Average level crossing rate and average fade duration of selectiondiversity

The average level crossing rate and average fade duration of the output signal envelope of a selection diversity combiner, operating on independent, but nonidentical fading input branch signals are derived. The exact closed-form results are valid for arbitrary diversity order, and are obtained for Rayleigh, Ricean, and Nakagami fading input signals     

Average level crossing rate and average outage duration of generalized selection combining

The paper presents an analytical methodology for the evaluation of the average level crossing rate and the average outage duration of generalized selection combining. More specifically, it presents a general approach when this scheme is employed over independent, but not necessarily identically distributed, fading channels. The general approach is then specialized to independent identically distributed Rayleigh fading paths. Selected numerical examples and plots are also provided and discussed.     

Level crossing rate and average fade duration of MRC and EGC diversity in Ricean fading

The average level crossing rate and average fade duration of the output signal of a maximal ratio combiner (MRC) and equal gain combiner (EGC), operating on independent Ricean fading input branch signals, are derived. Exact, closed-form results are obtained for MRC diversity, while precise expressions for EGC diversity are presented with an infinite series method. The results are valid for an arbitrary number of independent, identically distributed diversity branches, isotropic scattering, and a specular component perpendicular to the line of motion of the mobile.     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

Level crossing rate and average fade duration of the select-and-hold policy of selection diversity combining in a Rayleigh fading channel

The select-and-hold policy (SAH) is a general form of selection diversity combining (SDC). In this letter, we provide closed-form expressions for average level crossing rate and average fade duration for Nth-order SAH-SDC. The diversity branches are assumed to be independent and identical Rayleigh fading channels. A useful guideline for choice of the holding time is also obtained.     

Level crossing rate and average fade duration for pure selection and threshold selection diversity‐combining systems

Exact and closed‐form expressions for the level crossing rate and average fade duration are presented for the M‐branch Pure Selection Combining and for the two‐branch Threshold Selection Combining schemes, assuming independent branches in a Rayleigh environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The plots presented here are also compared with those of the general solution recently published for the Equal Gain and Maximal Ratio Combining and an agreeable coherence is found. Copyright © 2001 John Wiley & Sons, Ltd.     

Exact crossing rates of dual diversity over unbalanced correlated Rayleigh channels

General exact expressions for the level crossing rate of dual-branch selection, equal-gain, and maximal-ratio combiners operating over unbalanced correlated Rayleigh channels are derived. Sample numerical results are presented by specializing the general expressions to a space-diversity system with horizontally spaced omnidirectional antennas at the mobile station. It is observed that, whereas power imbalance is invariably prejudicial, fading correlation may be advantageous with closely spaced antennas arranged parallel to the direction of motion.     

Level-crossing rate and average duration of fades of deterministicsimulation models for Rice fading channels

The concept of Rice's sum of sinusoids is often applied to the design of deterministic simulation models for Rice fading channels. This paper investigates in detail the level-crossing rate (LCR), average duration of fades (ADF), and cumulative distribution function (CDF) of such classes of simulation models. Exact and simple approximative formulas are deduced for these statistical quantities. Several numerical results for the derived expressions are presented by using different procedures for the design of the parameters of the deterministic simulation model. Moreover, comparisons with the corresponding simulation results-obtained by evaluating the deterministic simulation models output data-are also given     

Analysis of 11 GHz slant path fade duration and fade slope

The letter presents results of an analysis of fade slope and fade duration data collected at 11 GHz within the framework of the OTS propagation experiments in Europe. Evidence is given of the fact that on a statistical basis, fade slope and fade duration are related. This could possibly be used in uplink power control systems.     

一种联合链路持续时间与平均速率的中继选择方法

针对中继系统中节点快速移动时采用传统中继选择方法造成系统可传输数据量较低的问题,提出一种联合链路持续时间与平均速率的中继选择方法.该方法首先分析了系统采用两跳传输及协作传输两种模式下的链路持续时间,分别给出了节点速度及相互之间距离满足不同条件时的链路持续时间表达式,然后计算两种模式下的链路平均可达速率,最后基于所提出的准则完成中继选择.仿真结果表明,与传统的中继选择方法相比,该方法可以使系统获得更多的数据传输,同时具有较低的中断概率.     

On the average outage rate and average outage duration of wireless communication systems with multiple cochannel interferers

This paper studies the average outage rate [or average level crossing rate (LCR)] and average outage duration (AOD) of wireless communication systems subject to cochannel interference. In particular, it presents closed-form expressions for the LCR and AOD when a minimum desired signal power requirement is specified for satisfactory reception. The results are quite general and account for systems operating over independent identically distributed Rician and/or Nakagami fading environments. When applicable, these new expressions are compared to those previously reported in the literature dealing with the LCR and AOD of 1) interference-limited systems when both the desired and interfering signals are subject to Rayleigh type of fading and 2) power-limited systems operating over Rician or Nakagami fading channels. Corresponding numerical examples that illustrate applications of the results are also provided and discussed. These results show that specifying a certain minimum desired signal power requirement induces a floor on the AOD. They also show that the AOD is essentially affected by the the maximum Doppler frequencies (or equivalently the speed) of the desired users.     

Noncoherent MT-MFSK signals with diversity reception in arbitrarily correlated and unbalanced Nakagami-m fading channels

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

On the average rate performance of hybrid-ARQ in quasi-static fading channels

The problem of efficient communication over a scalar quasi-static fading channel is considered. The single-layer transmission (SLT) and multi-layer transmission (MLT) schemes do not require any knowledge of the channel state information (CSI) at the transmitter, but their performance is also limited. It is shown that using Hybrid-ARQ (HARQ) can significantly improve the average rate performance, provided that the rate assignment between different ARQ rounds is carefully chosen. The average rate performance of several HARQ schemes is optimized and compared. In addition, optimal power allocation among retransmissions is derived and shown to further increase the average rate. This power allocation gain is remarkable at low signal-to-noise ratio (SNR), but becomes negligible at high SNR. Comparison of two different types of limited feedback, sequential feedback (ARQ) and one-shot feedback (quantized CSI), is made from several perspectives. Although the optimization problem is formed with respect to the average rate, simulation results give a comprehensive comparison under different metrics, including average rate, outage probability, and the combination of both. Substantial performance improvement is observed with even one ARQ retransmission in all simulations. More importantly, this gain appears to be robust with respect to the fading distributions.     

On the rain attenuation dynamics: spatial‐temporal analysis of rainfall rate and fade duration statistics

Knowledge about the dynamic characteristics of rain attenuation is of utmost importance for many applications in terrestrial and satellite communication systems operating at frequencies above 10 GHz. Long‐term rain rate statistics and rain rate duration statistics are usually available from meteorological data. In this paper, a spatial–temporal analysis is employed in order to evaluate the rain attenuation power spectrum of a terrestrial/satellite path. The predicted power spectrum is compared with experimental data. Based on the spectral analysis of rainfall rate a method for converting rain rate duration statistics to link fade duration statistics is also proposed. Fade duration statistics are presented for terrestrial and satellite links and compared with available experimental data. The agreement between the predicted results and the experimental data has been found to be quite encouraging. Finally, numerical results are presented for various climatic zones, elevation angles and frequencies. Some very useful conclusions concerning the dynamic properties of rain attenuation for a microwave path are deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Approximate equation of average bit-error rate in DS-CDMA systems over fading channels

The transmission quality in mobile wireless communications is affected not only by additive white Gaussian noise, but also by multipath fading, which drastically changes the amplitudes and phases of wireless signals. It is one of the key themes in direct-sequence code-division multiple-access systems to evaluate average bit error rate (BER) performances as parameters of the Doppler frequency, the delay profile, the number of simultaneous access users, and so on. This paper proposes the approximate equation for easily calculating the average BER over fading channels (multiray fading models). The performance evaluations are carried out in the two-ray model, the IMT2000 model, and the COST207 model. It is confirmed from the coincidence of approximate results with computer simulation results that the proposed approach is applicable to a variety of parameters.     

Performance evaluation of L-maximal ratio combining diversity with estimation error for Shadowed Beaulieu-Xie fading channels

To provide the increasing demand for wireless technologies, high capacity with lower latency is vital. New emerging technologies like 5G, millimeter wave, THz, and so forth are able to characterize such complex fading and shadowed environments. Spatial diversity is one of the techniques to minimize fading in the wireless communication channel. The performance of the wireless communication system can be further optimized by using estimators at the receivers. The influence of imperfect channel estimation on the performance over shadowed Beaulieu-Xie (SBX) fading channels with L-maximal ratio combining (MRC) diversity is studied. The probability density function (PDF) of the received output signal-to-noise ratio (SNR) with L-MRC over SBX fading channels is derived. Further PDF of the received output SNR, outage probability, and average bit error rate (ABER) using the derived PDF is evaluated for L-MRC diversity with channel estimation error over SBX fading channels. ABER expression for Gray-coded rectangular quadrature amplitude modulation over the SBX channel is also evaluated. The study also includes how the system performs under the effect of different shadowing and fading parameters.     

空间分集相关信道中信号误比特率研究

系统的分集情况对系统的影响是很大的。这里我们研究了空间分集对系统性能的影响。本文推导了在空间分集的情况下非相干检测 FSK信号的误比特率 ,并利用了多径信道的衰落相关性模型 ,通过计算机模拟的方法具体研究了空间分集中天线的距离和散射体分布对的非相干检测 FSK信号误比特率的影响。