Spreading Code Sequence Design via Mixed-Integer Convex Optimization

Binary spreading codes with good auto- and cross-correlation properties are critical for satellite navigation to ensuring precise synchronization and tracking with minimal inter-system interference. In this paper, we demonstrate that multiple instances of the spreading code design problem found in the literature may be cast as binary-constrained convex optimization problems. This approach enables new optimization methods that can exploit the convex structure of the problem. We demonstrate the approach using a block coordinate descent (BCD) method, which uses a convexity-exploiting branch-and-bound method to perform the block updates. With minimal tuning, the BCD method was able to identify GPS codes with better performance compared to the Gold codes and codes derived from a recently introduced natural evolution strategy.