Two-dimensionally spread multicarrier CDMA ranging signals with PAPR lower than 3dB

In this work we propose a methodology to design two-dimensional spreading codes for a multicarrier CDMA (code division multiple access) system with minimal multiple access interference (MAI) and minimal peak-to-average-power-ratio (PAPR). In particular, we minimise the cross-correlation peak between two two-dimensionally spread CDMA signals, with the side-constraints that both multicarrier signals must have a PAPR lower than 3 dB, and autocorrelation side-peaks lower than a certain value. The underlying principle of this work is that the users of a CDMA system need not be allocated exactly the same pulse shape, and that by assigning different pulse shapes, it is possible to increase the decorrelation among interfering signals. The resulting multi-dimensional non-linear optimization problem is solved by inspection of all possible solutions, as we show that the feasible region is a discrete countable set, whose size is reasonably small. The mathematical tool used in the solution of this paper consists of some radar pulse compression codes called Huffman codes.