Limited feedback signaling for spatially correlated broadcast channels employing 
linear beamforming is considered. Towards the goal of a systematic limited 
feedback codebook construction, we first study the performance of a pessimistic, 
but tractable statistical linear beamforming design. Leveraging the structure of 
the density function of weighted norms of isotropically distributed beamforming 
vectors, we establish the structure of the optimal statistical beamforming 
vectors. This optimal beamforming vector is the solution to a generalized 
distance maximization problem. Based on this intuition and building on 
single-user feedback design, we develop codebooks that significantly and 
consistently outperform naive RVQ codebooks (designed for i.i.d. channels) 
for the practically relevant small feedback bit regime.