Optimum Reception in an Impulsive Interference Environment--Part I: Coherent Detection

Joint outage identification and state estimation in power systems is studied. A Bayesian framework is employed, and a Gaussian prior distribution of the states is assumed. The joint posterior of the outage hypotheses and the network states is developed in closed form, which can be applied to obtain the optimal joint detector and estimator under any given performance criterion. Employing the minimum probability of error as the performance criterion in identifying outages with uncertain states, the optimal detector is obtained. Efficiently computable performance metrics that capture the probability of error of the optimal detector are developed. Under simplified model assumptions, closed-form expressions for these metrics are derived, and these lead to a mixed integer convex programming problem for optimizing sensor locations. Using convex relaxations, a branch and bound algorithm that finds the globally optimal sensor locations is developed. Significant performance gains from using the optimal detector with the optimal sensor locations are observed from simulations. Furthermore, performance with greedily selected sensor locations is shown to be very close to that with globally optimal sensor locations.

The optimum multiuser detection problem was shown to be NP-hard, i.e., its computational complexity increases exponentially with the number of users (Verdu 1986, 1989). In this letter, we show that the optimum multiuser detection problem for a synchronous code-division multiple access (CDMA) system is equivalent to the minimum capacity cut problem in a related network and propose an optimum multiuser detection algorithm with polynomial computational complexity for a certain class of signature sequences. The minimum cut problem is solvable in polynomial time if the capacities of the links not incident to source and sink are nonnegative. This condition in the optimum detection problem is equivalent to all cross correlations between the signature sequences of the users being negative. One example of such a set of signature sequences is obtained when shifted versions of the maximal length sequences (or m-sequences) are used. In this case the cross correlation between users i and j is given as /spl Gamma//sub ij/=-1/G for all i,j, where G is the processing gain.

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Sequential analysis has been used in many cases when the decision is supposed to be taken quickly such as for signal detection in statistical signal processing, namely sequential detector. For identical error probabilities, a sequential detector needs a smaller average sample number (ASN) than its counterpart of a fixed sample number quadrature detector based on Neyman-Pearson criteria. The optimum sequential detector was derived based on the assumption that the observations are uncorrelated (independent). However, in realistic scenario, such as in radar, the assumption is commonly violated. Using a sequential detector under correlated observations is sub-optimal and it poses a problem. It demands a high computational complexity, since it needs to recalculate the inverse and the determinant of the signal covariance matrix for each new sample taken. This paper presents a technique for reducing the computational complexity, which involves using recursive matrix inverse to subsequently calculate conditional probability density functions (pdf). This eliminates the need to recalculate the inverse and determinant, leading to a more reasonable solution in real-world scenario. We evaluate the performance of the proposed (recursive) sequential detector by using Monte-Carlo simulations and we use the conventional and non-recursive sequential detectors for comparisons. The results show that the recursive sequential detector has equal probabilities of false alarm and miss-detection with the conventional sequential detector and performs better than the non-recursive sequential detector. In terms of ASN, it maintains comparable results to the two conventional detectors. The recursive approach has reduced the computational complexity for matrix multiplication to from and it also has rendered the calculation of matrix determinant to be unnecessary. Therefore, by having better probabilities of error and reduced computational complexities under correlated observations, the proposed recursive sequential detector may become a viable alternative to obtain a more agile detection system as required in future applications, such as in radar and cognitive radio.

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

Near-far resistance is one of the most important performance measures in a multiuser communication system, especially in a code division multiple access (CDMA) system. The optimum multiuser detector can achieve the optimum near-far resistance. However, due to its high computational complexity, the optimum detector is impractical to implement. Nevertheless, computation of the near-far resistance of the optimum multiuser detector is still important since it is the least upper bound on the near-far resistance of any detector, as well as a benchmark for relative performance of any suboptimum detector. Lupas et al. and Zvonar et al. provided the computation of the optimum near-far resistance in the asynchronous AWGN and unipath channel case. In this paper, we extend the above results to the asynchronous multipath channel case. We derive the optimum near-far resistance under the assumption of a common identifiability condition in the blind multiuser detection/equalization literature. We also derive the ideal near-far resistance of three typical methods in blind multiuser detection/equalization (subspace, linear prediction, and constrained optimization) and compare them with that of the optimum detector. Two methods to enhance near-far resistance of suboptimum detectors are also presented. Furthermore, one possible cause that may affect the near-far resistance in a practical setting is analyzed. The computational complexity of the proposed methods is analyzed and compared. Simulations confirm the theoretical findings.

Finite memory detector formulations have provided some insight into the role of receiver memory in signal detection problems[1]-[5]. One design uses a finite set of integers to characterize a µ state memory such that a sequentially operating transition rule involving observation thresholding can offer performance comparable to the optimal infinite memory detector. This generally suboptimal algorithm generates time varying observation thresholds offering a convergent probability of decision error for a rather large class of problems, including SKE, SKEA, and M-ary detection problems[5]. Conversely, it has been shown that time invariant transition rules generally offer a non-convergent decision error probability[1]. The essential contribution here is an analytical analysis of a simple time invariant finite memory detector. These results are compared to the time varying finite memory detector, and the optimal infinite memory detector.

There has been much work done on deriving adaptive linear detectors for DS-CDMA systems corrupted by additive Gaussian noise. However, such communication systems are often interfered with by noises other than the classical white Gaussian noise; the present author considers DS-CDMA systems corrupted by natural impulsive noise sources, such as those found in low-frequency atmospheric channels, and for channels corrupted by man-made impulsive sources such as those occurring in urban or military radio networks. He develops an adaptive linear detector, for such impulsive noise channels, which directly minimizes the average probability of bit-error, using an infinitesimal perturbation analysis (IPA) based stochastic gradient algorithm. The implementation allows a very simple recursive structure, and the conditions for convergence of this algorithm are presented. The performance of the detector is uniformly better than that of the linear correlator even under the extreme cases when either the multiple access interference or the impulsive noise is dominant.

Spatial multiplexing multiple-input-multiple-output (MIMO) communication systems have recently drawn significant attention as a means to achieve tremendous gains in wireless system capacity and link reliability. The optimal hard decision detection for MIMO wireless systems is the maximum likelihood
\n(ML) detector. ML detection is attractive due to its superior performance (in terms of BER). However, direct implementation grows exponentially with the number of antennas and the modulation scheme, making its ASIC or FPGA implementation infeasible for all but low-density modulation schemes using a
\nsmall number of antennas. Sphere decoding (SD) solves the ML detection problem in a computationally efficient manner. However, even with this complexity reduction, real-time implementation on a DSP processor is generally not feasible and high-performance parallel computing platforms such as FPGAs
\nare increasingly being employed for this class of applications. The sphere detection problem affords many opportunities for algorithm and micro-architecture optimizations and tradeoffs. This paper provides an overview of techniques to simplify and minimize FPGA resource utilization of sphere detectors for high performance low-latency systems.

The design of detectors for binary signals in symmetric alpha-stable noise is considered. Since the optimal detector is impractically complex, many suboptimal detectors have been proposed such as the Gaussian, soft limiter, myriad and Cauchy detectors. However, no adequate explanation for the difference in performance between these detectors has been proposed. In this paper, we propose a novel framework, based on the optimal decision regions, that is used to justify the performance of many suboptimal detectors and compare them to the optimal one. Moreover, the analysis of the framework provides a novel method to significantly improve the performance of the soft limiter detector by employing an adaptive threshold that is a function of the signal level. As the number of samples per symbol increases, the performance of the proposed adaptive detector approaches the optimal performance at almost no additional complexity over the conventional Gaussian detector.

Optimum detectors for CPM use in general a large number of filters in order to calculate the optimum metrics. In this paper, we propose correlation detectors that calculate its metrics in a subspace of the signal space. The subspace is selected such that the asymptotic error performance is optimized for the given dimensionality. We focus on noncoherent detectors but show also some results for coherent detectors. The subspace metric calculation is combined with previously published reduced complexity decoding algorithms such as the SAN(B) and RSSD algorithms. Optimum subspace correlation detectors with different number of filters are found for both binary and quaternary CPM schemes. Their error performance on an AWGN channel is derived analytically through the use of a minimum Euclidean distance approach and is also simulated through the symbol error probability. Comparison is done with the optimum detectors. A close agreement between minimum distance and simulated symbol error probability is found for all considered detectors. We find that in most cases only 4 to 6 matched filters are needed in order to obtain a performance that is close to optimum. This corresponds to at least a five‐fold reduction in number of filters and with the reduced complexity search algorithms for making symbol decisions this leads to a dramatic reduction in overall complexity.

Near-far resistance is one of the most important performance measures in a CDMA multiuser communication system, especially when power control is difficult to implement, such as in an ad hoc wireless network. The optimum multiuser detector can achieve the optimum near-far resistance. But due to its high computational complexity, the optimum detector is impractical to implement. Cost-effective suboptimum detectors, i.e., linear detectors, are more practical to implement. However, the optimality in near-far resistance is generally lost. We examine the structural differences of the channel matrix between the optimum and the suboptimum detectors. A transmission scheme is then proposed that almost restores the near-far resistance of the suboptimum detectors to that of the optimum one, at least theoretically. Computer simulations are performed to verify the theoretical findings.

The receiver in a wireless communication system has the task of computing good estimates for the data symbols that have been transmitted. The best (optimum) detector is the Maximum Likelihood (ML) detector. However, it requires a high computational complexity. This work aims to efficiently detect the transmitted symbols with a reduced complexity. In order to produce a near optimum receiver, two methods are presented. These methods are obtained by convex optimization relaxations which yield global optimum solutions. The relaxations are combined with the idea of using the structure of the channel matrix to reduce the computational complexity. The channel matrix exhibits a banded Toeplitz structure. In each case, the dual problem of the convex optimization relaxation is solved to estimate the noise power. Gradient descent algorithm is used to solve the dual problem in the first relaxation while the bisection method is applied for the second relaxation. In both cases, the result is a Generalized Minimum Mean Squared Error (GMMSE) detector which has a form similar to the Minimum Mean Square Error (MMSE) detector and a performance almost the same as the MMSE detector, but it is not require the knowledge of the noise power. The GMMSE detectors can be used in scenarios where adapted or blind adaptive detection is not suitable, for instance when the channel is rapidly changing. Using a circular approximation of banded Toeplitz matrix the Fast Fourier Transform (FFT) can be applied to reduce the computational complexity of the detectors. Finally, the local search method is applied to enhance the performance of the proposed GMMSE detector. The proposed detector is a near optimum detector with low computational complexity.

By using compressive measurements, parameter estimation of LFM signal can be performed without completely reconstructing the original signal. Currently, estimation methods based on compressive measurements will not get good results for LFM signal with narrow-band interference. That is because, by using sparse decomposition of mixed-signal with a single dictionary, narrow-band interference cannot be separated effectively. Aiming at this situation, an improved parameter estimation method based on morphological component analysis is proposed in this paper, in which compositions with morphological differences in the mixed-signal are sparsely represented using corresponding dictionaries which are constructed according to different compositions. For the sparse representation of the mixed-signal is improved, the method leads to better parameter estimation of LFM signal. The experimental results indicate that in compare with the conventional method, with the same number of sampling, by using the method proposed in this paper, parameter estimation of LFM signal with narrow-band interference is more accurate.

The objective of in situ thermal treatment is typically to reduce the contaminant mass or average soil concentration below a specified value. Evaluation of whether the objective has been met is usually made by averaging soil concentrations from a limited number of soil samples. Results from several field sites indicate large performance uncertainty using this approach, even when the number of samples is large. We propose a method to estimate average soil concentration by fitting a log normal probability model to thermal mass recovery data. A statistical approach is presented for making termination decisions from mass recovery data, soil sample data, or both for an entire treatment volume or for subregions that explicitly considers estimation uncertainty which is coupled to a stochastic optimization algorithm to identify monitoring strategies to meet objectives with minimum expected cost. Early termination of heating in regions that reach cleanup targets sooner enables operating costs to be reduced while ensuring a high likelihood of meeting remediation objectives. Results for an example problem demonstrate that significant performance improvement and cost reductions can be achieved using this approach.