Wednesday, February 25, 2009

How Much Feedback Is Enough for MIMO? IV Channel Quantization

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]

Generally, MIMO channel quantizer or CQI generation, maps the input channel estimation vector to the index of a codeword in the codebook. The decode will do the reverse. It is similar to the vector coding in EVRC, AMR, MPEG-4, etc. The designing a best codebook as well as finding the general boundary of Voronoi cell is NP-hard.

Figure 1. MIMO Precoding Mismatching

With Figure 1, it is shown that there are multiple issues involving MIMO precoding mismatching. In most existing MIMO beamforming systems, the receiver tracks the channel norm information for link adaptation purpose and the phase information for beamforming precoding. In this case, Dh can be rewritten by

Dh = 2M σh2 [ 1 - ( 1- Dθ )1/2 ]

with Dθ denoting the phase quantization deviation. A lower bound for distortion rate of channel quantization for MIMO beamforming is

R( Dθ )   ≥ max{ - M log2[ 2 - 2( 1- Dθ )1/2 + σh2h2 ], 0 }

for each beam. With the feedback rate of R, it also tells us that the minimum precoding mismatch for forwardlink MIMO beamforming is

Dθ ≤ 1-[1-2-R/M-1 + σh2/(2σh2)]2

Figure 2. The rate-distortion region with M = 4

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