相干DS-SS/MPSK系统中频差影响的简化评估

该文针对单径慢衰落信道模型下的相干DS-SS/MPSK系统,分析了频差对系统性能的影响,得到了误比特率的封闭表达式。首先推导了匹配滤波解扩符号的信噪比特性和相干相位估计误差的分布;然后给出了衰落信道中误比特率的精确积分式,并利用MPSK条件误符号率的麦克劳林级数形式,推导了AWGN,Nakagami-m衰落和瑞利衰落信道中BPSK,QPSK误比特率的简化逼近式。最后的数值结果表明:逼近式的精度非常高,基本没有损失,可应用于实际系统设计和性能评估。     

Error probability for coherent and differential PSK over arbitraryRician fading channels with multiple cochannel interferers

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels     

New analytical probability of error expressions for classes of orthogonal signals in Rayleigh fading

New exact expressions for the symbol-error rate and bit-error rate of coherent 3-ary and 4-ary orthogonal and transorthogonal signaling in slowly fading Rayleigh channels are derived. New exact error probability expressions for coherent 6-ary and 8-ary biorthogonal signaling in slow Rayleigh fading are also presented. The use of these exact expressions as accurate approximations for the error rates of M-ary orthogonal, biorthogonal, and transorthogonal signaling with arbitrary M is illustrated.     

Exact symbol-error probability analysis for orthogonal space-time block codes: two- and higher dimensional constellations cases

Exact expressions are obtained for the symbol-error probability of orthogonal space-time block codes at the output of the coherent maximum-likelihood decoder in the general case of arbitrary input signal constellation and code. Such expressions are derived for the cases of both deterministic (fixed) and random Rayleigh/Ricean fading channels, and both the two- and higher dimensional constellations.     

Exact Performance Analysis of Dual-Branch Coherent Equal-Gain Combining in Nakagami- $m$, Rician, and Hoyt Fading

The exact symbol error rates (SERs) of several M-ary modulation schemes are obtained in a unified manner for mobile radio receivers employing dual-branch coherent equal-gain combining (EGC), where the received signals on each branch follow either similar or different fading distributions. Specifically, the cases considered are Nakagami-m, Rice, and Hoyt fading on both branches, but with not necessarily identical parameters, and mixed Nakagami-m/Rice and Nakagami-m/Hoyt fading; only the integer or half-integer values of the Nakagami-parameter are considered. While the previous exact expressions for the SERs of general M-ary modulations with L-branch EGC contained double integrals, the error probability expressions derived in this paper for the case of L=2 contain only a single integral. In addition, the derived probability distributions also allow the direct obtaining of other useful performance measures, such as the exact level crossing rates, average fade durations, and outage probabilities.     

Exact bit-error probability for optimum combining with a Rayleighfading Gaussian cochannel interferer

We derive expressions for the exact bit-error probability (BEP) for the detection of coherent binary phase-shift keying signals of the optimum combiner employing space diversity when both the desired signal and a Gaussian cochannel interferer are subject to flat Rayleigh fading. Two different methods are employed to reach two different, but numerically identical, expressions. With the direct method, the conditional BEP is averaged over the fading of both signal and interference, With the moment generating function based method, expressions are derived from an alternative representation of the Gaussian Q-function     

Performance of M-ary PSK signals in slow Rayleigh fading channels

The error rate performance of M-ary coherent phase shift keyed signals and M-ary differential phase shift keyed signals in slow Rayleigh fading channels is analysed. Closed-form expressions for the symbol error rate are presented. The coherent PSK signals are 3 dB stronger than the differential PSK signals at high SNR for given M in a Rayleigh fading environment.<>     

Unified analysis of MPSK and MDPSK with diversity reception indifferent fading environments

Computationally efficient expressions are presented for evaluating the symbol-error rates of coherent and differentially coherent M-ary phase-shift-keying signalling in conjunction with maximal-ratio combining diversity receivers in fading scenarios     

SEP calculations for coherent M‐ary FSK in different fading channels with MRC diversity

In this paper, the authors derive symbol error probability (SEP) expressions for coherent M‐ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small‐scale fading process is assumed to be slow and frequency non‐selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small‐scale fading statistics such as Rayleigh, Rician (Nakagami‐n), Hoyt (Nakagami‐q), and Nakagami‐m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front‐end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase‐coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (1≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different M, and gives exact values up to M=5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size M, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte‐Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication. Copyright © 2010 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     

Linear multipath-decorrelating receivers for CDMAfrequency-selective fading channels

Analytical expressions for the error probability of linear multipath-decorrelating receivers with coherent and differentially coherent reception are derived. Both multi-user receivers have superior performance compared to the RAKE receiver and eliminate error probability floor caused by multiple-access interference on a code-division multiple access (CDMA) reverse link. Results also emphasize benefits of using coherent multi-user reception with maximal-ratio combining in frequency-selective fading channels     

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     

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     

Selection diversity for wireless communications in Nakagami-fadingwith arbitrary parameters

By means of analytical and numerical methods, the probability of error and the outage probability of a selection diversity RAKE receiver system employing direct sequence/code division multiple access (DS/CDMA) is derived. A noise-limited propagation environment is modeled as a Nakagami (1960)-fading channel with arbitrary fading parameters and unequal mean power at the receiver. New analytical expressions are derived for the average probability of error and outage probability. Binary detection schemes are considered including binary phase-shift keying (PSK) and frequency-shift keying (FSK). Both coherent and noncoherent detection is considered as well as identical and arbitrary fading. It is shown that the effect of arbitrary fading on system performance is significant and may not be ignored     

A unified approach for calculating error rates of linearlymodulated signals over generalized fading channels

We present a unified analytical framework to determine the exact average symbol-error rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths, which are not necessarily identically distributed. In all cases, the proposed approach leads to an expression of the average SER involving a single finite-range integral, which can be easily computed numerically. In addition, as special cases, SER expressions for single-channel reception are obtained. These expressions reduce to well-known solutions, give alternative (often simpler) expressions for previous results, or provide new formulas that are either closed-form expressions or simple to compute numerically     

The error performance of Gray encoded QPSK and 8-PSK schemes in afading channel with cochannel interference

Closed-form BER (bit error rate) expressions are derived for Gray-encoded QPSK (quadrature phase shift keying) and 8-PSK schemes using coherent detection in a slow Rayleigh fading narrowband channel with fading cochannel interference. Earlier work has been limited to deriving the approximate BER using the canonical Stein (1961) receiver concept. The symbol error rate (SER) for the QPSK scheme is also derived. The desired signal and the cochannel interferer are both PSK signals, modulated by different baseband pulses with identical signaling rate     

Performance analysis of compact antenna arrays with MRC incorrelated Nakagami fading channels

This paper presents the average error probability performance of a compact space diversity receiver for the reception of binary coherent and noncoherent modulation signals through a correlated Nakagami (1960) fading channel. Analytical expressions of the average bit error rate (BER) are derived as a function of the covariance matrix of the multipath component signals at the antenna elements. Closed-form expressions for the spatial cross-correlation are obtained under a Gaussian angular power profile assumption, taking account of the mutual coupling between antenna elements. The effects of antenna array configuration (geometry and electromagnetic coupling) and the operating environment (fading, angular spread, mean angle-of-arrival) on the BER performance are illustrated     

Equal-gain and maximal-ratio combining over nonidentical Weibull fading channels

We study the performance of L-branch equal-gain combining (EGC) and maximal-ratio combining (MRC) receivers operating over nonidentical Weibull-fading channels. Closed-form expressions are derived for the moments of the signal-to-noise ratio (SNR) at the output of the combiner and significant performance criteria, for both independent and correlative fading, such as average output SNR, amount of fading and spectral efficiency at the low power regime, are studied. We also evaluate the outage and the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes, using a closed-form expression for the moment-generating function (mgf) of the output SNR for MRC receivers and the Pade/spl acute/ approximation to the mgf for EGC receivers. The ASEP of dual-branch EGC and MRC receivers is also obtained in correlative fading. The proposed mathematical analysis is complimented by various numerical results, which point out the effects of fading severity and correlation on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.     

The use of coding and diversity combining for mitigating fadingeffects in a DS/CDMA system

Spatial diversity is an attractive technology to cope with the fading channel encountered in mobile communications. This paper presents novel closed analytical expressions of the bit-error rate (BER) achievable in a coherent binary phase-shift-keying (CBPSK) direct-sequence code-division multiple-access (DS/CDMA) system for any power delay profile and for either postdetection selection or maximal ratio combining (MRC). In particular, expressions for the cutoff rate R _o and for its related parameter D are also formulated in order to assess the system performance under the consideration of some channel coding schemes. Finally, an exemplary study is carried out in order to illustrate the behavior of a realistic space-diversity code-division multiple-access (CDMA) system according to the analytical expressions that have been derived     

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

In this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.