George N. Karystinos

An iterative algorithm for the computation of the MVDR filter

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation.

New bounds on the total squared correlation and optimum design of DS-CDMA binary signature sets

The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.

On overfitting, generalization, and randomly expanded training sets

An algorithmic procedure is developed for the random expansion of a given training set to combat overfitting and improve the generalization ability of backpropagation trained multilayer perceptrons (MLPs). The training set is K-means clustered and locally most entropic colored Gaussian joint input-output probability density function (pdf) estimates are formed per cluster. The number of clusters is chosen such that the resulting overall colored Gaussian mixture exhibits minimum differential entropy upon global cross-validated shaping. Numerical studies on real data and synthetic data examples drawn from the literature illustrate and support these theoretical developments.

Optimal Algorithms for L 1 -subspace Signal Processing

We describe ways to define and calculate L1-norm signal subspaces that are less sensitive to outlying data than L2-calculated subspaces. We start with the computation of the L1 maximum-projection principal component of a data matrix containing N signal samples of dimension D. We show that while the general problem is formally NP-hard in asymptotically large N, D, the case of engineering interest of fixed dimension D and asymptotically large sample size N is not. In particular, for the case where the sample size is less than the fixed dimension , we present in explicit form an optimal algorithm of computational cost 2N. For the case N ≥ D, we present an optimal algorithm of complexity O(ND). We generalize to multiple L1-max-projection components and present an explicit optimal L1 subspace calculation algorithm of complexity O(NDK-K+1) where K is the desired number of L1 principal components (subspace rank). We conclude with illustrations of L1-subspace signal processing in the fields of data dimensionality reduction, direction-of-arrival estimation, and image conditioning/restoration.

The maximum squared correlation, sum capacity, and total asymptotic efficiency of minimum total-squared-correlation binary signature sets

The total squared correlation (TSC), maximum squared correlation (MSC), sum capacity (C/sub sum/), and total asymptotic efficiency (TAE) of underloaded signature sets, as well as the TSC and C/sub sum/ of overloaded signature sets are metrics that are optimized simultaneously over the real/complex field. In this present work, closed-form expressions are derived for the MSC, C/sub sum/, and TAE of minimum-TSC binary signature sets. The expressions disprove the general equivalence of these performance metrics over the binary field and establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible. The sum-capacity loss of the recently designed minimum-TSC binary sets is found to be rather negligible in comparison with minimum-TSC real/complex-valued (Welch-bound-equality) sets.

Rank-

Over the real/complex field, the spreading code that maximizes the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR linear filter is the minimum-eigenvalue eigenvector of the interference autocovariance matrix. In the context of binary spreading codes, the maximization problem is NP-hard with complexity exponential in the code length. A new method for the optimization of binary spreading codes under a rank-2 approximation of the inverse interference autocovariance matrix is presented where the rank-2-optimal binary code is obtained in lower than quadratic complexity. Significant SINR performance improvement is demonstrated over the common binary hard-limited eigenvector design which is shown to be equivalent to the rank-1-optimal solution.

2

This work derives and evaluates single-antenna detection schemes for collided radio frequency identification (RFID) signals, i.e. simultaneous transmission of two RFID tags, following FM0 (biphase-space) encoding. In sharp contrast to prior art, the proposed detection algorithms take explicitly into account the FM0 encoding characteristics, including its inherent memory. The detection algorithms are derived when error at either or only one out of two tags is considered. It is shown that careful design of one-bit-memory two-tag detection can improve bit-error-rate (BER) performance by 3dB, compared to its memoryless counterpart, on par with existing art for single-tag detection. Furthermore, this work calculates the total tag population inventory delay, i.e. how much time is saved when two-tag detection is utilized, as opposed to conventional, single-tag methods. It is found that two-tag detection could lead to significant inventory time reduction (in some cases on the order of 40%) for basic framed-Aloha access schemes. Analytic calculation of inventory time is confirmed by simulation. This work could augment detection software of existing commercial RFID readers, including single-antenna portable versions, without major modification of their RF front ends.

-Optimal Adaptive Design of Binary Spreading Codes

The maximization of a full-rank quadratic form over the binary alphabet can be performed through exponential-complexity exhaustive search. However, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient quadratic-form maximization problem is converted into a double maximization of a linear form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.

Single-Antenna Coherent Detection of Collided FM0 RFID Signals

We derive new bounds on the aperiodic total squared correlation (ATSC) of binary antipodal signature sets for any number of signatures K and any signature length L. We then present optimal designs that achieve the new bounds for several (K,L) cases. As interesting -arguably- side results, we show that individual maximal merit factor sequences (for example Barker sequences) are single-user ATSC-optimal, while neither the familiar Gold nor the Kasami set designs are ATSC-optimal in general. The ATSC-optimal signature set designs provided in this work are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.

Efficient Computation of the Binary Vector That Maximizes a Rank-Deficient Quadratic Form

The recent increased interest in large-scale multiple- input multiple-output systems, combined with the cost of analog radio-frequency (RF) chains, necessitates the use of efficient antenna selection (AS) schemes. Capacity or signal-to-noise ratio (SNR) optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this work, we prove that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas N is polynomially solvable and develop an algorithm that solves it with quartic complexity, independently of the number of selected antennas. The algorithm identifies with complexity O(N4) a cubic-size collection of antenna subsets that contains the one that maximizes the post-processing receiver SNR. From a different perspective, for any given two-row complex matrix, our algorithm computes with quartic complexity its two-row submatrix with the maximum principal singular value, for any number of selected columns. In addition, our method also applies to receive AS with two transmit antennas. Finally, if we enforce a per-antenna-element power constraint on the beamformer (i.e., constant-envelope transmission), then the set of transmit AS subsets that contains the optimal one is the same as in the total power constraint case. Therefore, our algorithm offers a practical solution to the maximum-SNR antenna selection problem when either the transmitter or the receiver consists of a large number of antennas.