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Let $\mathcal{C}_{R} = \left\{R_0 = 0, R_1, R_2, \ldots, R_{2^{B_1}-1}\right\}$ be the codebook for the fixed-length quantizer $\mathcal{Q}_{R}$. The selected rate for the transmitter will be $R_{s}$ such that $R_{s} < \left|\left|\pmb h\right|\right|^2 \leq R_{s+1}$, where $0 \leq s\leq 2^{B_1}-1$.   Let $\mathcal{Q}_{b}$ be the variable-length quantizer in our previous work. Then, for ${\pmb h}$ and the selected rate $R_s$, we can find an appropriate beamforming vector such that $\left|{\pmb h}^{+}{\pmb w}\right|^2 \geq R_s$ R_s$, and the average feedback rate is finite.   The left problem is to design the codebook $\mathcal{C}_R$.  \section{Power Allocation for Non-Orthogonal Multiple-Access (NOMA) Systems with Limited Feedback}