Convex synthesis of concentric ring arrays with quantized, dynamic-range-limited excitations

Concentric ring arrays radiate nearly azimuth-invariant sidelobes, but a realizable excitation must respect a finite amplitude resolution and a bounded feed dynamic range. Low-sidelobe design is cast as a second-order cone program in the per-ring excitations, the dynamic range ratio (DRR) is imposed as a convex constraint, and the b-bit quantization is solved by a mixed-integer second-order cone program coupling Dinkelbach fractional programming with cutting-plane sidelobe sampling, returning an optimality certificate. A deterministic greedy engine solves the same discrete problem without a solver, and the ring radii are updated by sequential convex programming with the quantized, DRR-bounded amplitude re-solved at each step. On a 385-element geometry without a DRR ceiling, the certified engine equals or exceeds re-implemented Firefly and particle-swarm designs at every resolution in a third of their runtime, while the greedy engine stays within 0.36 dB two orders of magnitude faster. A method-of-moments model with mutual coupling shows the array-factor model overstates a 4-bit design by 3.6 dB, chiefly through lost rotational invariance; re-solving the identical programs on the full-wave operator recovers 1.5 dB. Unconstrained, the certified design also has lower DRR and 0.20 dB less taper loss.