Radar and modern communication systems are both evaluating towards higher frequency bands and massive antenna arrays, thus increasing their similarities in terms of hardware structure, channel characteristics, and signal processing pipelines. To suppress the cross-system interference caused by communications and radar systems with shared spectral and hardware resources, the co-design philosophy, wherein the communications and radar/sensing systems can operate in parallel with jointly optimized performance, has drawn substantial attention from both academia and industry. In this paper, we propose a nullspace-based joint precoder-decoder design for spectrum sharing between multicarrier radar and multiuser multicarrier communication systems, by employing the maximizing signal interference noise ratio (max-SINR) criterion and interference alignment (IA) constraints. By projecting the cross-system interference to the designed null spaces, a maximum degree of freedom upper bound for the $K+1$-radar-communication-user interference channel can be achieved. Our simulation studies demonstrate that interference can be practically fully canceled in both communication and radar systems. This leads to improved detection performance in radar and a higher rate in communication subsystems. A significant performance gain over a nullspace-based precoder-only design is also obtained.