Correlation Properties Of Spreading Codes Research Articles

Spreading code optimization for low-earth orbit satellites via mixed-integer convex programming

Optimizing the correlation properties of spreading codes is critical for minimizing inter-channel interference in satellite navigation systems. By improving the codes’ correlation sidelobes, we can enhance navigation performance while minimizing the required spreading code lengths. In the case of low-earth orbit (LEO) satellite navigation, shorter code lengths (on the order of a hundred) are preferred due to their ability to achieve fast signal acquisition. Additionally, the relatively high signal-to-noise ratio in LEO systems reduces the need for longer spreading codes to mitigate inter-channel interference. In this work, we propose a two-stage block coordinate descent (BCD) method which optimizes the codes’ correlation properties while enforcing the autocorrelation sidelobe zero property. In each iteration of the BCD method, we solve a mixed-integer convex program over a block of 25 binary variables. Our method is applicable to spreading code families of arbitrary sizes and lengths, and we demonstrate its effectiveness for a problem with 66 length-127 codes and a problem with 130 length-257 codes.

Performance evaluation of DS-CDMA systems on multipath propagation channels with multilevel spreading sequences and RAKE receivers

Performance of small-cell wireless direct sequence code-division multiple access (DS-CDMA) systems with multilevel spreading sequences is investigated. An analytical methodology to evaluate both outage probability and mean bit error probability is presented; and its results are compared to those obtained with a semianalytical Monte Carlo based approach. Multipath propagation, the exact correlation properties of spreading codes, and both the simple correlator and RAKE receivers are taken into account in the analysis, which is oriented to asynchronous and synchronous environments. The spreading sequences investigated include multilevel sequences with complex isomorphic mapping, as well as some well-known two-level sequences. The numerical results show the impact of multilevel sequences on system performance, the improvements found in the absence of multiple access interference by using them rather than binary sequences, and the agreement between analytical and semianalytical evaluation.