Reduced Overhead Distributed Consensus-Based Estimation Algorithm Ban-Sok Shin, Henning Paul, Dirk W¨ ubben and Armin Dekorsy Department of Communications Engineering University of Bremen Bremen, Germany Email: {shin, paul, wuebben, dekorsy}@ant.uni-bremen.de Abstract—We consider a cooperation among nodes in a net- work which aim to reconstruct a common broadcast message. Distributed estimation algorithms are highly suited for such a scenario. Nevertheless, communication overhead due to an exchange of variables among nodes can be problematic con- cerning energy efficiency and costs. In this paper, we present a Reduced Overhead Distributed Consensus-based Estimation (RO-DiCE) algorithm exhibiting a significantly reduced com- munication overhead in comparison to its unreduced version, the DiCE algorithm. However, by reducing the overhead a possible degradation in estimation performance of the algorithm is introduced. We investigate the RO-DiCE algorithm in terms of communication overhead, convergence behavior and error rate performance for different network topologies. We will show that for a full mesh topology the RO-DiCE algorithm is identical to the DiCE algorithm. I. I NTRODUCTION In a cooperative scenario, a network consisting of connected nodes aims to recover a common message broadcast by a detached source. One approach for cooperative reconstruction is a centralized scheme: A central node, also termed Fusion Center (FC), processes the received information of all nodes jointly in order to estimate the broadcast message [1], [2]. Obviously, this scheme lacks robustness since an outage of the FC would corrupt the whole estimation process. A more robust scheme can be achieved by a distributed reconstruction of a common message via In-Network-Processing (INP). Here, no central node is needed since each node calculates an estimate of the broadcast message by incorporating informa- tion from neighboring nodes in the network improving the robustness e.g., against link failures. In [3], we presented a distributed consensus-based estimation (DiCE) algorithm derived from a Least Squares (LS) optimization problem. This algorithm establishes a scheme where nodes in a network exchange information with each other in order to reach the centralized solution iteratively. Other distributed consensus- based algorithms were proposed, e.g., in [4], [5]. Compared to [4], the DiCE algorithm showed a faster convergence and higher robustness against link failures while keeping the same estimation performance. The application of the DiCE algorithm for future mobile communication systems is topic of current research. In the EU FP7 ICT project iJOIN, dense networks consisting of small cells, termed iJOIN Small Cells (iSCs), are introduced. This deployment enables cooperation among small cells aiming to reconstruct the same message e.g., of one user equipment (UE). In [6], an application of the DiCE algorithm to Multi- User-Detection (MUD) in such a scenario is investigated. Further investigations of the DiCE algorithm concerning er- roneous inter-node links were discussed in [7]. Both [4] and [7] describe the necessity of exchanging quantities in a unicast fashion between the nodes. Obviously, this exchange causes a high communication overhead in the network since each quantity depends on the transmitting and receiving node. In contrast, for a broadcast transmission quantities depend on the transmitting node only. In this paper, we present a reduced overhead version of the DiCE algorithm in [3], the RO-DiCE, which avoids the exchange of quantities in a unicast fashion. We will compare the RO-DiCE algorithm to the DiCE algorithm in terms of communication overhead, convergence behavior and error rate performance. 1 2 J 3 4 s x 1 x J Fig. 1. Network consisting of J connected nodes, each receiving a different observation x j of the original message s. Dotted lines indicate an access link, solid lines an inter-node link. II. SYSTEM MODEL Fig. 1 depicts the basic transmission scenario. A message s ∈ R N×1 is broadcast by a source and received by J connected nodes which are set up to a network. The network is described by means of a graph G := {E , J} consisting of a set of nodes J := {1,...,J } and a set of undirected edges E⊂J×J assuming that inter-node links are symmetric. A set of neighbors N j is assigned to each node j containing