# Finite-Step Algorithms for Constructing
Optimal CDMA Signature Sequences

### Authors:

J. A. Tropp,
I. Dhillon,
and R. W. Heath,
Jr.,

### Reference:

Wireless Networking and Communications Group Technical Report
WNCG-TR-2003-05-08. Submitted to the *IEEE Trans. on Info. Theory*, May
2003.

### Abstract:

A description of optimal sequences for direct-spread code division multiple
access is a byproduct of recent characterizations of the sum capacity. This
correspondence restates the sequence design problem as an inverse singular value
problem that can be solved with finite-step algorithms from matrix theory. A new
one-sided construction is proposed that obtains the sequences directly instead
of computing the Gram matrix of the optimal signatures.

### Keywords:

Sequence design, code division multiple access, sum capacity, tight frames,
finite algorithms, majorization, Schur- Horn theorem

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