Bipolar sequences correlator and squarer for multiple-access systems

Novel architectures for squares, and sums of squares, of cross-correlations of bipolar sequences with applications to CDMA

“…Under favorable conditions and/or with good interference cancellation, the number of users supported K may be close to the spreading factor N . For such a case, and considering the last column, the direct methods have an advantage over the earlier methods in [7] by eliminating the expensive squaring operations.…”

“…The last column is the SSXC computation for all users, which is typically needed at the base station receiver. Note that the methods in [7] do not enjoy savings due to symmetry and hence the number of computations is in terms of N and not N r . The SSXC based on 6 carry out the inner summations first, then sum over all users.…”

“…Clearly, each of the OPM elements may be obtained using the XNOR gate in bipolar form, as in [7]. We note that the matrix Q is symmetric, and its diagonal elements are all equal to one.…”

“…Finally, we add all the elements of the matrix that results from the element-wise XNOR of the two matrices Q k and Q j . Since these elements take values of ±1, this last summation is implemented using the reduced complexity architecture introduced in [7], where we simply count the number of ones. Assuming the number of ones is x,…”

“…Efficient architectures for a cross-correlation and squaring unit were described in [7] by utilizing the special nature of bipolar code sequences. In the present paper, we propose novel architectures for directly computing the squares of crosscorrelations (SXC) and sums of squares of cross-correlations (SSXC).…”