due to the interest in wireless personal communications, there has been a lot of research on the performance of receivers with diversity. Most analyses assume the diversity branches are independent. This paper presents an analysis of the bit-error probability for receivers in which the diversity branches are correlated. Noncoherent orthogonal digital modulation (NCODM) with Rician and Rayleigh slow, nonselective fading models are assumed. Through the use of the diagonalization of quadratic forms, most of the calculations of the bit-error probability can be reduced to a two-dimensional numerical integration. For some cases for dual diversity, a closed-form expression for the error probability is given. A number of diversity combining laws, including square law and maximum likelihood, are considered. We find that Rician fading can be worse than Rayleigh fading in correlated diversity environments, a situation quite different from the independent diversity case. Also, for the Rayleigh fading model with correlated branch diversity, we find that an equal-weight, square-law combiner usually has the same error performance as the more complex maximum-likelihood combiner. However, this is not the case for a Rician fading model with the same correlation environment. Simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals     

Modeling of signal envelope correlation of line-of-sight fadingwith applications to frequency correlation analysis

Based on the theoretical method developed by Clarke (1968) for the analysis of correlation characteristics in Rayleigh fading conditions, we develop a general model for envelope correlation statistics of line-of-sight fading known as Nakagami-Rice fading. The model developed here has a considerable degree of universality and can be applied to the analysis of correlation statistics in frequency and spatial domains for microcellular mobile radio, maritime and aeronautical mobile-satellite communications. Using this model, we examine the frequency correlation statistics of two typical Nakagami-Rice fading environments     

An Improved Simulator for the Correlation-Based MIMO Channel in Multiple Cluster Scattering Environments

An improved MIMO radio channel simulator is proposed, based on the most popular correlation-based MIMO channel model called Kronecker model and the sum-of-sinusoids (SoS) method which is widely used to generate Rayleigh fading waveforms with temporal correlation. Firstly, a simplified simulation model for generating multiple independent Rayleigh fading waveforms is presented, which employs only one random variable to set all Doppler frequency components in all waveforms. Next, a fast spatial correlation calculation technique, in a closed-form expression implemented by the Fourier Transform both for outdoor and indoor multiple cluster scattering environments, is introduced, which accurately reproduces the desired spatial correlation properties and indicates a direct dependence between spatial correlation and channel physical parameters. The ergodic and outage capacity of the simulated channel are also evaluated with respect to different azimuth of arrival and azimuth of departure (AoA/AoD) under the condition of 3GPP SCM (3rd Generation Partnership Project Spatial channel model) [23]. The presented simulator is therefore suitable for the theoretical analysis of MIMO radio systems, including dynamic system simulation.     

Virtual branch analysis of symbol error probability for hybridselection/maximal-ratio combining in Rayleigh fading

We derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) “virtual branches,” which results in a simple derivation of the SEP for arbitrary L and N. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEPs of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with L≪N, can achieve a performance close to that of N-branch MRC     

Effect of correlation in diversity systems with Rayleigh fading,shadowing, and power capture

With the growth of wireless personal communications networks and wireless local area networks (WLAN's), the need for increased reliability of the radio link has become evident. The use of diversity techniques, such as dual receiving antennas, helps mitigate the effect of multipath fading in both the in-building and land mobile radio environments. A significant issue in the design of such systems is the degree to which correlation between the two or more diversity signals can be tolerated. In this paper, we consider the use of diversity techniques in radio systems that are subject to correlation. Rayleigh fading, lognormal shadowing, and the radio capture effect. In the presence of two simultaneously transmitting stations, the throughput, conditioned on the local-mean power, is determined exactly for the case of a dual diversity receiving station. The insight gained from the two-station analysis is used to develop an accurate approximation for cases with more than two stations. The degree to which correlation can be tolerated without significant performance loss relative to the case of independent diversity signals is quantified, as are the effects of different system parameters (i.e., the capture ratio, power roll-off coefficient, and the amount of shadowing). Furthermore, the relationship between the envelope and power correlation coefficients is presented. An application of the capture results to the slotted ALOHA protocol is also included     

Average level crossing rate and average fade duration of low-ordermaximal ratio diversity with unbalanced channels

The average level crossing rate and average fade duration of a maximal ratio diversity combiner, operating on independent, unequal power Rayleigh fading branches in isotropic scattering, are derived in closed-form for dual-branch diversity, and as definite integrals for threefold and fourfold diversity     

Performance of dual-diversity predetection EGC in correlated Rayleigh fading with unequal branch SNRs

The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series. In particular, we consider a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios. The BEP expression is in terms of the power correlation coefficient of the branches, is easy to compute, and depicts clearly the effect of correlated fading on the error performance.     

Unified error probability analysis for generalized selectioncombining in Nakagami fading channels

We study generalized selection combining (GSC) schemes in independent Nakagami fading channels, where N diversity branches with the largest instantaneous signal-to-noise ratios (SNRs) are selected from the total of L (N⩽L) branches and then coherently or noncoherently combined. We propose two different techniques to derive the moment generating function (MGF) expressions for the GSC output SNR in generalized Nakagami fading channels, where there are distinct and noninteger fading severity parameters, as well as different average SNRs in different diversity branches. For arbitrary fading severity parameter m_k, k=1, ···L, the MGF expression is given in a summation of N-dimensional definite integrals with the limits independent of SNR or channel parameters, and therefore can be evaluated very efficiently with numerical methods. Furthermore, for integer m_k closed-form MGF expressions are derived. Specializations of our results to Rayleigh channels and independent identically distributed (i.i.d.) Nakagami channels are presented, which are either new or equivalent to previously published results. Using the newly derived MGF expression, we provide a unified error probability analysis for many coherent and noncoherent modulation/detection schemes     

Level Crossing Rate and Average Fade Duration of Dual Selection Combining With Cochannel Interference and Nakagami Fading

This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analytical results reduce to known solutions in the cases of an interference-limited system in Rayleigh fading and an AWGN-limited system in Nakagami fading. The average LCR is determined by an original approach that does not require explicit knowledge of the joint PDF of the envelope and its time derivative, which also paves the way for similar analysis of other diversity systems.     

Performance of First-Order Digital Phase-Locked Loops in Mobile Radio Channels

The performance of a first-order digital phase-locked loop (DPLL) using nonuniform sampling is studied in the mobile radio environments. The mobile radio channel is characterized by introducing fast Rayleigh fading and random phase variation to the signal envelope and phase, respectively. The nonlinear stochastic difference equation describing the loop operation in fading environments is introduced. The joint probability density function (pdf) of the random variables of this equation is derived by transformation of random variables for fast Rayleigh fading channels. A closed-form expression for the transition probability of the ChapmanKolmogorov (C-K) equation is obtained for phase step plus noise input and for frequency step plus noise input. The probability density function of the steady-state phase error is obtained by solving the C-K equation numerically.     

Closed-Form Analysis of Equal-Gain Diversity in Wireless Radio Networks

This paper deals with the performance of predetection equal-gain combining (EGC) receivers operating over multipath fading plus cochannel interference (CCI) and additive white Gaussian noise channels. The desired components of the received signals are considered to experience independent but not-necessarily identically distributed Nakagami-m fading, while the interferers are subject to independent Rayleigh fading. The analysis is not only limited to equal average fading power interferers, but the case of interferers with distinct average powers is also examined. By following the coherent interference power calculation, novel closed-form expressions for the moments of the EGC output signal-to-interference-plus-noise ratio (SINR) are derived, which are being used to study the performance of the average output SINR. Furthermore, by assuming an interference-limited fading scenario, novel closed-form union performance bounds are derived. More specifically, tight upper bounds for the outage and average symbol error probability for several constant envelope modulation schemes, and lower bounds for the Shannon average spectral efficiency, are provided. Numerical results demonstrate the effect of the number of interferers, the number of the receiver branches, and the severity of fading on the EGC receiver performance. Computer simulations have been also performed to verify the tightness of the proposed bounds and the correctness of the mathematical analysis. It is shown that the performance of cellular radio systems in the uplink is degraded mainly from the first-tier CCI of the adjacent cells     

Cooperative Fading Regions for Decode and Forward Relaying

Cooperative transmission protocols over fading channels are based on a number of relaying nodes to form virtual multi-antenna transmissions. Diversity provided by these techniques has been widely analyzed for the Rayleigh fading case. However, short range or fixed wireless communications often experience propagation environments where the fading envelope distribution is meaningfully different from Rayleigh. The main focus in this paper is to investigate the impact of fading distribution on performances of collaborative communication. Cooperative protocols are compared to co-located multi-antenna systems by introducing the concept of cooperative fading region. This is the collection of fading distributions for which relayed transmission can be regarded as a competitive option (in terms of performances) compared to multi-antenna direct (noncooperative) transmission. The analysis is dealt with by adopting the information theoretic outage probability as the performance metric. Cooperative link performances at high SNR are conveniently expressed here in terms of diversity and coding gain as outage parameters that are provided by the fading statistics of the channels involved in collaborative transmission. Advantages of cooperative transmission compared to multi-antenna are related to the propagation environment so that the analysis can be used in network design.      

MIMO Diversity in the Presence of Double Scattering

The potential benefits of multiple-antenna systems may be limited by two types of channel degradations-rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multiple-input multiple-output (MIMO) systems, with an emphasis on orthogonal space-time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signal-to-noise ratio (SNR). In particular, we consider a general family of MIMO channels known as double-scattering channels-i.e., Rayleigh product MIMO channels-which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rank-deficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order in a double-scattering channel with effective scatterers. We also quantify the combined effect of the spatial correlation and the lack of scattering richness on the EFF and the low-SNR capacity in terms of the correlation figures of transmit, receive, and scatterer correlation matrices. We further show the monotonicity properties of these performance measures with respect to the strength of spatial correlation, characterized by the eigenvalue majorization relations of the correlation matrices.     

降雨环境中多径信道的包络概率密度函数

 利用随机介质中波传播理论研究了随机雨介质中信号的起伏特性,研究了降雨散射环境对多径信道中接收信号包络概率密度函数的影响,导出了降雨环境下单波和双波模型的计算公式,讨论了评估降雨环境中的莱斯衰落分布和瑞利衰落分布多径信道概率密度函数的研究方法.文中的研究方法对于雪、沙尘等环境中多径信道的信号包络概率密度函数也适用.     

Branch correlation measurements and analysis in an indoor Rayleigh fading channel for polarization diversity using a dual polarized patch antenna

Spatial diversity techniques are advantageous if the received signals of the diversity branches are sufficiently uncorrelated. Theoretical study using the power unbalance between the two branches employing Laplacian direction of arrival (DOA) distribution is carried out. It is shown that for low value of cross-polarization power ratio (XPR) the correlation has a negligible effect. In order to validate the theoretical results indoor NLOS measurements were carried out. The measurements were done to study the cross-correlation between two received signals of orthogonal polarization using a dual linear polarized patch antenna. The antenna has been designed, built and measured. The results of the channel measurements are given. It is concluded that received signals with orthogonal polarization in indoor Rayleigh fading channels have no significant envelope correlation.     

Capacity analysis of MIMO MRC systems in correlated rayleigh fading environments

In this paper, we analyze the capacity of multiple-input multiple-output systems employing maximal ratio combining under Rayleigh fading environments in the presence of spatial fading correlation at the transmitter or receiver. Based on statistical properties of the largest eigenvalue of correlated complex Wishart matrices, the exact closed-form expressions for the cumulative distribution function and the probability density function of the output signal-to-noise ratio are presented. The results are used to analyze the outage and ergodic capacities of the systems. The analysis shows that ergodic capacity improves with the increase of the channel correlation coefficient and the analytical results are validated by Monte Carlo simulations.     

Formulation of spatial correlation statistics in Nakagami-Ricefading environments

Propagation environments in line-of-sight (LOS) communications, such as mobile-satellite communications and indoor radio communications, can be expressed by a Nakagami-Rice (or Rician) fading model. Since the Nakagami-Rice fading model also covers the Rayleigh fading model as an extreme case, it seems a very widely applicable model. This paper gives a theoretical formulation of spatial correlation characteristics in the Nakagami-Rice fading environment. Based on this theoretical model, spatial correlation characteristics of Nakagami-Rice fading are clarified comparing with those of Rayleigh fading. Moreover, the difference in spatial correlation characteristics between wide-band signals and narrow-band signals is discussed