Figure 3

Channel direction quantizers, n _{g , m} and$n_{g_k,m_k}\in \mathcal{N}$, channel direction${\tilde{h}}_k$, and its quantized channel direction$n_{g_k,m_k}$. The blue surfaces, including${\mathbf{n}}_{g_k,m_k}$ and n_g,m, on the unit hypersphere describe the corresponding spherical caps,${\mathcal{C}}_{g_k,m_k}\left(\stackrel{2}{sin}\alpha \right)$ andx${\mathcal{C}}_{g,m}\left(\stackrel{2}{sin}\alpha \right)$. Their areas are the same. Here, the quantization error of channel direction, sin2θ _k , is larger than sin2α.