On Lattice Network Coding Based Cell-Free MIMO With Uncoordinated Base Stations

This paper studies a cell-free MIMO (cf-MIMO) system that consists of a central unit (CU),
$N$
distributed base stations (BSs) and
$K$
users. The BSs are connected to CU via
$N$
independent backhaul (BH) links of finite capacities. The BSs are uncoordinated, i.e. each one is ignorant of the others. We study a lattice network coding (LNC) scheme for cf-MIMO. In the uplink, the
$K$
users encode their messages with a practical
$2^{m}$
-ary channel code mapped to
$2^{m}$
-PAM, belonging to the ensemble of lattice codes, and transmit simultaneously. Each BS computes independent streams of integer-combinations of the users’ messages, referred to as network coding (NC) streams. The NC streams are forwarded to the CU via BH. The CU aggregates all NC streams from the
$N$
BSs, and recovers
$K $
users’ messages. We derive the achievable symmetric rate of the LNC scheme. Further, we solve a “bounded independent vectors problem” (BIVP) which identifies a near-optimal set of NC coefficient vectors. The solution maximizes the number of correctly computed NC streams at each BS. For practical implementation, we develop new soft detection algorithms for LNC decoding. The per-user complexity is proved to be no greater than
$O(K)$
, suitable for cf-MIMO with a large number of users. Our developed LNC based cf-MIMO exhibits superior frame error rate (FER) and spectral efficiency over existing non-LNC based schemes. Such advances are achieved with low-cost parallel processing and efficient usage of the BH.