Performance analysis of 2-D O-CDMA codes without the chip-synchronous assumption

In this paper, the performance of two-dimensional optical codes with cross-correlation functions of at most one, such as the carrier-hopping prime code (CHPC), is analyzed without the traditional chip-synchronous assumption. In addition to the Gaussian approximation method, we apply a combinatorial technique for a more accurate analysis, especially when there exists only a small number of simultaneous users. It is known that an optical hard-limiter can be placed at the front end of a receiver to reduce the effect of multiple-access interference. We also derive the hard-limiting error probability under the chip-asynchronous assumption. Finally, the performance improvement of the CHPC with the hard-limiting and chip-asynchronous assumptions is studied.