A millimeter-wave wireless multiple antenna system (80) and method (100) are provided in which a UE (120) uses a multi-antenna subsystem (81) to identify a plurality of m strongest transmit beams (122) from the base station (110) based on power measurements of a plurality of synchronization signal blocks (SSBs) transmitted on a corresponding plurality of transmit beams by the base station (110), and to generate a composite uplink random access channel (RACH) preamble (123) that is sent (124) to the base station (110) to identify the plurality of m strongest transmit beams and relative weights for each of the plurality of m strongest transmit beams which are used by the base station (112) to generate an optimal downlink transmit beam for use in sending a RACH response to the UE (120).