Analysis of equal gain diversity on Nakagami fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L -branch equal-gain (EG) diversity combiners in Nakagami (1960) fading channels is derived. The bit error rate for a matched filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase shift keying (CPSK) and differential coherent phase shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. Bit error rates for EG combining on Rayleigh fading channels are obtained for L>2. These results are presented as a special case of the more generalized Nakagami fading model     

Microdiversity on Rician fading channels

The performance of an L-branch equal gain (EG) combiner on slow and nonselective Rician fading channels is analyzed. Two performance criteria are considered; the probability distribution of signal-to-noise power ratio (SNR) at the output of the EG combiner and the average bit error rate (BER). Matched filter receivers are considered for two binary modulation formats, coherent phase shift keying (CPSK) and noncoherent frequency shift keying (NCFSK). Results using both maximal ratio combining (MRC) and selection diversity combining (SC) are presented for comparison. Our results show that from a feasibility and practical tradeoffs point of view, the performance of an EG combiner may be as good as that of a MR combiner. The effects of gain unbalance between branches of the EG combiner on the probability distribution of SNR and on the bit error rates are also investigated. The Rician fading model may be used to model bath the microcellular environment and the mobile satellite fading channel. Hence, the results of this paper may be useful in both of these areas. Furthermore, in the development of the analysis, we present an efficient method for computing the distribution of sums of Rician random variables. This may be useful for other problems involving Rician fading. The suitability of modeling a Rician fading environment by a properly chosen Nakagami model is examined. A formula for determining the corresponding values of Rician parameter K and Nakagami parameter m is also assessed     

Closed‐form analysis of multibranch switched diversity with noncoherent and differentially coherent detection

Exact closed‐form analytical expressions are derived for the average bit error probability of multibranch switched diversity systems over independent and identically Nakagami‐m distributed fading channels. Practical schemes that use noncoherent or differentially coherent symbol detection are considered. The general bit error probability expression derived in this paper includes as particular cases the following signaling formats: orthogonal binary signaling, correlated binary signaling, differential phase‐shift keying, and differential quadrature phase‐shift keying. Finally, we apply our analytical results to study the impact of the switching threshold selection on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance analysis of dual switched diversity over correlated Weibull fading channels with co‐channel interference

This paper studies the performance of switch and stay combining (SSC) diversity in the presence of co‐channel interference over correlated Weibull fading channels. SSC diversity based on signal‐to‐interference ratio (SIR) is a low‐complexity and a very efficient technique that reduces fading and co‐channel interference influence. New closed‐form expressions for the probability density function and cumulative distribution function of the output SIR's are derived. These formulas are used in a detailed analysis of the average output SIR and outage probability. The influence of fading severity and correlation coefficient on the optimum switching threshold and system performance is investigated. Monte Carlo simulations are performed to verify obtained theoretical results and determine average bit error rate in detecting binary phase‐shift keying (BPSK), differential BPSK and quadrature amplitude modulation signals. Copyright © 2011 John Wiley & Sons, Ltd.     

Digital transmission through a land mobile satellite channel

An analytical derivation of the probability of bit error noncoherent frequency-shift keying (FSK) and coherent phase-shift keying (PSK) signals transmitted through a land-mobile satellite channel is described. The channel characteristics used in the analysis are based on a recently developed model which includes the combined effects of fading and shadowing. Analytical expressions for the probability of bit error of FSK and coherent phase-shift keying (CPSK) signals are obtained. The results show that large amounts of signal-to-noise ratio (SNR) are required to compensate for the combined effect of fading and shadowing. An analytical expression for the irreducible probability of bit error of a CPSK signal due to phase variations caused by fading and shadowing is derived. The results described should be useful in the design of land mobile satellite communication systems     

Spread-spectrum path diversity in a shadowed Rician fadingland-mobile satellite channel

The effects of two types of path diversity techniques, namely selection diversity and maximal ratio combining, on the bit error probability are investigated for direct-sequence spread-spectrum (DS/SS) transmission in a land mobile satellite channel using coherent binary phase-shift keying (BPSK) modulation. It is assumed that the channel consists of a log-normally shadowed line-of-sight signal plus Rayleigh distributed multipath signals. The bit error probability is evaluated for light, average, and heavy shadowing. The performance is also measured in terms of the outage probability     

Dual-Space Diversity over Land Mobile Satellite Channels Operating in the L and K Frequency Bands

Land mobile satellite communication systems at Ka/K band (30/20 GHz) are attracting more and more attention to researchers because of its frequency band availability and the possibility of using small earth stations and satellite antennas for the systems. However, the Ka/K-band communications also give significant challenges in the system design due to severe channel impairments expected from the satellite links. In this paper, K-band channel characteristics are studied and compared with those at L band. The channel is modeled as Rayleigh multipath fading with the line-of-sight (LOS) component following a lognormal distribution. The first and second-order statistics of the fading channel are studied. Dual-space diversity reception is investigated to combat the flat channel fading. The bit error rate performance of coherent binary phase shift keying (BPSK) with ideal bit and carrier phase synchronization over the fading channel at K band is evaluated theoretically and verified by computer simulations in the case with and without diversity reception.     

基于分集接收技术的相干大气激光通信系统性能分析

分析了独立的双伽马衰落信道下采用分集接收技术的相干光通信系统的平均输出信噪比(SNR)、通信中断概率和平均误比特率。首先,利用多项式定理推导平均输出SNR的精确表达式;其次利用正随机变量的平均值不等式推导出SNR下界的概率密度函数(PDF),并进而得出通信中断概率和外差同步二进制相移键控(BPSK)平均误比特率的联合上界。回避了直接求取SNR的PDF,降低了性能分析的复杂度。结果表明,分集接收有效地克服了大气湍流对系统性能的影响,且分集路数越多,性能改善越明显,但强弱湍流区的性能差异也越大;所得到的性能上界与已有的Monte-Carlo模拟结果十分接近。     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

Error rate and outage of dual‐hop DF relay system with selection combining over Rice fading

Performance of dual‐hop decode‐and‐forward relay system with selection‐combining receiver is analyzed over Rice fading channels. The following closed‐form expressions of performance metrics are derived: moment generating function for selection‐combining receiver output signal‐to‐noise ratio, exact average bit error rate of noncoherent modulations, approximate average symbol error rate for coherent modulations, and outage probability. We also obtain simple asymptotic expressions for moment generating function, exact average bit error rate, average symbol error rate, and outage probability, which are useful to characterize the diversity order and the coding gain. The optimal power allocation analysis suggests that the optimal power allocation factor is independent of total signal‐to‐noise ratio and source‐to‐destination link fading parameters. The accuracy of the obtained analytical expressions are supported by computer simulation results.     

Diversity combining considerations for incoherent frequency hoppingmultiple access systems

This paper studies the problem of diversity combining for frequency hopped multiple access (FHMA) systems that operate in a mobile satellite environment characterized by frequency-nonselective Rician multipath fading. The modulation scheme considered is the incoherent M-ary frequency-shift keying (MFSK). The optimal diversity combining rule is derived under the assumptions that the number of active users (K) in the system is known, all users are chip (hop)-synchronous, and each user employs a random FH address. We suggest practical implementations that are close approximations of the optimal rule and examine the effects of various system parameters on the resulting receivers. The bit error probability performance is analyzed and numerical examples are provided. The effects of the diversity order (L), the signaling size (M) and unequal received powers are examined and related system design concerns such as system capacity and spectral efficiency are evaluated as well     

Dual MRC diversity reception of TCM-MPSK signals over Nakagamifading channels

Space diversity reception and forward error correction coding are powerful techniques for combating the multipath fading encountered in mobile radio communications. In this Letter, the authors analyse the performance of a dual maximal ratio combining (MRC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation is introduced for the pairwise error probability, used in calculating average bit error rate analytical upper bounds     

FSK With Limiter-Discriminator Detector in Nakagami Fading Channels With and Without Selection Combining

In this paper, an equation for the error probability of M-ary frequency shift keying with limiter-discriminator detection in Nakagami fading channels for arbitrary m is derived. The authors do the same for selection combining with L diversity channels for integer m and for switch and stay combining with two diversity channels for m=1 (Rayleigh fading). The error probability for various values of m, L, frequency deviation, and filter bandwidth is computed     

Dual predetection SC diversity reception of TCM-MPSK signals overNakagami fading channels

Space diversity reception and forward error correction coding are powerful techniques for combatting multipath fading encountered in mobile radio communications. The authors analyse the performance of a dual predetection selection combining (SC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation for the pairwise error probability, used in calculating average bit error rate analytical upper bounds, is introduced     

BPSK and QPSK non‐linear satellite communication system performance in the presence of cochannel interference

Taking the uplink and downlink cochannel interference and noise into account, the analytical expressions are derived for determining the bit error probability in detecting a binary phase‐shift‐keying (BPSK) and a quaternary phase‐shift‐keying (QPSK) Gray coded signal, transmitted over a satellite system exhibiting amplitude modulation‐to‐amplitude modulation (AM/AM) conversion effects and amplitude modulation‐to‐phase modulation (AM/PM) conversion effects. On the basis on the derived theoretic formulae, using real‐life system parameters, numerical results are obtained and presented. We point out the explicit comparisons of satellite communication system performance obtained when a satellite transponder amplifier is modelled by a hard‐limiter and those obtained when both AM/AM and AM/PM non‐linearities of the satellite transponder amplifier are taken into consideration. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.     

Nakagami衰落信道上组合SC/MRC的性能分析

研究Nakagami衰落信道上组合发射机选择合并(SC)/接收机最大比合并(MRC)天线分集系统的性能.使用矩生成函数方法,推导采用组合SC/MRC天线分集和相干检测的MPSK(M进制相移键控)、MQAM(M进制正交幅度调制)、MPAM(M进制脉冲幅度调制)、BFSK(二进制频移键控)、最小相关BFSK(BFSKmin)、差分编码BPSK(DE-BPSK)和预编码MSK(最小频移键控)等几种M进制数字调制方式在Nakagami衰落信道上的误符号率性能,获得了M进制数字调制系统误符号率性能的精确数学表达式.数值计算结果阐明了发射天线和接收天线数目以及衰落参数对数字调制系统误符号率性能的影响.     

Joint Detection and Diversity Techniques in CDMA Mobile Radio Systems

CDMA mobile radio systems suffer from intersymbol interference (ISI) and multiple access interference (MAI) which can be combated by using joint detection (JD) techniques. Furthermore, the time variation of the radio channels leads to degradations of the receiver performance due to fading. These degradations can be reduced by applying diversity techniques. Three suboptimum detection techniques based on matched filters (MF), zero forcing (ZF) and minimum mean square-error (MMSE) equalization are considered. For further improvements, switched and equal gain diversity techniques are employed to combat fading. The performance is depicted in terms of the average bit error probability versus the average SNR per bit in a single cell environment showing an appreciable improvement over the non diversity situation. Theoretical results for the SNR at the front end of the receiver and the BER for ideal channel are obtained and compared with the simulation results.