S.V. Maric

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. >

A new family of frequency-hop codes

We give an algebraic construction for a new family of frequency-hop codes. The construction is based on properties of finite fields: it is shown that for each field GF(p/sup m/), there exists a large number of codes of length p/sup m/. The codes are also shown to possess the best possible simultaneous two-dimensional autocorrelation and cross-correlation properties. Moreover, they include a family of codes: with a code length of a power of 2, which are ideally suitable for applications in digital communication systems.

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. >

Ambiguity properties of quadratic congruential coding

The ambiguity characteristics of multiple access frequency hop codes based on standard quadratic congruences are investigated in the light of results obtained for codes based on Costas arrays and extended quadratic congruences. While the autoambiguity properties are found to be very similar to those of Costa codes, i.e. nearly ideal, the cross-ambiguity properties of quadratic congruential codes are much better. These results are valid across the whole class of code sets considered, but they are obtained at some expense in the pulse compression characteristics of the codes. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time-bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of quadratic congruential coding with respect to Costas coding. >

On cross-ambiguity properties of Welch-Costas arrays

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar system, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers. >

Multiuser sonar properties for Costas array frequency hop coded signals

The cross-ambiguity properties of Costas-array frequency-hop coded signals for use in wideband multiuser sonar systems are established. In order to prevent system crosstalk, cross-ambiguity function for the signals should be minimized. The conditions under which Costas arrays achieve the minimum value of their cross-ambiguity functions are provided. The upper bound on the maximum number of hits in the cross-ambiguity function for Welch-Costas arrays is given, and it is shown that the maximum number of hits depends on the form of the prime over which the arrays are constructed.<<ETX>>

Microcell planning and channel allocation for Manhattan street environments

The demand for cellular service will increase dramatically in the near future. One way of increasing the cellular system capacity is by reducing the cell size. The authors discuss the problems associated with the new microcell environment. The propagation characteristics of the system are discussed and various types of microcell coverages introduced. In order to solve the cell planning problem, the authors introduce a new type of 1-0 array and show how they are used in maximizing the line-of-sight and nonline-of-sight distance between co-channel cells. The properties of the 1-0 array are established and examples of cell planing for various reuse distances are given.<<ETX>>

On cross-ambiguity properties of Welch-Costas arrays when applied in SS/FH multiuser radar and sonar systems

We discuss cross-ambiguity properties of a specific family of Costas (1984) arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar systems. Especially since Costas arrays are known to posses ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross-ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers.<<ETX>>

Address assignment for multiple-access systems based upon the theory of congruence equations

The authors discuss the address assignment via frequency hop patterns for a multiple-access spread-spectrum communication system. In such a system the receiver simultaneously communicates with a large number of transmitters (users), distinguished by their assigned addresses. In order to insure that the receiver correctly recognizes which users are active at the moment, it is necessary for the assigned addresses to possess minimum mutual interference. The authors define an algebraic construction for frequency hop patterns based upon the theory of congruence equations. The frequency hop patterns are constructed in such a way that they carry the address assignment and the message at the same time. The decoding scheme for the system is presented, and it is demonstrated that in both synchronous and nonsynchronous cases the mutual interference between the transmitted frequency hop patterns is minimal.<<ETX>>