We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with nonconvex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with nonconvex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing local consistency in support recovery, local convexity and estimation in high-dimensional settings is provided. We illustrate our approach with a numerical example.

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. The correlation function of the matrix series is Kronecker-decomposable. Unlike most past work on matrix graphical models, where independent and identically distributed (i.i.d.) observations of matrix-variate are assumed to be available, we allow time-dependent observations. We follow a time-delay embedding approach where with each matrix node, we associate a random vector consisting of a scalar series component and its time-delayed copies. A group-lasso penalized negative pseudo log-likelihood (NPLL) objective function is formulated to estimate a Kronecker-decomposable covariance matrix which allows for inference of the underlying CIG. The NPLL function is bi-convex and the Kronecker-decomposable covariance matrix is estimated via flip-flop optimization of the NPLL function. Each iteration of flip-flop optimization is solved via an alternating direction method of multipliers (ADMM) approach. Numerical results illustrate the proposed approach which outperforms an existing i.i.d. modeling based approach as well as an existing frequency-domain approach for dependent data, in correctly detecting the graph edges.

We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Existing methods for differential graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper, we analyze a group lasso penalized D-trace loss function approach for differential graph learning from multi-attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in support recovery and estimation in high-dimensional settings is provided. We illustrate our approach using a numerical example where the multi-attribute approach is shown to outperform a single-attribute approach.

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group logsum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data. Keywords: Sparse graph learning; graph estimation; time series; undirected graph; inverse spectral density estimation.

In this paper, the problem of effective and robust delivery of Dynamic Adaptive Streaming over HTTP (DASH) videos over an orthogonal frequency-division multiplexing access (OFDMA) network is studied. Motivated by a measurement study, we propose to explore the request interval and robust rate prediction for DASH over OFDMA. We first formulate an offline cross-layer optimization problem based on a novel quality of experience (QoE) model. Then the online reformulation is derived and proved to be asymptotically optimal. After analyzing the structure of the online problem, we propose a decomposition approach to obtain a user equipment (UE) rate adaptation problem and a BS resource allocation problem. We introduce stochastic model predictive control (SMPC) to achieve high robustness on video rate adaption and consider the request interval for more efficient resource allocation. Extensive simulations show that the proposed scheme can achieve a better QoE performance compared with other variations and a benchmark algorithm, which is mainly due to its lower rebuffering ratio and more stable bitrate choices.

We consider the problem of infemng the conditional independence graph (CIG) of both proper and improper, complex-valued, high- dimensional multivariate Gaussian vectors. A p-variate complex Gaussian graphical model (CGGM) associated with an undirected graph with p vemces is defined as the family of complex Gaussian distributions that obey the conditional independence restrictions im- plied by the edge set of the graph. For real random vectors, consider- able body of work exists, whereas that on proper complex Gaussian graphical models (PCGGMs) is sparse, while that on ICGGMs is non-existent. In this paper, we present a graphical lasso based penal- ized log-likelihood approach for both PCGGMs and ICGGMs. An alternating minimization algorithm is used to optimize the objective functions. Numerical examples illustrate the proposed algorithms.

In a time-division duplex multiple antenna system the channel state information (CSI) can be estimated using reverse training. In multi-cell multi-user massive MIMO systems, pilot contamination degrades CSI estimation performance and adversely affects massive MIMO system performance. In this paper we consider a subspace-based semi-blind approach where we have training data as well as information bearing data from various users (both in-cell and neighboring cells) at the base station (BS). Existing semi-blind approaches assume that the interfering users from neighboring cells are always at distinctly lower power levels at the BS compared with the in-cell users. This requires (perfect) power control. In this paper we do not make any such assumption. Unlike existing approaches, the BS estimates the channels of all users: in-cell and significant neighboring cell users, i.e., ones with comparable power levels at the BS. We exploit both subspace method using correlation as well as blind source separation using higher-order statistics. Finally, the estimated channels are used to detect information symbols, which, in turn, are used as pseudo-pilots to re-estimate the in-cell users' channels. The proposed approach is illustrated via simulation examples and compared with some existing semi-blind methods.

In a time-division duplex multiple antenna system, the channel state information can be estimated using reverse training. A pilot spoofing (contamination) attack occurs when during the training phase, an adversary (spoofer) also sends synchronized, identical training (pilot) signal as that of the legitimate receiver. This contaminates channel estimation and alters the legitimate beamforming/precoder design, facilitating eavesdropping. A recent approach proposed superimposing a random sequence on the training sequence at the legitimate receiver and then using the minimum description length (MDL) criterion to detect pilot contamination attack. In this paper, we augment this approach with estimation of both legitimate receiver and eavesdropper channels, and secure beamforming, to mitigate the effects of pilot spoofing. We consider two cases: 1) the spoofer transmits only the pilot signal and 2) the spoofer also adds a random sequence to its pilot, mimicking the legitimate receiver. We also employ a random matrix theory-based source enumeration approach instead of MDL, for spoofing detection, leading to improved detection performance. The proposed detection and mitigation approaches are illustrated via simulations.

In a time-division duplex (TDD) multiple antenna system, the channel state information (CSI) can be estimated using reverse training. A pilot contamination (spoofing) attack occurs when during the training phase, an adversary also sends identical training (pilot) signal as that of the legitimate receiver. This contaminates channel estimation and alters the legitimate beamformimg design, facilitating eavesdropping. A recent approach proposed superimposing a random sequence on the training sequence at the legitimate receiver and then using the minimum description length (MDL) criterion to detect pilot contamination attack. In this paper we augment this approach with joint estimation of both legitimate receiver and eavesdropper channels, and secure beamforming, to mitigate the effects of pilot spoofing. The proposed mitigation approach is illustrated via simulations.

This paper addresses the problem of detecting the presence of a complex-valued, possibly improper, but unknown signal, common among two or more sensors (channels) in the presence of spatially independent, unknown, possibly improper and colored, noise. Past work on this problem is limited to signals observed in proper noise. A source of improper noise is IQ imbalance during down-conversion of bandpass noise to baseband. A binary hypothesis testing approach is formulated and a generalized likelihood ratio test (GLRT) is derived using the power spectral density estimator of an augmented sequence. An analytical solution for calculating the test threshold is provided. The results are illustrated via simulations.

We consider detection of spoofing relay attack in time-division duplex (TDD) multiple antenna systems where an adversary operating in a full-duplex mode, amplifies and forwards the training signal of the legitimate receiver. In TDD systems, the channel state information (CSI) can be acquired using reverse training. The spoofing relay attack contaminates the channel estimation phase. Consequently the beamformer designed using the contaminated channel estimate can lead to a significant information leakage to the attacking adversary. A recent approach proposed using the minimum description length (MDL) criterion to detect spoofing relay attack. In this paper we augment this approach with joint channel estimation and secure beamforming to mitigate the effects of pilot contamination by spoofing relay. The proposed mitigation approach is illustrated via simulations.

In this paper, we investigate the problem of robust congestion control in infrastructure-based cognitive radio networks (CRN). We develop an active queue management algorithm, termed MAQ, which is based on multiple model predictive control. The goal is to stabilize the TCP queue at the base station under disturbances from the time-varying service capacity for secondary users. The proposed MAQ scheme is validated with extensive simulation studies under various types of background traffic and system/network configurations. It outperforms two benchmark schemes with considerable gains in all the scenarios considered.

In this paper, we investigate the problem of robust congestion control in infrastructure-based cognitive radio networks (CRN). We develop an active queue management (AQM) algorithm, termed MAQ, based on multiple model predictive control (MMPC). The goal is to stabilize the TCP queue at the base station (BS) under disturbances from the varying service capacity for secondary users (SU). The proposed MAQ scheme is validated with extensive simulation studies under various types of background traffic and system/network parameters. It outperforms two benchmark schemes with considerable gains in all the scenarios considered.

In this paper, we study the problem of video delivery over Orthogonal Frequency Division Multiple Access (OFDMA) networks using the Dynamic Adaptive Streaming over HTTP (DASH) framework. The goal is to integrate these two principal technologies to enable effective wireless video delivery. Based on a comprehensive QoE model, we develop a formulation to maximize the user QoE with joint OFDM resource allocation and DASH rate adaptation. The formulated problem is decomposed into a BS resource allocation problem and a user rate adaptation problem, which are then solved with effective algorithms. Our simulation study validates the efficacy of the proposed scheme.

In a time-division duplex (TDD) multiple antenna system, the channel state information (CSI) can be estimated using reverse training. A pilot contamination attack occurs when during the training phase, an adversary also sends identical training (pilot) signal as that of the legitimate receiver. This contaminates channel estimation and alters the legitimate pre-coder design, facilitating eavesdropping. We investigate superimposing a random sequence on the training sequence at the legitimate receivers and then using source enumeration methods to detect pilot contamination attack. The proposed method extends an existing TDD/TDMA uplink approach to TDD/SDMA uplink scenario. The detection performance is illustrated via simulations.

We consider multiple antenna spectrun sensing for improper complex primary user (PU) signals. Past work on this problem is limited to PU Gaussian signals over flat fading channels. We allow non-Gaussian signals over frequency-selective channels. A binary hypothesis testing approach is formulated and a generalized likelihood ratio test (GLRT) is derived using the power spectral density estimator of an augmented sequence. An analytical solution for calculating the test threshold is provided. The results are illustrated via simulations.

We consider the problem of testing whether a complex-valued vector random sequence is proper. Past work on this problem is limited to a sequence of independent Gaussian random vectors whereas we allow an arbitrary stationary vector sequence that can be non-Gaussian. A binary hypothesis testing approach is formulated and a generalized likelihood ratio test (GLRT) is derived using the power spectral density estimator of an augmented sequence. An asymptotic analytical solution for calculating the test threshold is provided. The results are illustrated via simulations.

This paper considers optimal multiband transmission under hostile jamming, where both the authorized user and the jammer are power-limited and operate against each other. The strategic decision making of the authorized user and the jammer is modeled as a two-party zero-sum game, where the payoff function is the capacity that can be achieved by the authorized user in the presence of the jammer. First, we investigate the game under AWGN channels. It is found that: either for the authorized user to maximize its capacity, or for the jammer to minimize the capacity of the authorized user, the best strategy for both of them is to distribute the transmission power or jamming power uniformly over all the available spectrum. The minimax capacity can be calculated based on the channel bandwidth and the signal-to-jamming and noise ratio, and it matches with the Shannon channel capacity formula. Second, we consider frequency selective fading channels. We characterize the dynamic relationship between the optimal signal power allocation and the optimal jamming power allocation in the minimax game, and then propose an iterative water pouring algorithm to find the optimal power allocation schemes for both the authorized user and the jammer.

We study the achievable secure degrees of freedom (DoF) in a cooperative MIMO cognitive radio system consisting of one primary source-destination pair, one or two secondary sourcedestination pairs, and one eavesdropper who is interested only in primary user's data. The cognitive radio users help to secure primary user's transmission against the eavesdropper and in return, the primary user allows the secondary users to access its licensed spectrum. All users are equipped with multiple antennas. We investigate the secure DoF using the interference alignment concept coupled with a zero inter-user interference constraint. We propose a beamforming design based only on the channel state information (CSI) between the primary and secondary user pairs which the legitimate users exchange among each other; no information data are exchanged and no eavesdropper CSI is needed. In the case of a single secondary user pair, we show that if all users have M antennas, secure DoF dpand DoF dsof primary and secondary users, respectively, are achievable if they satisfy 2dp≤ M and ds≤ M - 2dp. In the case of two secondary user pairs, secure DoF dpand DoFs ds1, ds2of primary user and two secondary users, respectively, are achievable if they satisfy 2dpp+ di≤ M, ds1+ ds2≤ M, i ∈ {s1,s2}, or 2dp= M, dp+ di≤ M, ds1+ ds21, s2}. Simulation examples corroborating the theoretical results are presented.

We study the secure degrees of freedom (DoF) in a cognitive radio system. A cognitive radio user helps to secure primary user's transmission against an eavesdropper and in return, primary users allows secondary user to access its licensed spectrum. All users are equipped with multiple antennas. We investigate the secure DoF using interference alignment concept with partial channel state information (CSI). When eavesdropper is interested only in primary user's data, it is shown that if all users, including primary transmitter-receiver pair, secondary transmitter-receiver pair and eavesdropper, have M antennas, achievable secure DoF dpand DoF dsof primary and secondary users, respectively, satisfy 2dp≤ M and ds≤ M - 2dp.

We consider a recently proposed generalized likelihood ratio test (GLRT) for comparing two complex multivariate random signal realizations to ascertain whether they have identical power spectral densities. In this paper we analyze the performance of this GLRT by deriving an approximate asymptotic distribution of the test statistic under the alternative hypothesis. We also provide robustification of this approach by adding artificial white noise to the received noisy signals. The results are illustrated via computer simulations which include application to user authentication in wireless networks with multiantenna receivers.

This paper develops two spectrally efficient orthogonal frequency division multiplexing (OFDM)-based multicarrier transmission schemes: a scheme with message-driven idle subcarriers (MC-MDIS) and another with message-driven strengthened subcarriers (MC-MDSS). The basic idea in MC-MDIS is to carry part of the information, which is named carrier bits, through an idle subcarrier selection while regularly transmitting the ordinary bits on all the other subcarriers. When the number of subcarriers is much larger than the adopted constellation size, higher spectral and power efficiency can be achieved compared with OFDM. The reason is that each idle subcarrier carries more bits than a regular symbol, with no power consumption. Moreover, the existence of idle subcarriers can also decrease possible intercarrier interference between their neighboring subcarriers. In MC-MDSS, the idle subcarriers are replaced by strengthened subcarriers, which, unlike idle subcarriers, can carry both carrier bits and ordinary bits. Therefore, MC-MDSS achieves even higher spectral efficiency than MC-MDIS. Both theoretical analysis and numerical results are provided to demonstrate the performance of the proposed schemes.

We consider a K-user multiple input multiple output (MIMO) Y channel consisting of K(≥ 3) users and a relay. Each user has K-1 independent messages for all the other K-1 users. Degrees of freedom (DoF) of such channels is not known in general but it is known that the DoF of K(K-1)/2 is achievable for a network operating in a half-duplex mode by using signal space alignment for network coding during both the multiple access phase and the broadcast phase. In this paper, a novel signal group based alignment scheme is proposed, which divides all K(K-1) signals into l groups where l = K or K-1. Then, the signals in each group are aligned into a smaller subspace at the relay. If the i-th user is equipped with Miantennas and the relay is equipped with N antennas where all antennas are used for both transmitting and receiving, we prove that when Mi= K-1, N = (K-1)2for even K and Mi= K-1, N = K(K-2) for odd K, the optimal total DoF of this K-user MIMO Y channel is K(K-1)/2. As a consequence, to achieve the total DoF of K(K-1)/2, the requirements on Miand N are Mi≥ K-1 and N ≥ (K-1)2for even K, and Mi≥ K-1 and N ≥ K(K-2) for odd K. In our proposed approach, we significantly decrease the minimum Miat the expense of higher N for a given number of users K and achievable DoF of K(K-1)/2, compared to an existing approach. This signal group alignment concept also motivates other signal grouping methods, which provide a tradeoff between number of antennas at end users and the relay. Also, for the K-user Y channel where all end users have a single antenna and the relay node has N antennas, it is shown that the DoF of min{K/2, (N + 1)/2} is achievable.

We study weighted energy efficiency maximization for multiple-input multiple-output cognitive multiple access channels under both secondary user transmit power constraint and primary user interference power constraint. Energy efficiency is defined as the ratio of weighted sum rate and energy consumption including both transmission and circuit energy consumption. The nonlinear (fractional programming) energy efficiency optimization problem is transformed into a series of parametrized convex optimization problems. A combination of bisection search method and cyclic coordinate ascent-based iterative water-filling algorithm is proposed to solve the parametrized problem. Computer simulation examples are provided to illustrate the proposed approach and to explore the trade-off between energy efficiency and spectrum efficiency.

We formulate the design of energy efficiency maximization for a single secondary link in an underlay spectrum sharing cognitive radio network under an SU (secondary user) transmit-power constraint and an upperbound on the interference power at the PU (primary user). We propose energy efficient precoding (beamforming) for the SU transmitter to maximize energy efficiency defined as the transmission rate to power ratio, when the terminals in the system are equipped with multiple antennas. The underlying channels are assumed to be known at the SU transmitter. The nonlinear optimization (fractional programming) problem is transformed into a parametrized convex optimization problem and the corresponding solution is discussed. Computer simulation examples are provided to illustrate the proposed approach and to explore the trade-off between energy efficiency and spectrum efficiency.

In this paper, we consider a K-user MIMO (multiple input multiple output) Y channel consisting of K, K ≥3, users and a relay. Each user has K - 1 independent messages for all the other K-1 users. With the deployment of multiple antennas at both end users and the relay, K(K - 1) messages can be conveyed to their desired receivers within two time slots for a network operating in a half-duplex mode. A signal group based alignment scheme is proposed which divide all K(K - 1) signals into K groups when K is odd and K - 1 groups when K is even. Then the signals in each group are aligned into a smaller subspace at the relay. If each user is equipped with M antennas and the relay is equipped with N antennas, we show that in order to exchange K(K - 1) messages, the requirements on M and N are KM ≥ N +K - 1 and N ≥ (K - 1)2for even K and (K - 1)M ≥ N +1 and N ≥ K(K - 2) for odd K. In our proposed approach we significantly decrease the minimum M at the expense of higher N for a given number of users K, compared to an existing approach.

We consider a physical layer approach to enhance wireless security by using the unique wireless channel state information (CSI) of a legitimate user to authenticate subsequent transmissions (messages) from this user, thereby denying access to any spoofer whose CSI would significantly differ from that of the legitimate user by virtue of a different spatial location. Past approaches have explicitly utilized underlying CSI estimated from data: is the CSI of the current message the same as that of the previous message? In this paper we formulate this problem as one of comparing two random signal realizations to ascertain whether they have identical power spectral densities. A binary hypothesis testing approach is formulated, analyzed and illustrated via simulations.

In this paper, we design relay precoder in a MIMO cognitive radio network where two-way transmission of multiple secondary user pairs occurs concurrently with primary network's transmission. We propose an interference alignment like precoder design which jointly aligns the direction of interference and the desired signal while interference to primary network is completely canceled. When the secondary transmitters and receivers are equipped with multiple antennas, sources, relay and receivers can all participate in aligning the interference and signal directions. It is shown that zero-forcing relay beamforming in which inter-pair interference is aligned to the null space of desired signal space is a special case of our algorithm. Our proposed algorithm can also work in the scenario where the number of antennas at relay node is not large enough and therefore zero-forcing is not possible. The effectiveness of the proposed algorithm is illustrated via simulations and compared with zero-forcing and MSE based designs.

We consider joint optimization of cooperative spectrum sensing, channel access and power allocation in an overlay multi-band cognitive radio network to maximize the secondary users' sum instantaneous throughput while keeping the interference to primary users under a specified threshold. A soft-decision cooperative spectrum sensing concept using the continuous-valued sensing test statistics is considered. The channel access decision about whether to access the channel or not is relaxed into allowing the secondary user to access channels with some probability. The decision is made at the secondary base station based on the sensing statistics received from all or a subset of secondary users. The problem is shown to be a convex optimization problem and the Lagrangian dual method is employed to obtain the optimal solution. Two heuristic algorithms are also proposed to reduce the complexity. Simulation results show that our soft sensing based algorithm significantly outperforms traditional hard decision sensing algorithms.

We consider joint design of source and relay pre-coders in a cognitive multiuser two-way relay system, which supports simultaneous transmission of multiple secondary users concurrently with primary network with the help of a relay node. The design criterion is to minimize the sum mean square error (MSE) of all users under a transmit power constraint for each transmitting node while causing no interference to the primary network. To solve this non-convex optimization problem, an iterative algorithm is proposed to iteratively solve for the precoding matrices at secondary source nodes and relay node, and then the decoding matrices at secondary nodes. To reduce the computational complexity, a matrix distance based non-iterative algorithm is also proposed. Simulation results show the effectiveness of our proposed algorithms.

Detection of cyclostationary primary user (PU) signals in colored Gaussian noise for cognitive radio systems is considered based on looking for a cycle frequency at a particular time lag in the cyclic autocorrelation function (CAF) of the noisy PU signal. We explicitly exploit the knowledge that under the null hypothesis of PU signal absent, the measurements originate from colored Gaussian noise with possibly unknown correlation function. We consider both single and multiple antenna receivers. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided using an OFDM PU signal and they show that our proposed approaches are computationally much cheaper than the Dandawate-Giannakis and related approaches while having quite similar detection performance for a given false alarm rate.

We consider joint optimization of spectrum sensing, channel access and power allocation in a multi-band cognitive radio network. Instead of making hard binary decisions as in traditional hypothesis testing spectrum sensing schemes, a soft spectrum sensing concept using the continuous-valued sensing test statistics is considered. The channel access decision about whether to access the channel or not is relaxed into allowing the secondary user to access channels with some probability. This joint optimization problem is aimed at maximizing the secondary users' sum throughput while keeping the interference to primary users under a specified threshold. The problem is shown to be a convex optimization problem and the Lagrangian dual method is employed to obtain the optimal solution. Two heuristic algorithms are also proposed to reduce the complexity while achieving a near optimal performance. Simulation results show that our soft sensing based algorithm significantly outperforms traditional hard decision sensing algorithms.

Recently several time-domain approaches relying on the generalized likelihood ratio test (GLRT) paradigm have been pro posed for multiple antenna spectrum sensing in cognitive radios. These approaches are suitable for flat-fading channels in white noise with equal noise variances across antennas; knowledge of the noise variance is not required, unlike the energy detector. In this paper we investigate a method based on the sample autocorrelation of the received multiantenna signal where we allow the noise variances to be different at different antennas without requiring knowledge of their values. A performance analysis of the proposed detector is carried out. Supporting simulation examples are provided.

Cognitive radio allows for usage of licensed frequency bands by unlicensed users when the licensed spectrum bands are unoccupied. Therefore, one of the first critical steps to be accomplished by a cognitive user is spectrum sensing: search for unoccupied spectrum bands (spectrum holes). A popular approach is that of energy detection whose implementation requires accurate knowledge of noise power. The performance of the energy detector deteriorates rapidly in the presence of noise power uncertainty. Recently several time-domain approaches relying on the generalized likelihood ratio test (GLRT) paradigm have been proposed for multiple antenna spectrum sensing which obviate the need for the knowledge of the noise variance, unlike the energy detector. That is, multiple antennas at the receivers are needed to tackle the problem of unknown noise power. In this paper we investigate a single-antenna method for signal detection in white noise based on analysis of the power spectral density (PSD) of the received signal relying on the bandlimited nature of the signal to be detected. Our proposed approach is also based on GLRT but exploits the fact that while noise is white, the signal is colored; it does not require knowledge of the noise power. Simulation examples are provided in support of the proposed approach.

This paper considers spectrally efficient anti-jamming system design based on code-controlled frequency hopping. Unlike conventional frequency hopping systems where hopping patterns are determined by preselected pseudo-random sequences, in the proposed scheme, part of source information is passed through a block encoder, and used to determine the selected frequency bands for signal transmission. By exploiting the redundancy provided by the block coding, the receiver can retrieve the hopping pattern without a priori knowledge. Through an integrated decoding-and-encoding process, the receiver can also perform partial jamming detection. It is observed that due to the combination of dynamic frequency hopping and coding diversities, the proposed system can effectively mitigate random jamming interference while maintaining high spectral efficiency.

We present a turbo (iterative) equalization receiver with fixed-lag nonlinear Kalman filtering for coded data transmission over doubly-selective channels. The proposed receiver exploits the complex exponential basis expansion model (CEBEM) for the overall channel variations, and an autoregressive (AR) model for the BEM coefficients. We extend an existing turbo equalization approach based on symbol-wise AR modeling of channels to channels based on BEM's. In the receiver an adaptive equalizer using nonlinear Kalman filters with delay is coupled with a soft-input soft-output (SISO) decoder to iteratively perform equalization and decoding. The adaptive equalizer jointly optimizes the estimates of the BEM coefficients and data symbols, thereby automatically accounting for correlation between data symbols and channel tap gains. An extrinsic information transfer (EXIT) chart analysis of the proposed approach is also presented. Simulation examples demonstrate that our CE-BEM-based approach significantly outperforms the existing symbol-wise AR model-based turbo equalizer.

We present a decision-directed tracking approach to doubly-selective channel estimation exploiting the complex exponential basis expansion model (CE-BEM). The time-varying nature of the channel is well captured by the CE-BEM while the time-variations of the (unknown) BEM coefficients are likely much slower than those of the channel. We track the BEM coefficients via the exponentially-weighted recursive least-squares (RLS) algorithm, aided by symbol decisions from a decision-feedback equalizer (DFE). Simulation examples demonstrate its superior performance over an existing subblock-wise channel tracking scheme.

In this paper, we exploit the Kalman filter as a time-varying linear minimum mean-square error equalizer for doubly-selective fading channels. We use a basis expansion model (BEM) to approximate the doubly-selective channel impulse response. Several time-varying linear equalizers have been proposed in the literature where both the channel and the equalizer impulse responses are approximated by complex exponential (CE) BEMs. Our proposed Kalman filter formulation does not rely on a specific BEM for the underlying channel, therefore, it can be applied to any BEM, including the CE-BEM and the discrete prolate spheroidal (DPS) BEM. Moreover, the Kalman filter relies solely on the channel model and therefore, does not incur any approximation error inherent in the CE-BEM representation of the equalizer. Through computer simulations, we show that compared to two of the existing algorithms, the proposed Kalman filter formulation yields the same or an improved bit error rate at a much lower computational cost, where the latter is measured in terms of the number of flops needed for the equalizer design and implementation.

We present a decision-directed tracking approach to doubly-selective MIMO channel estimation, exploiting the complex exponential basis expansion model (CE-BEM) for the overall channel variations, and an autoregressive (AR) model to update the BEM coefficients. We track the BEM coefficients via Kalman filtering, aided by symbol decisions from a decision-feedback equalizer (DFE). The time gap between symbol decisions and required channel estimates, arising from the decision-directed tracking, is bridged by CE-BEM-based channel prediction using the estimated BEM coefficients. Simulation examples demonstrate its superior performance over the existing AR-based and subblock-wise channel tracking schemes.

An adaptive channel estimation scheme, exploiting the over-sampled complex exponential basis expansion model (CE-BEM), is presented for doubly-selective channels where we track the BEM coefficients via a multiple model approach. In the past work the number of BEM coefficients used to model the doubly-selective channels for channel estimation has been based on an upperbound on the channel Doppler spread. Higher the Doppler spread, more the number of BEM coefficients leading to higher channel estimation variance. In this paper we propose to use a multiple model framework where several candidate Doppler spread values are used to cover the range from zero to an upperbound, leading to multiple CE-BEM channel models, each corresponding to an assumed value of the Doppler spread. Subsequently the well- known interacting multiple model (IMM) algorithm is used for symbol detection based on multiple state-space models corresponding to the multiple estimated channels. A simulation example is presented to illustrate the proposed approach.

An adaptive channel estimation scheme, exploiting the oversampled complex exponential basis expansion model (CEBEM), is presented for doubly-selective channels where we track the BEM coefficients. We extend/modify the subblockwise tracking method using time-multiplexed (TM) training recently proposed by [1]. Two finite-memory recursive least-squares (RLS) algorithms, including the exponentially-weighted and the sliding-window RLS algorithms, are respectively applied to track the channel BEM coefficients. Simulation examples illustrate the superior performance of our scheme to the conventional block-wise channel estimator, and demonstrate its improvement on our previous work in [1].

We present a decision-directed tracking approach to doubly-selective channel estimation, exploiting the complex exponential basis expansion model (CE-BEM) for overall channel variations, and an autoregressive (AR) model to update the BEM coefficients. We track the BEM coefficients via Kalman filtering, aided by symbol decisions from a decision-feedback equalizer (DFE). The time gap between symbol decisions and required channel estimates, arising from the decision-directed tracking, is bridged by CE-BEM-based channel prediction using the estimated BEM coefficients. Simulation examples demonstrate its superior performance over several existing AR- or CE-BEM-based channel tracking schemes.

We consider decision feedback equalization of doubly selective channels modeled via basis expansion models (BEM). Recently there has been some interest in designing time-variant serial FIR (finite impulse response) decision feedback equalizers (DFE) using complex exponential (CE-) BEMs for equalizers in addition to using CE-BEM for modeling the channel itself. In this paper we show that an alternative formulation of the FIR DFE based on a CE-BEM channel model yields the same or an improved BER at a lower computational cost, without incuring the approximation error inherent in CE-BEM modeling of equalizers.

We present a novel approach to doubly-selective channel estimation exploiting the complex exponential basis expansion model (CE-BEM) for the overall time-variant channel and an autoregressive (AR) model for the BEM coefficients. Since the time-varying nature of the channel is well captured in CE-BEM by the known exponential basis functions, the time variation of the (unknown) BEM coefficients is likely much slower than that of the channel. We propose a novel "subblock- wise" BEM coefficient tracking scheme based on Kalman filtering and time-multiplexed periodically transmitted training symbols. Simulation examples demonstrate its superior performance over several existing doubly-selective channel estimators.

Channel estimation for multiuser doubly-selective channels is considered using superimposed training. The time-varying channel is assumed to be described by a discrete prolate spheroidal basis expansion model (DPS-BEM). A user-specific periodic training sequence is arithmetically added (superimposed) at a low power to each user's information sequence at the transmitter before modulation and transmission. A two step approach is adopted where in the first step we estimate the channel using only the first-order statistics of the observations. Using the estimated channel from the first step, a Viterbi detector is used to estimate the information sequence. In the second step a deterministic maximum likelihood (DML) approach is used to iteratively estimate the multiuser channel and the information sequences sequentially.

Channel estimation for single-input single-output frequency- and time-selective channels is considered using time- multiplexed training. The time-varying channel is assumed to be well-described by a basis expansion model using discrete prolate spheroidal sequences as the bases (DPS-BEM). First, the popular linear least-squares approach is exploited to estimate the basis expansion coefficients. Then the issue of training power allocation is addressed. Finally, computer simulation examples are presented where the channel is generated via Jakes' model.

Channel estimation for frequency-selective time- varying channels is considered using superimposed training. We employ a discrete prolate spheroidal basis expansion model (DPS-BEM) to describe the time-varying channel. A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to- noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to either totally or partially cancel out the effects of the unknown information sequence at the receiver on channel estimation. In total cancellation, at certain frequencies, the information-bearing components are nulled. To compensate for this information loss, we propose a partially-data- dependent (PDD) superimposed training scheme where a tradeoff is made between interference cancellation and frequency integrity. An iterative method is also used to enhance channel estimation and data detection and illustrated via a simulation example.

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.

Channel estimation for single user frequency- selective time-varying channel is considered using superimposed training. The time-varying channel is assumed to be well- described by a basis expansion model using discrete prolate spheroidal sequences (DPS-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. A two-step approach is adopted where in the first step we estimate the channel using DPS-BEM and only the first-order statistics of the observations. Using the estimated channel from the first step, a Viterbi detector is used to estimate the information sequence. In the second step a deterministic maximum likelihood (DML) approach is used to iteratively estimate the channel and the information sequences sequentially, based on DPS-BEM. Illustrative computer simulation examples are presented where a frequency-selective channel is randomly generated with different Doppler spreads via Jakes' model. Simulations show that the proposed approaches are competitive with time-multiplexed training without incurring data-rate loss.

Design of doubly-selective linear equalizers for single user frequency-selective time-varying communications channels is considered using superimposed training and without first estimating the underlying channel response. Both the time-varying channel as well as the linear equalizers are assumed to be described by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. There is no loss in information rate. Knowledge of the superimposed training is exploited to design the FIR linear equalizer. An illustrative simulation example is presented.

The problem of multiple sensor scheduling for tracking a highly maneuvering target in clutter is considered. The objective is to schedule the sensors one or multiple time steps ahead so that the overall tracking performance of the system can be improved while minimizing the cost of resources. In the proposed scheduling algorithm, under the constraint that only one sensor may be used at any time step, we predict the expected cost one or multiple time steps ahead as a function of the candidate sensor scheduling sequences, and pick the sequence that minimizes an expected performance metric. We use a random sampling approach coupled with switching multiple kinematic models for target motion, to generate future (pseudo-)states and (pseudo-) measurements which allows computation of the relevant performance metric. Tracking of highly maneuvering target is achieved by an effective suboptimal filtering algorithm based on an interacting multiple model (IMM) filtering approach combined with probabilistic data association (PDA) technique and the proposed sensor scheduling scheme. The proposed algorithm is illustrated via a simulation example involving two geographically distributed radar sensors.

Channel estimation for single-input multiple-output (SIMO) time-invariant channels using superimposed training has been considered recently by several authors. In particular, J.K. Tugnait and Weilin Luo (see IEEE Commun. Lett., vol.CL-8, p.413-15, 2003) proposed channel estimation using only the first-order statistics of the data under a fixed power allocation for training. We first present a performance analysis of the approach of Tugnait and Luo to obtain a closed-form expression for the channel estimation variance. We then address the issue of superimposed training power allocation for complex Gaussian random (Rayleigh) channels. Using the developed channel estimation variance expression, we cast the power allocation problem as one of optimizing a signal-to-noise ratio (SNR) for equalizer design. Illustrative simulation examples are provided.

In this letter, blind detection of multirate code-division multiple-access (CDMA) signals is revisited by exploiting a fast converging blind deconvolution approach-the super-exponential algorithm. Here, only the desired user's spreading code is assumed to be known, while its transmission delay may be unknown. Compared with existing higher order statistics-based blind multiuser detectors in a paper by Ma and Tugnait, when the system actually converges to the desired user (generally needs SNR>10 dB for both existing methods and the proposed approach), the proposed approach can achieve much better performance with significantly faster convergence speed.

A modified bit-map-assisted dynamic queue (BMDQ) protocol is presented for wireless slotted networks with heterogeneous users and multiple packet reception (MPR) capability. As in our recently proposed BMDQ protocol, in the proposed protocol the traffic in the channel is viewed as a flow of transmission periods (TP). Each TP has a bit-map (BM) slot at the beginning followed by a data transmission period (DP). In the BMDQ protocol the BM slot is reserved for user detection so that accurate knowledge of the active user set (AUS) can be acquired. Then given the knowledge of the AUS and the channel MPR matrix, the number of users that can access the channel simultaneously in each packet slot in the DP is chosen to maximize the conditional throughput of every packet slot. In Wang et al. (2003), all users are assumed to have the same bit error probability, i.e. they were assumed to be homogeneous. In the proposed modified BMDQ protocol, we allow the users to have unequal bit error probability. In this case, given the AUS, the choice of users to transmit in a given slot to maximize the conditional throughput is no longer just the number of users, but also the specific choice of users. Simulation comparison of the performance of the modified BMDQ protocol with that of the original BMDQ protocol is presented.

Channel estimation for single-input multiple-output (SIMO) time-varying channels is considered using superimposed training. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. A two-step approach is adopted where, in the first step, we estimate the channel using only the first-order statistics of the data. Using the channel estimate from the first step, a Viterbi detector is used to estimate the information sequence. In the second step, a deterministic maximum likelihood (DML) approach is used to estimate the SIMO channel iteratively and the information sequences sequentially. An illustrative computer simulation example is presented where a frequency-selective channel is randomly generated with different Doppler spreads via Jakes' model.

Channel estimation for single-input multiple-output (SIMO) time-invariant or slowly time-varying channels is considered using superimposed training. A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. Two versions of a two-step approach are adopted where in the first step, following [11], we estimate the channel using only the first-order statistics of the data. Using the estimated channel from the first step, a linear MMSE equalizer and hard decisions, or a Viterbi detector, are used to estimate the information sequence. In the second step a deterministic maximum likelihood (DML) approach or an approximation to it, is used to iteratively estimate the SIMO channel and the information sequences sequentially. Illustrative computer simulation examples are presented where we compare the proposed approaches to the conventional (time-multiplexed) training based approach.

We consider the problem of tracking multiple maneuvering targets in the presence of clutter using switching multiple target motion models. A novel suboptimal fixed-lag smoothing algorithm is developed by applying the basic interacting multiple model (IMM) approach and joint probabilistic data association (JPDA) technique to a state augmented system. But unlike the standard single scan JPDA approach, we exploit a multiscan JPDA (Mscan-JPDA) approach to solve the data association problem. The algorithm is illustrated via a simulation example.

Channel estimation for single-input multiple-output (SIMO) time-invariant or slowly time-varying channels was recently considered in (J. K. Tugnait et al, IEEE Comm. Lett., vol.CL-8, p.413-415, 2003) using superimposed training. A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. In the Tugnait method, the channel is estimated using only the first-order statistics of the data, under the assumption that the superimposed training sequence at the receiver is time-synchronized with its transmitted counterpart. In this paper, we remove this assumption of synchronization and propose a novel approach to superimposed training synchronization. An illustrative computer simulation example is presented.

This paper considers blind channel identification and signal separation in long-code CDMA systems. First, by modeling the received signals and MUIs as cyclostationary processes with modulation introduced cyclostationarity, long-code CDMA system is characterized using a time-invariant system model. Secondly, based on the time-invariant model, multistep linear prediction method is used to reduce the intersymbol interference introduced by multipath propagation, and channel estimation can then be performed using the non-constant modulus precoding technique and the matrix pencil approach. After channel estimation, equalization is carried out using cyclic Wiener filter. Simulation examples arc provided to illustrate the proposed approaches.

Channel estimation for multiple-input multiple-output (MIMO) time-invariant or slowly time-varying channels is considered using superimposed training. A user-specific periodic (non-random) training sequence is arithmetically added (superimposed) at the low power of each user's information sequence at the transmitter before modulation and transmission. Two versions of a two-step approach are adopted wherein we first estimate the channel using only the first-order statistics of the data. Using the estimated channel from the first step, a linear MMSE equalizer and hard decisions, or a Viterbi detector, are used to estimate the information sequence. In the second step, a deterministic maximum likelihood (DML) approach or an approximation to it, is used to iteratively estimate the MIMO channel and the information sequences sequentially. Illustrative computer simulation examples are presented where we compare the proposed approaches to the conventional (time-multiplexed) training based approach to channel estimation and equalization.

In this letter, code-constrained super-exponential algorithms (CSEA) are presented for blind detection of asynchronous short-code direct-sequence code-division multiple-access signals over multipath channels. Constrained SEA leads to the extraction of the desired user whereas unconstrained SEA leads to the extraction of any one of the actives users. The results are further improved by following the constrained SEA by unconstrained SEA. Convergence of the constrained SEA is proved and simulation examples are provided to illustrate the proposed approaches.

Blind detection of a desired user's signal in a code-hopping (CH) direct sequence code-division multiple access (CDMA) system is considered. In CH CDMA systems each user switches between a predetermined set of short-code sequences. A user signal in such systems may be treated as the superposition of several virtual short-code signals. A code-constrained inverse filter criterion (IFC)-based blind detector for short-code CDMA signals in asynchronous multipath channels to detect a desired user's signal was recently presented by Tugnait and Li (2001). A novel approach combining the code-constrained IFC and a penalty function is proposed to simultaneously extract all virtual users associated with a given CH user. Global minima of the proposed cost function are analyzed. An extension of an existing subspace-based approach is also investigated. An illustrative simulation example is provided where the proposed algorithm is compared with a clairvoyant matched filter receiver, two linear minimum mean-square error (MMSE) receivers with channels known, and the subspace-based approach.

Blind detection of a desired user's signal in a direct sequence code-division multiple-access (DS-CDMA) system using multiple transmit and receive antennas and space-time (ST) block coding is considered. We consider Alamouti's ST coding scheme for two transmit antennas designed for flat-fading channels but allow the channel to be frequency selective. A (spreading) code-constrained inverse filter criterion (IFC)-based linear blind detector to detect a desired user's signal for uncoded CDMA signals exploiting only a single transmit and single receive antenna was recently presented. The IFC method exploits the higher order statistics of the data. In ST-coded multiantenna CDMA systems, a user signal may be treated as the superposition of several virtual user signals derived from the same parent user. In particular, for Alamouti's scheme, one has two virtual users for each user if the information symbols are real valued. The previously proposed code-constrained IFC-based detector is modified to detect a given virtual-user signal. The original user signal can then be recovered from the associated detected virtual user signals obtained by running two code-constrained IFC-based detectors in parallel. We also propose a novel approach combining the code-constrained IFC and a penalty function to simultaneously extract the two virtual user signals associated with a given user. Global minima of the proposed cost functions are analyzed. An illustrative simulation example is presented.

A modified bit-map-assisted dynamic queue (BMDQ) protocol is presented for wireless slotted systems with multiple packet reception (MPR) capability and finite user-buffers. As in our BMDQ protocol (Xin Wang and Tugnait, J.K., Proc. Joint Intern. Conf. Wireless LANs & Home Networks and Networking, p.549-60, 2002), in the proposed protocol, the traffic in the channel is viewed as a flow of transmission periods (TP). Each TP has a bit-map (BM) slot at the beginning followed by a data transmission period (DP). In the BMDQ protocol the BM slot is reserved for user detection so that accurate knowledge of the active user set (AUS) can be acquired and in any given TP, each active user is allowed to transmit only one data packet. In the proposed modified BMDQ protocol, the active users are allowed to transmit all data packets in their finite buffer. An active user with more than one packet in its buffer is modeled as several different active pseudo-users. In the BM slot, each user transmits information about the number of data packets in its buffer. Then, according to the number of the active pseudo-users and the channel MPR capability, the protocol attempts to minimize the expected duration of the DP in the same way as the BMDQ protocol. Simulation comparison of the performance of the proposed modified BMDQ protocol with that of the original BMDQ protocol is presented.

For long code DS-CDMA systems, where the spreading codes are aperiodic and extending over a large number of data symbols, chip-rate sampled signals and MUI (multiuser interferences) are generally modeled as time-varying vector processes. This complicates the application of traditional blind multiuser detectors, since consistent estimation of the needed signal statistics can not be obtained by time-averaging over received data record. In this paper, we propose an equivalent time-invariant system model for long code CDMA, in which the received signals and MUI are modeled as cyclostationary processes with modulation introduced cyclostationarity. Based on knowledge of the desired user's code sequences, channel estimation is carried out using a frequency domain subspace method.

A multistep linear prediction (MSLP) approach is presented for blind channel estimation for short-code DS-CDMA (direct sequence code division multiple access) signals in time-varying multipath channels. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). We first extend a recently proposed MSLP approach to blind channel estimation for time-varying SIMO (single-input multiple-output) systems, to time-varying MIMO systems in order to define a "signal" subspace. Then, the knowledge of the spreading code of a desired user is exploited in conjunction with the signal subspace to estimate the time-varying channel of the desired user. Sufficient conditions for channel identifiability are investigated. An illustrative simulation example is provided.

A code-constrained inverse filter criterion based approach was recently presented by J.K. Tugnait and Tongtong Li (see IEEE Trans. Sig. Processing, vol.SP-49, p.1300-9, 2001) for blind detection of a desired user in asynchronous short-code DS-CDMA (direct sequence code division multiple access) systems over multipath channels. The method proposed therein works well for low-to-moderate loading; however, it can converge to an undesired user under high loading. We augment this method with a binary hypothesis testing approach for extracted user identification (whether the desired user is acquired/extracted) and for successive user cancellation (if an undesired user is extracted, cancel its contribution and repeat). An illustrative simulation example is presented.

Channel estimation for single-input multiple-output (SIMO), possibly time-varying, channels is considered using only the first-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. Recently superimposed training has been used for time-invariant channel estimation assuming no mean-value uncertainty at the receiver. We propose a different method that explicitly exploits the underlying cyclostationary nature of the periodic training sequences. It is applicable to both time-invariant and time-varying systems. Unlike existing approaches we allow mean-value uncertainty at the receiver. Illustrative computer simulation examples are presented.

We revisit the recently presented code-constrained super-exponential algorithm (SEA) (Li-Tugnait, 2001) for blind detection. of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals over multipath channels. Convergence of the algorithm is proved by showing that the constrained SEA is a special case of “undermodeled” SEA which is equivalent to a gradient search algorithm. Given appropriate initialization, constrained SEA can lead to the extraction of the desired user, whereas unconstrained SEA leads to the extraction of any one of the actives users.

Blind channel estimation for single-input multiple-output (SIMO) time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The multistep linear predictors-based method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for identifiability are investigated. Cyclostationarity of the received signal is exploited to consistently estimate the time-varying correlation function of the data from a single observation. record. An illustrative computer simulation example is presented.

A code-constrained inverse Iter criterion based approach was recently presented in Tugnait & Li (IEEE Trans. SP, July 2001) for blind detection of a desired user in asynchronous short-code DS-CDMA (direct sequence code division multiple access) systems over multipath channels. The method proposed therein works well for low-to-moderate loading; however, it can converge to an undesired user under high loading. In this paper we augment this method with methods for extracted user identification (whether the desired user is acquired/extracted) and for successive user cancellation (if an undesired user is extracted, cancel its contribution and repeat). An illustrative simulation example is presented.

Blind detection of a desired user's signal in a code-hopping (CH) direct sequence code division multiple access (DS-CDMA) system is considered. In CH CDMA systems each user switches between a predetermined set of (short-)code sequences. A user signal in such systems may be treated as the superposition of several virtual short-code signals. A code-constrained inverse filter criterion (IFC)-based blind detector for short-code CDMA signals to detect a desired user's signal was recently presented by Tugnait and Li (2001). In this paper a novel approach combining the code-constrained IFC and a penalty function is proposed to simultaneously extract all virtual users associated with a given CH user. Global minima of the proposed cost function are analyzed. An illustrative simulation example is provided.

The problem of MIMO (multi-input multi-output) system identification given noisy input-output measurements is considered. The various noise processes affecting the system are zero-mean, jointly stationary Gaussian, whereas the system operates under a non-Gaussian input. First the MIMO transfer function is estimated using the integrated polyspectrum and cross-polyspectrum of the time-domain input-output measurements. Then an existing subspace-based technique for parametric system identification given noisy measurements of the underlying transfer function, is adapted to apply to the problem under consideration. We show that the resultant parametric transfer function estimator is strongly consistent. A simulation example is provided.

Blind channel estimation and blind equalization of single-input multiple-output communications channels is considered using only the second-order statistics of the data. Estimation of (partial) channel impulse response and design of finite-length minimum mean-square error blind equalizers is investigated. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite-impulse response channels are allowed. The proposed approach also works when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Three illustrative simulation examples using 4-QAM and 16-QAM signals are provided where the proposed approach is compared with several existing approaches.

A code-constrained inverse filter criterion (CC-IFC) based approach was presented Tugnait and Li (see Proc. IEEE 2000 ICASSP, p.V-246-64, Istanbul, Turkey, June 2000) for blind-detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. The equalizer was determined by maximizing the magnitude of the normalized fourth cumulant of inverse filtered (equalized) data with respect to the equalizer coefficients subject to the fact that the equalizer lies in a subspace associated with the desired user's code sequence. In this paper we analyze the identifiability properties of the approach of Tugnait and Li. Global maxima and some of the local maxima of the cost function are investigated. These aspects were not discussed by Tugnait and Li. More extensive simulation comparisons with existing approaches are also provided.

A code-constrained constant-modulus approach (CMA) was presented in Li and Tugnait (2000) for blind detection of asynchronous short-code DS-CDMA signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. The equalizer was determined by minimizing the Godard/CMA cost function of the equalizer output with respect to the equalizer coefficients subject to the fact that the equalizer lies in a subspace associated with the desired user's code sequence. An iterative projection approach was used in Li for constrained optimization where at each iteration the equalizer was projected onto the desired subspace. We investigate an alternative, penalty function-based approach to constrained optimization. Global minima and some of the local minima of the cost function are investigated. A simulation example is presented.

Blind channel estimation for SIMO time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The linear prediction error method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for identifiability are investigated. The cyclostationary nature of the received signal is exploited to estimate consistently the time-varying correlation function of the data from a single observation record. The focus of the paper is on certain theoretical issues.

Code-constrained super-exponential algorithms (SEA) are presented for blind detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals over multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. By exploiting the fact that the equalizer always lies in a subspace associated with the desired user's code sequence, a projection operator is imposed at every iteration so that the algorithm can extract the desired user. The results are further improved by following the constrained SEA by unconstrained SEA. An illustrative simulation example is provided.

Blind channel estimation and blind minimum mean square error (MMSE) equalization of multiple-input multiple-output (MIMO) communications channels arising in multiuser systems is considered, using primarily the second-order statistics of the data. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite impulse response (IIR) channels are allowed. Moreover, the multichannel transfer function need not be column-reduced. The proposed approach also works when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Using second-order statistics, the sources are recovered up to a unitary mixing matrix, and are further "unmixed" using higher order statistics of the data. Two illustrative simulation examples are provided where the proposed method is compared with its predecessors and an existing method to show its efficacy.

A multistep linear prediction approach is presented for blind channel estimation, multiuser interference (MUI) suppression, and detection of asynchronous short-code direct sequence code division multiple access signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We exploit the previously proposed multistep linear prediction approach for blind multiple-input multiple-output channel estimation in conjunction with the structure imposed by the desired user's spreading code sequence. With the knowledge of the desired user's code sequence, only the second-order statistics of the data are needed under certain sufficient conditions on the underlying multiuser MIMO transfer function. Based on the desired user's channel estimate, a linear minimum mean square error filter is designed for simultaneous equalization and MUI suppression. Three illustrative simulation examples are presented.

A code-aided constant modulus algorithm (CMA) based approach is presented for blind detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in intersymbol interference (ISI)/multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. A linear equalizer is designed by minimizing the Godard/CMA cost function of the equalizer output with respect to the equalizer coefficients subject to the fact that the equalizer lies in a subspace associated with the desired user's code sequence. Constrained CMA leads to the extraction of the desired user's signal whereas unconstrained minimization leads to the extraction of any one of the active users. The results are further improved by using unconstrained CMA initialized by the results of the code-aided CMA. Identifiability properties of the approach are analyzed. Illustrative simulation examples are provided.

A code-constrained inverse filter criterion based approach is presented for blind detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in multipath channels using a receiver antenna array. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We exploit maximization of the normalized fourth cumulant of inverse filtered (equalized) data w.r.t. the equalizer coefficients subject to the equalizer lying in a subspace associated with the desired user's code sequence. Constrained maximization leads to extraction of the desired user's signal whereas unconstrained maximization leads to the extraction of any one of the existing users. An illustrative simulation example is provided.

Blind channel estimation and blind equalization of MIMO (multiple-input multiple-output) communications channels is considered using primarily the second-order statistics of the data. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. The sources are recovered up to a unitary mixing matrix and are further 'unmixed' using higher-order statistics of the data. An illustrative simulation example is provided.

A multistep linear prediction approach is presented for blind channel estimation and detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We exploit the previously proposed multistep linear prediction (MSLP) approach for blind multiple-input multiple-output (MIMO) channel estimation in conjunction with the structure imposed by the desired user's spreading code sequence. With the knowledge of the desired user's code sequence, only the second-order statistics of the data are needed under certain sufficient conditions on the underlying multiuser MIMO transfer function. An illustrative simulation example is provided.

A code-constrained inverse filter criteria based approach is presented for blind detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We focus on maximization of the normalized fourth cumulant of inverse filtered (equalized) data w.r.t. the equalizer coefficients subject to the equalizer lying in a subspace associated with the desired user's code sequence. Constrained maximization leads to extraction of the desired user's signal whereas unconstrained maximization leads to the extraction of any one of the existing users. An illustrative simulation example is provided.

We show that a finite impulse response and multi-input-multi-output (FIR-MIMO) system with colored input is blindly identifiable up to a permutation and scaling using the second order statistics (SOS) of the system's output if (a) the system function is irreducible, and (b) the input signals are uncorrelated from each other and have distinct power spectra. Condition (a) is weaker than several conditions reported previously. It suggests a further potential of developing more robust blind algorithms.

The problem of closed loop system identification given noisy time-domain input-output measurements is considered. It is assumed that the various disturbances affecting the system are zero-mean stationary whereas the closed loop system operates under an external cyclostationary input which is not measured. Noisy measurements of the (direct) input and output of the plant are assumed to be available. The closed loop system must be stable but it is allowed to be unstable in the open loop. Tontiruttananon and Tugnait (1998) proposed two identification algorithms using cyclic-spectral analysis asymptotic performance analysis of the previously proposed parameter estimators. Computer simulation examples are presented in support of the analysis.

Channel estimation and blind equalization of MIMO (multiple-input multiple-output) communications channels is considered using primarily the second-order statistics of the data. We consider estimation of (partial) channel impulse response and design of finite-length MMSE (minimum mean-square error) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover /spl Gamma/ the multichannel transfer function need not be column-reduced. Our approaches also work when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further "unmixed" using higher-order statistics of the data. An illustrative simulation example is provided.

Blind equalization of MIMO (multiple-input multiple-output) communications channels is considered using primarily the second-order statistics of the data. In several applications the underlying equivalent discrete-time mathematical model is that of a MIMO linear system where the number of inputs equals the number of users (sources) and the number of outputs is related to the number of sensors and the sampling rate. Previously we investigated the structure of multi-step linear predictors for IIR/FIR MIMO systems with irreducible transfer functions and derived an upper bound on its length (Tugnait 1998). In the past multi-step linear predictors have been considered in the literature only for single-input multiple-output models. In this paper we apply the results of Tugnait (1998) for blind equalization of MIMO channels using MMSE linear equalizers. Extensions to the case where the "subchannel" transfer functions have common zeros/factors is also investigated. An illustrative simulation example is provided.

The problem of blind equalization of SIMO (single-input multiple-output) communications channels is considered using only the second-order statistics of the data. Such models arise when single receiver data is fractionally sampled (assuming that there is excess bandwidth), or when an antenna array is used with or without fractional sampling. We focus on the direct design of finite-length MMSE (minimum mean-square error) blind equalizers. Unlike the past work on this problem, we allow infinite impulse response (IIR) channels. Our approaches also work when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. Illustrative simulation examples are provided.

The problem of closed-loop system identification given noisy input-output measurements is considered. The closed-loop system operates under an external cyclostationary input which is not measured. Noisy measurements of the (direct) input and output of the plant are assumed to be available. The various disturbances affecting the system are either stationary or cyclostationary with cycle frequencies different from the input cycle frequencies. The closed-loop system must be stable but it is allowed to be unstable in open-loop. A frequency-domain parametric solution is proposed and analysed using an equation error formulation, and the cyclic spectrum and cross-spectrum of the input-output measurements. The parameter estimator is shown to be consistent. A simulation example using an unstable open-loop system is presented to illustrate the proposed approach.

This paper is concerned with the problem of blind separation of independent signals (sources) from their linear convolutive mixtures. The various signals are assumed to be linear non-Gaussian but not necessarily i.i.d. An iterative, normalized higher-order cumulant maximization based approach was developed previously using the fourth-order normalized cumulants of the: "beamformed" data. A byproduct of this approach is a decomposition of the given data, at each sensor into its independent signal components. In this paper an adaptive implementation of the above approach is developed using a stochastic gradient approach. Some further enhancements including a Wiener filter implementation for signal separation and adaptive filter reinitialization are also provided. A computer simulation example is presented.

Time-domain least-squares equation-error models are widely used for estimation of an input-output (I/O) parametric transfer function. It is known that an autoregressive constraint on the input is sufficient to ensure stability of the estimated multivariable model. In this letter, we consider a frequency-domain solution to the least-squares equation-error multivariable system identification problem using the power spectrum and the cross-spectrum of the I/O data to estimate the I/O parametric transfer function. The considered approach is shown to yield stable fitted multivariable models for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order.

The existence of finite-length one-step linear predictors plays a key role in several existing algorithms for blind identification and equalization of multiple-input multiple-output (MIMO) systems. An upper bound on the length of the predictor is known for the case when the underlying MIMO transfer function is irreducible and column-reduced. When the MIMO transfer function is irreducible but not necessarily column-reduced, it is known that a finite-length linear predictor exists; however, its length has not been specified in the literature. An upper bound on the length of a linear predictor for MIMO systems with irreducible transfer functions is derived.

Given a linear stationary non-Gaussian signal, suppose that we fit a linear model using higher-order statistics and one of several existing methods. The model is fitted under certain assumptions on the data and the underlying (true) model. Having obtained a model, how do we know if the fitted model is "good"? This paper is devoted to the problem of model diagnostics and validation. We propose some simple frequency-domain tests that are applicable to both third-order and fourth-order statistics-based model fitting unlike existing tests. A computer simulation example is presented to illustrate the proposed tests.

We consider a frequency-domain solution to the least-squares equation error identification problem using the power spectrum and the cross-spectrum of the IO (input-output) data to estimate the IO parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identification in colored noise and sufficient-order case, and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. Computer simulation results are presented to illustrate the proposed approach.

This paper is concerned with the problem of estimating the multichannel impulse response function of a 2-D multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. Such models arise in a variety of situations such as color images (textures), or image data from multiple frequency bands, multiple sensors or multiple time frames. We extend the approach of Tugnait (see IEEE Trans. Image Processing, vol.TP-3, p.109-27, 1994) (which deals with SISO 2-D systems) to MIMO 2-D systems. The paper is focused on certain theoretical aspects of the problem: estimation criteria, existence of a solution, and parameter identifiability. An iterative, inverse filter criteria based approach is developed using the third-order and/or fourth-order normalized cumulants of the inverse filtered data at zero-lag. The approach is input-iterative, i.e., the input sequences are extracted and removed one-by-one. The matrix impulse response is then obtained by cross-correlating the extracted inputs with the observed outputs.

The problem of blind equalization and channel estimation for partial-response signals (PRS) is considered. Three approaches are investigated; two of them exploit the prior knowledge of the PR code, and the third approach does not. We propose a constrained optimization approach involving a quadratic cumulant matching criterion where the coding structure of the transmitted signal is assumed to be a priori known. The other two approaches exploit the Godard blind equalizer. Computer simulation results using 16-QAM signals, and duobinary and modified duobinary PR codes, show that the constrained optimization approach yields the best performance as measured via the probability of symbol detection error.

Equalization and estimation of the matrix impulse response function of MIMO digital communications channels in the absence of any training sequences is considered. An iterative, Godard (1980) cost based approach is considered for spatio-temporal equalization and MIMO impulse response estimation. Stationary points of the cost function are investigated and it is shown that all stable local minima correspond to desirable minima when doubly infinite equalizers are used. The inputs are extracted and cancelled one-by-one. The matrix impulse response is then obtained by cross-correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. Computer simulation examples are presented to illustrate the proposed approach.

We consider the problem of blind estimation and equalization of digital communication finite impulse response (FIR) channels using fractionally spaced samples. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. The channel parameters are estimated by first estimating various subchannels using the second- and the fourth-order cumulant function of the received data, and then appropriately aligning and scaling them. The estimated channel impulse response is then used to construct a linear equalizer. Two illustrative simulation examples using four- and 16-QAM signals are presented where effect of symbol-timing-phase offset is studied via simulations.

The problem of fractionally-spaced (FS) blind adaptive equalization under symbol-timing-phase offsets is considered. It is well-known that in the case of trained (non-blind) equalizers, the performance of FS equalizers is independent of the timing-phase unlike that of baud-rate equalizers. Moreover, trained FS equalizers synthesize optimal filters in the MMSE sense, and hence are superior to baud-rate trained equalizers. These advantages of trained FS equalizers have not been shown to be true for blind equalizers, rather they have been simply assumed. The authors present a simulation example where such advantages do not materialize. Then they present a solution based upon a parallel, multimodel Godard adaptive filter bank approach which yields a performance almost invariant w.r.t. symbol-timing-phase. An illustrative simulation example 16-QAM (V22 source) signal is presented where the effect of symbol-timing-phase offset is studied via computer simulations.

The problem of estimating the difference in arrival times of a non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian (or a class of non-Gaussian) noise of unknown cross-correlation. We analyze the asymptotic performance of some recently proposed differential time-delay estimators which exploit the integrated polyspectrum of the measurements. The proposed estimators are asymptotically maximum-likelihood when attention is confined to the integrated polyspectra of the measurements. Therefore, the performance of the estimators approaches the Cramer-Rao (CR) bound asymptotically. Expressions for the relevant CR bound are derived. Computer simulations are presented comparing actual performance with the CR bounds for a simple example.

The problem of estimating the parameters of a non-Gaussian ARMA signal model using higher order statistics is considered. We propose and analyze a novel class of criteria involving explicit higher order whitening, where higher order cumulants of deconvolved data are exploited at a finite number of lags excluding the zero lag. In the presence of a class of measurement noise of unknown covariance/cumulant function, the proposed criteria are shown to yield strongly consistent parameter estimators unlike the Wiggins-Donoho-Shalvi-Weinstein class involving implicit higher order whitening, where higher order cumulants of deconvolved data are exploited only at zero lag.>

A frequency-domain, higher order whiteness testing approach to linear model validation and order selection for non-Gaussian signals was proposed in Tugnait (1994). It involves testing for the constancy of the bispectrum of inverse filtered data. In the present paper, an improved implementation of the statistical test used previously is presented. Simulation results show better performance (higher percentage of correct order selection) of the proposed approach with shorter data records when compared with the previous implementation.>

We consider the problem of blind estimation and equalization of digital communication FIR (finite impulse response) channels. The channel parameters are estimated by nonlinear batch optimization of a quadratic cumulant matching criterion involving second and fourth order cumulants of the received data. A new algorithm is proposed for (asymptotically) globally convergent, linear estimation of the FIR channel parameters where the FIR model order is not necessarily known. The nonlinear cumulant matching algorithm is initialized by the linear parameter estimator. The estimated channel impulse response is then used to construct a linear equalizer. Two illustrative simulation examples using 4, 16 and 64-QAM signals are presented.>

The problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. A necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived. This result provides an alternative but equivalent statement of an existing result. Using this result, it is shown that certain class of multipath channels cannot be identified from the second-order statistics irrespective of how the sampling rate is chosen.>

A typical assumption made in most of the existing blind channel estimation and/or equalization approaches is that the signal input to the digital communications channel is i.i.d. One important case where this is not true is that of correlative coded, or partial-response (PR), signals where a controlled amount of ISI (intersymbol interference) is introduced at the transmitting end in order to eliminate any need for "excess" bandwidth. We consider the problem of blind equalization for such signals. We propose a constrained optimization approach where the coding structure of the transmitted signal is assumed to be a priori known. Computer simulation results using 16-QAM signals, and duobinary and modified duobinary PR codes, are presented where the proposed approach is compared with two other possible approaches.>

The problem of estimating the parameters of a vector, stationary, ARMA(p,q) signal model driven by an i.i.d. vector non-Gaussian sequence is considered. The paper's focus is the problem of parameter identifiability of multichannel ARMA models given the higher-order cumulants of the signal on a finite set of lags. We specify the finite lag set for general ARMA(p,q) models. Our approach is to first derive the basic results via a diagonal canonical form and then to extend the parameter identifiability results to other (more parsimonious) canonical forms.>

The problem of estimating the difference in arrival times of a non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian (or a class of non-Gaussian) noise of unknown cross-correlation. The authors present two new frequency-domain approaches for differential time-delay estimation using bispectrum or integrated bispectrum of the measurements. The approaches are asymptotically maximum-likelihood, hence, are optimal unlike the existing frequency-domain (bispectrum-based) approaches. Unlike the existing time-domain approaches, the input does not need to be a linear process.>

The article propose novel approaches to the problem of blind channel impulse response estimation for data communication systems, including telephone channels as well as digital radio channels. No training sequence is assumed to be available. Two novel schemes are proposed for channel impulse response estimation. Only batch (nonrecursive) methods are considered. The higher order cumulant statistics is exploited, in addition to the usual second-order statistics, of the data and of appropriately defined error signals. The proposed methods yield (globally) optimal solutions. The estimated channel impulse response can be used for channel equalization, either for reliable ("open eye") initialization of the conventional decision-directed equalizers or as a channel estimator for a Viterbi algorithm based equalizer. Two illustrative examples one for a telephone channel and the other for a multipath channel, are given using an 8-level PAM signal.>

A general (possibly asymmetric noncausal and/or nonminimum phase) 2D autoregressive moving average random field model driven by an independent and identically distributed 2D nonGaussian sequence is considered. The model is restricted to be invertible, i.e., system zeros are not allowed to lie on the unit bicircle. Three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements (image pixels). The proposed criteria are functions of the higher order cumulant statistics of an inverse filter output. One of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency. In the paper strong consistency of the proposed methods under the assumption that the system order is known is proved. The convergence of the proposed parameter estimators under overparametrization is also analyzed. Experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches. Experimental results of synthesis of 128x128 textures visually resembling several real life textures in the Brodatz album (and other sources) are presented.

The author considers the problem of estimating the parameters of a general (possibly asymmetric noncausal and/or nonminimum phase) two-dimensional autoregressive moving average random field model driven by an independent and identically distributed two-dimensional non-Gaussian sequence. Several inverse filter criteria were recently considered for parameter estimation of the system parameters given only the output measurements (image pixels). These criteria were shown to yield strongly consistent parameter estimates. The focus is on the computational aspects. A computer simulation example is presented to illustrate the performance of the proposed approach.>

It is pointed out that certain criteria proposed in the paper by Shalvi and Weinstein (see ibid., vol.36, no.2, p.312-21, 1990) have been proposed before in the context of real-valued signals. Furthermore, it is noted that the assertion made in the paper that all local maxima of the proposed criteria correspond to the desired equalizer solution, holds true, strictly speaking, only for infinite length equalizers. There exist counterexamples which show existence of false local maxima when finite-length equalizers are used. Finally, it is also noted that in the presence of additive Gaussian noise of unknown power spectral density at the input to the equalizer (equivalently, at the channel output), it is not clear if the methods proposed in the paper will yield the desired response up to a constant gain.>

The problem of estimating the difference in arrival times of a nonGaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian noises of unknown cross correlation. The author proposes and analyzes two class methods for time delay estimation based on higher order statistics. The proposed methods are conceptually very similar to the traditional cross correlation based techniques in that the proposed criteria peak at the lag value equals the true delay. At the same time, the proposed methods are based on higher-order cumulant statistics of the data and are therefore unaffected by the Gaussian noises.>

The author considers the problem of estimating the parameters of a stable, scalar ARMA (autoregressive moving average) signal model (causal or noncausal, minimum phase or mixed phase) driven by an independent and identically distributed nonGaussian sequence. The driving noise sequence is not observed. The Wiggins-Donoho class of inverse filter criteria for estimation of model parameters are analyzed and extended to general ARMA inverses. A class of criteria for consistent parameter estimation in colored Gaussian noise is proposed and analyzed.>

The problem of estimating the parameters of a stable, scalar, noncausal autoregressive moving average (ARMA) (p,q) signal model driven by an i.i.d. non-Gaussian sequence is considered. The driving noise sequence is not observed. Two methods are proposed and analyzed: one is a multistep linear method and the other is a nonlinear optimization method. Both methods exploit both the second- and third- (or higher-) order cumulants of the observed signal. The strong consistency of the two estimators is proved. The main focus is on the linear method. Extensions to include i.i.d. measurement noise (Gaussian or non-Gaussian) can be done easily.>

A counterexample is presented to show that the solution to the stochastic realization problem given in the above-titled letter (ibid., vol.75, no.9, p.1333-4, Sept. 1987) does not apply, in general, to the infinite impulse response systems. The author expands on the comments.>

Recently two techniques that use both autocorrelations and third-order autocumulants of the noisy observations were proposed by the author (1987) for the estimation of the parameters of a noncausal autoregressive (AR) signal model. In the proposed methods the maximum cumulant lag parameters were specified as large but finite. The author gives specific values for the maximum cumulant lags, and proves strong consistency of the two estimators of the AR parameters under the specified choice of lags. In addition, he develops some fundamental results concerning the recovery of the system poles from the third-order statistics of the noisy observations.>

The problem of estimating parameters of a noncausal autoregresslve signal from noisy observations is considered. The signal is assumed to be non-Gaussian. The measurement noise is allowed to be non-Gaussian. Two techniques that use both autocorrelations and third-order autocumulants of the data are presented for parameter estimation. Strong consistency of the proposed techniques is proved under certain sufficient conditions. Knowledge of the probability distribution of the driving noise is not required. Simulation examples are presented to illustrate the two methods. The problem of model order selection is also addressed.

The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered. The system is not restricted to be minimum phase, and it is allowed to contain all-pass components. A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed. Knowledge of the probability distribution of the driving noise is not required. An order determination criterion that is a modification of the Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are presented to illustrate the method.

The problem of recursively estimating the unknown parameters of a scalar autoregressive (AR) signal observed in additive white noise, including signal power and noise variance, is considered. A state-space model in a canonical but noninnovations form is used to represent the noisy AR signal. An algorithm based on a system identification/parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation. Two simulation examples illustrate the effectiveness of the proposed algorithm.

The problem of consistent estimation of the unknown parameters of linear time-invariant continuous-time systems is considered. The unknown parameter set is assumed to be compact, and only noisy observations of the system output are available. Sufficient conditions are derived for global strong consistency of the maximum-likelihood parameter estimates. The consistency proof exploits a recent result due to Delchamps concerning smoothness of the algebraic Riccati equation in the system parameters. This smoothness result has been tacitly assumed in the literature on local consistency of the parameter estimates. The previous global consistency results have been obtained under the restrictive assumption of finite parameter sets.

The problem of estimating the unknown parameters of linear discrete-time stochastic system models is considered for the case when the observations may contain noise alone. The interruptions in the observations are modeled as an independent stationary binary (zero or one) sequence where the probability of an interruption may not be known. The criterion for parameter estimation is chosen to be minimization of the prediction errors using linear predictors. Sufficient conditions for strong consistency of the parameter estimates are derived. It is shown by means of an example that even a few missing observations can lead to a serious degradation in the quality of the parameter estimate.

Global convergence pf the maximum likelihood estimates of unknown parameters of a continuous-time stochastic linear dynamical system is investigated when the observation noise covariance is unknown. The unknown parameter set is assumed to be finite. The situation where the true parameter does not belong to the unknown parameter set is considered as well as the situation where the true model is included in the unknown parameter set. Convergence is proved under a certain sufficient condition called the identifiability condition.

Sufficient conditions for uniform asymptotic stability in the large of the optimal minimum mean-square error (MMSE) linear filter are developed for discrete linear systems whose observations may contain noise alone and where only the probability of occurrence of such cases is known to the estimator. Conditions for existence, uniqueness, and stability of the steady-state optimal filter are also considered for the case when the system is time-invariant.

The asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear discrete-time dynamical system with unknown Markovian noise statistics is investigated. Noise influencing the state equation and the measurement equation is assumed to come from a group of Gaussian distributions having different means and covariances, with transitions from one noise source to another determined by a Markov transition matrix. The transition probability matrix is unknown and can take values only from a finite set. An example is simulated to illustrate the convergence.