Polynomial complexity optimal multiuser detection for a wider class of problems

It is well known that jointly optimal multiuser detection for code division multiplex access (CDMA) systems has complexity which grows exponentially with the number of users. Recently, several authors [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] have reported that, for certain special sets of spreading sequences, optimal multiuser detection in synchronous CDMA systems can be performed with computational complexity which is polynomial in the number of users. In this paper, we show that the existing polynomial complexity (PC) algorithms of [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] lead to efficient algorithms for a wider class of spreading sequences than initially proposed. We identify these sequences and prove the existence of optimal polynomial-complexity algorithms for detecting synchronous CDMA signals using these sequences. We also give constructions of sets of binary antipodal spreading sequences for which optimal polynomial-complexity algorithms exist and show that for any sequence length N, we can construct at least N such sequences.