Base Station Cooperation With Feedback Optimization: A Large System Analysis

In this paper, we study feedback optimization problems that maximize the users' signal to interference plus noise ratio (SINR) in a two-cell multiple-input multiple-output broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this information to the base stations (BSs) over the uplink channels. The BSs then use the channel information to design their transmission scheme. Two types of feedback are considered: 1) analog and 2) digital. In the analog feedback case, the users send their unquantized and uncoded channel state information (CSI) over the uplink channels. In this context, given a user's fixed transmit power, we investigate how he/she should optimally allocate it to feed back the direct and interfering (or cross) CSI for two types of BS cooperation schemes, namely, multicell processing (MCP) and coordinated beamforming. In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using the random vector quantization scheme, with different size codebooks. The users then send the index of the quantization vector in the corresponding codebook to the BSs. Similar to the feedback optimization problem for the analog feedback, we investigate the optimal bit partitioning for the direct and interfering link for both types of cooperation. We focus on regularized channel inversion precoding structures and perform our analysis in the large system limit in which the number of users per cell $(K)$ and the number of antennas per BS $(N)$ tend to infinity with their ratio $\beta=({K}/{N})$ held fixed. We show that for both types of cooperation, for some values of interfering channel gain, usually at low values, no cooperation between the BSs is preferred. This is because, for these values of cross channel gain, the channel estimates for the cross link are not accurate enough for their knowledge to contribute to improving the SINR and there is no benefit in doing BS cooperation under that condition. We also show that for the MCP scheme, unlike in the perfect CSI case, the SINR improves only when the interfering channel gain is above a certain threshold.