Out-Sphere Decoder for Non-Coherent ML SIMO Detection and its Expected Complexity

In multi-antenna communication systems, channel information is often not known at the receiver. To fully exploit the bandwidth resources of the system and ensure the practical feasibility of the receiver, the channel parameters are often estimated and then employed in the design of signal detection algorithms. However, sometimes communication can occur in an environment where learning the channel coefficients becomes infeasible. In this paper we consider the problem of maximum-likelihood (ML)-detection in single- input multiple-output (SIMO) systems when the channel information is completely unavailable at the receiver and when the employed signalling at the transmitter is q-PSK. It is well known that finding the solution to this optimization requires solving an integer maximization of a quadratic form and is, in general, an NP hard problem. To solve it, we propose an exact algorithm based on the combination of branch and bound tree search and semi-definite program (SDP) relaxation. The algorithm resembles the standard sphere decoder except that, since we are maximizing we need to construct an upper bound at each level of the tree search. We derive an analytical upper bound on the expected complexity of the proposed algorithm.