Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Average bit error rate performance analysis of subcarrier intensity modulated MRC and EGC FSO systems with dual branches over M distribution turbulence channels

Based on the space diversity reception, the binary phase-shift keying (BPSK) modulated free space optical (FSO) system over Málaga (M) fading channels is investigated in detail. Under independently and identically distributed and independently and non-identically distributed dual branches, the analytical average bit error rate (ABER) expressions in terms of H-Fox function for maximal ratio combining (MRC) and equal gain combining (EGC) diversity techniques are derived, respectively, by transforming the modified Bessel function of the second kind into the integral form of Meijer G-function. Monte Carlo (MC) simulation is also provided to verify the accuracy of the presented models.     

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     

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     

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.      

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     

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.     

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.     

Simulation of bit error performance of FSK, BPSK, and π/4 DQPSKin flat fading indoor radio channels using a measurement-based channelmodel

The results of a simulation study that provides insight into the simulation methodology and bit error rate (BER) performance of frequency-shift keying (FSK), binary phase-shift keying (BPSK), and π/4 differential phase-shift keying (π/4 DQPSK) in flat fading channels inside open plan buildings are presented. A detailed measurement-based propagation channel model, SIRCIM (simulation of indoor radio channel impulse response models), which generates over 1000 closely spaced baseband equivalent complex impulse responses for a mobile radio operating at 1.3 GHz and traveling over a 1-m path, is used. The small-scale channel model, the communication system models used in the analysis and the methods used to predict BER are described. The channel simulator and the systems models have been thoroughly tested, and results from average instantaneous BER simulations are shown. The BER performances of the modulation techniques are presented. It is found that BPSK offers between a 2.8-dB and 3.0-dB improvement over π/4 DQPSK, although the latter offers a 3-dB increase in capacity for a given spectrum allocation     

The Distribution of Error Probability for Rayleigh Fading and Gaussian Noise

The distribution function of the probability of error in the presence of Rayleigh fading and Gaussian noise is determined for the basic binary modulation schemes of coherent frequencyshift keying (CFSK), noncoherent frequency-shift keying (NCFSK), differential phase-shift keying (DPSK), and coherent phase-shift keying (CPSK). General expressions for the distribution function of error probability are also derived when linear maximal-ratio diversity combining is employed. Results are given for various values of average error probability and various orders of diversity.     

Noncoherent diversity reception over Nakagami-fading channels

A method for computing the average bit-error probability of binary differential phase-shift keying (DPSK) and frequency shift-keying (FSK) signals transmitted over Nakagami asymptotically slow fading channels with postdetection diversity reception is presented to extend previously published results. The previously published results apply only for maximum ratio combining, i.e., with predetection combining, where phase coherency is necessary. The results for postdetection combining are derived with the explicit expressions for the most practical cases of independent channels and particular cases of correlated channels     

Performance of generalized selection combining for mobile radiocommunications with mixed cochannel interferers

The performance of generalized selection combining (GSC) space diversity for mobile radio systems in the presence of multiple cochannel interferers is studied. Two cochannel interference models are considered: (1) L cochannel interferers consisting of L-N Nakagami-m (1960) interferers and N Rayleigh interferers and (2) L cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining of time. The fading parameters of the Nakagami-m interferers are limited to integer values only. The desired signal is assumed to be Rayleigh faded. Also, all the desired signals and the cochannel interferers received on each branch are independent of each other. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the GSC for the two cochannel interference models. Using these SIR PDFs, closed-form expression for evaluating the outage probability and the average bit error probability (BEP) are subsequently derived. A differential phase-shift keying scheme is considered in the derivation. Numerical results showing the influences of various system parameters on the outage probability and the average BEP are then presented     

Combined adaptive RAKE diversity (ARD) and coding for DPSK DS/CDMAmobile radio

A diversity combining scheme, adaptive RAKE diversity (ARD), is proposed for a differential phase-shift keying (DPSK) direct sequence code division multiple access (DS/CDMA) mobile communications system. The ARD scheme minimizes the mean squared errors in the diversity combiner output. This suppresses the effects of the interference only paths in the time window for path diversity combining. Bit error rate (BER) performances with the proposed ARD and conventional equal gain combining (EGC) schemes are evaluated through laboratory experiments and compared. Block error rate (BKER) performance with the ARD scheme is also evaluated experimentally. Based upon the BKER evaluation results, an error correction scheme is proposed that is suitable for error occurrence characteristics of ARD output     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Closed-form analysis of dual-diversity equal-gain combining over Rayleigh fading channels

Starting with a new expression for the probability density function of the signal-to-noise ratio at the output of dual-diversity equal-gain combining (EGC) over Rayleigh channels, we provide closed-form expressions for the average bit and symbol error rate of M-ary phase-shift keying signals. Numerical examples indicate that EGC maintains a good diversity gain as long as the degree of unbalance is not very low but suffers a sharp and significant degradation when the degree of unbalance approaches zero.     

Analysis of M-ary phase-shift keying with diversity reception forland-mobile satellite channels

An analytical technique well suited to numerical analysis is presented for computing the average bit-error rate (BER) and outage probability of M-ary phase-shift keying (PSK) in the land-mobile satellite channel (LMSC) with microdiversity reception. Closed-form expressions are found for L-branch microdiversity using both selection diversity combining (SDC) and maximal ratio combining (MRC). These expressions are extended to include both M-ary coherent PSK (M-PSK) and differential PSK [M-differential PSK (DPSK)]. Following previous empirical studies, the LMSC is modeled as a weighted sum of Rice and Suzuki distributions. Numerical results are provided illustrating the achievable performance of both M-PSK and M-DPSK with diversity reception. Using measured channel parameters, the performance in various mobile environments for various satellite elevation angles is also found     

Performance of direct-sequence spread-spectrum RAKE receivers withrandom spreading sequences

In this paper, we derive error probability expressions for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) spread direct-sequence spread-spectrum (DSSS) systems employing random spreading sequences with RAKE receivers. The derived expressions accurately take into account the effect of interpath interference which usually has been neglected in previous analyses. Selection, equal gain, and maximal ratio techniques are considered for diversity combining. Two possible finger assignment strategies, one based on the instantaneous amplitudes and another based on the average powers of the multipath components, are considered for the assignment of multipath components to the available demodulating fingers in the RAKE receiver. Also, various simple, and in many cases, closed-form approximations for the error probabilities are derived and their accuracies are assessed     

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.     

Impact of nonlinear phase noise on direct-detection DQPSK WDM systems

The performance degradation of differential quadrature phase-shift keying (DQPSK) wavelength-division-multiplexed (WDM) systems due to self-phase modulation (SPM)- and cross-phase modulation (XPM)-induced nonlinear phase noise is evaluated in this letter. The XPM-induced nonlinear phase noise is approximated as Gaussian distribution and summed together with the SPM-induced nonlinear phase noise. We demonstrate that 10-Gb/s systems, whose walkoff length is larger than 40-Gb/s systems', are more sensitive to XPM-induced nonlinear phase noise than 40-Gb/s systems. Furthermore, DQPSK WDM systems show lower tolerance to both SPM- and XPM-induced nonlinear phase noise than differential phase-shift keying WDM systems.     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.