Efficient algorithms for sequence detection in non-Gaussian noise with intersymbol interference

In this paper, use of recurrent neural network equalizer (RNNE) in place of linear equalizer (LE) to combat both linear and nonlinear distortions corrupting the Magneto-optical (MO) readback signal is discussed. It is shown that RNNE can outperform LE without introducing significant complexity. RNNE is used to equalize the MO recording readback signal corrupted by transition jitter, intersymbol interference (ISI) and additive white Gaussian Noise (AWGN) at a density of 50 kbpi. The MO signal is equalized to a partial response (PR) (1 + D) using either the RNNE or the LE and the equalizer's mean- squared-error (MSE) performance is compared. Then, the equalized signal is passed through a detector and it is shown that a signal equalized to a PR (1 + D) shape can be detected using either a bit-by-bit type of detector (BD) or a sequence detector implemented via Viterbi Algorithm (VA). The bit-error-rate (BER) performance of BD is compared to that of the Viterbi detector and it is shown that PR equalization of MO readback signals using RNNE improves MSE performance over linear equalizer, allowing use of BD rather than LE + Viterbi Algorithm with comparable BERs.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The generalized stack algorithm GSA (L, K), where L denotes the number of branches per state and K the number of extended paths, is a tree or trellis search algorithm combining a metric-first and a breadth-first strategy. The GSA is applied in the equalization of signals disturbed by noise and intersymbol interference (ISI) and in the decoding of convolutional codes. For wide trellises it is not useful to implement a Viterbi algorithm (VA), as the complexity of the VA raises exponentially to the width of the trellis. The GSA follows only C paths (with normally C/spl Gt/K), where C is the capacity of the path memory and the complexity of the GSA increases much less than that of the VA. Instead of it, the GSA requires a sorting device, which is rather expensive. Additionally the number of paths varies during the detection process and the paths have different time indices. Extracting and inserting few paths from a more or less sorted path memory disturbs the order only slightly. So we need only little rearranging effort for the path memory. This paper presents a suitable sorting structure for the GSA for a large path number. The structure exploits the inherent parallelism by a new sorting scheme called extended systolic priority queue (ESPQ). It provides a faster sorting than previous designs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An optimal maximal ratio combiner (MRC) based on the expectation-maximization (EM) algorithm is devel- oped for noisy constant envelope signals transmitted over a Rayleigh fading channel. Instead of using a transmitted pilot signal with the data to estimate the combiner gains, the EM algorithm is used to perform this estimation. In the developed MRC, estimation of the transmitted data sequence is performed also by the EM algorithm. Estimation using the EM algo- rithm provides an iterative solution to the maximum likelihood (ML) approach. Therefore, the resulting receiver is opti- mum and does not suffer from the difficulties resulted from direct application of the ML procedure. One of these difficul- ties is the computational complexity which depends exponentially on the data sequence length. Introducing an iterative structure in the developed MRC achieves a linear computational complexity and enables efficient data extraction by the Viterbi algorithm when trellis coding is used.

Low complexity generalized EM algorithm for blind channel estimation and data detection in optical communication systems

Using a criterion of minimum average error probability we derive a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system. The transmitted data are binary and coded into pulses of shape <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\pm s(t)</tex> . The linear transmission medium introduces intersymbol interference and additive Gaussian noise. Because the intersymbol interference is not Gaussian and can be correlated with the binary digit being detected, our problem is one of deciding which of two waveforms is present in a special type of correlated, non-Gaussian noise. For signal-to-noise ratios in a range of practical interest, the optimum filter is found to be representable as a matched filter followed by a tapped delay line--the same form as that of the least mean square estimator of the pulse amplitude. The performance (error probability vs. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> ) of the optimum filter is compared with that of a matched-filter receiver in an example.

One of the key challenges in cognitive radio (CR) networks is to perform spectrum sensing in environments characterized by shadowing and fading effects as well as non-Gaussian noise distributions. Existing literature on spectrum sensing focuses mainly on the Gaussian noise model assumption, which does not properly characterize all the various noise types found in practical CR systems. This paper addresses the problem of spectrum sensing in the presence of non-Gaussian noise and interference for cognitive radio systems. A novel detector based on the Rao test is proposed for the detection of a primary user in the non-Gaussian noise environments described by the generalized Gaussian distribution (GGD). The test statistic of the proposed Rao detector is derived and its detection performance is analyzed and compared to that of the traditional energy detection. The Rao-based detection is then extended to a multi-user cooperative framework based on an improved decision fusion rule. It is shown through computer simulations that for a given probability of false alarm, the Rao detector can significantly enhance the spectrum sensing performance over conventional energy detection in non-Gaussian noise. Furthermore, the proposed cooperative detection scheme has a significantly higher global probability of detection than the non-cooperative scheme.

This paper describes an automatic text‐ and speaker‐independent language identification method based on hidden Markov models (HMMs) for acoustic features. The hidden Markov modeling is used to represent the phonotactics for each language. Each language has its proper phonotactics.The HMM topology here is a fully structured (ergodic) model wherein any state could transit to all states. Two kinds of HMMs are used: the discrete HMM (DHMM) with the codebook and the continuous density HMM (CHMM). The HMM was trained using both the Baum‐Welch (forward‐backward) algorithm and the Viterbi algorithm. The latter was used for emphasizing the state transition probability.For comparison, experiments also were conducted on the identification using a mixtured Gaussian distribution model with one state. This single‐state Gaussian distribution model gave the same performance as the HMM trained with the Baum‐Welch algorithm. This is because the transition between states which reflects the characteristics of each language does not affect the likelihood scores very much. This problem was addressed by emphasizing the transition probabilities and using the Viterbi algorithm, which resulted in an improvement in the recognition rates. The trigram for optimal state sequence is introduced. Combining it with the HMM produced the best results.

A differentially coherent receiver which uses the Viterbi algorithm is presented. This receiver compensates for intersymbol interference (ISI) and avoids noise enhancement. A phase estimate which takes into account the presence of inherent ISI in the signal is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. The complexity of the resulting receiver increases with the duration of observation used by the implicit phases estimator. A simple four-state Viterbi receiver with good performance is obtained when the phase estimate is based on one observable. Simulation results are given. >

In this paper, we consider diffusive molecular communication (MC) systems affected by signal-dependent diffusive noise, inter-symbol interference, and external noise. We design linear and nonlinear fractionally-spaced equalization schemes and a detection scheme which combines decision feedback and sequence detection (DFSD). In contrast to the symbol-rate equalization schemes in the MC literature, the proposed equalization and detection schemes exploit multiple samples of the received signal per symbol interval to achieve lower bit error rates (BERs) than existing schemes. The proposed DFSD scheme achieves a BER which is very close to that achieved by maximum likelihood sequence detection, but with lower computational complexity.

Autonomous Underwater Vehicles (AUVs) need accurate navigation and positioning data to carry out their operations in challenging marine environments. However, non-Gaussian environmental noise and sensor outliers in underwater environments degrade the positioning accuracy and stability of traditional algorithms. In such circumstances, the typical Unscented Kalman Filter (UKF) performs worse according to the Minimum Mean Square Error (MMSE) criteria. To reduce non-Gaussian environmental disturbances, a Maximum Correntropy Criterion (MCC) is created. This study extends the MCUKF by utilizing a mixture correntropy framework and an effective iterative optimization technique, and an improved Sage-Husa filtering mechanism is integrated into the iterative algorithm to address time-varying noise dynamics in complex scenarios. These changes increase the algorithm's resilience and flexibility in demanding underwater conditions. The algorithm's capability is confirmed using simulation and sea experiments, which show notable gains in Root Mean Square Error and navigation accuracy. Experimental results show that the proposed method outperforms other existing algorithms in terms of navigation accuracy performance in our simulations and experiments. To guarantee algorithm performance and resilience for the non-Gaussian time-varying measurement noise issue that AUVs encounter in intricate maritime settings, and to additionally enhance the precision and dependability of localization, this study uses the MCC-UKF to combat the environment's non-Gaussian noise, and the Levenberg-Marguardt iterative method to improve reliability of numbers and estimation precision, while the Maximum Mixture Correntropy Criterion (MMCC) serves the purpose of improve the filter flexibility and convergence speed, and finally, the improved Sage-Husa algorithm is combined to improve the robustness to time-varying noise. The following are the study's primary contributions. (1) In our study, we suggest an enhanced UKF algorithm that combines the MCC and iterated cost function, and adopt a Levenberg-Marquardt optimization strategy to accelerate the convergence. The mixture correntropy criterion was added in the construction of the LMIMC-UKF framework in order to achieve the synergistic enhancement of convergence performance and calculate accuracy. (2) Targeting the issue of time-varying environment noise interference, a fusion approach of iterative tuning and improved Sage-Husa filtering is suggested to achieve the systematic improvement of algorithm robustness. (3) By combining the Monte Carlo simulation with maritime measurement data, the algorithm's technical viability is confirmed, and the parameter sensitivity is quantitatively examined by methodical simulation tests. According to the results, the suggested algorithm performs noticeably better than the current maximum correntropy filtering techniques in terms of anti-interference capability, iteration speed, and navigation accuracy.

In this paper, we are going to discuss the error in determining the actual intersymbol interference noise (ISI) due to different circuit simulation methodology, while using a standard circuit simulator. In this paper, we have compared three different methods to predict accurately ISI noise. All three methods show that errors caused by circuit simulation can make the eye worst. We have also shown a method which allows one to determine that error and calculate the actual range of ISI noise. As we move towards sampling mVolt signals at the receiver end (Bhattacharyya, 2004 and Bhattacharyya, 2005), one needs to minimize the error that arises due to circuit simulation methodology. This is essential, in order to predict the actual performance of the interconnect.

In many applications non-stationary Gaussian or stationary non Gaussian noises can be observed. In this paper we present a maximum a posteriori estimation jointly of spectral amplitude and phase (JMAP). It principally allows for arbitrary speech models (Gaussian, super-Gaussian, ...), while the noise DFT coefficients pdf is modeled as Gaussian mixture (GMM). Such a GMM covers both a non-Gaussian stationary noise process, but also a non-stationary process that changes between Gaussian noise modes of different variance with probability of the GMM weight. Accordingly, we provide results for these two types of noise, showing superiority over the Gaussian noise model JMAP estimator even in case of ideal noise power estimation.

Unified low-complexity decision feedback equalizer with adjustable double radius constraint

Designing communication techniques for non-Gaussian impulsive noise has been attracting considerable attention from the research community. In this paper, we focus on the continuous phase frequency shift keying (CPFSK) signal detection for both white and bursty impulsive noises. The independent and identically distributed (i.i.d.) symmetric $\alpha $ -stable ( ${S\alpha S}$ ) process and the stationary $m$ -order $\alpha $ -sub-Gaussian [ ${{\alpha \mathit {SG}}}(m)$ ] model are adopted to model the white and the bursty impulsive noises, respectively. At first, both coherent and non-coherent detections of CPFSK signals are investigated for white ${S\alpha S}$ noises. For the coherent sequence detection, the Viterbi algorithm is used by replacing the maximum likelihood (ML) measure with the myriad measure. In non-coherent detection, a multiple symbol aided scheme is proposed, for which both the ML and myriad measures are considered. Subsequently, the detection of CPFSK signals is further addressed in ${{\alpha \mathit {SG}}}(m)$ noise. For coherent detection, based on the Markov property of ${{\alpha \mathit {SG}}}(m)$ noise, we first express the likelihood function as the sum of branch measures, and the myriad measure is also provided to replace the ML measure. The multiple symbol-aided methods are also applied to the non-coherent detection in ${{\alpha \mathit {SG}}}(m)$ noise, and the corresponding ML and myriad measure-based algorithms are given as well. For the sake of comparison, the Gaussian measure is also considered. The simulation results show that the performance of the myriad measure-based algorithms can closely approach that of the ML measure-based algorithms for both coherent and non-coherent detection, and is much better than that of the Gaussian measure-based algorithms.

A channel with inter-symbol interference and random perturbations to timing is approximated using a finite-state Markov model. The inter-symbol interference is approximated by a finite-impulse response and the timing perturbations are approximated by a first-order random walk. A Viterbi algorithm is then applied to find the maximum-likelihood sequence of states on this model. The resulting state sequence defines the data sequence and timing trajectory which jointly maximize a likelihood function on the observed signal. This approach provides a means of detecting data with rapidly fluctuating timing perturbations at low signal-to-noise ratio. This is particularly relevant to data storage applications where mechanical fluctuations are translated into timing perturbations. Codes can be incorporated into the detector. The coding gain improves the reliability of both data detection and timing recovery. Codes which can be represented using a reasonably small state machine, such as trellis codes and high rate block parity codes, can be incorporated directly into the finite state model. For iterative decoders a BCJR algorithm can also be applied to this state machine to yield a posteriori probabilities on the data bits.