Spreading Code Sequence Design via Mixed-Integer Convex Optimization

<title>Abstract</title> For a satellite navigation system, binary spreading codes with good autocor-relation and cross-correlation properties are critical for ensuring precise synchronization and tracking with minimal intrasystem 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 this approach using a block coordinate descent (BCD) method, which applies a convexity-exploiting branch-and-bound method to perform the block updates. With minimal tuning, the BCD method was able to identify Global Positioning System codes with better mean-squared correlation performance compared with the Gold codes and codes derived from a recently introduced natural evolution strategy.