This invention relates to communications systems and, more particularly, to wireless and other communications systems employing Orthogonal Frequency Division Multiplexing based Spread Spectrum Multiple Access. 
It is important that wireless communications systems be as efficient as possible in order to maximize the number of users that can be adequately served and to maximize data transmission rates, if data services are provided.  Wireless communications systems are typically shared media systems, i.e., there is a fixed available bandwidth that is shared by all users of the wireless system.  Such wireless communications systems are often implemented as so-called xe2x80x9ccellularxe2x80x9d communications systems, in which the territory being covered is divided into separate cells, and each cell is served by a base station. 
It is well known in the art that desirable features of cellular wireless communications systems are that intracell interference be as small as possible and that intercell interference be averaged across all users in adjacent cells. 
One prior known system of interest is disclosed in U.S. Pat.  No.  5,548,582 issued on Aug. 20, 1996 to Brajal et al.  The Brajal et al.  arrangement is a general wide-band orthogonal frequency division multiplexing (OFDM) based spread spectrum multiple access employed in a wireless communications systems.  However, the Brajal et al.  arrangement is not optimized for use in a cellular communications system, and fails to show, teach or suggest how to optimize frequency hopping patterns, tone assignment or bandwidth reuse. 
More recently, attempts have been made at overcoming the problems and limitations of arrangements like the one disclosed in Brajal et al.  One such attempt is disclosed in U.S. patent application of Laroia et al.  Ser.  No.  09/267,471, filed on Mar. 11, 1999, and assigned to the assignee of the instant United States Patent Application.  Although the wireless cellular communications system disclosed in the Laroia et al.  application operates satisfactorily in many applications, it is limited in that it is directed toward using a specific frequency hopping sequence.  Consequently, interference may not be minimized, and in data communications applications quality of service is not optimized. 
Problems and limitations of prior known frequency hopping arrangements are overcome by advantageously employing a unique combination of a sequence generator and a sequence assignor to generate sequences and assign them on a time slot by time slot basis.  In a transmitter, the sequence generator and sequence assignor, in combination with a user tone assignor are employed to generate and assign tone sequences to a user on a time slot by time slot basis.  In a receiver, the sequence generator and sequence assignor, in combination with a user tone identifier are employed to generate sequences and to identify incoming tone sequences to a user on a time slot by time slot basis in accordance with sequences assigned by the sequence assignor. 
Specifically, the sequence assignment in a time slot is such that a prescribed plurality of sequences is assigned to a particular user.  This partitioning of the tasks facilitates the use of a sequence generator that generates sequences with the desirable properties of interference and frequency diversity and, which, leaves the task of properly assigning these sequences among one or more users to the sequence assignor.  The sequence assignor functions in such a manner that the interference and frequency diversity properties for the one or more users are preserved, and this is further facilitated by assigning sequences in such a manner that they maximally overlap prior assigned sequences. 
In one embodiment of the invention, a Latin square based sequence is generated in accordance with a first prescribed process. 
In a second embodiment of the invention, a Latin cube based sequence is generated in accordance with a second prescribed process. 
In a third embodiment of the invention, a Latin hypercube of prescribed dimension based sequence is generated in accordance with a third prescribed process. 
In still another embodiment of the invention, the principles of the invention are employed to realize frequency band hopping.