A derivative of MQTT is called MQTT-SN (sometimes called MQTT-S) for sensor networks. It keeps to the same philosophy of MQTT as a lightweight protocol for edge devices but is architected specifically for the nuances of a wireless personal area network typical in sensor environments. These traits include support for low-bandwidth links, link failure, short message length, and resource-constrained hardware. MQTT-SN is, in fact, so light that it can be run successfully over BLE and Zigbee.
MQTT-SN does not require a TCP/IP stack. It can be used over a serial link (preferred way), where a simple link protocol (to distinguish different devices on the line) overhead is really small. Alternatively, it can be used over UDP, which is less hungry than TCP.