On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

On the stabilization of uniformly decoupled systems by state variable feedback

Conditions under which the asymptotic stabilization of uniformly decoupled time-varying multivariate systems is possible are explored. This is accomplished by developing a canonical form for integrator uniformly decoupled system in which the coefficient matrices have a simple structure. The procedures developed rely on certain conditions on the given system and yield explicit expressions for the stabilization compensators.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 x 2 and 4 x 2 MIMO Systems

This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 x 2) and the 4 transmit antenna, 2 receive antenna (4 x 2) MIMO systems. Presently, the best known STBC for the 2 2 system is the Golden code and that for the 4 x 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 x 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 x 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of for square QAM of size. In this paper, a scheme that reduces its ML-decoding complexity to M-2 root M is presented.

High-Rate Space-Time Coded Large-MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-multiple-input multiple-output (MIMO) systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16 X 16 and 32 X 32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.

A method of fraud & intrusion detection for e-payment systems in mobile

The need for paying with mobile devices has urged the development of payment systems for mobile electronic commerce. In this paper we have considered two important abuses in electronic payments systems for detection. The fraud, which is an intentional deception accomplished to secure an unfair gain, and an intrusion which are any set of actions that attempt to compromise the integrity, confidentiality or availability of a resource. Most of the available fraud and intrusion detection systems for e-payments are specific to the systems where they have been incorporated. This paper proposes a generic model called as Activity-Event-Symptoms(AES) model for detecting fraud and intrusion attacks which appears during payment process in the mobile commerce environment. The AES model is designed to identify the symptoms of fraud and intrusions by observing various events/transactions occurs during mobile commerce activity. The symptoms identification is followed by computing the suspicion factors for event attributes, and the certainty factor for a fraud and intrusion is generated using these suspicion factors. We have tested the proposed system by conducting various case studies, on the in-house established mobile commerce environment over wired and wire-less networks test bed.

A systematic design of high-rate full-diversity space-frequency codes for MIMO-OFDM systems

This paper presents a systematic construction of high-rate and full-diversity space-frequency block codes for MIMO-OFDM systems. While all prior constructions offer only a maximum rate of one complex symbol per channel use, our construction yields rate equal to the number of transmit antennas and simultaneously achieves full-diversity. The proposed construction works for arbitrary number of transmit antennas and arbitrary channel power delay profile. A key step in this construction is the generalization of the stacked matrix code design criteria given by Bolcskei et.al., (IEEE WCNC 2000). Explicit equivalence of our generalized code design criteria with the Hadamard-product based criteria of W. Su et.al., (lEEE Trans. Sig. Proc. Nov 2003) is established and new high-rate codes are constructed using our criteria.

BER-optimized linear parallel interference cancellers for multicarrier DS-CDMA systems

In this paper, we consider the design and bit-error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) systems. We propose an LPIC scheme where we estimate and cancel the multiple access interference (MAT) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit-error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. In addition, using an alternate approach involving the characteristic function of the decision variable, we derive BER expressions for the weighted LPIC scheme, matched filter (MF) detector, decorrelating detector, and minimum mean square error (MMSE) detector for the considered multicarrier DS-CDMA system. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating and MMSE detectors.

Tradeoff between PAPR reduction and decoding complexity in transformed OFDM systems

It is known that in an OFDM system using Hadamard transform or phase alteration before the IDFT operation can reduce the Peak-to-Average Power Ratio (PAPR). Both these techniques can be viewed as constellation precoding for PAPR reduction. In general, using non-diagonal transforms, like Hadamard transform, increases the ML decoding complexity. In this paper we propose the use of block-IDFT matrices and show that appropriate block-IDFT matrices give lower PAPR as well as lower decoding complexity compared to using Hadamard transform. Moreover, we present a detailed study of the tradeoff between PAPR reduction and the ML decoding complexity when using block-IDFT matrices with various sizes of the blocks.

Low PAPR full-diversity space-frequency codes for MIMO-OFDM systems

Use of precoding transforms such as Hadamard Transforms and Phase Alteration for Peak to Average Power Ratio (PAPR) reduction in OFDM systems are well known. In this paper we propose use of Inverse Discrete Fourier Transform (IDFT) and Hadamard transform as precoding transforms in MIMO-OFDM systems to achieve low peak to average power ratio (PAPR). We show that while our approach using IDFT does not disturb the diversity gains of the MIMO-OFDM systems (spatial, temporal and frequency diversity gains), it offers a better trade-off between PAPR reduction and ML decoding complexity compared to that of the Hadamard transform precoding. We study in detail the amount of PAPR reduction achieved for the following two recently proposed full-diversity Space-Frequency coded MIMO-OFDM systems using both the IDFT and the Hadamard transform: (i) W. Su. Z. Safar, M. Olfat, K. J. R. Liu (IEEE Trans. on Signal Processing, Nov. 2003), and (ii) W. Su, Z. Safar, K. J. R. Liu (IEEE Trans. on Information Theory, Jan. 2005).

On an asymptotic method of Krylov-Bogoliubov for overdamped nonlinear systems

A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria