Non-orthogonal Signals Research Articles

A New Method for Nonorthogonal Signal Decomposition

A new algorithm for nonorthogonal decomposition is proposed and applied to Gabor decomposition of images. The algorithm is iterative and its advantages are discussed. Proof of the convergence of the algorithm is given. Also, a modified version of the algorithm is considered which increases the rate of convergence. Image simulations show that this method gives much lower reconstruction error than the method using biorthogonal functions, at the cost of a greater amount of computer time.

Lattice architectures for multiple-scale gaussian convolution, image processing, sinusoid-based transforms and gabor filtering

This article describes a novel lattice architecture which performs multiple-scale Gaussian convolution of signals of any desired dimension. The principle of operation is based on the central limit theorem and involves repetitive convolution with small kernels to generate Gaussian smoothing. A pyramidal implementation of this architecture is also discussed which retains the fine scale (standard deviation) resolution, while reducing the complexity of the architecture. The lattice generates the scale-space description of the input signal which is very useful in image processing and vision applications. Applications of the lattice for Canny's and Laplacian of Gaussian edge detection are outlined. Using a novel Gaussian approximation to sinusoid kernels, the lattice is also capable of generating discrete Fourier, cosine, and sine transforms. Since the lattice can perform Gaussian smoothing and generate sinusoid kernels, it easily performs Gabor filtering and also reconstructs signals from their Gabor (or Gaussian) representations. An adaptive configuration of the lattice has been used for a hardware real-time implementation for our recently developed generalized nonorthogonal signal representations by Gaussians and Gaussian set wavelets.

Threshold detection of nonorthogonal signaling in turbulent optical channels

AbstractThe ever‐increasing demand for satellite links is motivating the search for techniques to enhance the utilization efficiency of optical communication systems. However, the performance of such a channel, in addition to background radiation and photodetector random gain, is highly affected by atmospheric turbulence along its propagation path. Multipulse nonorthogonal signaling has been recently introduced as a bandwidth‐efficient format for this channel [1]. In this article, threshold detection for this multipulse format is studied under different turbulence levels, concluding the optimum threshold setting for typical alphabet sizes. © 1993 John Wiley & sons, Inc.

Heterodyne and optically implemented dual-filter FSK systems: comparison based on a rigorous theory

The performance of heterodyne and optically implemented dual-filter FSK systems are compared based on a new rigorous theory that accounts for noise correlation (due to nonorthogonal signaling), laser phase noise, receiver noise, and amplifier spontaneous emission noise. Ideally, the two implementations have the same sensitivity with and without polarization control. The results emphasize the practical tradeoff between the heterodyne implementation (where receiver noise means that a low modulation index gives the best sensitivity) and the optical one (where the difficulty in making high-quality narrowband optical filters means that a larger modulation index gives the best sensitivity).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonorthogonal signal decomposition.

To gain physical interpretations and insights from observed phenomena, it is often desirable to decompose a given function, i.e., the observed signal, into a set of nonorthogonal functions. This paper describes a signal processing algorithm based on the minimization of the mean-square error formulation of the decomposition analysis. The computation scheme is derived from a recursive gradient descent method to approach the correct answer for a set of over-determined simultaneous equations. The traditional matrix inversion technique is usually not workable for numerical operation because the matrices are often ill-conditioned. This suggested approach not only alleviates the computation problem, but also can more easily be implemented in a parallel architecture computer or a neural-like network. The signal received from a synthetic circular array [N. Yen, IEEE/JOE, Jan. 1992, pp. 40–47] is used, as a practical example, to illustrate that a composite signal can be reduced to a combination of the corresponding signals from various directions. Comparison of the results obtained by this algorithm with the traditional beamforming method supports the use of this new signal processing technique.

A Terrestrial Rain Depolarization Compensation Experiment at 11.7 GHz

Depolarization caused by rain at 11.7 GHz is due to both differential phase shift and attenuation. In dual polarized communications systems it gives rise to interference which may be severe enough to cause an outage even though the allotted fade margin has not been exceeded. Described is a depolarization compensation experiment over a 10 km path with near circular polarization at 11.7 GHz. It made use of a turnstile junction feed system under computer control. Data presented demonstrate the stable performance of the method used during several rain events. At fades below about 15 dB significant isolation improvements were achieved, compared to a fixed cross-polarization channel. Finally, a method using the turnstile is suggested to receive two nonorthogonal signals without interference.

Performance of Nonorthogonal Signaling on an Asynchronous Multiple Access On-Off Channel

The results obtained by Cohen, Heller, and Viterbi [1] for an orthogonal coding technique for a particular asynchronous multiple access channel are generalized to nonorthogonal coding to investigate the gains that may be realized. It is shown that in the range of bit error probabilities of interest, for a given channel bandwidth, modest gains can be realized using nonorthogonai signaling.

Crosstalk Resistant Receiver for M-ary Multiplexed Communications

Attention is directed to the problem of M-ary signal transmission from a multiplicity of synchronized information sources. A receiver processor is derived which suppresses the effect of crosstalk between nonorthogonal signals. The processor is valid for a general zero mean, noise environment. A probability of error bound is derived for the processor. Several examples illustrate the processor.

Three-Frequency Nonlinear Heterodyne Detection 2: Digital Communications and Pulsed Radar

Part 1 of this paper [Appl. Opt. 14, 666 (1975)] dealt with the cw radar and analog communications uses of three-frequency nonlinear heterodyne detection. In this paper, we evaluate the technique for a number of specific pulsed radar and digital communications applications. Both the vacuum channel and the lognormal turbulent atmospheric channel are considered. It is found that the advantages of the technique in the pulsed/digital system are similar to those obtained in the cw/analog system. Computer generated error probability curves as a function of the input signal-to-noise ratio are presented for a variety of binary receiver parameters and configurations and for various levels of atmospheric turbulence. Orthogonal and nonorthogonal signaling schemes, as well as dependent and independent fading, are considered. When Doppler information is poor, performance is generally superior to that of the conventional heterodyne system.

Optimal multiple quantum statistical hypothesis testing

This paper is concerned with the problem of optimal M-alternative determination of quantum statistical states. A review of newest achievement of solving this problem is given. A notion of an effective decision Hilbert space is introduced and necessary and sufficient condkions for optimality of multiple quantum hypothesis testing in this space are formulated. The general solution is found for the case of a two-dimensional decision space. Another problem solved is that of discrimination of quantum pure non-orthogonal states. The result is represented in explicit analytical form for an equidiagonal case, which is quite general. In particular, we find explicit solutions of optimal discrimination problem of homogeneous and equiangle sets of pure states. These results are used for the M-ary detection problem in solving for the quantum coherent non-orthogonal signals. It is proved that the simplex signals are optimal elso in quantum case. The optimal estimatesof phaseandamplitude of quantum coherent signals ar...

Signal design for fast-fading Gaussian channels

The design of signals for digital communication over fast-fading Gaussian channels is considered; the emphasis is on nonorthogonal signaling schemes. A discrete channel model is used. Necessary and sufficient conditions on the transmitted signals are found that make the Bayes receiver independent of the channel parameters. By using a geometric interpretation of the resultant receiver a heuristic design criterion is developed. Then union bounds for particular nonorthogonal signaling schemes are evaluated. Nonorthogonal schemes based on modulation similar to differential-phase-shift-keyed (DPSK) modulation are found to use substantially less bandwidth than equivalent schemes based on generalized frequency-shift-keyed modulation.

Error probability for incoherent diversity reception

The problem of computing error probabilities for multi-channel communications using an incoherently terminated receiver is analyzed. The signaling alphabet is composed of two equal-energy, equiprobable, correlated waveforms and the multichannel model is presumed to be of the slowly fading "Rician" type, i.e., each subchannel is presumed to be composed of a fixed or specular component and a scatter-like or Rayleigh fading component. The main result of this paper is a generalization (21) of an earlier result derived by Helstrom. Novel by-products of this generalization include, as special cases, results derived by Turin, Pierce, Price, and Lindsey. Also closed-form solutions to very general integrals (22) (heretofore seemingly unknown) involving Bessel function products are presented as part of the main result. These integrals are known to arise in the analysis of multichannel adaptive communication systems. Numerical computations for the error probabilities are given for special values of the signal cross-correlation coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> and multi-channel order. These results graphically illustrate that the optimum set of equal-energy binary signals which minimize the error rate for the Rayleigh fading multichannel are orthogonal. Specifically, to maintain the same error probability in two systems, one employing nonorthogonal signals having correlation coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> , the other employing orthogonal signals, the transmitter power must be increased in the former. In fact, for large SNR's, the graphical data indicate that the required increase in transmitter power is approximately <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10 \log_{10}(1 - \lambda^{2})^{-1}</tex> dB.