Abstract

ABSTRACT are user signatures. The column vectors sk of S span This paper addresses the problem of signature set de- the space IRN. The noise, n, is a Gaussian vector of sign for uncoded multiple access (MA) communication mean zero and identity covariance, and a is the noise in which user signature waveforms are linearly depen- standard deviation. dent. In general, the linearly dependent or "over- Verdu has shown in [3] that for the general MA joint saturated " scenario requires an exponentially complex detection problem stated as above, i.e. for an arbitrary detector. signature matrix, S, the solution is N-P hard. In other The recent introduction of an optimal tree-structured words, the maximum likelihood estimate of b cannot be joint detector of extremely low complexity ([1, 2]) has found by an algorithm having polynomial complexity sparked our interest in signature set choice for over- in the number of users, K. saturated MA communications. The tree detector re- For the case in which the number of signal dimen-quires the set of linearly dependent user signatures sions is equal to the number of users, K = N,the MA to have tree-structured cross-correlations. This design optimal joint detection problem can be reduced from guideline is a natural by-product of redundant wavelet the N-P hard problem to K single-user problems by im-packet signals. In this paper we explore, via simula- posing users to be orthogonal. Restricting the users in a tions, the performance of wavelet packet signature sets MA communication system to be orthogonal results in and find them to do very well in general and to offer suboptimal total information transmission rates ([4]). promising behavior with the introduction of arbitrary Linearly dependent user waveform sets (K> N users carrier phase. in N dimensions) offer increased throughput relative to traditional orthogonal MA systems. A tree-structured