We design a custom spectrum sensing network, called RadioHound, capable of tuning from 25 MHz to 6 GHz, which covers nearly all widely-deployed wireless activity. We describe the system hardware and network infrastructure in detail with a view towards driving the cost, size, and power usage of the sensors as low as possible. The system estimates the spatial variation of radio-frequency power from an unknown random number of sources. System performance is measured by computing the mean square error against a simulated radio-frequency environment. We find that the system performance depends heavily on the deployment density of the sensors. Consequently, we derive an expression for the sensor density as a function of environmental characteristics and confidence in measurement quality.