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23
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy ..."
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Cited by 149 (51 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Performance Analysis of Existing and New Methods for Data Hiding with KnownHost Information in Additive Channels
 PROCESSING, SPECIAL ISSUE ON SIGNAL PROCESSING FOR DATA HIDING IN DIGITAL MEDIA AND SECURE CONTENT DELIVERY
, 2002
"... A considerable amount of attention has been lately payed to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper suppl ..."
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Cited by 43 (14 self)
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A considerable amount of attention has been lately payed to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper supplies a fair comparison between significant representatives of both this family of methods and the former spreadspectrum approaches that make use of nearoptimal ML decoding; the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions. Accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of Monte Carlo simulations. For Dithered Modulation (DM) a novel technique that allows to obtain tighter bounds to the probability of error is presented. Within the new framework, the strong points and weaknesses of both methods are distinctly displayed. This comparative study allows us to propose a new technique named "Quantized Projection" (QP), which by adequately combining elements of those previous approaches, produces gains in performance.
Computation Of ShotNoise Probability Distributions And Densities
 SIAM J. Comput
, 1996
"... . The computation of the cumulative distribution (cdf), the complementary cdf (ccdf), and the density of certain shotnoise random variables is discussed. After subtracting off a few terms that can be computed in closed form, what remains can be approximated by a general method for approximating samp ..."
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Cited by 11 (0 self)
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. The computation of the cumulative distribution (cdf), the complementary cdf (ccdf), and the density of certain shotnoise random variables is discussed. After subtracting off a few terms that can be computed in closed form, what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a Fourier series whose coefficients are modulated samples of their characteristic function. To approximate the density, a spline is fit to the cdf samples and then differentiated. When the density has corners, it is important that the spline have coincident knots at these locations. For shotnoise densities, these locations are easily identified. Key words. filtered point process, Poisson process AMS subject classification. 62E17 1. Introduction. The computation of the cumulative distribution (cdf) F (y), the complementary cdf (ccdf) F c (y) := 1 \Gamma F (y), and the probability density function f(y) of a shotnoise random variable Y := X A g(T ...
Ultrawideband small scale channel modeling and its application to receiver design
, 2003
"... and its Application to Receiver Design ..."
Nothing But a Kiss: A Novel and Accurate Approach to Assessing The Performance of Multidimensional DistortionCompensated Dither Modulation
 in Proc. of the 5th International Workshop on Information Hiding, Lecture Notes in Computer Science, (Noorwijkerhout, The
, 2002
"... A considerable amount of attention has been lately paid to a number of data hiding methods based on quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. In this paper we analyze a multidimensional extension of the implemen ..."
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Cited by 6 (4 self)
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A considerable amount of attention has been lately paid to a number of data hiding methods based on quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. In this paper we analyze a multidimensional extension of the implementation of Costa's result known as DCQIM. The presented analysis is based on measuring the probabilities of decoding error in the presence of two important kinds of additive channel distortions. DCQIM is able to achieve a probability of decoding error of less than 1e02 for 0 dB of watermark to noise ratio and only 20 samples per hidden bit. Empirical results supporting our analysis are given both for synthetic data and real images.
An Exact Error Probability Analysis of OFDM Systems with Frequency Offest
"... Abstract — In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for OFDM systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in frequency flat Rayleigh fading channel with BPSK and 4PSK modu ..."
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Cited by 4 (2 self)
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Abstract — In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for OFDM systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in frequency flat Rayleigh fading channel with BPSK and 4PSK modulation schemes. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions. I.
Exact outage probability for equal gain combining with cochannel interference in Rayleigh fading
 IEEE Trans. Wireless Commun
, 2003
"... Abstract—Equal gain combining (EGC) diversity has performance close to that of maximal ratio combining but at lower implementation complexity. We present a new outage performance analysis for EGC in mobile cellular radio systems that are limited by cochannel interference and undergo Rayleigh fading. ..."
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Cited by 3 (1 self)
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Abstract—Equal gain combining (EGC) diversity has performance close to that of maximal ratio combining but at lower implementation complexity. We present a new outage performance analysis for EGC in mobile cellular radio systems that are limited by cochannel interference and undergo Rayleigh fading. We utilize a new model where interfering signals add in amplitude and phase across antenna array elements. In addition, the interfering signals may each have a different power. In comparing our analysis to an existing method, we find that: 1) as much as 1.5 dB difference in signaltointerference ratio may exist at the same probability of outage and 2) the existing method can lead to overly optimistic outage performance prediction in certain situations. Index Terms—Cochannel interference (CCI), diversity methods, Rayleigh channels. I.
MultipleInput MultipleOutput Wireless Communication Systems with Cochannel Interference
, 2003
"... To meet the requirement of very high data rates for wireless Internet and multimedia services, multiple transmitting and multiple receiving antennas have been proposed for fourth generation wireless systems. In cellular systems, performance is limited by fading and cochannel interference from other ..."
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Cited by 3 (2 self)
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To meet the requirement of very high data rates for wireless Internet and multimedia services, multiple transmitting and multiple receiving antennas have been proposed for fourth generation wireless systems. In cellular systems, performance is limited by fading and cochannel interference from other users. Most of the current studies on multipleinput multipleoutput (MIMO) systems assume that the cochannel interference is both spatially and temporally white. In this thesis, we focus on MIMO systems under both spatially and temporally colored interference. In MIMO systems, diversity gain is effectively achieved by the multiple receiving antennas. Outage performances of several receive diversity schemes are analytically compared for an interferencelimited environment in a Rayleigh fading channel. We investigate three diversity schemes: a practical variation of maximalratio combining, equalgain combining (EGC) and selection combining (SC). An exact outage probability expression is derived for EGC by accurately calculating the interference power at the output of the combiner. It is found that the relative performance between EGC and SC depends on the
Throughput guarantees for wireless networks with opportunistic scheduling.” , http://folk.ntnu.no/vegardh/RateGuarver12.pdf. Accepted for presentation at
 IEEE Global Communications Conf. (GLOBECOM’06
, 2006
"... In this letter we develop an expression for the approximate throughput guarantee violation probability (TGVP) for users in timeslotted networks for any scheduling algorithm with a given mean and variance of the bitrate in a timeslot, and a given distribution for the number of timeslots allocate ..."
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Cited by 3 (0 self)
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In this letter we develop an expression for the approximate throughput guarantee violation probability (TGVP) for users in timeslotted networks for any scheduling algorithm with a given mean and variance of the bitrate in a timeslot, and a given distribution for the number of timeslots allocated within a timewindow. Based on this general result, we evaluate closedform expressions for the TGVPs for four wellknown scheduling algorithms. Through simulations we also show that our TGVP approximation is tight for a realistic network with moving users with correlated channels and realistic throughput guarantees. Index Terms Opportunistic scheduling, qualityofservice, wireless communications.