Radio-frequency interference (RFI) is a persistent threat to Earth-observing microwave radiometers. A number of test statistics are used for radiometric RFI detection. This paper presents a new RFI detection method that uses the information theoretic quantity known as negentropy. In particular, we study six negentropy-based test statistics and compare their performance against kurtosis, Jarque–Bera, Anderson–Darling, and Shapiro–Wilk normality tests for specific RFI signal models. The Neyman–Pearson decision rule is used to develop receiver operating characteristic curves for each test statistic. We show that although negentropy can be used to detect RFI, it does not outperform kurtosis, except for the kurtosis blind-spot case.

We present an importance sampling (IS) technique for evaluating the word-error rate (WER) and bit-error rate (BER) performance of binary linear block codes under hard-decision decoding. This IS technique takes advantage of the invariance of the decoding outcome to the transition probability of the binary symmetric channel given a received error pattern, and is equivalent to the method of stratification for variance reduction. A thorough analysis of the accuracy of the proposed signal-to-noise-ratio- invariant IS (IIS) estimator based on computing its relative bias and standard deviation is provided. Under certain conditions, which may be achieved fairly easily for certain code and decoder combinations, we demonstrate that it is possible to use the proposed IIS technique to accurately evaluate the WER and BER to arbitrarily low values. Further, in all cases, the probability estimates obtained via IIS always serve as a lower bound on the true probability values.

We study the word-error-rate (WER) performance and the WER-minimizing decision thresholds$\pm t^{\ast}$for the class of row-column-diagonal (RCD) array codes and their generalizations on the binary symmetric channel with erasures (BSC/E) where decoding is via an extended bounded-distance decoder (e-BDD). This model applies to very-high-data-rate systems where soft-decision iterative decoding is impractical. We demonstrate that substantial WER performance gain can be obtained, especially at higher channel signal-to-noise ratio (CSNR) ($\hbox{CSNR}\triangleq 10\log_{10} (1/2\sigma^{2})$) values, by employing two optimal thresholds$(\pm t^{\ast})$chosen to minimize WER. We study the WER improvement and signal-to-noise ratio (SNR) performance gain as a function of code length$(n)$for fixed minimum distance$(d_{\min})$, and as a function of$(d_{\min})$for fixed$(n)$. A distinct difference in the behavior of WER versus the threshold$t$, and the optimal threshold$t^{\ast}$versus SNR, is observed between codes with odd and even$d_{\min}$, with the even$d_{\min}$codes exhibiting larger performance improvements when employing a BSC/E instead of a BSC.

In this paper, we develop expressions for the transfer delay of an M-stage hybrid automatic repeat-request (HARQ) protocol. These generally applicable expressions make no assumptions about the quality of the feedback channel and explicitly account for both feedback errors and their associated delays. Both infinitely repeating and terminated HARQ protocols are considered. Through a series of examples, we demonstrate that these expressions admit earlier results as special cases or applications, while providing additional insight on the contributions of various error and delay terms.

Frames are the most widely used tool for signal representation in different domains. In this correspondence, we introduce the concept of product-function frames for l/sup 2/(/spl Zopf/). The frame elements of these frames are represented as products of two or more sequences. This forms a generalized structure for many currently existing transforms. We define necessary and sufficient conditions on the frame elements so that they form a frame for l/sup 2/(/spl Zopf/). We obtain windowed transforms as a special case and derive the biorthogonal-like condition. Finally, we introduce a new family of transforms for finite-dimensional subspaces of l/sup 2/(/spl Zopf/), which we call the "scalemodulation transforms". The frame elements of these transforms can be obtained via scaling and modulating a "mother" window. This transform, thus, complements the shift-modulation structure of the discrete-time Gabor transform and the shift-scale structure of the discrete wavelet transform.

Functional neuroimaging is a powerful biological tool to investigate the regions of the brain responsible for performing different mental functions. The traditional interpretation method is statistical analysis in the spatial domain, which is computationally expensive. We present a hybrid wavelet/neural network scheme to analyze functional brain images. Features are extracted in the wavelet domain and then fed to a neural network for detection. The proposed method is examined by exploring the differences between positron emission tomography (PET) images acquired under different experimental conditions during a tone recognition task. The performance shows its potential in the fast developing functional neuroimaging area.

A postphotodetection adaptive phase alignment system using an aperture array of photodetectors is presented to reduce the signal loss in an optical (free-space) heterodyne receiver resulting from wavefront misalignment (tilt) on a satellite platform. This paper compares two kinds of rectangular aperture configurations-full aperture and array aperture configurations-via a software simulation study of the error performance after DPSK demodulation for different angles of arrival (tilt) of the received signal wavefront. For the array configuration, an adaptive phase alignment system is used that phase aligns the signals from the different photodetector array elements, and constructively adds them to yield a higher signal magnitude as compared to that of signal of a single-element photodetector of the same total area. The optimum aperture length for a given wavefront misalignment is derived, and is verified via simulation.

In a recent letter, a complementary condition to the condition in Wexler and Raz (1990) for the discrete Gabor expansion (DGE) was derived and, consequently, the resulting DGE may admit rational oversampling rates. In the present letter, we first modify the condition in Li and Qian (1995), and then demonstrate a new relaxed complementary condition for the DGE in which the range of the time and frequency parameters is increased. Moreover, we will show that the new condition with the increased parameter range is equivalent to the condition in Wexler and Raz but with different parameters.

This letter presents a new frame condition for the Gabor expansion that avoids the estimation of frame bounds and the Zak transform and a fast new algorithm to compute the dual frame based on a biorthogonal condition. One of the main contributions of this work is that we can obtain a pair of analysis and synthesis functions that generate a frame and dual-frame pair without computation of frame bounds.

The burst error statistics of a soft-decision Viterbi decoder were simulated and obtained for the case when the transmitted signal is: (1) encoded with constraint length=3, rate 1/2 convolutional codes and rate 2/3, 3/4, 4/5, and 7/8 punctured convolutional codes; (2) modulated via noncoherent BFSK for the AWGN channel; and (3) subjected to slow and non-selective scintillation/fading modeled by the Nakagami-m and Rician pdfs. These statistics are evaluated to determine how Viterbi decoder burst error statistics vary with the channel and code parameters, and to compare the statistics of the Nakagami-m and Rician fading models (Morris and Chang 1990). The results have important implications for the design of interleaved or noninterleaved concatenated coding schemes, and to the development of burst error models and simulators for scintillating and fading channel environments. This extends the earlier burst-error-statistics results of Deutsch and Miller (1981), and Miller, Deutsch, and Butman who looked at the nonfading case for BPSK modulation and coherent demodulation.>

The random-threshold decision rule, which is an equalizer-rule in terms of probability-of-error for symmetrically distributed bounded-amplitude nonstationary noise, is compared with the sign detector and linear detector for bounded-amplitude noise via asymptotic relative efficiency (ARE). Explicit ARE expressions are derived for these detectors. The result shows that the random-threshold decision rule can be as effective as, or better than the sign detector and as effective as the linear detector, in terms of ARE, for some bounded-amplitude noise cases.>

The Wigner-Ville (WV) distribution has found favor in the processing of unknown or partially known signals because of its ability to portray the time-frequency distribution of signal energy. Signal independent methods for crossterm suppression of multicomponent signals, based on the crossterm-deleted representation, are discussed. In coupling the methods of Gabor and Wigner-Ville, effective crossterm suppression is possible through exploitation of partial knowledge of the signals to be encountered.>

The author presents and analyzes burst error statistics of a soft-decision Viterbi decoder when the transmitted signal is encoded with the 313 (3, 1/2) or 31123 (5, 1/2) convolutional codes, modulated via coherent binary phase-shift keying (BPSK) for the additive white Gaussian noise (AWGN) channel, and subjected to slow and nonselective scintillation/fading modeled by the Nakagami-m distribution. These statistics were generated by Monte-Carlo simulations, and presented in terms of burst error length average and quantile (90 and 99%) statistics versus SNR (E/sub b//N/sub 0/) parameterized by the fading intensity parameter m. The results indicate how Viterbi decoder burst error statistics vary with the fading/scintillation intensity m for Nakagami-m channels, and, consequently, provide information important to the design of interleaved or noninterleaved concatenated coding schemes for such channel environments.>

A pseudo-simulated annealing (PSA) technique for signal synthesis from smoothed versions of the Wigner distribution is proposed. The PSA adopts a deterministic local search strategy to complement the global search of traditional simulated annealing and accomplish a faster convergence. The squared-error in the joint time-frequency domain is minimized with relation to the real sample sequence directly and, thereby, reduces the phase ambiguity to either 0 or pi . Simulation results are provided to indicate the effectiveness of this approach.>

Expressions are obtained for specifying the optimal error probability (minimum P/sub e/) thresholds lambda /sub 01/ and lambda /sub 02/ for the traditional and modified sign detectors, respectively. These thresholds are shown to depend on the parameters p, P/sub 1/, and M where: M is the number of observations z/sub i/ used in the test statistic; P/sub 1/=P(H/sub 1/) is the prior probability for hypothesis H/sub 1/ that signal s/sub 1/ is present and 1-P/sub 1/=P(H/sub 0/) corresponds to the hypothesis H/sub 0/ that signal s/sub 0/ is present; and p=Pr(z/sub i/>or=0 mod H/sub 1/) with s/sub 0/=0 for the traditional sign detector and p=Pr(z/sub i/>or= lambda mod H/sub 1/)=Pr(z/sub i/>

The robust single-sample randomized decision rule for known signals in independent, unknown-mean, amplitude-bounded, additive noise is extended to a two-stage suboptimal multisample decision rule for independent finite-sample-size (M) nonstationary measurement sequences (x/sub 1/, . . ., x/sub M/). The first stage is a robust single-sample decision rule using N random thresholds; the second stage is the M-sample sign detector with N randomly chosen sample thresholds. This random-threshold detector, for a given number of thresholds N, is shown to be an equalizer decision rule for a class of nonstationary symmetrical noise; moreover, the equalizer rule P/sub e/ performance is a lower bound on independent, asymmetrical noise performance. The set of random-threshold detectors (N>1), when combined with the modified sign detector (N=1), forms a family of equalizer-rule multisample detectors for known signals in nonstationary bounded-amplitude noise where the choice of N and corresponding performance depend only on the ratio of bounded noise range to signal separation S/sub 1/-S/sub 0/.>

Specification of the worst case additive interference forM-ary signaling and receivers using predecision correlation is obtained. The interference is constrained by average power and peak amplitude upper bounds on its Fourier transform. In addition, no statistical description is assumed. The performance measure is a weighted(\pm 1)sum of the correlations between the received corrupted signal Fourier transformR_{m}(f)and each member of the signal set Fourier transforms\{S_{m}(f)\}. This measure also depends on the out-of-sync time shifttand the signal present probabilityp. Functional analysis concepts are utilized to state and solve the resulting generalized Lagrange multiplier problem inL_{2}. The worst case interference functionW^{0}(f)is shown to have an average power equal to the average power upper bound and is independent ofp, but dependent ont. A key parameter may need numerical techniques for evaluation. This power level is achieved withW^{0}as a clipped multiple of| \sum S_{m}|that follows the phase of\sum S_{m}(f). The clipping level is the peak amplitude upper bound. The worst case performance is explicitly expressed in terms ofW^{0}. Upper and lower bounds are also derived with respect to arbitrary signal sets. Additional bounds are obtained for interference functions independent of the signal set magnitudes or phases. As a recommendation to minimize the worst case performance, the communicator should transmit with a high average probability per signalpM^{-1}for a given fixed {\em sum}\sum S_{m}(f)and\tilde{S}_{m}(f)S_{n}(f)=0, m \neq n, allm,n. However, to weaken the effectiveness of some sub-worst case interference, compared with the worst case. the communicator should transmit with low average probability per signalpM^{-1}and a phase of\sum S_{m}(f)close to\pi. Further investigation of good signal sets is warranted.

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solution\phi^{0}uses an equaUy likely mixed strategy to chose one ofNBayesian single-threshold decision rules\phi_{i}^{0}, i = 1,\cdots , Nhaving been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability densityf_{0}, wheref_{0}is a picket fence function withNpickets on its domain. Thee pair(\phi^{0}, f_{0})is shown to satisfy the saddlepoint condition for probability of error, i.e.,P_{e}(\phi^{0} , f) \leq P_{e}(\phi^{0} , f_{0}) \leq P_{e}(\phi, f_{0})holds for allfand\phi. The decision rule\phi^{0}is also shown to be an eqoaliir rule, i.e.,P_{e}(\phi^{0}, f ) = P_{e}(\phi^{0},f_{0}), for allf, with4^{-1} \leq P_{e}(\phi^{0},f_{0})=2^{-1}(1-N^{-1})\leq2^{-1} , N \geq 2. Thus nature can force the communicator to use an {\em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.

The single-sample robust decision problem for known signals in additive unknown-mean amplitude-bounded random interference is investigated. The approach is based on the generalized Lagrange multiplier theory for infinite-dimensional linear spaces. For the probability-of-error performance measure (Bayes risk) and equally likely binary signaling both minimax and maximin subproblems are formulated and solved explicitly. There is no nonrandomized saddlepoint solution. Moreover, the respective solutions are not unique and the classes of maximin and minimax decision rules are not disjoint. A uniform density and its optimal decision rule are shown to yield performance slightly less than the maximin value.

Optimal blocklengths are investigated for various ARQ schemes used for error control in data transmission systems in independent-bit-error and Poisson-distributed block-error channels. A number of results relating to optimum block length for various ARQ schemes are collected for easy reference. New results are obtained for some of these schemes. The product of this investigation is suggested procedures for computing optimal blocklengths. Examples are given.

A modification to the basic Go-Back-NARQ error control technique is described which yields improved throughput efficiency performance for all block error rates.

An investigation is made of the performance of quantizers used as source encoders for noise-corrupted signal sources. The developmerit is pertinent to discrete-time, memoryless, signal-signal-sourse-independent noise sources with a given amplitude bound. A functional analysis approach is adopted to formulate the problem and derive the results. The derivations and intermediate results are in terms of an arbitrary quantizer and, consequently, are applicable to any quantizer and allow quantizer performance comparisons in the worstcase corrupting-noise source context. Examples are presented with this type of comparison in mind. These examples instructively illustrate the application of the results as well as file performance of the uniform quantizer and others under their worst-case additive noise conditions.

In this paper, theoretical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum. The Kalman filter is shown to be a minimax estimator for one class of problems and to satisfy a saddlepoint condition in the other two classes of problems. Equations for the worst case covariance matrices are given which allow the specifications of the minimax Kalman filter gains and the worst case distributions for the respective classes of problems. Both time-varying and time-invariant systems are treated.

TheN-level uniform quantizer on[-c,c]plus the assignment ofy_{0}\deg = -(a _{s}+ c)/2andy_{N+1}\deg = (a_{s}+ c)/2to signal values falling in the saturation regions[-a_{s},- c) and (c,a_{s}], respectively, is shown to be the minimax(N + 2)-level quantizer with a nonsaturating input range[-c,c]. The performance criterion considered is the mean weighted quantization error and the input signals are only required to be amplitude bounded by\pm a_{s}wherea_{s} > c > 0. The worst case input signal marginal probability distributions are shown to be discrete. From the derivation of this result, the minimax error can be computed. An example is given which illustrates the performance of the minimax quantizer for several input ranges against different input signal probability distributions.