Edward L. Titlebaum

Time-Frequency HOP Signals Part I: Coding Based upon the Theory of Linear Congruences

Time-frequency hop codes are developed based upon the theory of linear congruences. These codes can be used for multiuser radar and asynchronous spread spectrum communications systems. A uniform upper bound is placed on the cross-correlation function between any two elements of the code set. The upper bound is minimized by choice of time-bandwidth product and is shown to diminish as 2/N, where N is the number of elements in the code set. The size and position of spurious peaks in the autocorrelation functions are discussed. The results are extended to narrowband ambiguity functions.

A class of frequency hop codes with nearly ideal characteristics for use in multiple-access spread-spectrum communications and radar and sonar systems

The problem of constructing frequency hop codes for use in multiuser communication systems such as multiple-access spread-spectrum communications and multiuser radar and sonar systems is addressed. Previous frequency hopping techniques are reviewed. The construction of a new family of frequency hopping codes called hyperbolic frequency hop codes is given. The concepts of multiple-access spread-spectrum communication systems and multiuser radar and sonar systems are reviewed, and it is shown that the hyperbolic frequency hop codes possess nearly ideal characteristics for use in both types of system. Specifically, in multiple-access communications the codes achieve minimum error probability, while in radar and sonar systems the codes have at most two hits in their auto- and cross-ambiguity function. Examples of address assignment for multiple-access communications systems and radar and sonar auto- and cross-ambiguity functions are also given. >

A new family of optical code sequences for use in spread-spectrum fiber-optic local area networks

The problem of the algebraic construction of a particular family of optical codes for use in code-division multiple-access (CDMA) fiber-optic local area networks (LANs) is treated. The conditions that the code families have to satisfy when used in such systems are reviewed. The new codes are called quadratic congruence codes, and the construction of the corresponding sequences is based on the number-theoretic concept of quadratic congruences. It is shown that p-1 codes exist for every odd prime p and can serve as many as p-1 different users in the CDMA fiber-optic system. The codes belong to the family of optical orthogonal codes, their auto- and cross-correlation properties are established, and their performance is compared to that of the previous optical codes. Examples of the codes and examples of their auto- and cross-correlation functions are given. >

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.

Construction and performance analysis of a new family of optical orthogonal codes for CDMA fiber-optic networks

A construction of a new family of optical orthogonal codes (OOCs) for use in code division multiple access (CDMA) fiber-optic networks is given. Previous families of OOCs are reviewed and basic requirements for successful implementation of the fiber-optic CDMA system given. The new code construction is based on Costas (1970) arrays and the codes are proved to be (/spl omega/(2p-3), /spl omega/, 1, 1), p a prime and /spl omega/*Q/spl les/p-1, where Q is the maximum number of users, OOCs. The probability of error (using the Gaussian approximation) in the multiuser system as a performance measure is calculated and compared with that of existing OOCs. The size of the code family is compared against the Johnson bound. >

Frequency hop multiple access codes based upon the theory of cubic congruences

The need for families of frequency-hop codes which have mutually small auto-ambiguity and cross-ambiguity functions is discussed. Current coding methods are reviewed. A new family of frequency-hop codes based upon the number-theoretic concept of cubic congruences is introduced. It is shown that for about 50% of the prime numbers, families of full codes exist which have at most two coincidences for any time-frequency shift in their auto-ambiguity functions and at most three coincidences in the set of mutual cross-ambiguity functions. >

The design and performance analysis for several new classes of codes for optical synchronous CDMA and for arbitrary-medium time-hopping synchronous CDMA communication systems

New families of spread-spectrum codes are constructed, that are applicable to optical synchronous code-division multiple-access (CDMA) communications as well as to arbitrary-medium time-hopping synchronous CDMA communications. Proposed constructions are based on the mappings from integer sequences into binary sequences. The authors use the concept of number theoretic quadratic congruences and a subset of Reed-Solomon codes similar to the one utilized in the Welch-Costas frequency-hop (FH) patterns. The properties of the codes are as good as or better than the properties of existing codes for synchronous CDMA communications: both the number of code-sequences within a single code family and the number of code families with good properties are significantly increased when compared to the known code designs. Possible applications are presented. To evaluate the performance of the proposed codes, a new class of hit arrays called cyclical hit arrays is recalled, which give insight into the previously unknown properties of the few classes of number theoretic FH patterns. Cyclical hit arrays and the proposed mappings are used to determine the exact probability distribution functions of random variables that represent interference between users of a time-hopping or optical CDMA system. Expressions for the bit error probability in multi-user CDMA systems are derived as a function of the number of simultaneous CDMA system users, the length of signature sequences and the threshold of a matched filter detector. The performance results are compared with the results for some previously known codes. >

Deconvolution in the presence of Doppler with application to specular multipath parameter estimation

High-resolution multipath parameter estimates can be obtained through various deconvolution procedures, all of which-in the limit-rely on some form of inverse filtering. Although deconvolution in a multipath environment free from Doppler is well understood and well documented, this is not true for the case when motion of the multipath components relative to the receiver imposes a Doppler shift on the transmitted probing signal. This paper describes the effect of Doppler on a broad class of deconvolution methods by studying the effect of Doppler on the output of an inverse filter. It is shown that in the presence of Doppler, the deconvolution outputs are comprised chiefly of two signal-related functions, one of which may be designed in such a way as to be free from the range-Doppler coupling effects inherent in correlation processing. Knowledge of these two functions provides insight into the signal design issues relevant to deconvolution-based multipath parameter estimation systems and is useful in designing appropriate constraints and post-processing algorithms that may lead to an accurate extraction of the Doppler and delay parameters of the multipath channel. These results are applied to two known deconvolution methods: the method of projection onto convex sets (POCS) and the method of least squares (LS).

Cubic Spline Baseline Estimation In Ambulatory ECg Recordings For The Measurement Of ST Segment Displacements

Correction of baseline wander is one of the major problems in ambulatory ECG analysis. In this work, the isoelectric line of the ECG signal is estimated by interpolating consecutive isoelectric points with third order lines. A fiducial point is found with minimization techniques in a 100 msec window before the peak of the R wave. The definition of a continuous line permits synchronous measurements at any point of the ST segment. The technique (called cubic spline interpolation) allows the development of a reliable beat-by-beat ST segment displacement signal.

Cross-correlation properties of algebraically constructed Costas arrays

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically constructed Costas arrays for a given construction and dimension. Finding two arrays that minimally correlate implies that the signals based on these arrays also minimally correlate. The properties of finite fields are reviewed, and the major algebraic constructions for Costas arrays are presented, i.e. the Welch construction and the Golomb construction. The discrete cross-correlation properties of the Costas arrays are derived for arrays of the same dimension derived from the same construction. The use of Costas arrays in the signal design problem is discussed, and examples are given to show the cross-correlation of the signals based on the algebraically constructed arrays. >