Interleaving Channel Estimation and Limited Feedback for Point-to-Point Systems With a Large Number of Transmit Antennas

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 <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> transmit antennas, a short-term power constraint <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>, and target data rate <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula>. We show that for any <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>, the same outage probability as a system with perfect transmitter and receiver channel state information can be achieved with a feedback rate of <inline-formula> <tex-math notation="LaTeX">$R_{1}$ </tex-math></inline-formula> bits per channel state and via training <inline-formula> <tex-math notation="LaTeX">$R_{2}$ </tex-math></inline-formula> transmit antennas on average, where <inline-formula> <tex-math notation="LaTeX">$R_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$R_{2}$ </tex-math></inline-formula> <italic>are independent of t</italic>, and depend only on <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>. In addition, we design variable-rate quantizers for channel coefficients to further minimize the feedback rate of our scheme.