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Figure 1 Distribution of quantized 2-by-1 beamforming vector based on fixed feedback rate.
Compared with the fixed feedback rate scheme, the proposed method delivers a better performance without incurring additional feedback bandwidth.
The multiplexing gain of the downlink with DF and fixed feedback bits per user is zero due to the ceiling effect.
Although this upper bound is quite loose, it does also predict the ceiling effect on the achievable rate with fixed feedback bits per user.
From Figure 3, it can be seen that when using a variable feedback rate the codebook that appears in Figure 2 is closer to the optimal codebook than the one with a fixed feedback rate as shown in Figure 1. Figure 3 Optimal codebook trained using the maximum MSIP criterion.
The resulting controllers are compared with alternative suggested structures for adaptive tracking with fixed feedback, and differences are pointed out through simple interpretations of the respective schemes.
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For fixed feedback-link capacity constraint, the downlink achievable rates of ZF-DPC are bounded as the downlink SNR tends to infinity, which indicates that the downlink multiplexing gain with fixed feedback-link capacity constraint is zero.
From Corollary 1, it is obvious that the downlink multiplexing gain with fixed feedback-link capacity is zero.
We plot the lower and upper bounds on the achievable ergodic sum rates obtained in Theorems 1 and 2 with fixed feedback-link capacity constraint in Figure 1.
The achievable ergodic rate of ZF-DPC with AF and fixed feedback-link capacity is upper bounded for arbitrary downlink SNR: (27).
The lower and upper bounds on the achievable ergodic sum rate obtained in Theorems 5 and 6 with fixed feedback-link capacity constraint are plotted in Figure 6.
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