Edit J. Kaminsky

Fractional Fourier transform for sonar signal processing

In this paper we present an approach for processing of sonar signals with the ultimate goal of ocean bottom sediment classification. Work reported is based on sonar data collected by the volume search sonar (VSS) in the Gulf of Mexico, as well as on VSS synthetic data. The volume search sonar is a beam formed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back to above horizontal). Our investigation is focused on the bottom-return signals since we are interested in determination of the impulse response of the ocean bottom floor. The bottom-return signal is the convolution between the impulse response of the bottom floor and the transmitted sonar chirp signal. The method developed here is based on fractional Fourier transform, a fundamental tool for signal processing and optical information processing. Fractional Fourier transform is a generalization of the classical Fourier transform. The traditional Fourier transform decomposes signal by sinusoids whereas Fractional Fourier transform corresponds to expressing the signal in terms of an orthonormal basis formed by chirps. In recent years, interest in and use of time-frequency tools have increased and become more suitable for sonar applications. The fractional Fourier transform requires finding the optimum order of the transform that can be estimated based on the properties of the chirp signal. The bottom impulse response is given by the magnitude of the fractional Fourier transform applied to the bottom return signal. The technique used in this work has been tested both on synthetic data and real sonar data collected by the VSS. The synthetic sonar return signal has been generated by the convolution between the Green function, which has been utilized to simulate the impulse response of the seafloor and the transmitted VSS chirp. A study is carried out to compare the performance of our method to a conventional method based on deconvolution in the frequency domain (using standard Fourier transform). The amplitude and shape of an acoustic signal reflected from the sea floor is determined mainly by the seabottom roughness, the density difference between water and the sea floor, and reverberation within the substrate. Since the distribution of seafloor types is a very important tool in different applications, a sediment classification has been implemented based on a statistical analysis of the obtained impulse response. In order to perform a robust analysis of the signal, a joint time-frequency analysis is necessary. In this paper the analysis has been evaluated using the Wigner distribution, which can be thought of as a signal energy distribution in joint time-frequency domain. Singular value decomposition of the Wigner distribution has been used in order to perform the seafloor sediment classification. A comparative analysis of the experimental results for classical deconvolution and fractional Fourier method is presented. Results are shown and suggestions for future work are provided

Sonar signal enhancement using fractional Fourier transform

In this paper we present an approach for signal enhancement of sonar signals. Work reported is based on sonar data collected by the Volume Search Sonar (VSS), as well as VSS synthetic data. The Volume Search Sonar is a beamformed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back to above horizontal). The processing of a data set of measurement in shallow water is performed using the Fractional Fourier Transform algorithm. The proposed technique will allow efficient determination of seafloor bottom characteristics and bottom type using the reverberation signal. A study is carried out to compare the performance of the presented method with conventional methods. Results are shown and future work and recommendations are presented.

TCM without constellation expansion penalty

We present a family of constant-amplitude constellations of even dimensions 8 and above. These constellations allow trellis coded modulation to be implemented without the usual penalty paid for constellation expansion. The new constellations are generated by concatenating either n QPSK points or n QPSK points rotated by 45 degrees, for any n > 4. Our constellations double the number of points available for transmission without decreasing the distance between points and without increasing the average or peak energies, introducing asymmetry, or increasing the modulation level. Effective gains of 2.65 dB with minimum complexity through 6.42 dB with moderate complexity are demonstrated using the 8D constellation.

Status of Deregulation and Locational Marginal Pricing in Power Markets

In this paper, we present the status of electricity deregulation in the United States. Furthermore, we describe the use and advantages and disadvantages of locational marginal pricing (LMP) in deregulated power markets. Finally, we present the use of LMP in analyzing electricity pricing in a deregulated electric utility environment. Using LMP, our proposed methodology for determining electricity prices in deregulated power markets is presented as an optimization problem that aims to minimize the total system production cost subject to physical and operational power system constraints. As building blocks in our modeling and analysis, we consider NERC guidelines for regional generation and transmission planning. We show an application of LMP in analyzing a six-bus test system. The details of the test system are included in this paper.

A Novel Expanded 16-Dimensional Constant Envelope Q 2 PSK Constellation

We introduce a 16-dimensional constant-amplitude constellation that is generated by concatenating either four constant envelope quadrature-quadrature phase shift keying (CEQ2PSK) symbols from Saha and Birdsall or four CEQ2PSK symbols recently discovered by Cartwright and also introduced here. Our new constellation doubles the number of points available for data transmission without decreasing the distance between points or increasing energy, and may therefore be used in a trellis coded modulation (TCM) system without constellation expansion penalty. Because the new constellation has constant envelope, the modulation scheme becomes very attractive for nonlinear channels such as the magnetic recording channel or the satellite channel with traveling wave tube amplifiers.

An optimum hardware detector for constant envelope quadrature-quadrature phase-shift keying (CEQ/sup 2/PSK)

A hardware detector for constant envelope quadrature-quadrature phase-shift keying (CEQ/sup 2/PSK) is proposed. It uses appropriate hard decisions; yet, it achieves optimum probability of bit error performance, unlike the suboptimum detector of Saha and Birdsall. This optimum performance is verified through Monte Carlo computer simulations. Additionally, a more correct expression is given for the probability of bit error performance for CEQ/sup 2/PSK, which gives the gain over nonconstant Q/sup 2/PSK as 1.44 dB, rather than the previously published value of 1.76 dB.

Acoustic Seabed Classification using Fractional Fourier Transform and Time-Frequency Transform Techniques

In this paper we present an approach for processing sonar signals with the ultimate goal of ocean bottom sediment classification. Work reported is based on sonar data collected by the Volume Search Sonar (VSS), one of the five sonar systems in the AN/AQS-20. Our technique is based on the Fractional Fourier Transform (FrFT), a time-frequency analysis tool which has become attractive in signal processing. Because FrFT uses linear chirps as basis functions, this approach is better suited for sonar applications. The magnitude of the bottom impulse response is given by the magnitude of the Fractional Fourier transform for optimal order applied to the bottom return signal. Joint time-frequency representations of the signal offer the possibility to determine the time-frequency configuration of the signal as its characteristic features for classification purposes. The classification is based on singular value decomposition of the Choi William distribution applied to the impulse response obtained using Fractional Fourier transform. The set of the singular values represents the desired feature vectors that describe the properties of the signal. The singular value spectrum has a high data reduction potential. It encodes the following signal features: time-bandwidth product, frequency versus time dependence, number of signal components and their spacing. The spectrum is invariant to shifts of the signal in time and frequency and is well suited for pattern recognition and classification tasks. The most relevant features (singular values) have been mapped in a reduced dimension space where an unsupervised classification has been employed for acoustic seabed sediment classification. The theoretical method is addressed and then tested on field sonar data. In our classification we used the central beams. Good agreement between the experimental results and the ground truth is shown. A performance comparison of our method to a k-means based technique is also given. Results and recommendations for future work are presented

Blind phase recovery in cross QAM communication systems with the reducedconstellation eighth-order estimator (RCEOE)

A new method for blind phase estimation that uses eight-order statistics is described. For cross QAM constellations, it provides about the same root mean square error (RMSE) as the fourth power method with about one-sixth to one-fourth the number of samples. Monte Carlo simulations are provided to demonstrate the usefulness of the method.The eighth-order (EOE) phase estimator (K.V. Cartwright, 1999) is modified to work for an eight-symbol symmetrical constellation, so that the large signal-to-noise (SNR) performance is not limited by self-noise. By using only the eight highest energy points of cross-QAM constellations, a reduced constellation eighth-order estimator (RCEOE) is proposed. Computer simulations for 128-QAM show that this new method performs substantially better than the recently introduced APP phase estimator of Wang et al. (2003). However, simulations with 32-QAM show little performance advantage of the RCEOE over the APP estimator, for SNR values normally of interest, whereas for low SNR, the improvement is significant. Application to any constellation which can be reduced to an 8-symbol quadrant symmetrical sub-constellation is straight-forward

A Trellis-Coded Modulation Scheme with a Novel Expanded 16-Dimensional Constant Envelope Q2PSK Constellation

This paper presents a TCM scheme that uses a new expanded 16-Dimensional Constant Envelope Q2PSK constellation along with a simple convolutional encoder of rate 2/3. An effective gain of 2.67 dB over uncoded CEQ2PSK is achievable with low complexity, and without suffering from constellation expansion penalty. Larger coding gains are easily achieved with encoders of higher rates. In addition, an optimal hardware implementation of the required decoders is described.

TCM decoding using neural networks

Abstract This paper presents a neural decoder for trellis coded modulation (TCM) schemes. Decoding is performed with Radial Basis Function Networks and Multi-Layer Perceptrons. The neural decoder effectively implements an adaptive Viterbi algorithm for TCM which learns communication channel imperfections. The implementation and performance of the neural decoder for trellis encoded 16-QAM with amplitude imbalance are analyzed.