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     

Approximate average bit error probability for DQPSK over fading channels

The bit error probability (BEP) of DQPSK with Gray coding over an AWGN channel can be computed simply, although it is hard to integrate and derive the average BEP for fading channels. Presented are novel approximations of the average BEP of DQPSK with Gray coding over fading channels. Numerical results show that the novel formulations are quite accurate.     

A symbol-by-symbol channel estimation receiver for space-time block coded systems and its performance analysis on the nonselective rayleigh fading channel

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

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.     

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.     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.     

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 asynchronous DS-CDMA using a maximal ratio combiningdiversity over a Rician fading channel

The final closed-form expression for bit error probability (BEP) is presented for a DS-CDMA system using a maximal ratio combining (MRC) diversity over a Rician fading channel. The accuracy of the BEP estimate evaluated by this expression is verified by comparison with a semi-analytic simulation result. The effect that diversity order has on the BEP is also considered for typical multipath delay profiles with different Rician ratios     

Error probability analysis of multicarrier direct sequence code division multiple access system under imperfect channel estimation and jamming in a Rayleigh fading channel

The performance of a multicarrier direct sequence code division multiple access (MC-DS-CDMA) system in fading environment has been extensively analysed in the literatures. The analysis that is available in the literatures did not take into account the impact of jamming and channel estimation errors on the performance of the system. In this study, closed-form expressions of the average bit error probability (BEP) of the MC-DS-CDMA system with channel estimation errors in the presence of partial band, broadband and multitone jamming are derived in a Rayleigh fading channel. The analysis shows that the magnitude of the normalised correlation between the actual and the estimated complex fading channel gain, A, greatly affects the performance of the MC-DS-CDMA system. For large signal-to-noise ratio, the average BEP with A=1 and without multiple access interference (MAI) tends to zero. When A?1, the BEP of the system exhibits an error floor even without MAI. This error floor increases as the number of users increases. It is also shown that increasing the number of the system subcarriers enhances the system performance against jamming.     

Performance analysis of threshold digital relaying M2M cooperative networks

Exact average bit error probability (BEP) expressions for mobile-to-mobile cooperative networks employing threshold digital relaying over N-Nakagami fading channels are derived. The power allocation problem is formulated for performance optimization. The average BEP performance is evaluated via numerical simulation to verify the accuracy of the analysis with binary phase shift keying (BPSK) modulation. The simulation results showed that the fading coefficient, number of cascaded components, relative geometrical gain, and power-allocation parameter have a significant influence on the performance.     

Antijamming performance of space-frequency coding in partial-band noise

Space-frequency coded (SFC) orthogonal frequency-division multiple access (OFDMA) system is considered under partial band noise jamming (PBNJ). Analytical expressions for the bit error probability (BEP) are derived for OFDMA with and without SFC in a frequency-selective fading environment. It is shown that SFC increases the resistance of OFDMA against PBNJ and reduces the BEP considerably.     

Application of best relay selection approach to cooperative DF IDMA systems over Rayleigh/Weibull fading channels

This paper analyzes the performance of cooperative decode‐and‐forward (DF) interleave‐division multiple‐access (IDMA) networks with best relay selection over Rayleigh/Weibull fading environments. In the analysis, approximate outage probability (OP) and bit error probability (BEP) expressions are derived for the considered system. Further, a 2‐hop DF IDMA system is also designed to compare with cooperative one. We propose OP and BEP expression for 2‐hop DF IDMA systems. Numerical results are obtained by changing the number of relays and the value of fading parameter in the proposed expressions. Also, simulations are provided to corroborate the exactness of the derived approximate OP and BEP expressions.     

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.     

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.     

Coded OFDM with transmitter diversity for digital television terrestrial broadcasting

Space-frequency coded (SFC) and channel coded orthogonal frequency-division multiplexing (COFDM) is considered under narrow-band interference (NBI). Analytical expressions for the bit error probability (BEP) are derived for OFDM with SFC in a frequency-selective fading environment. It is shown that SFC increases the resistance of COFDM against the NBI and reduces the BEP considerably. Specific attention is paid to Digital Terrestrial Television Broadcasting (DTTB), and the associated coding gains are discussed.     

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     

On performance analysis and design criteria for trellis coded unitary space-time modulation

In this letter, we present formulas for the pairwise error-event probability (PEP) and bit error probability (BEP) of trellis-coded unitary space-time modulation (TC-USTM) operated in a piecewise constant Rayleigh fading channel. From these analyses we discovered design criteria for the TC-USTM encoder to achieve an optimal BEP performance. We conduct simulations and verify that our analyzes are accurate, especially at high signal-to-noise ratio (SNR).     

Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed