  A rate splitting based scheme is proposed to operate a broadcast setting with
two antennas at the transmit side and two single-antenna receiving terminals.
The transmitter knows the magnitude of the channel coefficients, and it is
oblivious to the phase information. Each transmit antenna, with a power
constraint, sends a private message and a common message to be decoded by both
receivers. An achievable rate region is obtained, which enlarges the capacity
region of the vector broadcast channel with vector channel magnitude feedback
by means of superposition coding.
