Envelope detection of orthogonal signals with phase noise

The authors analyze the performance of receivers that use envelope detection at an IF to detect optical signals with orthogonal modulation formats. Exact closed-form expressions for the error probability conditioned on the normalized envelope were obtained. The only information necessary for obtaining the unconditional error probability is a small set of tilted moments of the envelope. The authors then provide an approximation to this envelope which is not only accurate to the first order in phase noise strength, but also has the same range as the actual random envelope. This approximation was used to obtain the bit error performance of the three receiver models considered. A tight lower bound in closed form is given. The analysis is extended to the case of N-ary frequency-shift-keying (FSK) to provide very tight upper and lower bounds to the bit error probability     

A union bound on the error probability of binary codes over block-fading channels

Block-fading is a popular channel model that approximates the behavior of different wireless communication systems. In this paper, a union bound on the error probability of binary-coded systems over block-fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. The distribution of error bits over the fading blocks is computed. For a specific distribution pattern, the pairwise error probability is derived. Block-fading channels modeled as Rician and Nakagami distributions are studied. We consider coherent receivers with perfect and imperfect channel side information (SI) as well as noncoherent receivers employing square-law combining. Throughout the paper, imperfect SI is obtained using pilot-aided estimation. A lower bound on the performance of iterative receivers that perform joint decoding and channel estimation is obtained assuming the receiver knows the correct data and uses them as pilots. From this, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Furthermore, the optimal energy allocation for pilot signals is found for different channel memory lengths.     

A new approximation to the symbol error probability for codedmodulation schemes with maximum likelihood sequence detection

The power efficiency of coded modulation schemes in additive white Gaussian noise depends on the signal space distribution of their most common error events. Symbol error probability calculation allowing for the pairwise interaction of these error events is discussed. Two optimality criteria are considered for detectors. The first minimizes the probability of symbol error for each symbol decision. This is called the symbol-to-symbol detector. The second (which is superior) is the maximum likelihood sequence detector (MLSD). A lower bound for the symbol-to-symbol detector and an approximation to the MLSD symbol error probability are described. The theoretical performance difference between these two detectors is given. The results are more accurate than minimum squared Euclidean distance predictions, especially at low and intermediate signal-to-noise ratios. The MLSD symbol error probability approximation is obtained for considerably less cost than computer simulation and gives more insight into the signal space structure of the scheme being analyzed. Numerical results are presented for a continuous phase modulation (CPM) example     

Reliability approximation of a Markov queueing system with server breakdown and repair

This paper considers the reliability approximation of the queueing system PH/PH/1 with server breakdown and repair, where the life time of the server has the exponential distribution, and its repair time has the phase type distribution. First, we obtain the steady availability and steady failure frequency of the server. Then, we get the reliability function of the server, its probability density function and its Laplace-Stiltjes transform, which also gives an effective approximation of the reliability function of the server, where the error of the approximation can be easily bounded and is uniform in t. Finally, we discuss a special case and we can show that the reliability approximation has a wider application to various Markovian queueing systems with a repairable server.     

Packet throughput in slotted ALOHA DS/SSMA radio systems withrandom signature sequences

Packet throughput figures are obtained for direct sequence spread spectrum multiple access (DS/SSMA) slotted ALOHA radio systems where all users employ random signature sequences from bit-to-bit within all transmitted packets. These calculations use an improved Gaussian approximation technique which gives accurate bit error probabilities and also incorporates the effect of bit-to-bit error dependence within each packet in the multiaccess interference environment. Numerical results are given for packets which employ varying amounts of block error control, and a comparison is made with results obtained by other methods which ignore the effects of bit-to-bit error dependence within each packet in the multiaccess interference environment. Numerical results are given for packets which employ varying amount of block error control, and a comparison is made with results obtained by other methods which ignore the effects of bit-to-bit error and/or employ less-accurate Gaussian approximations to the probability of data bit error. Maximum throughput per unit bandwidth figures are calculated which compare favorably to similar figures for narrowband signaling techniques     

On the design of universal receivers for nonselective Rician-fadingchannels

The purpose of this paper is to illustrate the issues involved in designing the demodulator portion of a universal receiver for unknown or time-varying channels by means of a specific example. We consider the class of nonselective Rician fading channels with additive white Gaussian noise. The optimal receiver for a Rician channel depends on the parameters of the channel, and the collection of optimal receivers for channels in the class of interest forms an infinite receiver class. We find a finite number of receivers in this receiver class with the property that, regardless of the parameters of the channel in effect, at least one of these receivers provides a symbol error probability that is within a specified deviation from the optimal symbol error probability for the channel. These receivers are then used in parallel to perform a symbol-by-symbol demodulation of the received signal. The receiver output that gives the most reliable reproduction of the transmitted sequence is identified by means of a data verification mechanism. The resulting system is a universal receiver. Methods for data verification are developed in other papers. In this paper, we develop an algorithm for finding the required finite set of receivers. Typical issues, such as the tradeoff between the number of parallel receivers and the allowed deviation from optimality, are discussed     

Optical CDMA via temporal codes

The authors provide an analysis of the performance of optical orthogonal codes in an optical code division multiple access (CDMA) network by considering the probability distribution of the interference patterns. It is shown that the actual performance is close to a previous estimate. A less structured temporal code in which the code words are allowed to overlap at two pulse positions is also considered. The bit error probability for this class of codes is obtained for two cases: with and without optical hard-limiting at the receivers. It is shown that this code may increase the number of users in the network considerably without a significant loss in the performance     

Optimal detection of digital data over the nonselective Rayleighfading channel with diversity reception

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference     

Throughput performance of an unslotted direct-sequence SSMA packetradio network

A spread-spectrum multiple-access (SSMA) packet radio network model is presented. The topology is a fully connected network with identical message generation processes at all radios. Packet lengths are exponentially distributed, and packets are generated from a Poisson process, resulting in a Markovian model. This network model accounts for the availability of idle receivers in a finite population network. The model also allows the performance of the radio channel to be specified in detail. The channel considered is a BPSK (binary phase-shift keying) direct-sequence SSMA radio channel with hard-decision Viterbi decoding. An analysis of the Viterbi decoder leads to a bound on its performance which is valid for a system with a varying probability of error, as is the case for the network under consideration. The approximate analysis yields lower bounds on throughput and probability of successful packet transmission. Results are given which show the effects on throughput of the received energy-to-noise density ratio, the number of chips per symbol, and the number of radios, as well as the improvement due to error control coding     

Improving error probability of the prefiltered Viterbi equalizer

The article deals with the design of suboptimal data detectors for binary transmission over frequency selective channels. A detector consisting of a prefilter followed by a Viterbi processor with a number of states lower than that needed for maximum likelihood sequence estimation is considered. Often the parameters of the receiver are optimized according to the minimum mean square error criterion. Here a stochastic approximation algorithm that optimizes the parameters of the receiver according to a measure of the error probability is introduced. Simulation results show that the proposed design gives substantial benefits at moderate to high signal to noise ratio     

Optimal reception of digital data over the Gaussian channel with unknown delay and phase jitter

Asymptotically optimum (in the sense of minimum per-symbol error rate) receiver structures for data communication over the white Gaussian channel with unknown time delay and carrier phase jitter are developed. The receiver structures apply to the following suppressed-carrier modulation systems: double sideband (DSB), quadrature amplitude modulation (QAM) with an arbitrary constellation, vestigial sideband (VSB) and single sideband. The resulting minimum error probability receivers are asymptotically equivalent to maximum-likelihood digital {em sequence}-estimating receivers. The optimum structures implicitly derive joint maximum-likelihood estimates of the unknown parameters and of the sequence of data symbols. It is shown that the parameter estimates can be obtained from two data-directed stochastic approximation algorithms. Unlike traditional theoretical treatments of this communication situation, which have separated the highly important carrier phase and timing recovery problem from the detection problem, a unified theory is presented from which the complete ideal receiver structure can be deduced.     

Performance of Coherent PSK and DSPK Systems in an Impulsive and Gaussian Noise Environment

General probability of error expressions of coherent PSK and differentially coherent DPSK systems in the presence of both impulsive and Gaussian noise are derived. The presented impulsive and Gaussian channel disturbance is a first-order approximation to operational multichannel satellite and terrestrial microwave systems in which in addition to front-end Gaussian noise, out-of-band intermodulation noise is also present. Our analysis contains an extension of the method developed by Bello and Esposito [1], [2] to include the Gaussian as well as the impulsive noise environment. Computed results are presented for a one-pole bandpass filter and a lognormal impulse amplitude distribution. The numerical results show that a welldefined threshold region exists, above which the effect of the impulsive noise on the system performance is predominant. A comparative study of system performance having integrate-sample-and-dump receivers with sample-only receivers is presented.     

A Trivariate Nakagami-m Distribution with Arbitrary Covariance Matrix and Applications to Generalized-Selection Diversity Receivers

This paper deals with a trivariate Nakagami-m distribution derived from the diagonal elements of a Wishart matrix. For this distribution, infinite series representations for its probability density and cumulative distribution functions are derived having an arbitrary covariance matrix and integer-order fading parameters. Moreover, upper bounds on the error resulting from truncating the infinite series are obtained. Based on the derived formulas, the performance of triple-branch generalized selection combining (GSC) receivers is analyzed. For this type of receivers, the outage and the average bit error probability for a variety of modulation schemes are analytically obtained. The performance of GSC receivers is compared to that of conventional selection and maximal-ratio diversity schemes. In order to check the accuracy and convergence of the derived formulas, various performance evaluation results are presented and compared to equivalent simulation ones.     

非时槽FH—CDMA系统分组错误概率分析＊

对采用RS-(n,k)编码的非时槽FH-CDMA系统,分组区间内干扰用户数目是变化的.本文提出了一种简易模型,并找到了当干扰数目N>1时分组区间内的干扰分布与N=1时的内在联系,首次使用计算干扰状态概率平均的方法求得分组错误概率。通过比较,指出目前采用的上、下界及近似法效果欠佳。     

Efficient estimation of call blocking probabilities in cellularmobile telephony networks with customer retrials

A novel approximate technique is proposed for the estimation of call blocking probabilities in cellular mobile telephony networks where call blocking triggers customer retrials. The approximate analysis technique is based on Markovian models with state spaces whose cardinalities are proportional to the maximum number of calls that can be simultaneously in progress within cells. The accuracy of the approximate technique is assessed by comparison against results of detailed simulation experiments, results of a previously proposed Markovian analysis approach, and upper and lower bounds to the call blocking probability. Numerical results show that the proposed approximate technique is very accurate, in spite of the remarkably small state spaces of the Markovian models     

An analysis of nonlinear direct-sequence correlators

An analysis of the performance of nonlinear correlation reception of direct-sequence signals in single- and multiuser channels is presented. The communications channel is modeled as containing non-Gaussian background noise and, in some cases, multiple-access interference as well. The error-probability behavior is studied asymptotically as the lengths of the spreading codes increase without bound, and conditions on the spreading sequences are obtained that assure asymptotic achievement of single-user performance in a multiuser system. A long-spreading sequence approximation to the average error probability is also derived, and this result is applied to the analysis of smooth-limiting correlation receivers in impulsive channels. Simulation results are also provided to verify the analysis. Average bit-error probabilities are computed by Monte Carlo simulations for linear, hard-limiting, and smooth-limiting correlation receivers in both single- and two-user impulsive channels. The simulation results are compared to the error rates by asymptotic approximations for the smooth limiter and also to those from previous studies on linear and hard-limiting correlators     

Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multiple-antenna multiple-input multiple-output (MIMO) communications. In this paper, we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-signal-to noise-ratio (SNR) regime in terms of the diversity-multiplexing tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas.As far as the DMT is concerned, we report a negative result: we show that both linear zero-forcing (ZF) and linear minimum mean- square error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and deAcircnot coding is performed across the antennas. We also provide an apAcircnot proximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of an MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear reAcircnot ceiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.     

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.     

Blind Source Separation: The Location of Local Minima in the Case of Finitely Many Samples

Cost functions used in blind source separation are often defined in terms of expectations, i.e., an infinite number of samples is assumed. An open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case. To answer this question, we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions. In particular, we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix. The method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function. This shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function. We also answer a long-standing problem of the mean-squared error (MSE) behavior of the (finite sample) least squares constant modulus algorithm (LS-CMA), namely whether there exist LS-CMA receivers with good MSE performance. We demonstrate how the proposed techniques can be used to determine the required number of samples for LS-CMA to exceed a specified performance. The paper concludes with simulations that validate the results.      

Bit Error Rate of TH-BPSK UWB Receivers in Multiuser Interference

It is well known that the Gaussian distribution is not an accurate model for approximating the probability density function (PDF) of the multiple access interference (MAI) in time-hopping UWB (TH-UWB) systems. An exact theoretical model which explains the key features of the PDF of the MAI in TH-UWB systems is discussed. These features, which can be precisely anticipated by the proposed model include impulses, singularities, and the tail behaviour in the distribution of the MAI. The model reveals in quantitative terms why a Gaussian approximation for the MAI in TH-UWB systems is highly imprecise even in an environment with a large number of independent interferers. Based on the model obtained for the PDF of the MAI and exploiting the maximum a posteriori (MAP) receiver design rule, the optimal attainable BER performance of binary TH-UWB receivers in additive white Gaussian noise channels is numerically determined. The performances of some recently proposed UWB receivers are benchmarked against the optimal performance showing that some of them achieve near-optimal performance.