Author's reply to `On the generalized multinomial distribution,optimal multinomial detectors, and generalized weighted partial decisiondetectors' by N.C. Beaulieu

Beaulieu (see ibid., vol.39, no.2, p.193, 1991) states that the equivalence between the generalized multinomial detectors and the generalized weighted partial decision detectors is obscured by E.K. Al-Hussaini (see ibid., vol.37, p.1099, 1989), who concluded that the former outperforms the latter. In reply, Al-Hussaini clarifies his results     

An algorithm for the design of generalized quantizers for detection

A procedure based on the generalized Lloyd algorithm approach using a sequence of independent noise samples to design M-region generalized quantizers for signal detection is presented. Included in this case are the conventional M-interval quantizer detectors. The quantizer parameters for S.A. Kassam's (1985) four-region generalized quantizer detector are computed using various sample sizes for the known sequence of independent noise samples. Two families of densities which cover a wide spectrum of possible nonGaussian densities are considered: the generalized Gaussian densities and the Johnson S_u family of densities. The performance of the quantizer detector is compared to that of the locally optimum detector, and the results are presented as the asymptotic relative efficiencies of the respective detectors. The case when the noise density is not known before analysis is considered, and the detection performance is examined using an estimate of the density. A mean-squared-error distortion criterion is used in the proposed algorithm to obtain quantizers that yield maximum efficacy. It is shown through numerical examples that the design procedure is simple, fast, and applicable to a wide range of nonGaussian distributions     

Locally optimum detection of signals in a generalized observationmodel: the random signal case

Locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal-dependent and multiplicative noise. It is shown that the locally optimum random-signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model. Examples of explicit results for the locally optimum detector test statistics are given for some typical cases. Both asymptotic and finite sample-size performances of the locally optimum detectors are considered and compared with those of other standard detector structures     

Subspace-based adaptive generalized likelihood ratio detection

Subspace-based adaptive detection performance is examined for the generalized likelihood ratio detector based on Wilks' Λ statistic. The problem considered here is detecting the presence of one or more signals of known shape embedded in Gaussian distributed noise with unknown covariance structure. The data is mapped into a subspace prior to detection. The probability of false alarm is independent of the subspace transformation and depends only on subspace dimension. The probability of detection depends on the subspace transformation through a nonadaptive signal-to-noise ratio (SNR) parameter. Subspace processing results in an SNR loss that tends to decrease performance and a gain in statistical stability that tends to increase performance. It is shown that the statistical stability effect dominates the SNR loss for short data records, and subspace detectors can require substantially less SNR than full space detectors for equivalent performance. A method for designing the subspace transformation to minimize the SNR loss is proposed and illustrated through simulations     

Locally optimum detection of signals in a generalized observationmodel: the known signal case

A generalized observation model for signal detection problems is proposed. The model allows consideration of several interesting special cases including additive noise, multiplicative noise, and signal-dependent noise, and includes both deterministic and random signals. Locally optimum (LO) detectors are interesting generalizations of those for the additive noise model. Under the proposed observation model the performance of the LO detectors is compared with that of other common detectors     

Maximum transition run codes for generalized partial responsechannels

A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at dc and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrained or j-constrained are studied. Deterministic finite-state transition diagrams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between (G,I) constraints and MTR(j) constraints is clarified. Code design methodologies that are based on look-ahead coding in combination with violation detection/substitution as well as on state splitting are used to obtain several specific constructions of high-rate MTR codes     

基于空间交替广义最大似然的低复杂度列表检测

针对V-BLAST系统,提出了一种低复杂度的空间交替广义最大似然（SAGL）列表检测算法。该算法的子检测器由简化最大似然（SML）检测器和连续干扰抵消（SIC）检测器组成。传统SIC算法每次只能对单一符号进行检测,而所提算法则利用相邻符号进行联合滑动检测,可以获得更高的分集增益。此外,所提SAGL算法对检测结果进行迭代修正来进一步提升检测性能。分析与仿真结果表明,与传统列表检测算法相比,所提SAGL列表检测算法以少许复杂度的增加为代价显著提升了检测性能。     

Optimal waveform design for generalized likelihood ratio and adaptive matched filter detectors using a diversely polarized antenna

In this paper, we address the performance optimization of adaptive detectors in Gaussian noise with unknown covariance matrix, based on a diversely polarized antenna (DPA). First, a general signal model is presented, where the system response is related to the characteristics of its transmitted pulses. Two adaptive detectors, i.e., generalized likelihood ratio and adaptive matched filter, are then adopted, and their expressions for the probabilities of false alarm and detection are provided. In particular, a waveform design algorithm to enhance the detection performance of both the detectors is proposed. Finally, simulation results illustrate the performance gain obtained with the proposed waveform design algorithm, i.e., by optimally selecting the polarization of the transmitted pulses of the DPA.     

The asymptotic performance of two-sample nonparametric detectors when detecting nonfluctuating signals in non-Gaussian noise (Corresp.)

The asymptotic relative efficiencies (ARE) of generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) two-sample nonparametric detectors are compared with those of the mean and median parametric detectors. The signal is assumed to be nonfluctuating, and the background noise is assumed to be lognormal or to be characterized by a contaminated normal distribution. It is shown that using the asymptotic relative efficiency measure the performance of nonparametric detectors increases appreciably as the noise distribution deviates from normality.     

Efficient performance evaluation for generalized selection combining on generalized fading channels

The authors propose an efficient moment generating function (MGF)-based method to evaluate the performance of generalized selection combining (GSC) over different fading channels. Employing a recently proposed method which is, however, only applicable to GSC diversity with independent and identically distributed branches, they derive a general MGF expression for the GSC output signal-to-noise ratio (SNR) for generalized fading channels, where the channel statistics in different diversity branches may be nonidentical or even distributed according to different distribution families. The resulting MGF expression is applicable to the analysis of the error probability, the outage probability, and the SNR statistics for GSC in a number of wireless communications scenarios with generalized fading. Numerical examples are presented to illustrate the application of the new analysis.     

A generalized two-threshold detection procedure

A modified sequential procedure for testing binary hypotheses with different means, proposed by C.C. Lee and J.B. Thomas (ibid., vol.IT-30, no.1, p.16-23, Jan. 1984), is generalized for application to the case of multiple hypotheses with different means/variances of the Gaussian distribution. The method constitutes a two-threshold test for fixed-size packages of samples with a sequential procedure of discarding the package for which no decision is reached and subsequently testing a new package. The objective is to find an optimum package size N₀ which leads to the minimum overall average sample number (ASN) for a given overall error probability. An optimization algorithm is developed to extend the application of the Lee-Thomas procedure to the M-ary case. Performance characteristics of the generalized two-threshold (GTT) test procedure are compared with those of conventional sequential as well as fixed-sample-size (FSS) methods. It is shown for the M-ary different means/variances cases that for low error rates the number of samples required by the GTT test is, on the average, approximately half that needed by a FSS test. However, it is somewhat more than the ASN obtained with a conventional sequential test. With decreasing error probabilities the GTT test performance approaches that of conventional sequential methods     

PERFORMANCE OF TWO GENERALIZED ORDER STATISTICS CFAR DETECTORS WITH AUTOMATIC CENSORING TECHNIQUE IN MULTIPLE TARGET SITUATIONS

This paper presents two generalized modified OS-CFAR detectors and an automatic censoring technique. For these two new OS-CFAR detectors, analytic expressions of the false alarm rate, the detection probabilities and the measure of ADT under the Swerling 2 assumption are obtained. Their detection performances are analyzed in homogeneous background and in the presence of strong interfering targets, and they are compared with several previously proposed CFARs.     

Alias-free generalized discrete-time time-frequency distributions

A definition of generalized discrete-time time-frequency distribution that utilizes all of the outer product terms from a data sequence, so that one can avoid aliasing, is introduced. The new approach provides (1) proper implementation of the discrete-time spectrogram, (2) correct evaluation of the instantaneous frequency of the underlying continuous-time signal, and (3) correct frequency marginal. The formulation provides a unified framework for implementing members of Cohen's class, which was formulated in the continuous-time domain. Some requirements for the discrete-time kernel in the new approach are discussed in association with desirable distribution properties. Some experimental results are provided to illustrate the features of the proposed method     

An invariance property of the generalized coherence estimate

The distribution of the M-channel generalized coherence estimate is shown not to depend on the statistical behavior of the data on one channel, provided that the other M-1 channels contain only white Gaussian noise, and an channels are independent. This confirms a previously published conjecture and extends the utility of the GC estimate as a detection statistic to include active as well as passive scenarios     

On the generalized Cramer-Rao bound for the estimation of thelocation

It is shown that the generalized Gaussian distribution maximizes the generalized Cramer-Rao (CR) bound for the pth absolute central moment of any classical location parameter unbiased estimator. The underlying maximization is taken over the class of distributions with fixed and finite pth-order moment and exhibits particular utility in minimax designs as well as in worst-case performance analysis. The relationship between the generalized Gaussian density and the generalized CR bound is further examined for the model of a mixture of generalized Gaussian distributions as well as for scenarios where multiple independent generalized Gaussian observations are involved     

Unification of generalized hybrid analysis and generalized diakoptics

First, the concept of generalized hybrid basis is introduced and the generalized hybrid analysis for the special linear network having no coupling between its subnetworksN ₁ andN ₂ in Chua and Chen’s paper (1976) is extended to that for the general linear network having coupling betweenN ₁ andN ₂. Second, the concept of generalized diakoptics is introduced and the one-to-one correspondence between it and the generalized hybrid analysis is established. Thus the two analysis methods are unified. Third, the multilevel generalized diakoptics and its algorithm are presented. Fourth, the concepts of the equivalent tree-flower type network and the equivalent interconnected network for fundamental diakoptics are presented.     

广义三次DP曲线的形状分析

基于包络理论和拓扑映射的方法对广义三次DP曲线进行了形状分析,首先讨论了空间曲线的变挠性;接着讨论了曲线含有奇点、拐点、局部凸和全局凸的充分必要条件,得出了其形状分布图;最后就参数对形状分布图的影响作了进一步的讨论。     

一类广义非线性sine-Gordon方程新的显式解

将行波变换推广为一般的函数变换,给出一种改进的试探方程法.应用该方法求解一类广义的非线性sine-Gordon方程,获得了多种形式的新显式解,包括三角函数型解,双曲函数型解.     

Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.     

Another generalized Golomb-Posner code

Through the use of mutually orthogonal frequency squares, a generalization of the original Golomb-Posner code is constructed. The minimum distance and weight distribution of the generalized code when it is constructed from a complete set of orthogonal squares over a finite field are also determined