Base Station Cooperation With Feedback Optimization: A Large System Analysis

Abstract

In this paper, we study feedback optimization problems that maximize the users' signal to interference plus noise ratio (SINR) in a two-cell MIMO 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. TheBSs then use the channel information to design their transmission scheme. Two types of feedback are considered: analog and digital. In the analog feedback case, the users send their unquantized and uncoded 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 base station cooperation schemes, namely, Multi-Cell Processing (MCP) and Coordinated Beamforming (CBf). In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using RVQ, 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 in 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 β = 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 base stations 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 base station 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.

Base Station Cooperation for Confidential Broadcasting in Multi-Cell Networks

“…Actually, the advantage of using α * MCP againstα * MCP can be very obvious as well if some other network parameters are considered, e.g., β = 1. These observations indicate that the optimal values of α without secrecy considerations given by [24] are no longer optimal for the networks with secrecy considerations.…”

“…Figure 4 plots the large-system secrecy rate per transmit antenna, R ∞ s /(2N ), versus . Specifically, we compare the performances for two different designs of α: 1) the optimal α that maximizes the large-system secrecy sum rate, i.e., α * MCP given by (26) for the MCP or α * CBf obtained by Algorithm 1 for the CBf and 2) the optimal α that maximizes the largesystem sum rate without secrecy considerations given by [24], i.e.,α * MCP for the MCP orα * CBf for the CBf. We find that the performance achieved by α * MCP or α * CBf is always better than that achieved byα * MCP orα * CBf .…”

“…Proof: See Appendix A. Theorem 2: In the large-system regime, the secrecy sum rate achieved by the generalized RCI precoder for the CBf converges almost surely to a deterministic quantity given by (24), where ρ C = α/N , Λ is the solution of x to…”

Optimal Power Allocation and User Loading for Multiuser MISO Channels with Regularized Channel Inversion

“…We should note that in evaluating R (i),∞ sum , we use {β j } allocation scheme in Lemma 3, β = i j=1 β j and also the stationary conditions in (19) and (20) to determine ρ andp respectively. The value for β M must satisfy (21) with ν M = 0 and η M = 0, i.e.,…”

“…The analysis in this paper assumes perfect CSI at the BS even though this is hard to obtain in practical scenarios. The impact of imperfect CSI at the BS with RCI precoder has been investigated in some work, e.g., [18], [19] and [20]. The optimization problems considered in this paper together with imperfect CSI can be a subject for future investigation.…”