Nakagami衰落上DE-QPSK在联合收发分集下的性能分析

利用高斯Q函数的高阶次幂在最大比合并（MRC）分集接收瑞利衰落信道上统计平均的结果,推导了Nakagami 衰落信道上采用组合发射选择合并（SC）/接收 MRC 天线分集的相干检测差分编码四相相移键控（DE-QPSK）的平均误符号率（ASER）精确表达式。利用高斯Q函数的近似表达式和矩生成函数（MGF）方法,推导了Nakagami衰落信道上采用组合SC/MRC天线分集的相干检测DE-QPSK 的ASER近似表达式。通过数值计算和仿真,验证了DE-QPSK的ASER精确表达式的正确性以及近似表达式的准确性。利用精确表达式和近似表达式可研究收发天线数目和衰落参数对DE-QPSK的ASER性能的影响,为实际SC/MRC天线分集方案的设计提供了理论指导。     

Ordered Statistic Analysis for Diversity Combining Schemes over Nakagami-m Fading Channel

Order diversity combining technique is one of efficient methods to lower the complexity but not to significantly degrade performance. Recently, Eng and Milstein [1] proposed a novel order-combining technique, called the second order diversity combining (SC2) and third order diversity combining (SC3) and applied to Rayleigh fading channel. SC2 and SC3 schemes mean that the two (three) signals with the first two (three) largest amplitudes among the branches are chosen and coherently combined. However, when compared to Rayleigh distribution, the Nakagami-m distribution [10] provides a more general and versatile way to model wireless channel. For the reason, the bit error rate (BER) performance of proposed schemes were then analyzed with order statistic method and compared to the traditional diversity technique over Nakagami fading environment in this paper. The results are compared to maximal ratio combining (MRC), and conventional selection combining (SC) in coherent reception and to equal gain combining (EGC) in noncoherent reception. The results show that SC is in performance the worst for either in coherent or in noncoherent schemes, as expected. The performance differences between SC2 (SC3) and MRC (EGC) are not significant when the diversity order L 3, but the difference will increase when L 5. It is worth noting that the result of [1] is a special case with fading figure, m = 1. It is also observed the performance is much affected by the number of diversity branches L, the fading figure m, and the signal-to-noise ratio (SNR).     

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.     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

Performance Analysis of Ranging Process in Diversity Incorporated Wireless Systems Suffering from Narrowband Jamming

Ranging is a process where the base station (BS) identifies a mobile station (MS) among many other MSs with the help of Ranging code set, which is unique to each MS. Also, an estimation process is made to find the transition time delay which is the difference between the time at which the MS sends some data and the time at which the BS receives data. In this paper, the effect caused by jamming on the Ranging process will be analyzed. Jamming destroys orthogonality/pseudo orthogonality of the Ranging code set which affects the estimation of the codes. This in turn affects parameters like detection miss rate. This paper also discusses the improvement in the Ranging process where diversity techniques like maximal ratio combining (MRC), selection combining (SC), and equal gain combining are used. These diversity techniques are used in various fading channel models like Rayleigh, Rician, and Nakagami. The analyses indicate that for a Rayleigh fading channel, the code word error rate (CER) decreases by two orders of magnitude for a SC case as compared to the no diversity case, and that CER reduces by three orders of magnitude for an Equal Gain/MRC case as compared to the no diversity case. Similar results are observed for Rician and Nakagami fading channels also.     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

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     

A Unified Capacity Analysis for Wireless Systems With Joint Multiuser Scheduling and Antenna Diversity in Nakagami Fading Channels

A Unified Capacity Analysis for Wireless Systems With Joint Multiuser Scheduling and Antenna Diversity in Nakagami Fading Channels In this paper, we present a cross-layer analytical framework to jointly investigate antenna diversity and multiuser scheduling under the generalized Nakagami fading channels. We derive a unified capacity formula for the multiuser scheduling system with different multiple-input multiple-output antenna schemes, including: 1) selective transmission/selective combining (ST/SC); (2) maximum ratio transmission/maximum ratio combining (MRT/MRC); 3) ST/MRC; and 4) space–time block codes (STBC). Our analytical results lead to the following four observations regarding the interplay of multiuser scheduling and antenna diversity. First, the higher the Nakagami fading parameter, the lower the multiuser diversity gain for all the considered antenna schemes. Second, from the standpoint of multiuser scheduling, the multiple antennas with the ST/SC method can be viewed as virtual users to amplify multiuser diversity order. Third, the boosted array gain of the MRT/MRC scheme can compensate the detrimental impact of the reduced amount of fading gain on multiuser scheduling, thereby resulting in greater capacity than the ST/SC method. Last, employing the STBC scheme together with multiuser diversity may cause capacity loss due to the reduced amount of fading gain, but without the supplement of array gain.     

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     

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of noise imbalance on dual-MRC over Rayleigh fading channels

The performance analysis of dual (two-branch) maximal ratio combining (MRC) under imperfect weight, named imperfect MRC, due to the noise imbalance is derived over independent but non-identical Rayleigh fading channels. Considering the system (or channel) conditions that the noise level of each branch is different, we present the accurate performance analysis of imperfect dual MRC in terms of average combined signal-to-noise ratio (SNR), outage probability and average symbol error rate for a large class of modulations in closed-form and compare them with the performance of the perfect MRC and the perfect selection combining (SC) over non-identical but independent Rayleigh fading channels based on the interesting statistical results on the combined SNR. From the performance results we provide the criterion in choosing the imperfect MRC, perfect MRC, or SC depending on the degree of the difference of the noise level between branches.     

BER of Differentially Detected π/4-DQPSK with Selection Combining in Nakagami-m Fading

Nakagami’s m distribution is a versatile statistical model to characterize small-scale multipath fading in wireless channels. On the other hand, selection combining (SC) is a widely practiced diversity technique to mitigate the detrimental effects of multipath fading. Thus, when SC is applied over Nakagami fading channel, the error performance improvement for any given modulation format is of considerable interest. Since the last decade, π/4-shifted differential quadrature phase shift keying (π/4-DQPSK) modulation has attracted much attention as it is used for high-capacity code division multiple access (CDMA) based digital cellular systems. One of the major reasons behind this is the provision for differential detection which allows production of low complexity mobile units. In this paper, we present analytical expressions for bit error rate (BER) of π/4-DQPSK modulation with L-branch SC diversity in Nakagami-m fading channels perturbed by additive white Gaussian noise (AWGN). The derived end expressions are in closed form and contain finite series of Gaussian hypergeometric function. This makes evaluation of error rates much more straightforward compared to earlier approaches that required single or even double numerical integration. Some special instances such as the nondiversity case and Rayleigh fading case are also investigated and plotted along with the main findings. For different fading parameter (m) values and for different diversity orders (L), simulated results are shown to be in excellent agreement with the derived analytical results. All the results are, however, limited to integer values of fading severity parameter m.     

Sum of Squared Shadowed-Rice Random Variables and its Application to Communication Systems Performance Prediction

The distribution of the sum of non-negative random variables plays an essential role in the performance analysis of diversity schemes for wireless communications over fading channels. While for common fading models such as the Rayleigh, Rice, and Nakagami, the performance of diversity systems is well understood, a minor attention has been devoted to the shadowed-Rice (SR) case, namely a Rice fading channel with fluctuating (e.g. random) Line of Sight (LOS) component. Indeed, the analytical performance evaluation of diversity systems on SR fading channels requires the availability of handy expressions for the distribution of the combined received power. To this end, the rationale of this paper is twofold: first, to evaluate the distribution of the sum of SR random variables, both for the case of independent as well as correlated LOS components, and then to carry out an extensive performance analysis of maximal ratio combining (MRC) detection scheme on SR fading channels.     

Performance of coherent receivers with hybrid SC/MRC overNakagami-m fading channels

A performance analysis of two hybrid selective combining/maximal ratio combining (SC/MRC) diversity receivers over Nakagami-m (1960) fading channels with a flat multipath intensity profile is presented and numerically compared with that of the conventional SC and MRC schemes. Numerical results for particular cases of interest show that the bit error rate (BER) degradation arising from the use of hybrid SC/MRC instead of MRC is independent of the average signal-to-noise ratio (SNR) regardless of the severity of the fading and that MRC provides a higher rate of improvement than the hybrid SC/MRC as the severity of fading decreases     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Capacity of MRC on Correlated Rician Fading Channels

A new exact explicit expression is derived for the ergodic capacity of maximal ratio combining (MRC) schemes over arbitrarily correlated Rician fading channels. This is used to study the effects of channel correlation on the ergodic capacity. Numerical results reveal that both the phase and the magnitude of correlation have an impact on the ergodic capacity of Rician fading channels. This is in contrast to correlated Rayleigh fading, where the phase of the correlation has no effect on the ergodic capacity. It is also observed that negatively correlated branches in Rician fading may lead to an increase in ergodic capacity beyond that obtained by uncorrelated branches.     

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.     

Analysis of hybrid selection/maximal-ratio diversity combiners withGaussian errors

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on both the output statistics of a hybrid selection/maximal-ratio (SC/MRC) receiver and the degradation of the average symbol-error rate (ASER) performance as compared with the ideal case. New expressions are derived for the probability density function, cumulative distribution function and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR). The MGF is then used to derive exact, closed-form, ASER expressions for binary and M-ary modulations in conjunction a nonideal hybrid SC/MRC receiver in a Rayleigh fading environment. Results for both selection combining (SC) and maximal-ratio combining (MRC) are obtained as limiting cases. Additionally, the effect of the weighting errors on both the outage rate of error probability and the average combined SNR is investigated. These analytical results provide insights into the tradeoff between diversity gain and combination losses, in concert with increasing orders of diversity branches in an energy-sharing communication system     

Error probability performance of L-branch diversity reception ofMQAM in Rayleigh fading

New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed     

A general analytical approach to multi-branch selection combining over various spatially correlated fading channels

Driven by the potential application to wireless communications, intensive research efforts have been made on the study of various selective combining (SC) schemes in the past decade. Nevertheless, regardless of its practical importance, performance analysis of multi-branch SC over spatially correlated fading channels is not available in literature except for the simplest case of dual diversity. The major difficulty lies in the fact that SC has its root in the theory of order statistics, and yet systematic methodology has been developed mainly for order statistics obtained from an independent population. In this paper, we formulate the problem in a very general framework, whereby a general solution is derived. The application of the new solution to SC with different modulation schemes and operational environments is elaborated. The fading environments to be addressed include correlated Nakagami, Rayleigh, and Rician channels. Numerical examples are also presented to illustrate the use of the theory.