Quasi-omnidirectional beamforming for uniform rectangular array

This letter studies omnidirectional beamforming based on a uniform rectangular array (URA) for common message broadcasting. Noticing a subtle yet important fact that the whole (theta, phi)-angular domain maps to a circular region in the (u, v)-domain, we propose to optimize the beamforming weights to make the power radiation as even as possible only in the circle. The resultant scheme, termed as quasi-omnidirectional beamforming (quasi-OBF), yields near-omnidirectional radiation while the peak-to-average power ratio (PAPR) of the array elements is significantly lower than the state-of-the-art approach, which can help improve the energy efficiency of the power amplifiers (PAs) driving the antenna array. We also prove that even constraining the beamforming weights to be unimodular for maximizing the energy efficiency of the PAs, the omnidirectional beamforming is asymptotically achievable by convergence in L-2 as the number of the URA elements increases to infinity. The theoretical results are corroborated by the numerical simulations.