Antenna and user selection for a cloud base station with (Reverse) Compute and Forward

We consider a distributed antenna system where L antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity R₀, and serve K user terminals (UTs). The uplink is a special case of a multi-source, single destination relay network. The downlink is a special case of a broadcast relay network. Recently, novel uplink and downlink schemes called Compute-and-Forward and Reverse Compute-and-Forward were proposed, showing attractive performance-complexity tradeoff in certain regimes. In this work we focus on the ATs (uplink) or UTs (downlink) selection problem. For the uplink, for a given set of active UTs, we wish to select a subset of the ATs such that the resulting system matrix is full-rank and the sum rate is maximum. For the downlink, for a given set of transmitting ATs, we wish to select a subset of UTs such that the resulting system matrix is full-rank and the sum rate is maximum. We present antenna and user terminal selection algorithms suited for the proposed cloud base station architecture and demonstrate by simulation, in a realistic environment with fading and pathloss, that selection essentially eliminates the problem of rank deficiency of the system matrix, which represents the main performance impairment effect for a naive assignment of the active terminals.