J. O. Coleman

Optimal array-pattern synthesis for wideband digital transmit arrays
D. P. Scholnik and J. O. Coleman
Some next-generation RF 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 DSP would generally represent an inefficient use of computational resources; thus we propose instead to place an FIR 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 polarizationsn.
authors' two-column manuscript, unofficial but with nicely typeset math (3.1 Mbytes)
IEEE version, official but with badly typeset math (9.9 Mbytes)
Published in the IEEE Journal on Selected Topics in Signal Processing, Special Issue on Convex Optimization Methods for Signal Processing, vol. 1, no. 4, December 2007, pp. 660-677.
September 2007.