Codebook Design for the Finite Rate MIMO Broadcast Channel with Zero-Forcing Precoding

We present a novel codebook design criterion for the limited feedback MIMO broadcast channel with zero-forcing precoding. To reduce system implementation complexity, each user has the same codebook. We derive a new sum-rate bound, show the bound maximization problem is invex and explicitly solve it using the Karush-Kuhn-Tucker (KKT) conditions. We show that the solution has the same structure as Grassmannian frames. We also derive a new lower bound on the outage probability. We show via simulations that our codebooks designed using Grassmannian frames outperform random vector quantization with different codebooks at each user for codebook sizes greater than 9 bits.