Distributed MIMO (DMIMO) communications and specifically the idea of distributed transmit beamforming involves multiple transmitters coordinating among themselves to form a virtual antenna array and steer a beam to one or more receivers. Recent works have successfully demonstrated this concept of beamforming with narrowband, frequency-flat wireless channels. We consider the generalization of this concept to wideband, frequency selective channels and propose two Figures of Merit (FOMs), namely, communication capacity and received power to measure the performance of beamforming.
We formulate the precoder design that maximizes the two FOMs as optimization problems and derive general properties of the optimal precoders. The two metrics are equivalent with frequency-flat channels, whereas, they result in vastly different optimal criteria with wideband channels. The capacity maximizing solution also differs from classical water-filling due to the per-transmitter power constraints of the distributed beamforming setting, whereas, the power maximizing solution involves the array nodes concentrating their power in a small, finite set of frequencies resulting in an overall received signal consisting of a small number of sinusoidal tones. We have not been able to derive closed-form solutions for the optimal precoders, but we provide fixed point algorithms that efficiently computes these precoders numerically. We show using simulations that solution to both these maximization problems can yield substantially better performance as compared to simple alternatives such as equal power allocation. The fixed point algorithms also suggest a distributed implementation where each node can compute these precoders on their own iteratively using feedback from a cooperating receiver. We also establish the relationship between various precoders.
The idea of maximizing received power suggests a natural application of wireless power transfer(WPT). However, the large-scale propagation losses associated with radiative fields makes antennas unattractive for WPT systems. Motivated by this observation, we also consider the problem of optimizing the efficiency of WPT to a receiver coil from multiple transmitters using near-field coupling. This idea of WPT using near-field coupling is not new; however, the difficulty of constructing tractable and realistic circuit models has limited the ability to accurately predicting and optimizing the performance of these systems. We present a new simple theoretical model and take the more abstract approach of modeling the WPT system as a linear circuit whose input-output relationship is expressed in terms of a small number of unknown parameters. We present a simple derivation of the optimal voltage excitations to be applied at the transmitters to maximize efficiency, and also some general properties of the optimal solution. Obviously, the optimal solution is a function of unknown parameters, and we describe a procedure to estimate these parameters using a set of direct measurements. We also present a series of experimental results, first, with two transmitter coils and a receiver coil in a variety of configurations and then with four transmitter coils and two receiver coils to illustrate our approach and the efficiency increase achieved by using the calculated optimal solution from our model.