Precoding Performance with Codebook Feedback in a MIMO-OFDM System

Limited feedback precoding is part of the LTE standard. Despite standardization, important fundamental questions, especially relating to the performance due to the use of codebooks and receiver processing techniques, remain to be explored. In order to understand these questions, we consider a single user in a single cell employing single or multi-stream transmission using a variety of codebooks and a choice of different receiver types. We derive expressions for capacity loss relative to perfect feedback due to the limited size of codebook. When multistream transmission is deployed, we show that codebook feedback manifests itself as inter-stream interference resulting in a capacity loss for all receiver types. In the case of SVD receivers, this interference results in a capacity floor. We define a precoding matrix index (PMI) coherence time and bandwidth and show how these parameters are respectively related to channel coherence time and bandwidth. The PMI coherence parameters shed new light on how often feedback is required, both in time and frequency domains, and help us to determine the capacity penalty if feedback is delayed beyond the coherence parameters. Finally, we show the distribution of PMI and also show that this is environment dependent. This supports the need for codebooks that are adaptable to different environments and are not strictly tied to i.i.d. channels.