Optimum Antenna Separation for V2V MIMO with Ground Reflections

The problem of optimum antenna separation for a vehicle-to-vehicle (V2V) multiple antenna system is addressed here by considering the combined effects of line-of-sight (LOS), path loss, and ground reflections. Our work extends previous approaches that were based exclusively on LOS assumptions. It is shown that by introducing the new impairments, the LOS solution no longer complies with the orthogonality condition, thus being sub-optimal in more general settings. A more accurate solution is proposed, which is based on a series expansion model that numerically boils down to a polynomial root problem. To reduce the complexity of this solution we propose a reformulation of the problem as the minimization of a cost function. A two-stage approach is employed to address this optimization: 1) the LOS solution is used as an initial approximation to the optimum separation, and 2) the approximation is improved using a gradient descent iterative tool. The LOS solution is shown to improve its accuracy for the more realistic scenario when the inter-vehicular distance increases. The solutions presented here partially fill a gap in V2V antenna design by increasing robustness under changing propagation/configuration settings.