Zero-forcing precoding: Difference between revisions

Revision as of 06:02, 30 September 2014

Revision as of 04:44, 7 June 2015

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where <math>b = \Omega_{FB} T_{FB}</math> is the feedback resource consisted by multiplying the feedback frequency resource and the frequency temporal resource subsequently and <math>\rho_{FB}</math> is SNR of the feedback channel. Then, the required feedback resource to satisfy <math>\Delta R \leq \log_2 g</math> is

:<math> b_{FB} \geq \frac{B}{\log_2(1+\rho_{FB})} = \frac{(M-1) \log_2 \rho_{b,m} - (M-1) \log_2 (g-1)}{\log_2(1+\rho_{FB})} </math>.

Note that differently from the feedback bits case, the required feedback resource is a function of both downlink and uplink channel conditions. It is reasonable to include the uplink channel status in the calculation of the feedback resource since the uplink channel status determines the capacity, i.e., bits/second per unit frequency band (Hz), of the feedback link. ConsidedConsider a case when SNR of the downlink and uplink are proportion such that <math>\rho_{b,m} / \rho_{FB}) = C_{up,dn}</math> is constant and both SNRs are sufficiently high. Then, the feedback resource will be only proportional to the number of transmit antennas

:<math> b_{FB,min}^* = \lim_{\rho_{FB} \to \infty } \frac{(M-1) \log_2 \rho_{b,m} - (M-1) \log_2 (g-1)}{\log_2(1+\rho_{FB})} = M - 1</math>.