Zero-forcing precoding: Difference between revisions

Revision as of 22:52, 15 February 2012

Revision as of 23:03, 4 July 2012

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=== Quantify the feedback amount ===

Quantify the amount of the feedback resource required to maintain at least a given throughput performance gap between zero-forcing with perfect feedback and with limited feedback, i.e.,,

:<math>\Delta R = R_{ZF} - R_{FB} \leq log_2 g</math>.

Jindal showed that the required feedback bits of ana [[Spatial Correlation|spatially uncorrelated]] channel should be scaled according to SNR of the downlink channel, which is given by<ref name="Jindal_ZF"/>:

:<math> B = (M-1) \log_2 \rho_{b,m} - (M-1) \log_2 (g-1) </math>

where ''M'', is the number of transmit antennas and <math>\rho_{b,m}</math> is the SNR of the downlink channel.

To feedbackfeed back ''B'' bits though the uplink channel, the throughput performance of the uplink channel should be larger than or equal to 'B'

:<math> b_{FB} \log_2(1+\rho_{FB}) \geq B </math>

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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 chanel conditions. It is reasonable to include the uplink channel status in the calcurationcalculation 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. ConsidedrConsided 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 proportionproportional 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>.

It follows from the above equation that the feebackfeedback resource (<math>b_{FB}</math>) is not necessary to scale according to SNR of the downlink channel, which is almost contradict to the case of the feedback bits. WeOne, hence, seesees that the whole systematic analysis can reverse the facts resulted from each reductioned situation.

==See also==