In this two-part paper, an integrated maritime surveillance (IMS) system, based on high-frequency surface-wave radars (HFSWR), is described. IMS provides low-cost, 24-hour, real-time, over-the-horizon surveillance of large ocean areas, out to the 200 nautical mile Exclusive Economic Zone (EEZ). The system can be used to coordinate search and rescue operations, and to combat smuggling, drug trafficking, illegal dumping of pollutants, and other undesirable activities. The major challenges in using HFSWR are (i) operating within the crowded HF spectrum; and (ii) maintaining effective operation in high environmental noise, ocean clutter, ionospheric clutter and other undesirable sources of interferences. In Part 1, the system is outlined and these problems are addressed. Numerical simulation, as well as stochastic modeling, are presented to demonstrate the physics behind the system.