Multi-antenna theorems

This is the wikia page for collecting theorems in the paper. Now, I'll order according to the extracted paper first. Later on, I'll revise the grouping rule based on the issues.

The abbreviations are listed as follows:

• Zero-forcing beamforming (ZFBF)
• Channel state information at the transmitter (CSIT)

MAT-J06NOV

• N. Jindal, MIMO Broadcast Channels with Finite Rate Feedback, IEEE Trans. Information Theory, Vol. 52, No. 11, pp. 5045-5059, Nov. 2006.

MAT-J06NOVT1

We denote the signal-to-noise ratio (SNR) as $P$, the sum-rate of the perfect CSIT zeroforcing beamformin as $R(P)$ and the sum-rate of imperfect CSIT zeroforcing beamforming with limited feedback digital signaling as $R_\mathrm{LF}$. The number of transmit antennas are assumed to be $M$.

The sum-rate loss of the limited feedback zero-forcing beamforming (ZFBF) with $B$ bit feedback relative to the perfect channel state information at the transmitter (CSIT) system with the constant performance gap of $\log b$ is given by

$\Delta R(P) < \log_2 \left( 1 + P 2^{-\frac{B}{M-1}} \right)$

where $\Delta R(P) = R(P) - R_\mathrm{LF}(P)$.