On Achievable Multiplexing Gain of BD in MIMO Broadcast Channels with Limited Feedback

To maintain a specific degree of multiplexing gain with limited feedback in multiple-input/multiple-output broadcast channels, the number of feedback bits has been increased linearly with the signal-to-noise ratio (SNR) measured in decibel, and conditions for the slope of this increase have been derived in previous studies. However, previous studies mostly focused on the chordal distance (ChD) for channel quantization, although it is not an optimally designed distance measure. Thus, the possibility exists that the same degree of multiplexing gain can be obtained by using fewer feedback bits than the existing method requires. In this paper, we propose an optimal distance measure that can maximize the multiplexing gain achieved by limited-feedback-based block diagonalization over broadcast channels. Then, we provide a sufficient condition for the number of feedback bits to achieve a specific degree of multiplexing gain with the proposed method. The sufficient number of feedback bits is given by a linear function of the SNR (decibel) as in previous studies, but the slope of the linear increase can be much less than that obtained in previous studies. As a consequence, the proposed method achieves higher multiplexing gain and corresponding throughput than the existing methods with the same number of feedback bits.