This paper presents a new optimization framework dedicated for integrated sensing and communication (ISAC) waveform design. In particular, the problem aims at maximizing the total achievable sum-rate, through multi-user interference minimization, while preserving a certain level of similarity to a given desired radar waveform. Aiming towards feasible and practical PHY architectures, we also offer the flexibility of tuning the peak-to-average power ratio to a desired level. Towards this design, a non-convex optimization problem is formulated, and an alternating direction method of multipliers based solution is derived to converge towards the superiority of the final ISAC waveform. Finally, simulation results validate the proposed ISAC waveform design, as compared to state-of-the-art solutions.