Optimum Sequence Multisets for Symbol-Synchronous Code-Division Multiple-Access Channels

A discrete-time symbol-synchronous code-division multiple-access (S-CDMA) system is considered where K independent users spread their real-valued encoded symbols 1?k, k = 1, . . . , li, by individual real signature sequences L?,, of length L ‘chips’ and, then, transmit the L-dimensional symbols B k Z k over a Gaussian multiple-access (GMAC, [l]) channel with noise correlation matrix E[zdT] = o 2 I ~ (T denotes transposition and IL is the L x L identity matrix). Moreover, the same symbol-energy constraint is assumed for all users, i.e., E[Bi] 5 &c and s : & = L. For convenience, the L-dimensional observation vector at the output of the GMAC channel is written as