LightSquared Chief Executive Officer Sanjiv Ahuja has resigned, the company announced Tuesday. The news comes two weeks after the Federal Communications Commission rejected plans by the wireless broadband firm to build a 4G network on spectrum adjacent to Global Positioning System signals. Tests by the National Telecommunications and Information Administration (NTIA) and others warned of the harm LightSquared’s proposed network would pose to GPS services critical for first responders, the airline industry and others. “During my tenure at LightSquared, we all worked tirelessly to create the nation’s first open wireless broadband network and provide consumers with a new wireless broadband…