Millimeter-wave and Terahertz frequencies, while promising high throughput and abundant spectrum, are highly susceptible to hardware non-idealities like phase-noise, which degrade the system performance and make transceiver implementation difficult. While several phase-noise compensation techniques have been proposed, there are limited results on the post-compensation system performance. Consequently, in this paper, a generalized reference-signal (RS) aided low-complexity phase-noise compensation technique is proposed for high-frequency, multi-carrier systems. The technique generalizes several existing solutions and involves an RS that is transmitted in each symbol, occupies adjacent sub-carriers, and is separated from the data by null sub-carriers. A detailed theoretical analysis of the post-phase-noise compensation performance is presented for an analog beamforming receiver under an arbitrary phase-noise model. Using this analysis, the performance-impact of several system parameters is examined and the throughput-optimal designs for the RS sequence, RS bandwidth, power allocation, number of null sub-carriers, and the number of estimated phase-noise spectral components are also derived. Simulations performed under 3GPP compliant settings suggest that the proposed scheme is robust to phase-noise modeling errors and can, with the optimized parameters, achieve better performance than several existing solutions.