Noncoherent decision feedback multiuser detection: optimality, performance bounds, and rules for ordering users

A systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of K simultaneously transmitting users of a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. A new performance criterion called symmetric energy is defined which is a low-noise indicator of the joint error rate that at least one user is detected erroneously. Even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum-likelihood detector. A general class of decision feedback detectors (DFDs) is defined with O(K) implementational complexity per user. The symmetric energy of arbitrary DFD and bounds on their asymptotic effective energy (AEE) performance are obtained along with an exact bit-error rate and AEE analysis for the decorrelating DFD. The optimum DFD that maximizes symmetric energy is obtained. Each one of the K! optimum, decorrelating, and conventional DFDs, that correspond to the K! orders in which the users can be detected, are shown to outperform the linear optimum, decorrelating, and conventional detectors, respectively, in terms of symmetric energy. Moreover, algorithms are obtained for determining the choice of order of detection for the three DFDs which guarantee that they uniformly (user-wise) outperform their linear counterparts. In addition to optimality in symmetric energy, it is also shown that under certain conditions, the optimum DFD achieves the AEE performance of the exponentially complex maximum-likelihood detector for all users simultaneously. None of the results of this paper make the perfect feedback assumption. The implications of our work on power control for multiuser detection are also discussed.

This paper considers the joint design of bit loading, precoding and receive filters for a multiple-input multiple-output (MIMO) digital communication system employing decision feedback (DF) detection at the receiver. Both the transmitter as well as the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, a diagonal transmission (i.e., orthogonalization of the matrix channel) is optimal for some criteria. Surprisingly, it was shown five years ago that for the family of Schur-convex functions an additional rotation of the symbols is necessary. However, if the bit loading is optimized jointly with the linear transceiver, then the rotation is unnecessary. Similarly, for DF MIMO transceivers, a rotation of the symbols is sometimes needed. The main result of this paper shows that for a DF MIMO transceiver where the bit loading is jointly optimized with the transceiver filters, the rotation of the symbols becomes unnecessary and, consequently, also the DF part of the receiver is not required.

For the single-carrier M-ary differential phase-shift keying (MDPSK), the multiple-symbol differential detector, or the noncoherent maximum-likelihood sequence detector (NSD), and its three special cases, namely, the noncoherent one-shot detector, the linearly predictive decision-feedback (DF) detector, and the linearly predictive Viterbi receiver are reviewed based on a hierarchical interpretation. For the multicarrier transmission, the differential orthogonal frequency division multiplexing (OFDM) systems with diversity reception are discussed. It is well known that there are two types of differential OFDM systems, namely, the time domain differential OFDM (TD-OFDM) and the frequency domain differential OFDM (FD-OFDM). In this paper, the NSD and its special cases are incorporated to the differential OFDM systems. Furthermore, we provide a simple closed-form bit-error-rate (BER) expression for the differential OFDM systems utilizing the noncoherent one-shot detector with diversity reception in the time-varying multipath Rayleigh fading channels. Numerical results have revealed that, with multi-antenna diversity reception, the performance of the noncoherent one-shot detector is improved significantly. However, when only one or two receive antennas are available, the implementation of the linearly predictive DF detector or the linearly predictive Viterbi receiver is necessary for achieving better and satisfactory performance.

Spectrum sensing exploiting polarization has been identified as an effective method for improving detection performance. However, the optimal polarization-based sensing algorithm with an upper bound performance has yet to be developed. The polarization likelihood ratio test (PLRT) is derived using the Neyman–Pearson theorem, resulting in an optimal detector with regard to the likelihood ratio. The best linear polarization processor or filter, i.e., the polarization matched filter (PMF), which processes the observed polarization data to provide the maximum signal-to-noise ratio (SNR) to the output of the filter, is also derived. Although the PLRT and the PMF provide an ideal upper bound on the performance of all detection methods that exploit polarization when likelihood functions or statistic parameters of likelihood functions are exactly known, their performance for realistic blind sensing remains unknown. Using the generalized likelihood ratio test (GLRT) method, we formulate two practical polarization-based detectors, i.e., GLRT based on received electric-field vector (GLRT-EV) and GLRT of the Stokes subvector, according to the statistical distribution of observed data expressed as a received electric-field vector and a Stokes vector, respectively. The two GLRT detectors can serve as a practical bound when all statistical parameters are unknown. Theoretical and numerical simulation results of the detection performance for the proposed detectors are presented. Additionally, these polarization-based detectors were thoroughly tested via a realistic wireless regional area network. Our experimental results show that the GLRT-EV detector exhibits better performance than other polarization-based detectors in terms of sample complexity and computational complexity, which is particularly critical in real-time applications.

In an estimation framework, the suspected sparsity of an unknown vector of deterministic parameters is classically accounted for through thresholding functions, some of which being related to Maximum A Posteriori estimates with specific priors. In a detection framework, statistical tests applied to sparse vectors are classically designed so as to limit the focus of the test to a few active components, leading to test statistics of thresholded data. We propose a study of the connections between these two problems. The detection tests we consider are the Generalized Likelihood Ratio Test (GLRT), the Bayes Factor, the Posterior Density Ratio and a LRT using a Maximum A Posteriori estimate with Generalized Gaussian priors. In the case of scalar parameter first, we derive sufficient conditions that any detection test must obey to be equivalent to a GLRT, and prove that the tests above verify them. In the vector case, the LRT with a MAP estimate and the PDR outperform the GLRT and the BF thanks to the thresholding effect of the MAP estimation. The connections between thresholding functions used in estimation and the resulting ”thresholded test statistics” are precisely investigated.

The problem of signal detection in unknown Gaussian interference with an adaptive array is considered in this paper. A modified Generalized Likelihood Ratio Test (GLRT) detector is suggested to improve the performance of Kelly's GLRT, when the sample that estimating the covariance matrix is limited. The modified GLRT detector proposed in this paper is noiseless unloaded GLRT (NUGLRT). Advantages of the proposed detector are illustrated by simulations comparing with some typical diagonalloaded detectors.

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

Integration of Information and Communication Technology (ICT) in modern smart grids (SGs) offers many advantages including the use of renewables and an effective way to protect, control and monitor the energy transmission and distribution. To reach an optimal operation of future energy systems, availability, integrity and confidentiality of data should be guaranteed. Research on the cyber-physical security of electrical substations based on IEC 61850 is still at an early stage. In the present work, we first model the network traffic data in electrical substations, then, we present a statistical Anomaly Detection (AD) method to detect Denial of Service (DoS) attacks against the Generic Object Oriented Substation Event (GOOSE) network communication. According to interpretations on the self-similarity and the Long-Range Dependency (LRD) of the data, an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model was shown to describe well the GOOSE communication in the substation process network. Based on this ARFIMA-model and in view of cyber-physical security, an effective model-based AD method is developed and analyzed. Two variants of the statistical AD considering statistical hypothesis testing based on the Generalized Likelihood Ratio Test (GLRT) and the cumulative sum (CUSUM) are presented to detect flooding attacks that might affect the availability of the data. Our work presents a novel AD method, with two different variants, tailored to the specific features of the GOOSE traffic in IEC 61850 substations. The statistical AD is capable of detecting anomalies at unknown change times under the realistic assumption of unknown model parameters. The performance of both variants of the AD method is validated and assessed using data collected from a simulation case study. We perform several Monte-Carlo simulations under different noise variances. The detection delay is provided for each detector and it represents the number of discrete time samples after which an anomaly is detected. In fact, our statistical AD method with both variants (CUSUM and GLRT) has around half the false positive rate and a smaller detection delay when compared with two of the closest works found in the literature. Our AD approach based on the GLRT detector has the smallest false positive rate among all considered approaches. Whereas, our AD approach based on the CUSUM test has the lowest false negative rate thus the best detection rate. Depending on the requirements as well as the costs of false alarms or missed anomalies, both variants of our statistical detection method can be used and are further analyzed using composite detection metrics.

In this paper, using the recurrent neural network (RNN) for non-coherent differential phase-shift keying (DPSK) signal detection is proposed. While deep-learning has been utilized for estimating the channel and detecting the signal in various communication systems models, making use of the time series encoding of DPSK modulation along with the time series feature of the recurrent neural networks for Rayleigh fading communication channel has not been studied before. The use of both of deep neural network (DNN) and recurrent neural network to detect the differential encoded time series signal is considered and compared. Both of the DNN-based and RNN-based detectors are compared to conventional non-coherent DPSK detection, coherent phase-shift keying (PSK) detection, and the analytical error rate of coherent and non-coherent detection. Extensive simulation results exhibit that the proposed RNN-based signal detector outperforms both of conventional non-coherent differential detection, and the DNN-based detector in terms of symbol error rate performance. In addition, it does not need any statistical information about the channel or require complex online calculations.

The sensing scheme based on the generalized likelihood ratio test (GLRT) technique has attracted a lot of research interest in the field of cognitive radios (CR). Although its potential advantages in detecting correlated primary signal have been illustrated in prior work, no theoretical analysis of the positive effects of the correlation has appeared in the literature. In this letter, we derive the theoretical false-alarm and detection probabilities of GLRT detector. The theoretical analysis shows that, in the low signal-to-noise ratio (SNR) region, the detector's performance can be improved by exploiting the high correlations between the primary signal samples. The conclusions of the analysis are verified by numerical simulation results.

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

This paper describes a new approximate maximum-likelihood (ML) MIMO detection approach by studying a Lagrangian dual relaxation (LDR) of ML. Unlike many existing relaxed ML methods, the proposed LDR employs a discrete domain for the problem formulation. We find that the proposed LDR exhibits an intriguing relationship to the lattice decoders (LDs) and the lattice reduction aided (LRA) detectors, both of which have caught much attention recently. Specifically, regularization in LDs, which was proposed to mitigate out-of-bounds symbol effects, can alternatively be interpreted as a way to constrain the symbol decision within bounds in a Lagrangian sense. We handle the LDR problem by using a projected subgradient method. The resultant method may physically be viewed as an adaptive regularization control in which a sequence of LDs are involved. Based on this newly developed insight, we propose two additional iterative LDR-based detectors using LRA decision-feedback (DF) and "lazy" DF. By simulation results, we show that the LDR LRA-DF and lazy-DF detectors yield better symbol error rate performance than the MMSE-regularized LRA-DF and DF detectors, respectively, where the SNR gaps can be more than 3dB.

We consider interference rejection for code-division multiple-access (CDMA) channels using decision-feedback detectors. Performance of zero-forcing and the minimum mean square error (MMSE) multiuser decision-feedback detectors is studied, and the full and partial feedback approaches are investigated. We also derive the maximum-likelihood detector based on the white noise CDMA channel model. Comparison among the decision-feedback detectors, the two-stage receivers, the conventional detector, and the linear decorrelating detector is undertaken for a four-user bandwidth-efficient asynchronous CDMA channel. We find that the decision-feedback detectors compare favorably to other suboptimal methods and maintain good performance under diverse channel conditions. This conclusion is further strengthened by performance analysis of the decision-feedback detector for a two-user synchronous CDMA flat Rayleigh fading channel. >

Detection and estimation of t-wave alternans (TWA) in presence of indispensable physiological artifacts is still a challenging task, as in most of the cases, the signal of interest resides well below the noise levels. In this paper, a generalized detection theoretic framework (GDFT) is proposed for the detection and estimation of TWA from the stress test ECG signal. The analytical foundations, TWA signal modeling, and finally simulations of nine TWA detectors and estimators belonging to median match filtering, empirical mode decomposition (EMD) based match filtering, and generalized likelihood ratio test (GLRT) for GDTF are presented. GLRT schemes require noise statistics for parameter estimation and are computationally efficient. GLRT detectors outperform all the detectors including the benchmark spectral method by ≥ 2 dB for a broad spectrum of SNR ranging from -15 dB to 30 dB under Gaussian noise. EMD based strategies also outperform spectral method under Gaussian and Laplacian noise by ≥ 1 dB.

The performance analysis for an optimal tonal detector is described . The detector is based on the generalized likelihood ratio test (GLRT) by using the statistical properties of the power spectrum observations. Unlike the conventional average power processor (AVGPR), which performs simple integration by averaging, the tonal detector is developed by optimally integrating the power spectrum observations and exploits the statistical characteristics of the power spectrum. The exact performance of the proposed detector is difficult to be evaluated, since the probability distribution of the log likelihood ratio cannot be obtained easily. Also, there is no general result for the GLRT detector. Here we adopt two methods to solve the problem. One is Van Trees' (1968) method and the other is the central limit theorem method. Using the second method, we derive the approximate probability density functions (PDF) of the detector under both hypotheses. They approach the Gaussian distribution with shifted mean for large data records. The Monte Carlo simulations support our conclusion about the PDF. On the basis of that, we derive the receiver operating characteristics (ROC) of the optimal detector. Then we compare it with the AVGPR, the performance of which is also studied. The simulation results show that the performance of our detector is better than the conventional AVGPR.