Abstract The design of an optimal non‐orthogonal multiple access (NOMA) transmission scheme with finite alphabet inputs for a typical two‐user uplink wireless communication system is investigated in which each terminal is equipped with a single antenna. Each of the two users utilises a four quadrature amplitude modulation (4‐QAM) constellation to transmit information data to a common base station, and the receiver employs a maximum likelihood (ML) detector to jointly estimate both transmitted signals. Assuming the availability of channel state information at both the transmitters and the receiver, it is aimed to design a pair of scalar beamformers for the two users such that the minimum Euclidean distance between elements of the received sum‐constellation is maximised subject to the power constraints on the users. A thorough consideration of all the different conditions results in the derivation of a closed‐form optimal beamformer design. As well, examination of the construction of sum‐constellation resulted from the optimum design directly leads to the unique decoding of the original transmitted signal of each user. To facilitate practical implementation, a fast decoding procedure of the optimum NOMA scheme is further developed. The corresponding theoretic probability of ML detection error is also derived. The theoretical development of an optimum sum‐constellation for the basic 2‐user 4‐QAM system provides a solid platform for the derivation of an optimum sum‐constellation for a K ‐user and/or M ‐QAM system. Indeed, a simple development of the basic sum‐constellation map facilitates such extensions. Numerical simulations not only demonstrate that the performance of the fast decoder agrees closely with the theoretical analysis, but also verify that it is superior in performance to other existing NOMA designs for the same system under high signal‐to‐noise ratio.

Quantum illumination (QI) is a technique exploiting the quantum entanglement between the transmitted signal and the idler to enhance the detection performance of a quantum radar over the classical radar. Here, we propose the double optical parameter amplifier (OPA) detector for QI so that the effect of entanglement between the idler and the returned signal beams is maximized. We show here how even when a weak returned signal is embedded in a large background noise, the probability of detection can be significantly increased.

Abstract A design technique is developed for the probing signals of a Multi‐Input Multi‐Output (MIMO) radar. The concentration of the energy of the signal in its essential duration and essential bandwidth is achieved through the use of a class of time‐frequency concentrated functions called the WLJ functions as the synthesizing signal set. The goal is to design a signal vector having a pre‐specified desired covariance (CoV) matrix while ensuring that the side‐lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED); rather, the distance should be measured along the surface of the manifold, that is, in terms of a Riemannian distance (RD). In either case, the signal optimisation problem is non‐convex in the design variables, involving, respectively, a quartic and a square‐root objective function. An efficient algorithm based on successive convex approximation is developed in which the original non‐convex problems are transformed so that they can be approximated by a convex quadratically constrained quadratic problem at each stage, resulting in good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster when optimising over the manifold (RD) than when optimising over the whole space (ED). More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.

Massive machine-type communications (mMTC) is a key enabling technology for Internet of Things (IoT) services in 5G and beyond. Efficient data collection from massive machine-type communication devices (MTCDs) performing sensing tasks is an important part of the service. In this paper, we consider an unmanned aerial vehicle (UAV) being deployed to facilitate data collection from MTCDs. Taking into account the limited energy of battery-powered MTCDs, the UAV trajectory is optimized to improve the energy efficiency of data collection. By fixing the starting and ending points of the UAV trajectory, a globally optimal (GO) trajectory can be obtained, based on the assumption that the UAV's serving radius and access capacity (number of served MTCDs) are unlimited. Interestingly, it is shown that the optimal trajectory always exists as long as the UAV flying height is greater than its service radius multiplied by a constant. However, the increase of the UAV flying height deteriorates the channel, leading to reduced efficiency of energy consumption. Alternatively, a greedy dynamic (GD) trajectory optimization scheme with limited UAV service radius and access capacity is then investigated, resulting in the optimal service location of the UAV being at a lower flying height, and the energy consumption for accomplishing the data collection task being reduced. Specifically, the UAV sorts the MTCDs within its serving radius based on the distance and selects its closest serving MTCD set. In a serving MTCD set, there is an optimal hovering location that maximizes the data collection efficiency. The UAV dynamically adjusts its service set and the optimal data collection location when MTCDs finish their data transmission and exit the service set. The process continues until all the MTCDs are served and the UAV arrives at the ending point of the trajectory. Simulation results show that both the GO and GD algorithm can improve the efficiency of overall energy consumption. In particular, the online dynamic trajectory optimization scheme is less restrictive and achieves higher efficiency.

We consider the signal design problem for a Multi-Input Multi-Output (MIMO) radar. The goal is to design a signal vector having a desired covariance (CoV) matrix while ensuring that the side-lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED), rather, the distance should be measured along the surface of the manifold, i.e., in terms of a Riemannian distance (RD). In either case, the signal optimization problem is quartic in the design variables. An efficient algorithm based on successive convex quadratic optimization is developed and is effective in producing good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster by optimizing over the manifold (RD) than by optimizing in ED. More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.

This paper develops a power allocation strategy for multiple networks of Poisson-distributed single-antenna nodes that share the available spectrum in a spectrum underlay scenario. This strategy aims to maximize the overall throughput obtained by sharing the spectrum while limiting the degradation of the successful transmission probability of each network. In its original form, this joint power allocation problem is difficult to solve. However, we demonstrate that the problem can be transformed into a convex optimization formulation, which can be efficiently solved. Furthermore, we obtain a quasi-closed-form solution that has a water-filling interpretation by analyzing the optimality conditions. Numerical results indicate that, when a spectrum-sharing scheme employs the proposed optimal strategy of power allocation, the throughput substantially improves over that obtained by exclusively allocating the spectrum to the primary network. Moreover, when the number of spectrum-sharing networks increases, the enhancement is significant, being up to the limit imposed by the maximum allowable degradation in the performance of each network.

This paper develops a power control strategy for multiple spectrum-sharing networks of single antenna nodes in a spectrum underlay scenario. A distinguishing feature of the proposed strategy is that it requires only knowledge of the spatial distribution of the nodes, rather than instantaneous channel state information. The strategy seeks to maximize a weighted sum of the throughput of each network while guaranteeing specified successful transmission probabilities. In its native form, this joint power allocation problem is difficult to solve. However, we show that the problem can be transformed into a convex optimization formulation that can be efficiently solved using general purpose tools. Furthermore, we analyze the optimality conditions and obtain a quasi-closed form solution reminiscent of waterfilling. Numerical results demonstrate that spectrum sharing employing the proposed optimal power yields a substantial throughput gain over allocating the spectrum to a single network.

The direct application of orthogonal space-time block coding (OSTBC) for multiple input and multiple output (MIMO) systems to distributed cooperative relay networks makes the equivalent channel matrix for maximum likelihood (ML) detection lose its orthogonality. Hence, this paper proposes a new design that makes the channel matrix be orthogonally distributed (OD) for a suboptimal symbol-by-symbol detector (SBSD). Using ODSTBC, an asymptotic symbol error probability (SEP) formula with SBSD is derived, showing the optimal diversity gain function is achieved. In addition, two kinds of ODSTBC designs for the distributed relay networks are presented, which interestingly renders that SBSD is equivalent to the ML detector. Numerical results verify the diversity analysis and indicate competitive error performance to currently available orthogonal distributed STBC designs with much simpler complexity.

In this paper we take a new perspective on the worst case robust multiuser downlink beamforming problem with imperfect second order channel state information at the transmitter. Recognizing that all channel covariance matrices form a Riemannian manifold, we propose to use a measure properly defined along this manifold in order to model the set of mismatched channel covariance matrices for which robustness shall be guaranteed. This leads to a new robust beamforming problem formulation for which a convex approximation is derived. Simulation results show a dramatically improved performance of the proposed scheme, both in terms of transmission power and constraint satisfaction, as compared to the previous methods.

This work presents a novel full generalized likelihood ratio test (GLRT) for signal detection in a sensor array environment. The multiple hypothesis test approach is well known to have excellent detection performance among several popular methods. Existing multiple test procedures consider the relation between two adjacent models. When the number of signals or the assumed number of signals is large, it tends to overestimate the number of signals. The proposed full GLRT procedure overcomes this disadvantage by employing complete information between candidate models and leads to gain in test power. A further advantage is that a confidence interval for the true number of signals can be constructed based on the outcome of the GLRT procedure. Numerical results show that the full GLRT procedure improves detection performance significantly in comparison with existing multiple test based approaches in challenging scenarios.

In this work, the authors study the classification of electroencephalogram (EEG) signals for the determination of the state of sleep of a patient. They employ the power spectral density (PSD) matrices as the feature for the distinction between different classes of EEG signals. This not only allows us to examine the power spectrum contents of each signal as well as the correlation between the multi-channel signals, but also complies with what clinical experts use in their visual judgement of EEG signals. To establish a metric facilitating the classification, the authors exploit the specific geometric properties, and develop, with the aid of fibre bundle theory, an appropriate metric in the Riemannian manifold described by the PSD matrices. To use this new metric effectively for the EEG signal classification, the authors further need to find a weighting for the PSD matrices so that the distances of similar features are minimised whereas those for dissimilar features are maximised. A closed form of this weighting matrix is obtained by solving an equivalent convex optimisation problem. The effectiveness of using these new metrics is examined by applying them to a collection of recorded EEG signals for sleep pattern classification based on the k-nearest neighbour decision algorithm with excellent outcome.

It is shown that binary low-density generator matrix codes can achieve the rate-distortion bound of discrete memoryless sources with general distortion measure via multilevel quantization. A practical encoding scheme based on the survey-propagation algorithm is proposed. The effectiveness of the proposed scheme is verified through simulation.

We consider asynchronous Slepian-Wolf coding where the two encoders may not have completely accurate timing information to synchronize their individual block code boundaries, and propose LDPC code design in this scenario. A new information-theoretic coding scheme based on source splitting is provided, which can achieve the entire asynchronous Slepian-Wolf rate region. Unlike existing methods based on source splitting, the proposed scheme does not require common randomness at the encoder and the decoder, or the construction of super-letter from several individual symbols. We then design LDPC codes based on this new scheme, by applying the recently discovered source-channel code correspondence. Experimental results validate the effectiveness of the proposed method.

This paper addresses the problem of designing optimum full-symbol-rate linear space-time block codes (STBC) for a multi-input multi-output (MIMO) communication system with M transmitter and N ≥ M receiver antennas and a linear minimum mean square error (MMSE) receiver. By analyzing the detection error probability expression for the optimized STBC, it is shown that for QAM signaling, the maximum diversity gain for such a system is N - M + 1. The minimum probability of error STBC design is then extended to systems in which the transmission spans L independent realizations from a block fading channel model, and a (multiblock) linear MMSE receiver is employed. Necessary and sufficient conditions for the optimality of the code are obtained, and a systematic design method for generating codes that satisfy these conditions is presented. The detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed. It is proved that the error probability decreases with L, and it is shown numerically that the diversity gain increases with L. Thus, if the corresponding latency can be accommodated, for sufficiently large L an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block-fading channel and achieve higher diversity gain than that of any single-block system of the same symbol rate with a maximum likelihood (ML) receiver. The optimized multiblock linear system achieves this diversity at a substantially lower computational cost. In fact, the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver.

In a parallel distributed detection in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. In this paper, we propose a blind technique for the M-ary distributed detection problem. We derive the probability mass function of the local decisions and use this result to develop maximum likelihood estimates of unknown parameters. We also derive analytically the overall detection performance for both binary and M-ary distributed detection and discuss the difference of the overall detection performance obtained using the estimated values of unknown parameters and their true values. Finally, we demonstrate the applicability of our results through numerical examples.

We consider asynchronous Slepian-Wolf coding where the two encoders may not have completely accurate timing information to synchronize their individual block code boundaries, and propose LDPC code design in this scenario. A new information-theoretic coding scheme based on source splitting is provided, which can achieve the entire asynchronous Slepian-Wolf rate region. Unlike existing methods based on source splitting, the proposed scheme does not require common randomness at the encoder and the decoder, or constructing super-letter from several individual symbols. Furthermore, we show that linear codes are sufficient for each coding step of this scheme. We subsequently design LDPC codes based on this new scheme, by applying the recently discovered source-channel code correspondence. Experimental results validate the effectiveness of the proposed method.

In this paper, the ergodic channel capacities are established for the amplify-and-forward (AF) half-duplex cooperative systems, which consist of a source node, a destination, and multiple-relay nodes. The relay nodes assist the transmission from the source node to the destination. Since the channel matrices for the cooperative systems involve product of Gaussian random variables, which are no longer Gaussian, the approach in obtaining the ergodic channel capacity for conventional multiple-input-multiple-output (MIMO) Gaussian channels (Telatar, 1999) is not applicable. By using a novel approach, we have arrived at the following conclusions about the ergodic channel capacities for the AF cooperative systems. For the single antenna AF relay systems in which all nodes are equipped with one antenna, the optimal covariance matrix of the input signals to achieve the ergodic channel capacity is diagonal, and the diagonal elements are obtained by solving optimization problems of multidimensional integrals. These diagonal entries are not all equal even if all the channel gains in the cooperative systems are independent and identically distributed (i.i.d.) Gaussian with unit variance. Therefore, a white input signal for the AF cooperative system may not achieve the ergodic channel capacity of the system. This is in direct contrast to the case of conventional multiple-input-single-output (MISO) systems having i.i.d. Gaussian channel gains of unit variance, in which case, the ergodic capacity is achieved if the input covariance matrix is a scaled identity matrix. For the MIMO relay system in which the nodes have multiple antennas, the input covariance matrix to achieve the ergodic capacity is block diagonal and each block diagonalizes the autocorrelation of channel matrix from the source to the destination. This is different from the case of conventional MIMO systems, where the input covariance matrix to achieve the ergodic channel capacity diagonalizes the channel autocorrelation matrix of the MIMO system (Tulina, Lozano, and Verdu, 2006). If the channel gains in conventional MIMO systems are correlated Gaussian random variables, the input covariance matrix is a full matrix, not block diagonal; and if the channel gains are i.i.d. Gaussians, the optimal input covariance matrix is a scaled identity. The observations obtained in this paper reveal useful insights of how the AF cooperative systems ldquomimicrdquo the conventional MISO and MIMO systems from the ergodic channel capacity perspective.

In this paper, a new algorithm for robust adaptive beamforming is developed. The basic idea of the proposed algorithm is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Unlike other robust beamforming techniques, our algorithm does not assume that the norm of the mismatch vector is upper bounded, and hence it does not suffer from the negative effects of over/under estimation of the upper bound. Simulation results show the effectiveness of the proposed algorithm.

We proposed a new signal transmission scheme for a multi-input multi-output (MIMO) communication system, in which the signals are encoded to span multi-block channel realizations and received by a linear equalizer followed by a maximum likelihood (ML) detector. The proposed system achieves a diversity gain proportional to the number of blocks of channels over which the signals span. The detection complexity is comparable to that of a linear receiver, with additional complexity independent of the number of antennas. A general criterion for designing the optimal precoder is presented. A design example is provided. Simulation results verify the effectiveness of such a combination.

We consider the problem of space-time block code (STBC) design for Ricean fading channels in a multiple-input multiple-output (MIMO) communication system equipped with a linear minimum mean square error (MMSE) receiver. Two criteria, i.e., ergodic channel capacity and mean square error (MSE) are used for the design. Due to the complexity of the mathematics involved, no general solution has yet been proposed for a Ricean channel with arbitrary mean. In this paper, we present the necessary and sufficient conditions for the design of the optimal precoder applicable to any channel condition and any range of signal-to-noise ratio (SNR). Simulations verify that the performance of the MIMO system using the optimum precoder is indeed superior in performance.

We consider a flat fading wireless link having multiple M transmitter antennas and a single receiver antenna (MISO). This system is often useful in mobile downlink communications for which the mobile receiver may not be able to support multiple antennas. For such a system, we propose a novel and very simple design of full diversity two-group and four-group decodable block diagonal linear dispersion codes with rate one for any number of the transmitter antennas. For M = 2nand M = 2n− 1, we also prove that for K-ary Quadrature Amplitude Modulation (QAM) transmission equipped with a maximum likelihood (ML) detector, our proposed code minimizes the worst case average pair-wise error probability, i.e., it achieve optimal coding gain.

In this paper, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach depends on explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices, worst-case performance optimization and guarantees that the quality of service (QoS) constraints are satisfied for all users using minimum amount of power. An iterative algorithm to find the optimum power allocation is proposed. The key to this algorithm is to solve an optimization problem to obtain worst-case uncertainty matrices. When the uncertainty is small enough to guarantee that the DCC matrices are positive semidefinite, we obtain a closed-form solution of the subproblem. When the uncertainty is large, we transform this intractable problem into a convex problem. Simulation results show that our proposed robust downlink power control using the approach of worst-case performance optimization reduces the transmission power effectively under imperfect knowledge of the channel condition.

We consider the design of the precoder for a multi-input multi-output (MIMO) communication system equipped with a decision feedback equalizer (DFE) receiver. For such design problems, perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver is usually required. However, in the wireless communications environment, it is often difficult to provide sufficiently timely and accurate feedback of CSI from the receiver to the transmitter for such designs to be practically viable. In this paper, we consider the optimum design of a precoder for a wireless communication link having M transmitter antennas and N receiver antennas (M ≪ N), in which the channels are assumed to be flat fading and may be correlated. We assume that full knowledge of CSI is available at the receiver. At the transmitter however, only the second order statistics of the channels are available. Our goal here is to come up with an efficient design of the optimal precoder for such a MIMO system by minimizing the average arithmetic mean-squared error (MSE) of zero-forcing (ZF) decision feedback detection subject to a constraint on the total transmitting power. Applying some of the properties of the matrix parameters, this non-convex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method. The superior performance of our MIMO system equipped with the optimum precoder is verified by computer simulations.

A new approach to the design of robust adaptive beamforming is introduced. The essence of the new approach is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Contrary to the worst-case performance-based and the probability-constrained-based approaches, our approach does not make any assumptions on either the norm of the mismatch vector or its probability distribution. Hence, it avoids the need for estimating their values.

In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input-single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: (1) the symbol transmission rate can be made to approach unity; (2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability.

In this paper, an optimal unitary precoder is designed for an amplify-and-forward (AF) half-duplex relay system to obtain the maximum coding gain while the original ergodic channel capacity for the relay system is kept unchanged. A closed-form design is derived for quadrature amplitude modulation (QAM) signals by employing the properties of Farey sequence in number theory. Simulation results indicate that the proposed design greatly improves the bit error rate (BER) performance for the relay system.

Recently, distributed space-time code designs with high cooperative diversity for wireless communication networks, such as ad hoc and sensor networks, have received much attention. Amplify forward and decoding forward are widely used protocols for the cooperative diversity in the wireless communication networks. In both protocols, the information received by relay terminals are "forwarded" to destination or next relay terminals. Since the signals transmitted by relay terminals and those transmitted from the source terminal are correlated, there is information redundancy. To improve the energy efficiency of cooperative networks, we propose an encoding protocol, which is referred to as a nested cooperative encoding protocol. In our proposed protocol, the received signal at each relay terminal is divided into several sub-signals with the nest lattice structure of source information. Each of the sub-signals contains only a partial information with a smaller size of constellation compared to the original information sent by the source terminal. Do a new encoding or modulation by using these sub-signals before transmitting at relay terminals. It is shown that the proposed new protocols can achieve both high cooperative diversity and high energy efficiency.

In this paper, we design an optimal precoder for the amplify-and-forward (AF) half-duplex cooperative system. We first present asymptotic pairwise error probability (PEP) expression and identify the corresponding terms for diversity and coding gains. By employing the properties of the Farey sequence in number theory, we obtain a closed form optimal precoder to achieve both full diversity as well as maximum coding gain for square quadrature amplitude modulation (QAM) signals. Simulation results indicate that the proposed design significantly improves the BER performance of the relay system.

A new algorithm for estimating the parameters of multiple wideband polynomial-phase signals (PPSs) in sensor arrays is developed. The spatial high-order instantaneous moments (SHIMs) are first defined using a nonlinear transformation of the array snapshot vectors. Then, the properties of SHIMs of multiple wideband PPSs are employed to obtain recursive estimates of the PPS frequency parameters. The time-frequency properties of SHIMs are then exploited for estimating the source directions-of-arrival (DOAs) using spatial time-frequency distributions (STFDs). The proposed algorithm is shown to have an improved performance compared to the chirp beamformer technique. Since our algorithm is based on multiple one-dimensional searches, it also offers a much simpler implementation avoiding multi-dimensional search, which is needed for other algorithms.

In a parallel distributed detection system each local detector makes a decision based on its own observation, then transmits its local decision to a fusion center. Given fixed local decision rules, in order to design the optimal fusion rule for the M hypotheses, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probability of the hypotheses. Such knowledge may not be available in practice. In this paper, we propose a suboptimal algorithm for M-ary decision fusion based on binary groupings of multiple hypotheses. Simulation results show that this method is effective in practice.

We consider a multi-input multi-output (MIMO) communication system equipped with a linear minimum mean-square error (MMSE) receiver. We design a full-rate linear space-time block code (STBC) for blocks of data that span several realizations of a block-static fading channel to achieve high diversity gain. The proposed code structures are necessary and sufficient to minimize the detection error probability. They also enable the detection computations to be partitioned into separate blocks such that the normalized complexity is reduced to little more than that for a single block. The additional complexity grows only linearly with L, the number of blocks for which the code design covers. Analysis shows that the diversity gain achieved by the code also grows linearly with L. This is confirmed by simulation results

The design of a linear space-time code with full rate, large diversity product, and non-vanishing minimum determinant of codewords continues to attract great attention. However, in most available no-vanishing determinant space-time codes for three, four, and six transmitter antennas, the average power at each layer is different, which results in a high peak to average power ratio. In this paper, a new cyclic algebraic space-time design scheme is proposed and the optimal codes in this class are provided by using some specific cyclic field extensions. Our proposed codes not only include the available non-vanishing determinant cyclotomic space-time codes for three, four, and six transmitter antennas, but also have the desirable property that the optimal codes can be achieved with the same average power at each layer.

This paper presents a method for jointly designing the transmitter-receiver pair in a block-by-block transmission system that employs minimum mean square error intra-block decision feedback detection. We provide a recursive closed-form expression for a transceiver which maximizes the Gaussian mutual information and also minimizes the bit error rate at moderate-to-high signal-to-noise ratios (in the absence of error propagation). The proposed design generates uncorrelated inputs to the decision device with equal signal-to-interference-and-noise ratios. These properties suggest that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceiver performs significantly better than standard transceivers, and that it retains its performance advantages in the presence of error propagation.

In this paper, we introduce the definitions of a full diversity integer generating matrix and the corresponding norm form space-time code for MIMO systems. Subject to a power constraint, we characterize all full diversity integer generating matrices with the first three largest gains in the Gaussian integer ring and the Eisenstein integer ring for two transmitter antennas. Using this generating matrix family to separately design space-time codes layer by layer for two transmitter antenna and two receiver antenna MIMO systems, we obtain the optimal norm form integer space-time codes both in the Gaussian integer ring and the Eisenstein integer ring in the sense of maximizing the minimum determinant of codeword matrices. As a consequence, we prove that the golden code constructed by Dayal and Varanasi, Belfiore, Rekaya and Viterbo is optimal in the Gaussian integer ring. Also, we find the optimal code in the Eisentein integer ring, the coding gain of which is greater than that of the golden code.

We consider efficient techniques for the design of a transceiver for a matrix channel with minimum mean square error (MMSE) decision-feedback (DF) detection when perfect channel information is available at both the transmitter and receiver. By combining the canonical property of the MMSE-DF detector and our recently developed equal-diagonal QRS decomposition of a matrix we obtain a uniform decomposition of mutual information in which each of the synthesized scalar subchannels has the same mutual information (under the assumption of error-free feedback). To assist our analysis of this uniform decomposition, we provide a new QR interpretation of the MMSE-DF receiver. This enables us to show that the natural detection order is optimal (in an SINR sense), and that for the proposed transmitter, the MMSE-DF detector is asymptotically equivalent to the maximum likelihood detector when the SNR is high. We also derive a low-complexity quadratic recursive algorithm for the characterization of all eligible S-factors in the QRS decomposition. When coupled with our QR interpretation of the MMSE-DF detector, this enables us to efficiently design the optimal transmitter and to efficiently implement the MMSE-DF receiver

In this paper we consider coherent flat fading wireless communication systems with multiple transmitter antennas and single receiver antenna (MISO). We propose a Toeplitz linear space time block code (STBC) that converts an original MISO flat fading channel into a Toeplitz virtual multiple inputs multiple outputs (MIMO) channel. We show that our proposed code has the following main features: (a) The symbol transmission rate is (T-M + 1)/T, where M is the number of transmitter antenna and T is the number of channel uses (T > M). (b) Linear receivers (zero-forcing and minimum mean square error) can extract full diversity. Moreover, when the channel coefficients are independent and the maximum likelihood (ML) detector is employed, our Toeplitz STBC minimizes the exact worst case average pair-wise error probability, (c) When channels are correlated, we design our Toeplitz STBC that minimizes the exact average worst case pair-wise error probability. By transforming this non-convex optimization problem into a convex one, the problem can be solved efficiently by employing an interior point method. In particular, when the design criterion in question is approximated by the Chernoff bound, we obtain a closed form solution, (d) Finally, for the independent MISO flat fading system, we prove that our proposed codes can approach the optimal diversity-vs-multiplexing tradeoff developed by Zheng and Tse with a linear zero-forcing receiver when the number of channel uses is large

Radar emitter classification is a special application of data clustering for classifying unknown radar emitters from received radar pulse samples. The main challenges of this task are the high dimensionality of radar pulse samples, small sample group size, and closely located radar pulse clusters. In this paper, two new online clustering algorithms are developed for radar emitter classification: One is model-based using the Minimum Description Length (MDL) criterion and the other is based on competitive learning. Computational complexity is analyzed for each algorithm and then compared. Simulation results show the superior performance of the model-based algorithm over competitive learning in terms of better classification accuracy, flexibility, and stability.

In multiple-input multiple-output (MIMO) multiuser detection theory, the QR decomposition of the channel matrix H can be used to form the back-cancellation detector. In this paper, we propose an optimal QR decomposition, which we call the equal-diagonal QR decomposition, or briefly the QRS decomposition. We apply the decomposition to precoded successive-cancellation detection, where we assume that both the transmitter and the receiver have perfect channel knowledge. We show that, for any channel matrix H, there exists a unitary precoder matrix S, such that HS=QR, where the nonzero diagonal entries of the upper triangular matrix R in the QR decomposition of HS are all equal to each other. The precoder and the resulting successive-cancellation detector have the following properties. a) The minimum Euclidean distance between two signal points at the channel output is equal to the minimum Euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the R-factor. b) The superchannel HS naturally exhibits an optimally ordered column permutation, i.e., the optimal detection order for the vertical Bell Labs layered space-time (V-BLAST) detector is the natural order. c) The precoder S minimizes the block error probability of the QR successive cancellation detector. d) A lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the R-factor in the QR decomposition of a channel matrix. e) The precoder S maximizes the lower bound of the channel's free distance subject to a power constraint. f) For the optimal precoder S, the performance of the QR detector is asymptotically (at large signal-to-noise ratios (SNRs)) equivalent to that of the maximum-likelihood detector (MLD) that uses the same precoder. Further, We consider two multiplexing schemes: time-division multiple access (TDMA) and orthogonal frequency-division multiplexing (OFDM). We d

We study the problem of direction-of-arrival (DOA) estimation using partly calibrated arrays composed of multiple subarrays with unknown inter-subarray parameters and imperfectly known subarray orientations. The recently developed spectral and root variants of the rank reduction estimator (RARE) can handle scenarios where no calibration between subarrays is available but, unfortunately, they are very sensitive to subarray orientation errors. Therefore conventional RARE can be applied to such partly calibrated arrays only if all subarray misorientations are negligibly small. In this paper, we develop a new modification of RARE which improves its robustness against subarray misorientations. The performance of the proposed robust RARE algorithm is demonstrated to be close to the stochastic Cramer-Rao bound (CRB) of the considered estimation problem.

In this paper, we present a design of linear codes which improves the bit error rate (BER) performance for multiple-input multiple-output (MIMO) communication systems, under a flat-fading environment, in which the channel information is unknown for the transmitter but known at the receiver. Recently, space-time codes have been designed to achieve capacity and/or minimize the overall mean square error. Our codes here simultaneously achieve the lower bound of BER, the upper bound of the overall signal to interference plus noise ratio (SINR) and the lower bound of substream minimum mean square error. Our code structure is orthogonal in both overall and individual senses.

It has recently been determined (by others) that one can construct full rate full diversity linear space-time block codes without a reduction in the achievable information rate. In this paper, we address two issues in those designs. One issue is whether the rotation matrix and the Diophantine number can be systematically and efficiently constructed for an arbitrary number of transmitter antennas and receiver antennas and whether the signal constellation is necessarily limited to PAM or QAM. The other issue is whether the currently available square designs can be generalized to a rectangular design and in particular, to a linear dispersion code design. This paper resolves these issues by proposing a trace-orthonormal linear space-time block code and linear dispersion code, and giving a systematic method to design such a code family. By carefully selecting V-structured matrices or conjugate V-structured matrices in this family, we can systematically and efficiently design information lossless full rate full diversity cyclotomic space-time codes.

The problem of joint space-time decoding and multiple-access interference (MAI) rejection in multiple-access multiple-input multiple-output (MIMO) wireless communication systems is addressed. We assume that both the receiver and multiple transmitters are equipped with multiple antennas and that space-time block codes are used to send the data simultaneously from each transmitter to the receiver. A new linear minimum variance (MV) receiver structure is developed to decode the data sent from the transmitter-of-interest and to reject MAI, self-interference, and noise. Simulation results show that in multiple-access MIMO scenarios, the proposed receivers have a substantially lower symbol error rate as compared to the matched filter (MF) receiver which is equivalent to the maximum likelihood (ML) space-time decoder in the point-to-point MIMO communications case.

In this paper we propose a trace-orthonormal linear dispersion code that is an extension of the generalized complex orthogonal space-time block codes and present a method to systematically design such code family. We prove that our proposed codes can minimize the average bit error probability for the QPSK modulation when the minimum mean square error (MMSE) detector is employed. Furthermore, we establish a unified framework to systematically and efficiently construct trace-orthonormal full diversity cyclotomic linear dispersion codes with any integer symbol transmission rate which is less than or equals to the number of transmitter antennas. This result generalizes the currently available linear space-time block code designs into a full diversity linear dispersion code design

Two strategies for improving the (uncoded) bit error rate (BER) performance of practical rate-adaptive block-by-block communication schemes, such as discrete multitone modulation (DMT) is proposed. Our strategies are inspired by some recent work which showed that for uniformly bit-loaded schemes, the transmission strategy which minimizes the BER for a linear receiver involves allocating power to the subchannels that are implicit in the block-by-block framework in a minimum mean square error (MMSE) fashion and linearly combining these subchannels using a normalized discrete Fourier transform (DFT) matrix. This combining equalizes the decision point signal-to-noise ratios (SNRs) of the subchannels. Given a nonuniformly bit-loaded scheme, our first design strategy simply performs a DFT-based linear combination within the groups of subchannels which share the same constellation. Our second strategy provides further reduction in the BER by reallocating power within these groups in a MMSE fashion prior to DFT combining. Our examples indicate that our design strategies can provide significant reductions in the BER, and give rise to substantial SNR gains (of the order of several decibels).

The performance of adaptive beamforming methods may degrade in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. This paper addresses the problem of robust adaptive beamforming in the presence of unknown arbitrary (yet norm-bounded) mismatches of such type as well as interference-plus-noise covariance matrix mismatch. Our approach is developed for the case of an arbitrary dimension of the signal subspace and, therefore, it can be applied to both rank-one and higher-rank signal models. The proposed beamformer is based on the optimization of the worst-case signal-to-interference-plus-noise ratio (SINR). The obtained closed-form solution combines two different types of diagonal loading (DL) applied to the signal and data covariance matrices. An efficient on-line implementation of our beamformer is developed. Simulations validate substantial performance improvements relative to other popular adaptive beamforming techniques.

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless channels. We propose a soft quasi-ML detector, which maximizes the log-likelihood function by developing a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML detector achieves the performance of the optimal ML detector in both coded and uncoded multiple-input multiple-output (MIMO) channels with quadrature phase-shift keying modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, and, thus, the quasi-ML detector offers more favorable performance/complexity trade-off. Compared to the existing sphere decoder the quasi-ML detector enjoys low polynomial worst-case complexity, as well as guaranteed near capacity performance.

A new approach to adaptive beamforming with sidelobe control is developed. The proposed beamformer represents a modification of the popular minimum variance distortionless response (MVDR) beamformer. It minimizes the array output power while maintaining the distortionless response in the direction of the desired signal and a sidelobe level that is strictly guaranteed to be lower than some given (prescribed) threshold value. The resulting modified MVDR problem is shown to be convex, and its second-order cone (SOC) formulation is obtained that facilitates a computationally efficient way to implement our beamformer using the interior point method.

In this paper we derive an analytic expression for the linear precoder which minimizes the bit error rate (BER) for block transmission systems with zero-forcing equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference; viz, zero padding (ZP) and cyclic prefix (CP). The CP minimum BER precoder has a structure similar to that of the conventional water-filling discrete multitone (DMT) modulation scheme, but the diagonal water-filling power loading matrix is replaced by a full matrix consisting of a diagonal minimum mean square error (MMSE) power loading matrix post-multiplied by a Discrete Fourier Transform (DFT) matrix. The ZP minimum BER precoder has a corresponding structure. Performance evaluations indicate that the signal-to-noise ratio (SNR) gain of the ZP and CP minimum BER precoders over conventional water-filling DMT, MMSE, and orthogonal frequency division multiplexing (OFDM) schemes can be as much as several decibels.

Maximum-likelihood (ML) multiuser detection provides attractive bit error rate performance, but it is computationally prohibitive to implement (except in certain restricted cases). Recently, it has been shown that ML detection for synchronous CDMA can be efficiently and accurately approximated using the semi-definite relaxation (SDR) method. In this work, we consider the application of SDR to the more general scenario of asynchronous CDMA. To make this application computationally feasible, we incorporate a block coordinate ascent (BCA) technique into our detector. Simulation studies show that the resulting BCA-SDR detector has significantly better BER performance than several typical suboptimal multiuser detectors.

We study the uniqueness of the signal Direction Of Arrival (DOA) estimates obtained using the RAnk Reduction Estimator (RARE) [I] in partly calibrated subarray-based sensor arrays. A new identifiability condition is derived for such class of arrays which guarantees that the array manifold is unambiguous. The equivalence of the MUSIC solution for the signal DOA's (obtained in the fully calibrated array case) and the RARE solution (obtained in the case of partly calibrated array of the same configuration) is proved and the uniqueness of the RARE DOA estimates is established.

Redundancy introduced using filterbank precoders at the transmitter builds a unified framework for modulation schems. Taking advantage of this diversity can offer a powerful tool for removing interblock interference and devising simple but effective precoders for suppressing the intersymbol interference (ISI) and being robust to frequency selective channels‥ In this paper, we assume that the transmitter knows the autocorrelation sequences of the channel impulse response. Under this assumption, we derive a lower and an upper bound on the free distance for a precoded channel and with this, design the precoder that maximizes the lower bound subject to a power constraint. It turns out that the optimal precoder is a unitary matrix which makes QR decomposition of its super-channel exhibit equal diagonal entries in R-factor and the lower and the upper bounds of its free distance equal. We show that for the optimal precoded channel, the detection performance using the decision feedback equalizer (DFE) based on QR decomposition is asymptotically equivalent to that of the mamximum likehood detector (MLD) when the signal to noise ratio (SNR) is large.

We consider the direction finding problem in time-varying arrays composed of identically oriented subarrays displaced by unknown vector translations. A new eigenstructure-based estimator is proposed for such a class of partly calibrated sensor arrays.

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing scheme in which the message signals are waveform-coded onto wavelet packet basis functions for transmission. However, WPDM suffers from severe performance degradation in the presence of high-power amplifier (HPA) nonlinearities. Data predistortion using the pth-order Volterra inverse is proposed to combat the amplifier nonlinearities in a WPDM system. A 5th-order Volterra inverse with truncated memory length is designed based on the Volterra series channel model. Computer simulations are presented to demonstrate the capability of the proposed technique in compensating amplifier nonlinearities even under system parameter discrepancies. Guidelines are also proposed for designing a wavelet filter which leads to better predistortion with the truncated Volterra inverse.

In multiuser detection, maximum-likelihood detection (MLD) is optimum in the sense of minimum error probability. Unfortunately, MLD involves a computationally difficult optimization problem for which there is no known polynomial-time solution (with respect to the number of users). In this paper, we develop an approximate maximum-likelihood (ML) detector using semi-definite (SD) relaxation for the case of anti-podal data transmission, SD relaxation is an accurate and efficient approximation algorithm for certain difficult optimization problems. In MLD, SD relaxation is efficient in that its complexity is O(K/sup 3.5/), where K stands for the number of users. Simulation results indicate that the SD relaxation ML detector has its bit error performance close to the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.

The upper bound derived by Verdu (1986) is often used to evaluate the bit error performance of both the maximum-likelihood (ML) sequence detector for single-user systems and the ML multiuser detector for code-division multiple-access (CDMA) systems. This upper bound, which is based on the concept of indecomposable error vectors (IEVs), can be expensive to compute because in general the IEVs may only be obtained using an exhaustive search. We consider the identification of IEVs for a particular class of ML detection problems commonly encountered in communications. By exploiting the properties of the IEVs for this case, we develop an IEV generation algorithm which has a complexity substantially lower than that of the exhaustive search. We also show that for specific communication systems, such as duobinary signaling, the expressions of Verdu's upper bound can be considerably simplified.

We consider the problem of identity fusion for a multisensor target tracking system whereby the sensors generate reports on the target identities. Since sensor reports are typically fuzzy, incomplete, or inconsistent, the fusion of such sensor reports becomes a major challenge. In this paper, we introduce a new identity fusion method based on the minimization of inconsistencies among the sensor reports by using a convex quadratic programming formulation. In contrast to Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing complexity, our approach is highly efficient (polynomial time solvable). Moreover, our approach can fuse sensor reports of the form more general than that allowed by the evidential reasoning theory. Simulation results show that our method generates reasonable fusion results which are similar to that obtained via the evidential reasoning theory.

In many communication systems training sequences are used to help the receiver identify and/or equalize the channel. The amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization. In this paper we propose the use of a new adaptive filtering method, interior point least squares (IPLS), for adaptive equalization. One of the main features of the algorithm is its fast transient convergence: it thus requires fewer training bits than for example RLS. We apply the IPLS algorithm to update the weight vector for a minimum-mean-square-error decision-feedback equalizer (MMSE-DFE)in a CDMA downlink scenario. Numerical simulations show that when training sequences are short IPLS consistently outperforms RLS in terms of system bit-error-rate. As the training sequence gets longer IPLS matches the performance of the RLS algorithm.

Investigation of detection schemes for non-orthogonal multicarrier modulation (MCM) is motivated by two reasons. Firstly, non-orthogonal MCM offers a higher degree of freedom in pulse-shaping design. Secondly, the problem of detecting orthogonal MCM under channel distortion can be viewed as a problem of detecting non-orthogonal MCM. In this work, the maximum likelihood detector (MLD) is considered for non-orthogonal multicarrier systems. In the absence of inter-block interference, it is shown that the MLD can be efficiently achieved by a Viterbi algorithm (VA). In contrast to using the VA for channel equalization, the proposed VA has its survivor metrics running in the""frequency domain". Incorporating this VA with an interference-canceling approach, we also develop a decision feedback MLD for the case of non-zero inter-block interference. Superior bit error performance of the MLDs is demonstrated by simulations.

Redundant multirate filter bank transceivers have been proposed for block-based transmission over channels whose characteristics are known at both the receiver and the transmitter. We propose a criterion for the design of such transceivers for applications in which the channel is not known at the transmitter. The design objective is the minimization of the average mean square error of the data estimates produced by a zero-forcing equalizer over a statistically modelled class of channels. Two solution methods are proposed, one of which appears to be amenable to modification for the solution of certain other robust performance problems. It is shown that the optimal transmitter provides substantially improved performance over a scheme based on multicarrier modulation.

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing scheme in which wavelet packet basis functions are chosen as the coding waveforms. In this paper, characterization of the effects of amplifier nonlinearities over the WPDM signal is performed for a 16-QAM signal constellation. An expression for the symbol error probability in the presence of Gaussian noise and amplifier nonlinearities is derived.

Wavelet packet-division multiplexing (WPDM) is a high-capacity, flexible, and robust multiple-signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. We derive an expression for the probability of error for a WPDM scheme in the presence of both impulsive and Gaussian noise sources and demonstrate that WPDM can provide greater immunity to impulsive noise than both a time-division multiplexing scheme and an orthogonal frequency-division multiplexing scheme.

In digital communications, orthogonal pulse shapes are often used to represent message symbols for transmission through a channel. The design of such pulse shapes is formulated as a convex semidefinite programming problem, from which a globally optimal pulse shape can be efficiently found using interior point methods. The formulation is used to design filters which achieve the minimal bandwidth for a given filter length, and the minimal filter length for a given bandwidth. The effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the 'chip' waveforms specified in the standards for digital mobile telecommunications.

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing technique in which wavelet packet basis functions are chosen as the coding waveforms. By analogy with frequency-hopped communication schemes, incorporation of time variation into the WPDM scheme offers the potential for further performance improvements, especially in frequency-selective fading channels. We consider a 'branch-hopped' WPDM scheme which employs an efficient modular switched transmultiplexer structure to induce the time variation. We determine classes of 'slow' and 'fast' hopping schemes analogous to their frequency-hopped counterparts, and evaluate several switching strategies for the transmultiplexer. For a given switching strategy we then design the filters within the transmultiplexer modules to provide further robustness to frequency-selective fading channels.

A prime objective of array processing is to estimate the location of signal sources. The signals in many applications such as ocean exploration, radar and radio communications could appear to be from either point sources or spatially dispersed ones. Previously, a few methods have been proposed to estimate the DOA of dispersed sources. Among them, VEC-MUSIC [Wu et al. 1994] has the property of jointly estimating the DOA of point and dispersed sources. In this paper, the the unique ability of VEC-MUSIC to distinguish a point source from a dispersed source using different noise subspaces is demonstrated. The asymptotic performance of VEC-MUSIC is also analyzed.

The paper describes and analyses, in a unifying manner, the spatial and temporal IV-SSF (instrumental variable-signal subspace fitting) approaches recently proposed for array signal processing in colored noise fields. We derive a general, optimally-weighted, IV-SSF direction estimator and show that this estimator encompasses the UNCLE estimator of Wong and Wu (see IEEE Trans.SP, vol.42, Sept. 1994), which is a spatial IV-SSF method; and the temporal IV-SSF estimator of Viberg, Stoica and Ottersten (see IEEE Trans.SP, May 1995). The latter two estimators have seemingly different forms, so their asymptotic equivalence shown in this paper comes as a surprising unifying result.

In this paper, two types of adaptive FREquency SHift filters are proposed. One is LMS adaptive FRESH filter. The other is blind adaptive FRESH filter. By exploiting the spectral correlation of cyclostationary signals, these adaptive filters can separate the signals which overlap in both frequency and time domain. Theoretical development and simulations of these filters are given in this paper. The results show that for signals which spectrally overlap, the adaptive FRESH filters can perform very well while ordinary adaptive filters fail.

Recently, it has been proposed to apply array beamforming in digital mobile communication systems, such as mobile cellular communication systems and mobile-satellite communication systems, in order to increase channel capacity and suppress co-channel interference. However, the conventional beamforming methods are not suitable for such use, since these methods were mainly developed for signal detection and DOA estimation in radar and sonar. In this paper, utilizing the cyclostationarities of communication signals, we propose three blind cyclic adaptive algorithms (CAB's) and associated fast implementation schemes. We also investigate the characteristics of the new beamforming methods.>

In array signal processing, signal number detection is a necessary step for high resolution directions of arrival (DOA) estimation. With the assumption of spatially white noise, several methods have been proposed for detecting both coherent and uncoherent signals. A new parametric signal number detector for unknown noise environments is proposed. The new detector is suitable for both coherent and uncoherent signals.>

Derives a new set of basis functions which have high energy concentration in both time and frequency. The approach is based on transforming a signal energy maximization problem into an equivalent eigenvalue problem for a certain integral operator, and then showing that the eigenvectors of this integral operator form a complete orthonormal basis. This basis set is in some sense optimal since each basis function has the highest energy concentration within a certain subspace of /spl Lscr//sup 2/. Furthermore, this basis can be employed to analyze and design communication signals for which the energy concentration within the essential duration and essential bandwidth is important and some other optimum characteristics would also be required.>

An approach to detecting the number of signals in an unknown noise environment based on applying canonical correlation analysis to the outputs of two spatially separated arrays is presented. The method, called the canonical correlation test (CCT) method, works very well in a wide variety of colored noise situations and gives a quantitatively controllable performance. Compared with other methods, it shows robust performance even when both AIC and MDL fail completely. Thus, it gives a very attractive, simple, statistically rigorous approach.>

In array signal processing, the spatially white noise model is most commonly used, and most of the high-resolution methods are established on such a noise model. However, in real environments, the noise model is often either unknown or undeterminable. This may cause the high-resolution methods to suffer severe performance degradation. An approach for consistent and parametric direction of arrival (DOA) estimation in unknown noise environments using two separated arrays is proposed under the assumption that noise correlation is spatially limited. This new method can be also applied in radar or sonar tracking and time series analysis.>

Two new information theoretic criteria for detecting the number of signals in spatially correlated noise with unknown covariance matrix are presented. The new criteria take a very simple form involving the canonical correlation coefficients of sensor data, and are applicable to the cases either two sensor arrays or a single array are available. In both cases, the new schemes are significantly superior to the conventional information criteria.>

The authors address the issue of design of linear arrays of sensors with application to high-resolution direction-of-arrival (DOA) algorithms, and present the D-optimality based design criterion (DOBC). The design technique employs certain prior information in the cases of low-angle tracking and where targets are close to each other, and provides an array which minimizes the joint estimation error in angles of arrival. Two examples are given, and both theoretical analysis and computer simulation are carried out, showing that significant improvement in performance can be achieved with this design over the conventional uniform arrays and a class of minimum redundancy (MR) arrays.>

Among high-resolution direction-of-arrival (DOA) estimators, it is known that the maximum likelihood estimation (MLE) has the most desirable performance in resolution. However, when the SNR falls below a certain threshold, its performance degrades considerably. The prime concern of this research is to try to provide a new estimator which can maintain an acceptable performance for the hard conditions under which the MLE fails. The way to achieve this estimator is to introduce a robust hierarchical statistical model to the sampled data. Simulation results have verified that the resultant robust estimator provides improvement in resolution and possesses certain robustness with respect to the misspecification on the signal model.>

By comparing the second-order statistics of the resolution cells under test with those obtained from their neighboring range cells, a detection scheme for detecting a target in a locally stationary two-dimensional random noise field is derived. The assumptions made are: (1) the noise field is uncorrelated in range but correlated in azimuth; (2) the correlation of the data in azimuth can be modeled by a Gaussian autoregressive process of relatively low order. The detection scheme exploits the full information of the second-order statistics in the data to make a detection decision. Its performance is superior to those schemes based on the amplitude or on Doppler shift information only. The proposed scheme is a constant false-alarm rate processor; its threshold can be evaluated by using a central chi-square probability distribution factor and its detection probability can be predicted by a non-central one.>

The entropy of a sequence of random variables under order restrictions is examined. A theorem that shows the amount of entropy reduction when the sequence is ordered is presented. Upper and lower bounds to the entropy reduction and conditions under which they are achieved are derived. Some interesting properties of the entropy of the individual order statistics are also presented. It is shown that the difference between the average entropy of the individual order statistics and the entropy of a member of the original independent identically distributed (IID) population is a constant, regardless of the original distribution. Finally, the entropies of the individual order statistics are found to be symmetric about the median when the probability density function (PDF) of the original IID sequence is symmetric about its mean.>

A novel method for estimating directions of arrival of plane waves impinging on arrays of sensors is proposed. The method is particularly well suited t the case in which the background noise field is nonisotropic, with arbitrary covariance matrix. The joint posterior probability density function of the signal parameters and the noise covariance matrix Sigma is formed, and then the dependence on Sigma is integrated out, after a suitable noninformative prior p( Sigma ) is defined. The resulting estimator structure is then modified to reduce the computational requirements substantially. Significantly improved performance over the MUSIC algorithm, particularly with regard to threshold, is observed.>

A method for the detection of the number of signals in array processing is proposed. This technique can provide the number of signals irrespective of the signal-to-noise ratio, whereas existing detection techniques fail to perform at low signal-to-noise ratios even asymptotically. The asymptotic error performance of the proposed technique is studied, and it is shown that the probability of error is nearly zero. An objective criterion is given to obtain the number of signals for the case in which the number of snapshots are finite. The concept of detectability is introduced, and a methodology is developed to obtain the detectability of an array system together with number of signals.>

A problem central to most high-resolution methods of array processing is the determination of the number of signals K from a finite set of observations. Two common criteria which do not make use of a subjective threshold are the AIC (Akaida information criterion) and MDL (minimum distance length), both of which consist of a likelihood-function term and a penalty term. The idea is to find a number of K such that either of the criteria is minimized. Examination of both criteria reveals that the likelihood function encompasses irrelevant parameters resulting in the relatively inaccurate estimation of the relevant parameters. A criterion is proposed such that a new likelihood function is derived, consisting of only the parameters having some bearing on the determination of K. The improvement of the accuracy in the estimation of the relevant parameters is evaluated. Computer simulations indicate that considerable improvement in performance is attained.>

Severe congestion of the communications spectrum illustrates the need to seek a communication technique that offers the potential to utilize the spectrum efficiently. Communication efficiency and multiple access capability are the two factors influencing the design of signalling systems. In this paper, a technique is proposed to address this problem. A unique continuous baseband waveform is designed for each of the many users. All users are allowed to access the channel at the same time. A waveform estimator followed by a correlator has been postulated as the detection processor. Based on such a processor, the baseband waveforms for individual users are found by maximizing the correlator's output signal-to-noise ratio, subject to the constraint of a finite bandwidth. The resulting waveforms are linear combinations of sinusoids or of prolate spheroidal functions, depending on whether the r.m.s. or the Slepian [1] definition of bandwidth is used. The use of unique continuous baseband waveforms for the individual users avoids the use of rectangular code sequences which spreads the spectrum in conventional code division multiple-access systems.

Proper Orthogonal Projection - Multiple signal classification (POP-MUSIC) is introduced. Two spectral estimates are derived using geometrical approach based on POP-MUSIC which appear to be the counterparts of the Maximum Likelihood (ML) spectral estimate and Linear Prediction (LP) spectral estimate. POP-MUSIC based on linear prediction (POP-MUSIC-LP) provides a superior resolution compared to POP-MUSIC based on maximum likelihood (POP-MUSIC-ML), and this is justified mathematically. Quantitative measures such as degrading factor due to spurious peaks (F) and sharpness factor (Y) are introduced to facilitate the comparative performance of the spectral estimates. A systolic array structure which is suitable for VLSI implementation is given for adaptive estimation of the cross spectral density matrix and the POP-MUSIC spectral estimation. Computer simulation is presented.

Dyadic inverse of a finite length sequence is considered. Properties related to the inverse sequence in sequency domain is derived and compared with the inverse wavelet in the frequency domain. Possibilities of obtaining an exact solution to the inverse filtering problem through sequency domain is investigated.

This paper provides a capsular introduction to the theoretical framework and experimental applications of the Polar Exponential Grid (PEG) transformation, in the context of image analysis. The PEG transformation is an isomorphic (1) representation of the image intensity array that simplifies, and potentially offers new insights about, a variety of tasks in computational vision. We describe the PEG transform representation; we briefly survey its functional precursors in optical computing and image processing. We then give an example of PEG-based image analysis for rotation-and-scale variant template matching and, present the PEG transform as a motif for a class of problems in stochastic estimation of object boundaries.