Symbol error probability of hop-by-hop beamforming in Nakagami-m fading

The symbol error probability (SEP) of amplify-and-forward (AF) multiple-input multiple-output (MIMO) cooperative networks where beamforming is adopted at both the source and destination is investigated. In particular, the tight lower bound for SEP of AF MIMO relay systems is presented with hop-by-hop beamforming over independent, but not necessarily identically distributed, Nakagami-m fading channels. Furthermore, assessing the high SNR, an asymptotic SEP expression is derived which reveals the array and diversity gain. Numerical results are shown to verify the analysis in some representative scenarios.     

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.     

Symbol error rate on fading self-interference channel in full-duplex

In-band full-duplex (FD) is being considered as a promising technology for the next generation wireless communication systems. In this paper, the performance of orthogonal frequency division multiplexing (OFDM) modulation system with different symbol duration and the code spreading system with different spreading sequence lengths under time-varying self-interference (SI) channel in FD mode is investigated respectively. Typically, the SI channel is estimated during the SI cancellation duration and used for SI suppression in the whole data transmission duration. First, the expressions of the residual SI power during the data transmission duration are derived under the classical, the uniform, and the two-way Doppler SI channels. Second, the signal-to-interference-and-noise-ratio after the SI mitigation is obtained. Third, the symbol error rates for the OFDM modulation and the code spreading systems are given. Simulation results show that OFDM symbol length should be selected longer when the symbol duration is significantly lower than the SI coherent time while the length of the coding spreading system should be chosen shorter.     

Symbol error probability of low-order orthogonal signalings in Rayleigh fading with general diversity combining

New analytical expressions for the symbol error probability of 3-ary and 4-ary orthogonal signaling and 6-ary and 8-ary biorthogonal signaling with general diversity combining in Rayleigh fading are derived.     

Outage analysis of ANC in the FDD two-way fading channel with channel estimation error

This paper considers a frequency-division duplex (FDD) two-way channel with channel estimation error, where channel gains are independent of each other. It derives the exact closed-form outage probability expressions in the FDD system with analog network coding (ANC) by use of probability theory. To provide more insights, an approximated version for the exact outage probability is also developed in the medium-to-high signal-to-noise ratio (SNR) region. The simulation results show that the derived exact outage probabilities match the results of Monte Carlo simulations in all SNR regions, while the approximated outage probabilities also approach the simulation results when the channel condition is good. It is interesting that ANC in the FDD two-way channel is proved to outperform that of in the time-division duplex (TDD) channel by the computer simulation.     

Ricean信道下Turbo码性能研究

针对Ricean衰落信道,在信道估计误差给定的情况下,提出一种新的Turbo码译码度量,推导出信道置信因子Lc新的表达形式。仿真结果表明,与采用传统近似译码度量相比,采用新的译码度量可以提高译码性能,信噪比改善0.1～0.6dB。而且在大主径衰落因子和小信道估计误差的情况下,译码性能优越,接近AWGN信道下Turbo码性能。     

Symbol error probability for guided scrambling over a recording channel

We derive expressions for the symbol error probabilities for a recording code concatenated with a Reed-Solomon (RS) code. The recording code is structured by a guided scrambling (GS) code for the direct current (DC) suppression in conjunction with a runlength-limited (RLL) code. As for the GS codes, convolutional GS and Galois field (GF) addition GS schemes are examined. As for the RLL codes, two types of RLL codes are investigated. One is a traditional RLL code where a bit length m of an RS symbol is an integer multiple of a bit length p of an RLL source symbol. The other is a new type of high-rate RLL code where p>m. We compute the RS symbol error rates when these RLL codes are combined with the two GS schemes.     

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.     

Optimal and mismatched detection of QAM signals in fast fading channels with imperfect channel estimation

In this paper, we derive an optimal detector for pilot-assisted transmission in Rayleigh fading channels with imperfect channel estimation. The classical approach is based on obtaining channel estimates and treating them as perfect in a minimum distance detector (this is called mismatched detector). The optimal detector jointly processes the received pilot and data symbols to recover the data. The optimal detector is specified for fast frequency-flat fading channels.We consider spline approximation of the channel gain time variations and compare the detection performance of different mismatched detectors with the optimal one. Further, we investigate the detection performance of an iterative receiver in a system transmitting turbo-encoded data, where a channel estimator provides either maximum likelihood estimates, minimum mean square error (MMSE) estimates or statistics for the optimal detector. Simulation results show that the optimal detector outperforms the mismatched detectors. However, the improvement in the detection performance compared to the mismatched detector with the MMSE channel estimates is modest.     

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.     

A simple approach to error probability with binary signaling over generalized fading channels with maximal ratio combining and noisy channel estimates

In this letter, we study the performance of binary signaling on generalized fading channels with maximal ratio combining (MRC) and imperfect channel estimates. With the assumption of the channel estimate being corrupted by a complex Gaussian random variable, an expression for the average probability of error is provided in the form of a simple single integral which involves the moment generating function of the normalized signal-to-noise ratio corresponding to the case of ideal MRC. Various examples are given to illustrate the usefulness of the derived expression under various fading conditions with different distributions, and with a possible correlation between the diversity branches.     

Diversity combining with imperfect channel estimation

The optimal diversity-combining technique is investigated for a multipath Rayleigh fading channel with imperfect channel state information at the receiver. Applying minimum mean-square error channel estimation, the channel state can be decomposed into the channel estimator spanned by channel observation, and the estimation error orthogonal to channel observation. The optimal combining weight is obtained from the first principle of maximum a posteriori detection, taking into consideration the imperfect channel estimation. The bit-error performance using the optimal diversity combining is derived and compared with that of the suboptimal application of maximal ratio combining. Numerical results are presented for specific channel models and estimation methods to illustrate the combined effect of channel estimation and detection on bit-error rate performance.     

Average error probability for quadriphase modulated DS-SSMA communications through Nakagami fading channel

An asynchronous direct sequence spread spectrum multiple access system using quadrature phase shift keying modulation through Nakagami'sm-distributed fading channel is considered for nondiversity reception. Approximation to the average error probability is evaluated in two steps. Using the Gauss quadrature rule, the moments of the multiple interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. The probability density function of the desired signal is Nakagami distributed. The average error probability which is the expected value of the conditional probability is evaluated by the trapezoidal integration method. This method provides a good approximation to the average error probability for a small to a fairly large number of users. Numerical results are presented for a set of Gold code of code length 127.     

Effect of channel estimation error on M-QAM BER performance inRayleigh fading

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider     

Impact of channel estimation error on adaptive modulation performance in flat fading

Presented here is an approach to analyzing the effect of imperfect channel estimation on adaptive modulation. The sensitivity of the main performance parameters to short-term and long-term estimation error sources is summarized in a set of new formulas that are either closed-form expressions or simple to compute numerically.     

Maximum likelihood estimation of the K factor in Ricean fading channels

Estimation of the K factor in a Ricean fading channel is studied. Unlike most previous estimators which employ exclusively samples of the fading envelope, new maximum likelihood estimators that use samples of both the fading envelope and the fading phase, or samples of the fading phase only, are derived and examined. Simulation results show that these estimators have good performances when operating in a Ricean fading channel, and in some cases outperform envelope-sample-based estimators.     

Error performance of selection combining and switched combining systems in Rayleigh fading channels with imperfect channel estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.     

Upper bound on the bit error probability of TCM overfrequency-selective Rayleigh fading channel

A new upper bound on the bit error probability using Chernoff's bound of trellis code modulation (TCM) is introduced. It can be applied to a frequency-selective Rayleigh fading channel. The bound indicates a new design criterion, which is the product of the intersymbol interference (ISI) distance     

Random coding error exponents for flat fading channels withrealistic channel estimation

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied