Combined scintillation and terrestrial fadings occur in mobile satellite communication channels as the signal passes through the ionosphere and the lower atmosphere. This results in a product fading channel, which negatively affects the performance of the system. The challenge is to evaluate the performance of the system, in terms of the average bit error probability (BEP). In this paper, through the use of the moment generating function, we derive expressions for the average BEP and an upper bound for M-ary phase-shift keying (M-PSK) modulation with maximal-ratio combining (MRC) diversity over the product RiciantimesRician channel. The results are expressed as double summations in terms of the generalized hypergeometric function, which can be computed using standard commercial software. For a large Rician factor, the expression is simplified to a single summation. Numerical results are obtained from the derived expressions and compared with simulation results. They show very good agreement for various Rician factors and the number of diversity branches. The upper bound is also evaluated and shown to be reasonably tight.

The performance analysis of wireless digital communication systems employing optimum combining (OC) at antenna arrays of the receiver is investigated in a non-Gaussian multipath fading channel called spherically invariant random process (SIRP). The outage probability and probability of error are then analyzed with the existence of cochannel interference

Since 2-D Gabor filter can be separated into 1-D Gaussian band-pass filter and 1-D low-pass filter to the perpendicular, separable Gabor filter realization for any selected orientation is introduced for fast fingerprint enhancement. The experimental results showed that the separable Gabor enhancement significantly reduced computational complexity, approximately 1:2.8 times, faster than traditional Gabor enhancement, with comparable enhancement quality. Moreover, this separable Gabor filter is generalized for any desired orientation resulting in faster execution time (1:1.46), less memory space, and better quality enhancement comparing to the traditional Gabor filter with 8 orientations.

We propose a joint PN phase and carrier phase acquisition scheme by using a new auxiliary sequence for a DS/SS system. The auxiliary sequence helps provide the direction for each update of the local PN code phase and carrier phase adjustment. Performance of the proposed scheme is obtained by simulation and compared with a previously proposed joint PN phase and carrier phase acquisition scheme and the conventional serial search scheme. Results show that the proposed scheme acquires the PN phase faster than the other schemes, at the cost of a modest increase in hardware.

We propose a closed-loop system with a pre-loop code phase estimator (PLE) for acquisition of the pseudonoise (PN) signal in direct-sequence spread-spectrum systems. It consists of two major parts: a PLE and a closed-loop acquisition subsystem. The system uses an auxiliary signal, as opposed to the PN signal itself, to correlate with the incoming signal. The PLE uses the correlation result to obtain an estimate of the incoming code phase. Then, starting with this initial estimate, the closed-loop subsystem will acquire the code phase of the incoming PN signal. With coherent carrier demodulation, mean and variance of the acquisition time of the proposed scheme are obtained and compared to those of the conventional serial-search acquisition receiver and the closed-loop system without the pre-loop estimator. Results show that, with proper choices of parameters, the proposed system acquires the PN phase significantly faster than the other two systems.

We propose a closed-loop system for the acquisition of the pseudo-noise (PN) signal in direct-sequence spread-spectrum (DS/SS) systems. We introduce a novel idea of using an auxiliary signal, as opposed to the PN signal itself, for correlation with the incoming signal. The cross-correlation function of the auxiliary signal and the PN signal has a triangle shape that covers essentially the entire period of the PN signal. Consequently, their correlation provides the direction for the phase update of the local signal generator in the acquisition scheme. With coherent demodulation, the mean and variance of the acquisition time are derived under additive white Gaussian noise (AWGN). They are compared to those of the conventional serial-search acquisition system. Results suggest that the proposed system acquires the PN phase at least twice faster, with significantly smaller acquisition time variance, than the conventional system.

Almost all previous acquisition schemes for direct-sequence spread-spectrum systems assume that there is no data modulation. However, in some applications, there is need for acquisition systems with the presence of data modulation, which is what we consider in this paper. First, we derive an optimal scheme using maximum likelihood estimate, by treating the phase of the incoming sequence as a signal parameter to be estimated. Two practical parallel search schemes as approximations to the optimal scheme are presented. We also consider serial and hybrid search schemes. Numerical results show that significant degradation of the standard coherent acquisition schemes occurs when there is data modulation. Using the proposed search schemes, performance is restored to the level which is almost equal to that of the standard schemes without data modulation.>

We study a direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with M-ary phase-shift-keyed (MPSK) signaling. Users in the system employ complex signature sequences, which are modeled as deterministic sequences. We present upper and lower bounds for the probability of bit error (p.b.e.) of a reference transmission. First, the conditional p.b.e., given the multiple-user interference (MUI), is obtained. Then, the conditioning is removed by averaging over the discretized probability density function (p.d.f.) of the MUI. The result is an upper (or lower) bound when the discretized p.d.f. is a shifted-high (or shifted-low) version of a sectioned p.d.f. This process requires the two-dimensional p.d.f. of the MUI, which is derived. Arbitrarily tight bounds can be obtained at the cost of increased computation. Numerical results are presented for complex FZC and near optimal 4-phase sequences, as well as real binary Gold sequences, for BPSK, 4-PSK, and 8-PSK. Gray code bit mapping is assumed, although the analysis can be applied to other bit mappings. Results show that complex sequences can yield better performance than binary sequences in MPSK signaling. Using complex sequences, the number of available signature sequences is greatly enlarged.>

Studies sequential acquisition schemes of m-sequences, based on the sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT), with noncoherent demodulation. Most reported results on sequential acquisition schemes assume that independent samples are available for the decision process. The assumption of independent and identically distributed (i.i.d.) samples requires the integrator in the receiver to be reset periodically. This introduces loss in the effective signal-to-noise ratio, degrading the performance. In the present paper, on the contrary, the authors' two sequential schemes use continuous integration. It can be shown that the likelihood ratio is monotonic; consequently, the tests can be easily implemented in realtime. Methods are proposed for designing the decision thresholds to achieve the desired false-alarm and miss probabilities. Performances of the proposed schemes are obtained and they suggest that the TSPRT is more desirable. The effect of slowly-varying channel fading is also investigated. Results show that fading does not affect the false alarm probabilities, but it can drastically reduce the probability of detecting the alignment of the two PN sequences, especially when the fading is severe.>

The performance of sequential acquisition of m sequences, based on the sequential probability ratio test (SPRT), is studied. The authors consider a sliding correlator-type structure for the acquisition scheme, which the mean acquisition time is proportional to the average number of samples used for a synchronization test. Sequential acquisition requires the knowledge of the partial correlation of the pseudonoise (PN) sequence, however, as the partial correlation of an m sequence is difficult to model the authors propose an approximate upper bound. This is then piecewise linearized and used for designing the SPRT which is then compared to the fixed-dwell time technique, a scheme using the fixed sample size test. Numerical results show that the saving of acquisition time by the SPRT increases as the desired probabilities of errors and/or the input SNR decrease. Analytic results are verified by computer simulation.>

The idea of the Wilcoxon detector using a conditional test is extended to two-stage detectors, which constitute a class of sequential detectors. Three different two-stage detectors are considered, using the Wilcoxon statistic with conditional tests. The three detectors differ in the usage of the samples of the first stage for computing the test statistic in the second stage. In computing the test statistic in the second stage, the first detector disregards all the samples of the first stage, the second detector uses the value of the test statistic of the first stage, and the third detector uses all the samples of the first stage. The asymptotic relative efficiency improves from the first to the second detector. Comparisons of these detectors with fixed-sample-size (FSS) detectors show that they are better than both the FSS linear detector and the FSS conditional Wilcoxon detector under the same false-alarm and detection probabilities.>

A multiplierless realization of IIR (infinite impulse response) filters is proposed. It is achieve by cascading biquad units (second-order filters), and each biquad unit is realized by a periodically time-varying state-space (PTV-SS) structure, preceded and followed by a first-order interpolator (hold circuit) and a decimator (down-sampler), respectively. The coefficients of the PTV-SS structure are powers of two, so that multiplications are performed by shift operations. Design examples show that the resulting frequency response closely matches that of the target filter with infinite-precision coefficients.>

The performances of some proposed sequential constant-false-alarm-rate (CFAR) detectors are evaluated. The observations are passed through a dead-zone limiter, the output of which is -1, 0, or +1, depending on whether the input is less than -c, between -c, and c, or greater than c, where c is a constant. The test statistic is the sum of the outputs. The test is performed on a reduced set of data (those with absolute value larger than c), with the test statistic being the sum of the signs of the reduced set of data. Both constant and linear boundaries are considered. Numerical results show a significant reduction of the average number of observations needed to achieve the same false alarm and detection probabilities as compared to a fixed-sample-size CFAR detector using the same kind of test statistic.>

A filter which combines L-type structure with a modified median filter (MMF) is proposed for suppressing nonimpulsive as well as impulsive noise. The MMF is designed to reduce edge jitter caused by the median filter. The MMF output is obtained by modifying the median filter output, based on results of hypothesis tests. The proposed filter, named the decision-based order statistic filter (DBOSF), generates the output by using asymmetrical alpha -trimming with respect to the MMF output. In addition to noise suppression, the DBOSF can enhance the gradient of blurred edges provided that the size of the window is greater than twice the transition with width of the blurred edges. Experimental results for one- and two-dimensional signals are presented to demonstrate performances of the proposed filter.>

The sequential probability ratio test (SPRT) with constant thresholds and the sequential linear detector (SLD) are compared under an autoregressive noise assumption in terms of the average sample number (ASN) when both detectors have the same error probabilities. For small ASN their performances are evaluated numerically. Results show that the SLD is better when\rho(the parameter in the autoregressive noise) is positive and the SPRT is better when\rhois negative. However, their asymptotic efficiencies (as the signal approaches zero) are found to be the same.

Asymptotic relative efficiencies of two-stage and multistage tests of a simple null hypothesis Versus a simple location alternative are considered. Observations are taken in groups, not necessarily of the same size, and a test statistic is computed for comparison with thresholds. In a two-stage test, if the test statistic of the first group of observations exceeds an upper threshold, the alternative is accepted, and if it crosses a lower threshold, the null hypothesis is accepted. Otherwise, a second group of samples is taken and a second test is performed. Two different classes of two-stage tests are considered. One of them computes the test statistic in the second stage from observations in the second group alone, while the other uses both the first and the second groups of observations. It is shown that these tests are asymptotically more efficient than fixed-sample-size tests but are less efficient than sequential probability ratio tests. With proper choices of parameters, the improvement over fixed-sample-size tests can be significant, especially when the error probabilities are small. However, the complexity of two-stage tests is comparable to that of fixed-sample-size tests, making their use desirable. The efficiency ofk-stage tests,k > 2, is also investigated with the conclusion that the behavior of a two-stage test can be enhanced by adding stages up to a point beyond which the effect of adding stages diminishes.

Truncation of a sequential test with constant boundaries is considered for the problem of testing a location hypothesis:f(x- \theta_{0})versusf(x- \theta_{1}). A test design procedure is developed by using bounds for the error probabilities under the hypothesis and alternative. By viewing the truncated sequential test as a mixture of a sequential probability ratio test and a fixed sample size test, its boundaries and truncation point can be obtained once the degree of mixture is specified. Asymptotically correct approximations for the operating characteristic function and the average sample number function of the resulting test are derived. Numerical results show that an appropriately designed truncated sequential test performs favorably as compared to both the fixed sample size test and the sequential probability ratio test with the same error probabilities. The average sample number function of the truncated test is uniformly smaller than that of the fixed sample size test, and the truncated test maintains average sample sizes under the hypothesis and the alternative that are close to those optimum values achieved by Wald's sequential probability ratio test. Moreover, the truncated test is more favorable than the sequential probability ratio test in the sense that is has smaller average sample size when the actual location parameter is between\theta_{0}and\theta_{1}. This behavior becomes more pronounced as the error probabilities become smaller, implying that the truncated sequential test becomes more favorable as the error probabilities become smaller.

A class of nonparametric sequential tests is considered for testing a symmetric density under the hypothesis against a one-sided shift alternative. The test statistic at each observation is the sum of intermediate statistics obtained from the ranks within the most recentmobservations, where tn is a fixed ranking size. Excessive ranking of the data can be avoided with a proper choice of tn so that real-time implementation of the sequential rank test is feasible. Approximate expressions for the power and average sample number functions are given. Comparison with existing nonparametric tests is studied. Results show that the ranking sizemneed not be very large in order that the performance of the proposed test be almost as good as sequential rank tests which require ranking of all the data.

The relative efficiency of a sequential hypothesis test compared to a fixed sample size test is defined as the ratio of the expected sample size of the sequential test to the sample size of the fixed sample size test with the same size and power. Asymptotic behavior of the relative efficiency is studied for the detection of a constant signal in additive noise. With some regularity conditions imposed on the noise density, the asymptotic relative efficiency of the sequential probability ratio test with respect to the corresponding fixed sample size likelihood ratio test is a function of the size and the power. As the size a approaches zero and the power approaches unity, this asymptotic relative efficiency has a limiting value depending on the functional relationship of a and1 - \betaas they approach zero. Comparison of the power functions is also studied.

The quantization of the observed data for sequential signal detection is studied. The criteria used are the minimizations of the average sample number under the hypothesis, the average sample number under the alternative, and the maximum average sample number. Numerical results show that the performance is not very sensitive to different criteria. Using a sequential probability ratio test (SPRT), the performances of optimum quantizers are compared to systems with unquantized data. The asymptotic relative efficiencies of the quantizerSPRT's with respect to the SPRT for unquantized data are derived for symmetric noise densities. The relation between these asymptotic relative efficiencies and those of fixed-sample-size detectors is noted.

In fixed sample size signal detection, the sign detector is easier to implement and requires much less knowledge of the noise density than does the optimum fixed sample size detector. These advantages accrue at a cost of more observations needed to achieve the same performance. By utilizing the sign detector sequentially, it is shown that considerable saving in the (average) number of observations is obtained over the corresponding optimal fixed sample size detector. The asymptotic relative efficiencies, as the signal-to-noise ratio and both probabilities of error approach zero, of the sequential sign detector compared to fixed sample size detectors are derived. The possibility of truncating the test to avoid excessively large numbers of observations is considered.