Above is a picture of a primary / secondary surveillance radar combo (top is secondary, bottom is primary).
What does the ASDE-X radar unit look like in real life?
This page claims to show the Raetheon ASDE antenna at Boston Logan. However, Saab Sensis appears to be the prime contractor for the ASDE-X system. Boston does have an ASDE-X system, according to the FAA.
According to the above link, Saab provides the "Multi-Sensor Data Processor" that "fuses the surface movement radar, multilateration, ADS-B and terminal radar data into a single track that is correlated with flight plan information." So my guess is that Raetheon provides the radar antenna and Saab does the software integration, alerting, fusing, etc. Since the contract is in the US there may have been a requirement to use a US radar supplier.