In this paper, the distributed cooperative communication of unmanned aerial vehicles (UAVs) is studied, where the condition number (CN) and the inner product (InP) are used to measure the quality of communication links. By optimizing the relative position of UAVs, large channel capacity and stable communication links can be obtained. Using the spherical wave model under the line of sight (LOS) channel, CN expression of the channel matrix is derived when there are N_t transmitters and two receivers in the system. In order to maximize channel capacity, we derive the UAVs position constraint equation (UAVs-PCE), and the constraint between BS elements distance and carrier wavelength is analyzed. The result shows there is an area where no matter how the UAVs' positions are adjusted, the CN is still very large. Then a special scenario is considered where UAVs form a rectangular lattice array, and the optimal constraint between communication distance and UAVs distance is derived. After that, we derive the InP of channel matrix and the gradient expression of InP with respect to UAVs' position. The particle swarm optimization (PSO) algorithm is used to minimize the CN and the gradient descent (GD) algorithm is used to minimize the InP by optimizing UAVs' position iteratively. Both of the two algorithms present great potentials for optimizing the CN and InP respectively. Furthermore, a hybrid algorithm named PSO-GD combining the advantage of the two algorithms is proposed to maximize the communication capacity with lower complexity. Simulations show that PSO-GD is more efficient than PSO and GD. PSO helps GD to break away from local extremum and provides better positions for GD, and GD can converge to an optimal solution quickly by using the gradient information based on the better positions. Simulations also reveal that a better channel can be obtained when those parameters satisfy the UAVs position constraint equation (UAVs-PCE), meanwhile, theory analysis also explains the abnormal phenomena in simulations.