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Maximum signal-to-noise ratio (SNR) designs for space-time formatting transmissions over multiple input multiple output (MIMO) flat channels under various power constraints is discussed. Examples of power constraints include the total power constraint (TPC), the elemental power constraint (EPC) and the total and elemental power constraint (TEPC).

A recent paper by Ranheim considered the problem of separating signal sources using an array of sensors. A main algebraic result in that paper states that a certain noise covariance matrix can be replaced in a weighted least squares criterion by the sample version of the data covariance matrix without changing the asymptotic properties of the signal estimates. As we demonstrate in this paper, this result appears to be flawed in the general case. However, despite this fact, we also demonstrate that the method in Ranheim's paper is statistically sound under fairly weak conditions. Since it is also computationally attractive, we believe that it can be useful in practical applications. Index Terms--Adaptive arrays, array signal processing, interference suppression, signal separation.

The problem of direction finding in the presence of an intermittent jammer is discussed. Using an array of sensors to mitigate the effects of interference is investigated.

The amplitude and phase estimation (APES) algorithm is extended to deal with the circumstance when some samples are missing. The new algorithm, called gapped-data APES (GAPES), was developed for the 2-D case with 1-D treated as a special case.

A paradigm for designing trasmitter space-time coding is described. The paradigm, referred to as linear precoding, yields simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with regard to number of antennas, size of the coding block, and transmit average/peak power.

Space-time coding (STC) procedures for communication systems that rely on multiple antennas are discussed. The emphasis is on two interrelated problems: detection of space-time codes under differing interference conditions; and information transfer from the STC detector to an error-correcting channel decoder.

We address the problem of designing jointly optimum linear precoder and decoder for a MIMO channel possibly with delay-spread, using a weighted minimum mean-squared error (MMSE) criterion subject to a transmit power constraint. We show that the optimum linear precoder and decoder diagonalize the MIMO channel into eigen subchannels, for any set of error weights. Furthermore, we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights. We show how to obtain: 1) the maximum information rate design; 2) QoS-based design (we show how to achieve any set of relative SNRs across the subchannels); and 3) the (unweighted) MMSE and equal-error design for fixed rate systems. Index Terms--MIMO, MMSE, precoding, space-time coding, spatial multiplexing.

Fast alternative formulations of the moving average (MA) covariance fitting problems are proposed. Guidelines are provided for their implementation, using semidefinite quadratic programming.

New procedures are described, for direction-of-arrival (DOA) estimation, relying on arrays consisting of multiple translated and uncalibrated subarrays. The procedures can be regarded as generalized versi9ons of the MUSIC, Root-MUSIC, and MODE techniques, originally developed for fully calibrated arrays.

We propose to use the APES (amplitude and phase estimation) approach for the spectral estimation of gapped data and synthetic aperture radar (SAR) imaging with angular diversity. A relaxation-based algorithm, referred to as GAPES (Gapped-data APES), is proposed, which includes estimating the spectrum via APES and filling in the gaps via a least squares (LS) fitting. For SAR imaging with angular diversity data fusion, we perform one-dimensional (I-D) windowed fast Fourier transforms (FFTs) in range, use the GAPES algorithm to interpolate the gaps in the aperture for each range, apply I-D inverse FFTs (IFFTs) and dewindow in range, and finally apply the two-dimensional (2-D) APES algorithm to the interpolated matrix to obtain the 2-D SAR image. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

Research is presented concerning the derivation and accuracy of the array output covariance matrix. The multiple signal classification algorithm is used for direction-of-arrival estimations.

The direction finding problem is considered in the imperfect spatial coherence case.

Research is presented concerning the elimination of all the distortion parameters from wavefront amplitude distorted in an arbitrary manner. The accuracy of the estimator is discussed.

Singular information matrices problems are considered.

The weighted noise subspace fitting algorithm with optimal weight is shown to have the same statistical efficiency as the unconditional maximum likelihood algorithm, but is more effective than the conditional maximum likelihood algorithm.

Blind multichannel deconvolution and generalized quadratic minimization are discussed relative to the problem of quadratic minimization with linear equality limitations. The most general case of a possibly singular quadratic form is assumed. The new approach is free from most common drawbacks, is simple to interpret and relatively easy to implement. It has numerous real-world applications, making it important.

A statistical test to determine whether the amplitude of an exponential signal is constant or time varying has been developed. The statistics of two frequency estimates were derived and then used to design a chi-square test. The results showed that the proposed detection test provides consistent frequency estimates under either hypothesis. Simulation results showed the good detection performance of the proposed test.

A study was conducted to find solutions to the problem of computing the time delays and Doppler shifts of a known waveform received through several different paths by an array of antennas. A number of approaches was developed to resolve this problem. These include the general maximum likelihood estimator, which only requires a 2d-dimensional nonlinear minimization and two signal and noise subspace fitting solutions.

A study was conducted to examine forward-backward matched-filterbank (MAFI) spectral estimators using a higher order expansion method. Two dimensional extension analyses were carried out to analyze the behavior of two-dimensional MAFI estimators. The bias of the forward-backward Capon was nearly half of the forward-only Capon. Results indicated that the bias for the forward-only Capon spectral estimate can easily be determined by substituting the forward-backward sample covariance by the forward-only sample covariance matrix.

A comparative study of the iterative quadratic maximum likelihood (IQML) and the method of direction estimation (MODE) in direction-of-arrival (DOA) estimation of narrowband incident signals having uniform linear array, is presented. DOE estimates via MODE were asymptotically statistically efficient, but those obtained through IQML were mostly inconsistent with larger mean squared errors.

Two eigenvalue-based rules for estimating the number of signals impinging on an array of sensors along with the spatially correlated noise field have been introduced. The first rule is derived from the assumption that the noise spatial covariance is block diagonal or branded. The second rule is based on the assumption that the temporal correlation of the noise has a shorter length than that of the signals. Matrix is built from the array output data covariances. Both rules are mathematically simple and can be used with a noncalibrated array.

The asymptotic Cramer-Rao bound matrix, the maximum likelihood method (MLM), and the nonlinear least-squares method (NLSM) were considered to address the problem of estimating the parameters of ciscoids from data corrupted by colored noise. The ultimate large-sample statistical performance of the exact MLM estimator of the signal parameters was found achievable by a computationally much simpler NLSM method.