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     

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     

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.     

Differentially amplitude and phase-encoded QAM for the correlatedRayleigh-fading channel with diversity reception

This paper studies the differentially amplitude and phase-encoded (DAPE) quadrature amplitude modulation (QAM) transmission over correlated Rayleigh channels with diversity reception. Operating over two successive received symbols, the optimum and an asymptotic maximum-likelihood (AML) differentially coherent receiver are developed and compared with a conventional switched diversity combining (SDC) grid receiver. It is shown that the AML and SDC grid receivers are much simpler in complexity than the optimum receiver in that no channel side information is required in their realization. An exact expression of the bit-error probability (BEP) is obtained for the SDC grid receiver. Based on a union bound argument, a BEP upper bound for the AML receiver is also derived and verified by simulation. Numerical results on 16- and 64-point constellations show that the AML receiver exhibits an almost optimum performance and the SDC grid receiver with a small level of diversity is nearly optimum. It is also shown by simulation that the conventional equal-gain diversity receiver is almost optimal for demodulating a 16-point DAPE QAM signal     

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.     

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

The effect of spatial correlation on the performance of orthogonal space-time block codes (OSTBCs) over multiple-input-multiple-output (MIMO) Rician fading channels is studied. Asymptotic error-rate formulas for OSTBC with high average signal-to-noise ratios (ASNRs) over arbitrarily correlated Rician MIMO channels are derived in terms of the diversity and coding gains. Our results show that, in correlated fading, the phase vector phi of the channel line-of-sight (LOS) components affects the effective Rice K-factor at the OSTBC receiver output and, hence, may result in a coding gain that is significantly higher than that for independent Rician MIMO channels. Furthermore, when the channel covariance matrix is rank deficient and under some additional mild conditions, the error and outage probabilities of OSTBC achieve those in a nonfading additive-white-Gaussian-noise channel. For both cases of full-rank and rank-deficient channel covariance matrices, analytical expressions of optimal and worst case phase vectors phi, and exact upper and lower bounds of OSTBC performance are derived. These results provide new insights into the achievable performance of OSTBC over correlated Rician MIMO channels and, if incorporated into future multiple antenna systems design, will bring about significant performance enhancement     

Efficient BER evaluation of linear multiuser detectors with imperfect channel estimation for CDMA fading channels

In this paper, we present a unified mathematical framework to analyze the bit-error rate (BER) performance of general linear coherent multiuser receivers with diversity reception and imperfect channel estimation for doubly selective Rician-fading asynchronous code-division multiple-access channels. BERs of linear receivers with channel state information and data-aided channel estimation are analyzed, and both exact and low-complexity approximate BER evaluation formulas are presented. Furthermore, by using a Markov chain steady-state analysis, a tight BER approximation for receivers with decision-directed channel estimation is proposed. Numerical and simulation results verify the accuracy of the proposed BER evaluation methods.     

Performance study of suboptimum maximum-likelihood receivers for FFH/MFSK systems with multitone jamming over fading channels

We derive two suboptimum maximum-likelihood (ML) receivers for fast frequency-hopped M-ary frequency-shift-keying (FSK) spread-spectrum (SS) communication systems. These two receiver structures attempt to countermeasure the effects of the worst case multitone jamming (MTJ) and additive white Gaussian noise over Rayleigh- and Rician-fading channels, respectively. In addition, analytical bit-error-rate (BER) expressions for the two proposed suboptimum structures are derived and validated by simulation results. Performance comparisons among various receivers show that the proposed suboptimum receivers significantly outperform the other existing receivers over fading channels. The optimum diversity level of the suboptimum ML receiver for the Rayleigh-fading case is found to be higher than that of the Rician-fading case. In addition, the proposed suboptimum ML receivers with optimum diversity levels can effectively remove the effect of MTJ, even under very low signal-to-jamming ratio conditions.     

Performance of S + N Selection Diversity Receivers in Correlated Rician and Rayleigh Fading

The performances of two signal-/?/wi-noise (S + N) selection diversity receivers employing noncoherent M-ary frequency shift keying (MFSK) in slow, flat, correlated Rayleigh and Rician fading channels are examined. The branches are assumed to be equally correlated for Rician fading. The correlation model for Rayleigh fading is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.     

Performance of FFH/BFSK product combining receiver over aRician-fading channel with partial-band jamming

A theoretical performance evaluation for an FFH/BFSK spread spectrum product combining receiver over a Rician-fading channel in the presence of partial-band jamming and AWGN is presented. The BER of this receiver is better than that of a linear combining receiver for a strong direct signal, and improvement is significant when diversity is increased     

Performance analysis of linear multisensor multiuser receivers forCDMA in fading channels

Bit-error probability (BEP) analysis for linear multiuser receivers with multiple sensors in frequency selective Rayleigh fading channels is presented. The analysis is applied to evaluate the BEP in antenna diversity reception and in a cellular CDMA system. Diversity and multiuser receivers are compared based on the examples. It is observed that adding new diversity antenna elements improves performance even if the correlation between the antenna elements is relatively large (up to 0.7). However, the large correlation values pose a significant reduction in the diversity gain in comparison to the zero correlation. It is also seen that the macroscopic diversity improves the performance of receivers significantly in cellular CDMA networks. When comparing diversity and multiuser receivers it is concluded that multiuser receivers are necessary to provide low BEPs. It is also highly beneficial to have at least two diversity antennas available, in particular, if there is no multipath diversity provided by the channel. The results also show that the reduction of intercell multiple-access interference yields a significant performance advantage in cellular networks. It is also demonstrated that the combination of spatial diversity and a multiuser receiver provides a significant receiver performance or system capacity gain in comparison to implementing only one of them     

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     

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.     

Universal receivers with side information from the demodulators: anexample for nonselective Rician fading channels

We consider binary orthogonal signaling over a nonselective Rician-fading channel with additive white Gaussian noise. The received signal over such a channel may have both a specular component and a scatter (Rayleigh-faded) component. If there is only a scatter component, the noncoherent receiver is optimal. If there is only a specular component, the optimal receiver is the coherent receiver. In general, the optimal receiver for a Rician channel depends on the strengths of the two signal components and the noise density, and the set of possible optimal receivers is infinite. We consider a system in which the noncoherent receiver and the coherent receiver are employed in a parallel configuration for a symbol-by-symbol demodulation of the received signal. Each sequence of transmitted symbols produces a sequence at the output of each of the parallel receivers. The task of identifying which of these received sequences is a more reliable reproduction of the transmitted sequence is the data verification problem. In this paper, we show that data verification can be accomplished by combining side information from the demodulators with a suitable error-control coding scheme. The resulting system is a universal receiver that provides good performance over the entire range of channel parameters. In particular, the universal receiver performs better than the traditional noncoherent receiver     

M-ary CPFSK-DPD with L-diversity maximum ratio combining in Ricianfast-fading channels

We derive a formula for the bit error probability (BEP) of M-ary continuous phase frequency shift keying with differential phase detection and maximum ratio combining diversity in Rician fast-fading channels. We assume that transmitter and receiver filters distort the signal and limit the noise. We compute the BEP as a function of energy-to-noise ratio per bit (E_b/N₀) and other system and channel parameters: Rician factor K=0, 6 dB, 10, ∞; number of diversity channels L=1, 2, 3; Doppler frequency shift f_D T=0, 0.01, 0.02; Butterworth filters in transmitter and receiver of order N_T=3 and N_R=4; optimal sampling time and filter bandwidth. In all cases the BEP is significantly reduced by diversity     

The performance of the maximum ratio combining method in correlated rician-fading channels for antenna-diversity signal combining

The performance of the maximum ratio combining method for the combining of antenna-diversity signals in correlated Rician-fading channels is rigorously studied. The distribution function of the normalized signal-to-noise ratio (SNR) is expanded in terms of a power series and calculated numerically. This power series can easily take into account the signal correlations and antenna gains and can be applied to any number of receiving antennas. An application of the method to dual-antenna diversity systems produces useful distribution curves for the normalized SNR which can be used to find the diversity gain. It is revealed that signal correlation in Rician-fading channels helps to increase the diversity gain rather than to decrease it as in the Rayleigh fading channels. It is also shown that with a relative strong direct signal component, the diversity gain can be much higher than that without a direct signal component.     

Robust linear MIMO receivers: a minimum error-rate approach

This paper looks at the linear reception of spatially multiplexed signals across MIMO channels. We address the problem of robustness in the presence of detrimental effects such as correlation and Ricean components. We consider the error-rate performance of MIMO linear filters as these can be used in purely linear receivers or as part of each stage in successive interference canceling (SIC) receivers. We know from multiuser detection theory that minimum error-rate (MER) linear receivers significantly outperform minimum mean-square error (MMSE) receivers when correlation is high; however, no direct method exist to design the MER receiver simply. We derive a scheme allowing a closed-form approximate solution to this problem. The solution is a good approximation to the true MER receiver upon fulfillment of a certain, easily checkable, channel-related condition. The algorithms are derived first for the two-input many-output case. A generalized scheme is provided for the case of arbitrary number of inputs and outputs. The performance gain compared with that MMSE is significant and evaluated for various correlated and Ricean channels and transmit power allocation strategies.     

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.     

Performance of ultra-wideband communications with suboptimal receivers in multipath channels

The performance of a single-user ultra-wideband (UWB) communication system employing binary block-coded pulse-position modulation (PPM) and suboptimal receivers in multipath channels is considered. The receivers examined include a RAKE receiver with various diversity combining schemes and an autocorrelation receiver, which is used in conjunction with transmitted reference (TR) signaling. A general framework is provided for deriving the performance of these receivers in multipath channels corrupted by additive white Gaussian noise (AWGN). By employing previous measurements of indoor UWB channels, we obtain numerical results for several cases which illustrate the tradeoff between performance and receiver complexity.     

Postdetection diversity receiver for DAPSK signals on the Rayleigh and Rician-fading channel

In this paper, the optimum decision boundaries for (N, M) differential amplitude phase-shift keying on the Rayleigh-fading channel are analyzed. A postdetection maximal ratio combining (MRC) and weighted maximal ratio combining (WMRC) diversity receivers are proposed. In the Rayleigh-fading channel, assuming a high signal-to-noise ratio and a small normalized Doppler frequency, the analytical optimum decision boundaries are obtained. In addition, it is shown that an outer optimum decision boundary is the inverse of the inner optimum decision boundary. In the proposed MRC receiver, the decision at each branch is made based on the minimum distance criterion. The performance of the MRC receiver is analyzed, in terms of the union bound for bit error probability. The proposed WMRC receiver assigns weighting factors to the decision variable at each branch, based on the optimum decision boundaries. The performance of the WMRC is investigated through computer simulation and compared with those of MRC and equal gain combining (EGC). From the results, the performances of MRC and WMRC are found to be better than those of the EGC receiver on both the Rayleigh- and Rician-fading channels. It is also found that the performance improvement of WMRC over MRC is more pronounced as the number of diversity branches increases