Approximate bounds for limited backhaul uplink multicell processing with single-user compression

This paper studies single-user compression for the uplink multi-cell processing (MCP) model where multiple base-stations are connected to a central processor via noiseless backhaul links with a sum capacity constraint. The proposed scheme is based on the virtual multiple-access channel (V-MAC) architecture, where the base-stations quantize the received signals and send the quantized bits to the central processor, and at the decoder side the central processor first recovers the quantized signals then decodes the user messages in a successive manner. This paper focuses on the use of single-user compression in the V-MAC architecture, which is significantly simpler to implement than Wyner-Ziv compression. The main result of this paper is that single-user compression can achieve the sum capacity of the MCP model to within a constant gap under two specific scenarios. First, we define a diagonally dominant channel criterion and show the constant-gap result for the case when the covariance matrix of the received signals across the base-stations is κ-strictly diagonally dominant for some constant κ > 1. Second, we show that the constant-gap result holds for a special class of Wyner channel models in the weak interference regime.