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     

Bit-error probability for optimum combining of binary signals in the presence of interference and noise

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N/sub A/ denote the number of antennas and N/sub I/ the number of interferers. We consider both the cases of an overloaded system, in which N/sub I//spl ges/N/sub A/, and an underloaded system, in which N/sub I/相似文献   

Symbol-error probability and bit-error probability for optimum combining with MPSK modulation

New expressions are derived for the exact symbol error probability and bit-error probability for optimum combining with multiple phase-shift keying. The expressions are for any numbers of equal-power cochannel interferers and receive branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to flat Rayleigh fading. The new expressions have low computational complexity, as they contain only a single integral form with finite limits and finite integrand.     

Clipped diversity combining for channels with partial-bandinterference. II. Ratio-statistic combining

For pt.I see ibid., vol.COM-3, no.12, p.1320 (1987). Ratio-statistic combining is proposed for mitigating partial-band interference in systems with diversity transmission and frequency-hop signaling. Systems with noncoherent demodulation and binary orthogonal signaling are covered. The partial-band interference is Gaussian, and Gaussian quiescent noise is included in the analysis to account for wideband noise sources. The exact probability of error is found for a receiver using ratio-statistic combining, and this is compared to the exact error probabilities for receivers with optimum combining with perfect side information, clipped-linear combining, the ratio-threshold test with majority-logic decoding, and self-normalization diversity combining. Numerical results are also given for a frequency-hop system which uses ratio-statistic combining for channels with Rayleigh fading and partial-band interference. It is determined that ratio-statistic combining is an excellent diversity combining scheme for systems with partial-band interference and fading     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

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     

Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Asymptotic BEP and SEP of Quadratic Diversity Combining Receivers in Correlated Ricean Fading, Non?Gaussian Noise, and Interference

In this paper, we study the asymptotic behavior of the bit-error probability (BEP) and the symbol-error probability (SEP) of quadratic diversity combining schemes such as coherent maximum-ratio combining (MRC), differential equal-gain combining (EGC), and noncoherent combining (NC) in correlated Ricean fading and non-Gaussian noise, which in our definition also includes interference. We provide simple and easy-to-evaluate asymptotic BEP and SEP expressions which show that at high signal-to-noise ratios (SNRs) the performance of the considered combining schemes depends on certain moments of the noise and interference impairing the transmission. We derive general rules for calculation of these moments and we provide closed-form expressions for the moments of several practically important types of noise such as spatially dependent and spatially independent Gaussian mixture noise, correlated synchronous and asynchronous co-channel interference, and correlated Gaussian interference. From our asymptotic results we conclude that (a) the asymptotic performance loss of binary frequency-shift keying (BFSK) with NC compared to binary phase-shift keying (BPSK) with MRC is always 6 dB independent of the type of noise and the number of diversity branches, (b) the asymptotic performance loss of differential EGC compared to MRC is always 3 dB for additive white Gaussian noise but depends on the number of diversity branches and may be larger or smaller than 3 dB for other types of noise, and (c) not only fading correlation but also noise correlation negatively affects the performance of quadratic diversity combiners.     

Performance of Optimum and Suboptimum Combining Diversity Reception for Binary and Quadrature DPSK Over Independent, Nonidentical Rayleigh Fading Channels

dThis paper is concerned with the error-performance analysis of binary and quadrature differential phase-shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. The diversity channels are independent, but have nonidentical statistics. The fading process in each channel is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of second-order diversity and require numerical integration for their actual evaluation. Our results are more general in that the order of diversity is arbitrary. Moreover, the bit-error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-symbol-interval fading correlation coefficient at the matched-filter output, the mean received signal-to-noise ratio per symbol per channel, and the order of diveristy.      

Analytical Framework for Optimal Combining With Arbitrary-Power Interferers and Thermal Noise

The performance of multiple-input-multiple-output systems with optimum combining (OC) is studied in a Rayleigh fading environment with arbitrary-power cochannel interference and thermal noise. Based on the joint eigenvalue distributions of quadratic functions of complex Gaussian matrices, a closed-form expression for the exact distribution of the output signal-to-interference-plus-noise ratio (SINR) is derived. A closed-form expression for the exact moment-generating function (MGF) of the output SINR of single-input-multiple-output (SIMO) systems is also derived. From the exact MGF, the moments of the output SINR and the symbol error rate of various M-ary modulation schemes are obtained. We verify the accuracy of our analytical results with numerical examples. The new analytical framework provides a simple and accurate way to assess the effects of equal- and unequal-power cochannel interferers and thermal noise on the performance of OC.     

Simple error probability derivation for binary DPSK over fast Rician channels with diversity

Bit error probability (BEP) performance of binary differential phase shift keying (DPSK) with differential detection over the nonselective, fast Rician fading channels with combining diversity reception is analysed. The analytical approach that exists in previously published literature for computing the BEP relied on a special case of the derivation given by Proakis that was concerned with the probability that a general quadratic form in complex Gaussian random variables is less than zero. However, evaluating the various coefficients required in the derivation leads to a computationally intensive solution. A simple derivation is presented which leads to a new, alternative BEP expression.     

A simple bit error probability analysis for square QAM in rayleigh fading with channel estimation

A new approach is presented for analyzing the bit error probability (BEP) of square, multilevel, quadrature amplitude modulation over a nonselective Rayleigh fading channel, with imperfect channel estimation employing pilot-symbolassisted- modulation. It is much simpler and more powerful than those in the literature, and the average BEP is obtained by calculating the BEP for each individual bit. The results are given in simple, exact, closed-form expressions that do not require any numerical integration. These expressions show explicitly the behavior of the BEP as a function of various system parameters. Three channel estimation schemes are investigated. It is shown that existing channel estimation schemes using sinc interpolation and Gaussian interpolation can be improved.     

Performance bounds for optimum multiuser DS-CDMA systems

In this letter we estimate the bit error probability (BEP) of optimum multiuser detection for synchronous and asynchronous code division multiple access (CDMA) systems on Gaussian and fading channels. We first compute an upper bound and a lower bound on the bit error probability for a given spreading code, then average the bounds over a few thousand sets of spreading codes. These bounds are obtained from a partial distance spectrum. On Gaussian channels, the upper bound converges to the lower bound at moderate to large signal-to-noise ratios. However, on fading channels the upper bound does not converge, hence we present our results for the lower bound only. The numerical results show that: 1) the BEP of a 31-user CDMA system with binary random spreading codes of length 31 is only two to four times higher than the BEP of the single user system; 2) the number of users that can be accommodated in an asynchronous CDMA system is larger than the processing gain; and 3) optimum multiuser detection outperforms linear detection (e.g., the decorrelating detector) by about 2.8 to 5.7 dB     

Performance comparison of selection combining schemes for binary DPSK on nonselective Rayleigh-fading channels with interference

This paper is concerned with the error performance analysis of binary differential phase shift keying (DPSK) with differential detection over the nonselective Rayleigh-fading channel with selection diversity reception and with an additive, correlated, Gaussian interference process in each diversity channel. The fading process is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The selection schemes investigated are: 1) the selection combining (SC) scheme based on signal-to-noise power ratio (SNR); 2) the SC scheme based on signal-plus-noise (S+N); and 3) the SC scheme based on maximum output (MO). New, exact, closed-form bit-error probability (BEP) expressions are derived, and a performance comparison among the three SC schemes and combining diversity reception is given. The results obtained reduce to previously known results when the correlated interference process is absent, and when the fading process does not fluctuate over the duration of several symbol intervals. The results indicate that the performance of each scheme depends on the tradeoff between the number of diversity branches, the SNR, the interference level, and the correlation of the interference process. However, the SC-(S+N) scheme generally performs worse than the SC-SNR scheme, the SC-MO scheme and combining diversity reception scheme. The findings presented here are not only of fundamental theoretical value, but are also of practical interest to the designers of future mobile communication systems.     

GMSK with limiter-discriminator detector in Nakagami fading channel with and without selection combining

We derive an equation for the bit-error probability (BEP) of Gaussian minimum-shift keying with limiter discriminator detection in Nakagami-m fading channels including selection and switch-and-stay combining. We compute the BEP for various selections of system parameters.     

Linear Diversity Analysis for M‐ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

We derive and analyze the exact closed‐form expression for the average bit error probability (BEP) of M‐ary square quadrature amplitude modulation (QAM) for diversity reception in frequency‐nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M‐ary square QAM with an MRC diversity combiner for various cases of practical interest.     

Multiple symbol differential detection with diversity reception

In this letter we first consider the maximum-likelihood sequence estimator for multiple symbol differential detection (MSDD) over the slow fading diversity channel. Since this optimum decision metric results in a complex receiver implementation whose average bit-error probability (BEP) performance is difficult (if not impossible) to obtain analytically, we then focus our attention on evaluating the average BEP for MSDD with diversity reception in the form of postdetection equal-gain combining (EGC) giving emphasis to its ability to bridge the gap between EGC of conventional differentially detected M-PSK and maximal-ratio combining of coherently detected M-PSK with differential encoding     

Performance of QDPSK signals with postdetection equal gaindiversity combining in arbitrarily correlated Nakagami-m fading channels

This letter derives a bit-error probability (BEP) expression for quadrature differential phase-shift keying (QDPSK) signals with post-detection equal gain combining (EGC) in additive white Gaussian noise and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. Unlike previous work, the effects of arbitrary values of fading severity parameter m and the arbitrary correlation between the L diversity channels are considered. The derived expression can be easily computed via numerical integration routines, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems     

Optimum diversity combiner based multiuser detection fortime-dispersive Rician fading CDMA channels

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity     

Performance Analysis for OFDMA in the Presence of Tone Interference

Space-frequency coded (SFC) orthogonal frequency-division multiple access (OFDMA) is considered in the presence of multitone (MT) interference. Analytical expressions for the bit-error probability (BEP) are derived for OFDMA with SFC in a frequency-selective fading environment. It is shown that SFC increases the resistance of OFDMA against the MT interference and reduces BEP considerably