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.     

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 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.     

Performance of M-PSK in mobile satellite communication over combined ionospheric scintillation and flat fading channels with MRC diversity

Combined scintillation and terrestrial fadings occur in mobile satellite communication channels as the signal passes through the ionosphere and the lower atmosphere. This results in a product fading channel, which negatively affects the performance of the system. The challenge is to evaluate the performance of the system, in terms of the average bit error probability (BEP). In this paper, through the use of the moment generating function, we derive expressions for the average BEP and an upper bound for M-ary phase-shift keying (M-PSK) modulation with maximal-ratio combining (MRC) diversity over the product RicianxRician channel. The results are expressed as double summations in terms of the generalized hypergeometric function, which can be computed using standard commercial software. For a large Rician factor, the expression is simplified to a single summation. Numerical results are obtained from the derived expressions and compared with simulation results. They show very good agreement for various Rician factors and the number of diversity branches. The upper bound is also evaluated and shown to be reasonably tight.     

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.     

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.     

Optimal detection of coded differentially encoded QAM and PSKsignals with diversity reception in correlated fast Rician fadingchannels

The optimal sequence estimator for digital signals received over Λ different channels is derived. Each of these channels corrupts the transmitted signal by a mixture of additive white Gaussian noise (AWGN) and frequency-nonselective, correlated, fast Rician fading. By analysis it is shown that for the lth (1⩽l⩽Λ) diversity channel, the basic hardware structure of the optimal receiver consists of a combination of envelope, multiple differential, and coherent detectors. In order to reduce the overall implementation complexity, suboptimal, e.g., having a small number of differential detectors and equal combining diversity structures, versions of the optimal receivers are proposed and evaluated. Two modulation schemes are chosen in order to evaluate the overall performance of the proposed reduced-complexity diversity receivers: the π/4-shift 8-DQAM (differential quadrature amplitude modulation) and the 8-DPSK (differential phase shift keying). Bit-error-rate (BER) performance evaluation results are given. By means of computer simulation, the effect of correlation between the fading processes on the Λ diversity channels is investigated     

Analysis of differentially coherent linear receivers over Rician-faded CDMA channels

RicianAccurate performance analysis for linear receivers over frequency- and time-selective asynchronous code-division multiple-access Rician-fading channels is very useful and a general approach to this topic is very desirable. In this paper, by using a decision variable-based moment generating function approach, we provide a unified bit-error probability (BEP) analysis framework for different linear detectors with binary or quaternary differential phase-shift keying and postdetection combining over Rician-fading channels, taking into account the effects of the spreading code correlation, the system and fading-channel parameters, diversity combining, and branch correlation. To reduce the complexity of the exact BEP evaluation, we furthermore provide an approximate multivariate Gaussian assumption (MGA)-based method which entails a low complexity for BEP evaluation. Ideal and approximate linear minimum mean-squared error diversity receivers for correlated Rician-fading channels are proposed. Numerical results show that the phases of the line-of-sight (LOS) components of the desired user significantly affect the receiver performance over correlated multipath Rician channels, and this may be exploited to improve performance. Also, when the LOS components are affected by a significant Doppler shift, automatic frequency control is very useful in improving the receiver performance.     

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.     

Linear diversity analyses for M-PSK in Rician fading channels

Symbol and bit error rates of M-ary differentially encoded/differentially decoded phase-shift keying (MDPSK) and coherent M-ary phase-shift keying (M-PSK) over slow, flat, Rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading. These closed-form solutions are general enough to cover several cases of nondiversity, additive white Gaussian noise (the nonfading mode), Rayleigh fading, mixtures of Rayleigh and Rician fading (the mixed mode), and Rician fading. The results presented here can also be applied to predict the error-rate performance when recent transmit diversity techniques are employed. The solutions for the nonuniform fading profile are included as well. Error probabilities are graphically displayed for both modulation schemes.     

An approximate analytical framework for performance analysis of equal gain combining technique over independent Nakagami,Rician and Weibull fading channels

In this paper, an approximate analytical method for performance analysis of equal gain combiner (EGC) receiver over independent Nakagami and Rician fading channels is presented. We use a convergent infinite series approach which makes it possible to describe the probability of error of EGC receiver in the form of an infinite series. In this paper, we develop a new approximation method for computation of the required coefficients in this series which lets us to derive simple analytical closed-form expressions with good accuracy compared with the exact results existing in the literatures. Our proposed approximation method only needs the mean and the variance of the fading envelope, which are known for various fading distributions, and hence, bypasses the required integration over the fading envelope distribution while computing the required coefficients. This feature lets us to extend our approximation method for performance analysis of EGC receiver over independent Weibull fading channels where the required integration has not any closed-form or tabulated solutions. To give an application of our developed method, we analyze the probability of error of an EGC receiver for binary, coherent PSK (CPSK) modulation over independent Nakagami, Rician and weibull fading channels and study the effect of the fading conditions on the system performance.     

Performance analysis of generalized-faded coherent PSK channels with equal-gain combining and carrier phase error

A new method is developed to analyze the performance of partially coherent PSK systems in wireless channels with equal-gain combining diversity receiver. Two performance criteria are considered: the average bit error probability and the probability distribution of the combiner SNR (SNR reliability). Tikhonov-distributed phase error processes are assumed and generalized fading channels including Rayleigh, Rician, and Nakagami-m are investigated. We evaluate the detection loss suffered by the carrier recovery for different SNR reliability levels when BPSK and QPSK systems are used in wireless channels. The analysis is based on a convergent infinite series for the distribution of the sum of random variables. The convergence rate of the proposed series is investigated and the analytical results are presented along with providing results obtained by simulation.     

Modulation and coding for mobile radio communications: channelswith correlated Rice fading and Doppler frequency shift

We discuss the relative performance of coherent phase-shift keying (PSK), differential PSK (DPSK), and double differential PSK (DDPSK) modulation schemes over a mobile radio channel in which transmission is affected by additive noise, a constant carrier phase offset, a constant Doppler frequency shift, and correlated Rice fading. We first compare the performance of these schemes to assess the amount of degradation caused on each one of them by fading. Among our findings, we observe that DDPSK turns out to be less sensitive to the effects of correlated fading than the other two schemes and that in these conditions interleaving may not be beneficial. We then consider the introduction of trellis-coded modulation (TCM). The system we advocate as offering the best tradeoff between performance and complexity with the channel model assumed here includes double-differential encoding, differential detection, an open-loop Doppler phase tracking circuit, and differential decoding in addition to a simple TCM scheme     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Multiple-symbol differential detection for MPSK space-time block codes: decision metric and performance analysis

Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.     

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     

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.<>     

Binary PRCPM with differential phase detection and maximal ratiocombining diversity in fading channels

We derive a formula for the bit-error probability (BEP) of binary partial-response continuous-phase modulation (PRCPM) with N-bit differential phase detection (DPD) in a Rician fading channel subject to L-branch maximum ratio combining (MRC) diversity. We compute the BEP for minimum-shift keying (MSK), Gaussian MSK (GMSK), and 2 RC (2-b-duration raised cosine) frequency signals as a function of the energy-to-noise ratio per bit E_b/N₀ and other system and channel parameters [N=1 and 2 and L=1, 2, and 3, Rician factor K=-∞, 0, 6, 10, and ∝ dB, Doppler frequency shift f_DT=0, 0.01, and 0.02, Gaussian premodulation filter bandwidth B_gT=∞, 0.5, 0.25, and the presence or absence of a Doppler frequency tracking loop (DFTL) in the receiver]. In all cases, the BEP is significantly reduced by diversity     

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