Optimal Array-Pattern Synthesis for Wideband Digital Transmit Arrays

Some next-generation radio frequency systems are expected to share a common transmit aperture among multiple users across a wide range of frequencies and functions such as radar and communications. The requisite linear architectures and digital signal generation will permit far greater flexibility in the design of array patterns than traditional time-delay steered wideband transmit arrays. Merely replicating the traditional architecture in digital signal processing would generally represent an inefficient use of computational resources; thus, we propose instead to place a finite-impulse response filter per input signal at each element and to directly optimize the resulting wideband array pattern. For this architecture, we present a passband-equivalent transmit-array model and derive expressions for wideband directivity, efficiency, error sensitivity, gain, peak and mean-square sidelobes, mainlobe frequency-response flatness, and polarization. All can be constrained using second-order cone programming, a highly-efficient type of convex optimization. Several examples illustrate the design tradeoffs, including the need to limit undesirable superdirective effects in wideband arrays. The system model and the derivations are general enough to admit almost any array architecture, including arbitrary element locations, nonuniform element responses, and multiple polarizations.