MRC performance for binary signals in Nakagami fading with generalbranch correlation

Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation     

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 performance analysis of M-ary QAM with MRC diversity in Rician fading channels

The exact expression of symbol error rate (SER) is derived for coherent square M-ary quadrature amplitude modulation (M-QAM) using Lth order maximal-ratio combining (MRC) diversity in Rician fading channels with an arbitrary fading parameter. The accuracy of the SER estimates evaluated by this expression is verified through comparison with the results evaluated by numerical integration.     

Precise error-rate analysis of bandwidth-efficient BPSK in Nakagami fading and cochannel interference

The bit-error rate (BER) of bandlimited binary phase-shift keying in a fading and cochannel interference (CCI) environment is derived for the case of perfect coherent detection. The fading-and-interference model assumed is general and of interest for microcellular system studies. The model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity. A precise BER expression is derived using a characteristic function method. Using this accurate analytical result, the impact of the interfering users' fading severity on the desired user-error rate is examined. The BERs obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement. The error-rate performance of a novel bandwidth-efficient pulse shape is determined for the general fading and CCI environment. Analysis and numerical results show that the new pulse can provide better BER performance than the widely used raised-cosine pulse.     

Performance of DS-CDMA receivers with MRC in nakagami-m fading channels with arbitrary fading parameters

The receivers that combine spatial antenna diversity with temporal multipath diversity are known as two-dimensional (2-D) RAKE receivers. In this paper, we consider the outage probability and the bit error rate performance of a coherent binary phase shift keying 2-D RAKE receiver in the context of an asynchronous direct sequence (DS)-code division multiple access (CDMA) system operating in a Nakagami-m fading channel with real and arbitrary fading parameters. The closed-form expressions derived for the two wireless performance measures are easily evaluated numerically and enable the link designer to examine the effects of system parameters, such as the number of receive antennas, RAKE fingers per antenna, and asynchronous CDMA users in the cell, as well as channel conditions, such as the amount of fading in the combined paths and the multipath intensity profile of the channel on the link performance. In addition, the diversity loss due to correlated fading among the spatially separated RAKE fingers is quantified.     

Exponential-type bounds on the generalized Marcum Q-function withapplication to error probability analysis over fading channels

Strict upper and lower bounds of exponential-type are derived for the generalized (mth order) Marcum Q-function which enable simple evaluation of a tight upper bound on the average bit-error probability performance of a wide class of noncoherent and differentially coherent communication systems operating over generalized fading channels. For the case of frequency selective fading with arbitrary statistics per independent fading path, the resulting upper hound on performance is expressed in the form of a product of moment generating functions of the instantaneous power random variables that characterize these paths     

Performance analysis of SIR-based dual selection diversity over correlated Nakagami-m fading channels

Signal-to-interference-ratio (SIR)-based selection diversity is an efficient technique to mitigate fading and cochannel interference in wireless communications systems. An approach to the performance analysis of dual SIR-based selection diversity over correlated Nakagami-m fading channels with arbitrary parameters is presented. Useful formulae for the outage probability, the average output SIR, and the average error probability for coherent, noncoherent, and multilevel modulation schemes are derived. The main contribution of the paper is that, for the first time, the proposed analysis is carried out assuming correlated Nakagami-m fading with arbitrary parameters for both the desired signals and the cochannel interferers, which is the real scenario in practical dual selection diversity systems with insufficient antenna spacing. It is shown that the presented general results reduce to the specific ones for the independent fading case, previously published. Numerical and simulation results are also presented to show the effects of various parameters, such as the fading severity, input SIR unbalance, and level of correlation, to the system's performance.     

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     

SEP performance of coherent MPSK over fading channels in the presence of phase/quadrature error and I-Q gain mismatch

This letter presents a joint approach to the symbol-error probability (SEP) of coherent M-ary phase-shift keying in a situation where the phase error, quadrature error, and in-phase-quadrature (I-Q) gain mismatch problems take place all concurrently over an additive white Gaussian noise and arbitrary fading channel. A set of equations that characterizes the conditional SEP on an instantaneous fading signal-to-noise ratio is derived in the form of the Craig representation.     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.     

Error rate analysis for peaky signaling over fading channels

In this paper, the performance of signaling strategies with high peak-to-average power ratio is analyzed in both coherent and noncoherent fading channels. Two modulation schemes, namely on-off phase-shift keying (OOPSK) and on-off frequency-shift keying (OOFSK), are considered. The optimal detector structures are identified and analytical expressions for the error probabilities are obtained for arbitrary constellation sizes. Numerical techniques are employed to compute the error rates. It is concluded that increasing the peakedness of the signals results in reduced error rates for a given power level and hence equivalently improves the energy efficiency for fixed error probabilities.     

Gaussian class multivariate Weibull distributions: theory and applications in fading channels

Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance.     

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     

Pilot-symbol aided coherent M-ary PSK in frequency-selective fastRayleigh fading channels

Pilot-symbol aided coherent M-ary PSK modems in digital cellular mobile radio systems are analyzed theoretically. The error-floors caused by the Doppler spread in a fast fading channel are removed in both flat and selective fading channels. However, the error-floors caused by the delay spread are lower-bounded by those that exist in the ideal coherent detection. The systems are modeled as frequency-selective fast Rayleigh fading channels, corrupted by co-channel interference (CCI) and additive white Gaussian noise (AWGN). In the proposed scheme, pilot symbols are inserted periodically to monitor the channel characteristics. The fading processes experienced by the pilot symbols are used to estimate those suffered by the data symbols using interpolation or filtering. The estimated fade characteristics are used to compensate the random phase variation caused by the Doppler spread, so that the signals can be demodulated coherently. The theoretical performances of the fade compensated coherent modems are evaluated. The results show that the fade compensated coherent demodulation with the least redundancy achieves the same performance as the ideal differential detection in a fading channel. The performance approaches that of the ideal coherent demodulation as more redundancy is allowed. The pilot-symbol-insertion (PSI) scheme is also applicable to M-ary QAM modems and Rician channels. The residual frequency offset can also be compensated by the PSI technique     

Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading

Using a circular contour integral representation for the generalized Marcum-Q function, Q/sub m/(a,b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in Q/sub m/(a,b). As an aside, we show that previous integral representations for Q/sub m/(a,b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for Q/sub m/(a,b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems.     

Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters

Nakagami fading model is widely used in modeling wireless communication systems. In this paper, we present methods to generate Nakagami fading signals with arbitrary cross-correlation and fading parameters by taking the square root of correlated Gamma random variables (RVs) with the corresponding shape parameters. To generate correlated Gamma RVs with different noninteger values of m-parameters, two methods, namely the decomposition method and Sim's method, are proposed. The former is more flexible and efficient. The latter is mathematically exact but carries constraints on the permissible simulation parameters. Simulations show that both methods produce outputs that match well with the specifications.     

Adaptive reception of MPSK on fading channels

An adaptive estimator of the complex gain of a fading channel is proposed. Tracking of the fading process is achieved without knowledge of the fading spectrum. This enables coherent detection of MPSK to be performed. Simulations show good error rate performance. The receiver finds applications in mobile radio communications     

Selective decode-and-forward cooperation over Nakagami-m fading channels

The asymptotic performance analysis is presented for selective fixed decode-and-forward (DF) cooperation over independent but not identically distributed Nakagami-m fading channels. A tractable closed-form average bit error probability expression is derived at the high signal-tonoise ratio region. The presented expression is quite simple and general for cooperative systems with an arbitrary number of DF relays and fading environment with arbitrary values of severity parameters m ⩾ 0.5.     

Moments-based approach to the performance analysis of equal gain diversity in Nakagami-m fading

In this letter, an alternative moments-based approach for the performance analysis of an L-branch predetection equal gain combiner (EGC) over independent or correlated Nakagami-m fading channels is presented. Exact closed-form expressions are derived for the moments of the EGC output signal-to-noise ratio (SNR), while the corresponding moment-generating function (MGF) is accurately approximated with the aid of Pade/spl acute/ approximants theory. Important performance criteria are studied; the average output SNR, which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters, the average symbol-error probability for several coherent, noncoherent, and multilevel modulation schemes, and the outage probability, which are both accurately approximated using the well-known MGF approach. The proposed mathematical analysis is illustrated by various numerical results, and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach.     

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