In this work, spatially-discrete traveling-wave modulation (SDTWM) is applied to an electrically small antenna (ESA) to increase its efficiency-bandwidth product. The antenna is formed of closely coupled sectors and is rotationally symmetric. It supports a fundamental radiating mode as well as non-radiating modes that are analogous to discrete orbital angular momentum modes. Time-modulated capacitors, placed in each sector, couple these modes using SDTWM. The modulation scheme is similar to that of a classic negative-resistance parametric amplifier, but instead of using the modulation to obtain gain from the system, the modulation parameters are chosen to enhance the matching bandwidth of the antenna. We show how this can be done by choosing an appropriate combination of the modulation depth and modulation frequency. After extending the definition of radiation efficiency and mismatch loss to the case of a parametrically time-varying antenna, the extended definitions are used to characterize the simulated performance of the time-varying antenna under two different SDTWM modulation schemes. The first modulation scheme couples the radiative mode to a single non-radiative mode, while the second modulation scheme couples the radiative mode to two different non-radiative modes. Both schemes yield efficiency-bandwidth products that are 6.4-7.6 dB larger than that of the time-invariant version of the antenna.