MLD and mse algorithms for adaptive detection of digital signals in the presence of interchannel interference

Adaptive mean-square error (mse) and maximum-likelihood detection (MLD) algorithms for a dual-channel digital communication system in the presence of interchannel interference and white Gaussian noise are presented. The mse algorithm forms estimates of the transmitted symbols from a linear combination of received symbols using weights that minimize the mse between transmitted and estimated symbols. The nonlinear MLD algorithm minimizes the probability of symbol error by maximizing the probability of the received signal samples on the two channels over ail possible transmitted symbol pairs. The probability of error is derived for the two algorithms when quadrature phase-shift keying (QPSK) is used as a modulation technique, and is compared with that of a dual-channel QPSK system having no compensation for the crosstalk.     

Upper bounds to the error probability of decision feedbackequalization

The exact computation of the symbol error probability of systems using decision feedback equalization is difficult due to the propagation of errors. New upper bounds to the error probability of decision feedback equalization, which take error propagation into account, are developed. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are valid for any noise process that has a symmetric and unimodal probability density function. In some cases, the new bounds are significantly tighter than a well-known upper bound of D.L. Duttweiler et al. (1974)     

Error performance of differentially coherent detection of binary DPSK data transmission on the hard-limiting satellite channel

The error performance of differentially coherent detection of a binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective is to show the extent of error rate degradation of a DPSK system when a power imbalance exists between the two symbol pulses that are used in a bit decision interval. Consideration is also given to the DPSK error rate performance for the special case of {em uncorrelated} uplink and {em correlated} downlink noises at the sampling instants in adjacent time slots. Error probabilities are given as functions of uplink signal-to-noise ratio (SNR) and downlink SNR with different levels of SNR imbalance and different downlink SNR and uplink SNR as parameters, respectively. Our numerical results show that 1) as long as the symbols are equiprobable, the error probability is not dependent upon the downlink noise correlation, regardless of whether there is a power imbalance; 2) error performance is definitely affected by the power imbalance for all cases of symbol distributions; and 3) the error probability does depend upon downlink noise correlation for all levels of power imbalance if the symbol probabilities are not equal.     

On the Binary DPSK Communication Systems in Correlated Gaussian Noise

Using the recently developed probability density function we obtain "directly" the error rate expressions for the binary differential phase-shift keyed (DPSK) systems when the noise values at the sampling instants in adjacent time slots are statistically dependent. Two cases are considered: One corresponding to equal SNR at each of the two sampling instants, and the other to unequal SNR's. The consideration of the former case, together with the assumption of unequal a priori symbol probabilities P0and P1results in an error rate expressionP_{E} =1/2[1 + (P_{0} - P_{1})rho] exp (-h^{2})where ρ is the noise correlation coefficient, and h²is the SNR. This expression shows clearly why PEis independent of noise correlation when the source symbols are equi-probable provided intersymbol interference is assumed absent. We then obtain the error probability expression in terms of unequal SNR's (at the two sampling instants) and the correlation coefficient ρ. Since intersymbol interference in a binary DPSK system gives rise to unequal SNR's, this expression provides a useful formula for estimating the system performance under such circumstances.     

An upper bound on the error probability in decision-feedback equalization

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the firstJfeedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of2^Jrelative to the error probability in the absence of decision errors at highS/Nratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a highS/Nratio and a fast roll-off of the feedback tap gains.     

Performance of asynchronous slow frequency-hop multiple-accessnetworks with MFSK modulation

The performance of asynchronous slow frequency-hop spread-spectrum multiple-access networks where each user transmits L, M-ary symbols per hop using M-ary frequency-shift keying (FSK) modulation with noncoherent demodulation is investigated. Expressions for the decision variables are derived for a given multiple FSK (MFSK) symbol within a hop hit by K' interfering users under additive white Gaussian noise and Rayleigh fading channel models. For the special case when M=2, an accurate analytic approximation for the average error probability is derived as a function of L and K' and semianalytic Monte Carlo simulations are performed to estimate the probability of error for M larger than 2. The results are used to investigate the dependence of the average symbol error probability on L and M. Finally, the effect of enforcing phase transition between the MFSK symbols within a hop is investigated     

Numerically efficient Fourier-based technique for calculating errorprobabilities with intersymbol interference

We propose a numerically efficient technique for calculating the probability of symbol error for arbitrary coherent modulation schemes in the presence of intersymbol interference (ISI) and additive noise. The probability of error is formulated in terms of an inverse Fourier transform of the windowed characteristic function of the random variable representing the interfering symbols and the noise process. The integral is evaluated numerically using the sampling theorem     

Intersymbol Interference Performance of Systems with Correlated Digital Signals

For a digital system with correlated digital symbols, we derive upper and lower bounds on the probability of error when the system is subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite number of intersymbol interference terms and some parameters associated with the remainder terms. We also show that the difference between the upper and lower bounds can be made arbitrarily small and that the error probability can be computed to any desired degree of accuracy. We give some examples to illustrate the method.     

Decision feedback differential phase detection of M-ary DPSKsignals

Multiple-symbol differential phase detection (DFDPD) based on decision feedback of past detected symbols is presented for M-ary DPSK modulation. Adopting a Gaussian phase noise assumption, we obtain the a posteriori joint probability density function (PDF) of the outputs of L DPD defectors of orders of 1 to L symbols and derive a DF-DPD algorithm which is based on feeding back the L-1 past detected symbols and minimizing the sum of phase errors of L DPD detectors. A practical implementation of the DF-DPD receiver is presented that uses a single conventional (one-symbol) DPD detector. The bit error rate (BER) performance in an additive white Gaussian noise (AWGN) channel is analyzed taking into account decision error propagation. Performance improvements are evaluated by computer simulations in AWGN and Rayleigh fading channels     

Considerations on Error Probability in Correlated-Symbol Systems

An approach to evaluate the error probability in conventional PAM digital data transmission systems with correlated symbols in the presence of intersymbol interference and additive noise is formulated in general and it is applied to the Gram-Charlier series expansion method. It is shown that the technique of conditioning few symbols before and/or after the symbol to be detected increases substantially the range of signal-to-noise ratios with an acceptable increase of numerical work. This technique also improves existing bounds on error probability, as, e.g, Glave's bound.     

Binary DPSK transmission over terrestrial and satellite links (Corresp.)

It has been observed previously that downlink noise correlation has no effect on the average error probability of a differentially phase shift keyed (DPSK) satellite system when the symbols are equiprobable. We show thai this observation holds for a satellite system exhibiting amplitude-modulation-to-amplitude-modulation (AM-AM) conversion effects and amplitude-modulation-to-phase-modulation (AM-PM) conversion effects. It is also shown thai noise correlation has no effect even when a constant phase error is caused by the delay line of the DPSK receiver in terrestrial and satellite links.     

An Error Probability Formula for Linear Coded Digital Signals

A formula for the probability of error in a digital system subjected to noise and intersymbol interference is derived. The transmitted symbols are encoded by forming the weighted sum of theMmost recent, independent, multilevel source digits. This linear coding operation in cludes, as a special case, the family of partial response codes.     

Effects of correlated fading on frequency-hop communications with Reed-Solomon coding

The transmission of frequency-hop spread-spectrum signals over a frequency-selective fading channel results in correlation between the amplitudes of signals that occupy different frequency slots. This correlation produces dependent errors among symbols transmitted at different frequencies. For a system that employs block coding, this dependence results in dependent errors, even if the code symbols are interleaved over the dwell intervals. Using an appropriate mathematical model for wideband frequency-selective fading channel, we present analytical results on the code-word error probability for a simple coding scheme and simulation results for more complex codes.     

The evaluation of error probabilities for low-frequency attenuationchannels

Channels having large low-frequency attenuation are of much interest. Low-frequency removal may result from transformer or capacitor coupling. Examples include ISDN loop transmission (transformer coupling) and wireless systems (capacitor coupled amplifiers). Despite this interest, few works have explicitly examined the problem of calculating the average probability of error for these systems, in which the intersymbol interference from a single pulse may extend over hundreds or even thousands of symbols. Efficient series techniques for evaluation of the error probabilities of multilevel pulse amplitude modulations and multilevel duobinary signaling are derived. The method is applicable to any additive noise possessing an even probability density function. The Gaussian noise case is examined in detail. Examples of Nyquist I signaling and suboptimal detection of nonreturn-to-zero pulse codes are considered. The results are compared to previous published results. It is seen that an often cited upper bound, though within a factor of about ten in error probability for small to medium intersymbol interference conditions, may significantly overestimate the system degradation due to low-frequency attenuation when the intersymbol interference is large     

Error probabilities for QAM systems on partially coherent channelswith intersymbol interference and crosstalk

We describe an efficient procedure to calculate the probability of error P_e for a quadrature amplitude modulation (QAM) communications system operating over a channel that introduces distortion, interference, and noise. The method is an extension of the saddlepoint integration technique introduced by Helstrom (1986) to efficiently evaluate P_e for one-dimensional pulse-amplitude modulation (PAM) systems with intersymbol interference (ISI) and crosstalk. We consider the effects of noise, random carrier phase offset, ISI, and crosstalk between the I and Q channels. The error probability is written as a double Laplace inversion integral and can be easily applied to any rectangular constellation. This integral is calculated by extending the saddlepoint integration technique to two complex dimensions. Results are presented for QAM systems with 16, 64, and 256 symbols. The technique can be directly extended to environments with cochannel interference consisting of other QAM signals     

On the probability of error for decision-feedback equalizers (Corresp.)

Methods for calculating or bounding the probability of error in a decision-feedback equalizer when the noise component at the input of the quantizer is a sequence of independent and identically distributed random variables are briefly reviewed. A new upper bound on the probability of error of a decision-feedback equalizer is then derived. Unlike the methods reviewed, this bound is valid even when the noise component at the input of the quantizer is a serially dependent stationary stochastic process.     

Joint parameter estimation and symbol detection for linear ornonlinear unknown channels

We present an iterative method for joint channel parameter estimation and symbol selection via the Baum-Welch algorithm, or equivalently the Expectation-Maximization (EM) algorithm. Channel parameters, including noise variance, are estimated using a maximum likelihood criterion. The Markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward-backward algorithm. The calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability. The proposed receiver can be used for both linear and nonlinear channels. It improves the system throughput by making saving in the transmission of known symbols, usually employed for channel identification. Simulation results which show fast convergence are presented     

Performance evaluation of HDAF relaying systems for pilot and data symbol burst transmission over quasi‐static Rayleigh fading channels

This paper analyzes averaged symbol error probabilities of burst transmission consisting of pilot and data symbols for hybrid adaptive decode‐or‐amplify‐forward (HDAF) relaying systems. Under the assumption of quasi‐static Rayleigh fading channels with independent and non‐identically distribution, we consider a channel estimation scheme based on pilot symbols and show how channel estimation error affects received signal‐to‐noise ratio (SNR) and symbol error probability (SEP). Firstly, all the possible detection error‐events are presented for all the relay nodes, and their probabilities are derived as forms related with data symbol burst transmission. For the given error event, we analyze the conditional SEP as an exact form and then, the averaged SEP (ASEP) is approximately derived as a closed‐form. The simulation results verify that our derived ASEP expression is accurate over all the regions of SNR. Utilizing the proposed expressions, we can evaluate ASEP performance of HDAF relay systems easily and fast. Copyright © 2015 John Wiley & Sons, Ltd.     

Tail Extrapolation in MLSE Receivers Using Nonparametric Channel Model Estimation

This paper presents a method for determining the probability of rare events, in particular for probability density function (pdf) and bit error rate (BER) estimation. The derivation of the method is based on the presumption that the pdf is a member of a family of distributions very often named as the generalized exponential (GE) class of distributions. Based on high reliability estimations obtained in short simulation/measurement times, the low probably events are estimated accurately by extrapolation. The suggested method can be applied to some distributions that are different from GE distributions, such as noncentral chi-square distributions, to extrapolate to low probability events, with some extrapolation error. It can also be applied to BER estimation. The method is in particular helpful for estimating channels suffering from both severe signal distortion causing undesired intersymbol interference (ISI) of several symbols, and from severe noise. Such conditions prevail, for example, in metro and long haul high-speed optical fiber communication systems. So the method may be implemented in particular in maximum-likelihood sequence estimation (MLSE) optical receivers using nonparametric channel model estimation. A special use of the extrapolation method is explained for practical systems using trellis branch metrics derived from the estimated pdf to decode the transmitted sequence of symbols.     

A bit error probability analysis of a digital PLL based demodulatorof differentially encoded BPSK and QPSK modulation

Presents a bit error probability analysis of a digital phase-locked loop based demodulator, of differentially encoded BPSK and QPSK modulations. Differential decoding is a method of resolving a phase ambiguity, typical of fully modulated signals, that uses two consecutive demodulated symbols to estimate the information symbols. The effects of a noisy phase reference on demodulator performance are well documented for uncoded modulations (single symbol demodulation). The paper investigates performance for phase reference time variations between the two symbols. The time varying reference investigated is produced by a digital phase-locked loop. The noisy phase reference has negligible additional effect on the bit error probability for differentially encoded BPSK and QPSK