Interleaving training and limited feedback for point-to-point massive multiple-antenna systems

We introduce and investigate the opportunities of multi-antenna communication schemes whose training and feedback stages are interleaved and mutually interacting. Specifically, unlike the traditional schemes where the transmitter first trains all of its antennas at once and then receives a single feedback message, we consider a scenario where the transmitter instead trains its antennas one by one and receives feedback information immediately after training each one of its antennas. The feedback message may ask the transmitter to train another antenna; or, it may terminate the feedback/training phase and provide the quantized codeword (e.g., a beamforming vector) to be utilized for data transmission. As a specific application, we consider a multiple-input single-output system with t transmitter antennas, a short-term power constraint P, and target data rate ρ. We show that for any t, the same outage probability as a system with perfect transmitter and receiver channel state information can be achieved with a feedback rate of R1 bits per channel state and via training R2 transmitter antennas on average, where R1 and R2 are independent of t, and depend only on ρ and P.