Gradient-Based Optimization of Coherent Distributed Arrays

In a coherent communication system consisting of an open-loop distributed transmit array sending messages to a distributed receive array, the combined transmit-receive gain is characterized by the coherent communication gain. We consider the problem of optimizing coherent communication gain using the positions of the individual transmitter and receiver nodes as well as the beam angle of the transmit array as degrees of freedom. We focus on the use of gradient descent to find locally optimal configurations for node positions, which is motivated by two observations: first, the NP-hardness of the problem precludes an exhaustive search for the globally optimal configuration of node positions; and second, the positions of the network nodes are likely not arbitrary. That is, the initial, non-optimized node placement is intentional and is determined by higher-layer network objectives. The hypothesis is that the coherent communication gain of a communication network can be improved in a deterministic fashion using a steepest descent algorithm to make relatively small adjustments to node positions. We develop the closed-form expressions for the rate of change of coherent communication gain with respect to node positions and transmit array beam angle. Next, we use the expressions to implement a spherical quadratic steepest descent (SQSD) algorithm and use simulations to test SQSD alongside pattern search and particle swarm optimization to determine theoretical gain improvements achieved by the algorithms, as well as the expected average node displacement.