Spatial shaping in cognitive system with coded legacy transmission

We consider the coexistence of a secondary user with a single-antenna primary link which is not fully loaded. The secondary user has multiple antennas and performs spatial shaping. First we consider the case when single-user decoding is deployed at the cognitive receiver. By spatial shaping, the secondary user can optimize its achievable rate under the rate constraint of the primary user, and a closed-form solution is derived. Then we study the case when successive decoding is viable at the cognitive receiver and rate splitting is applied at the cognitive transmitter. In both cases the cognitive transmitter can operate at its full power. Both theoretical analysis and simulation results show that spatial shaping with single-user decoding converges to maximum ratio transmission (MRT) as the primary link approaches null load, and converges to zero forcing (ZF) as the primary link approaches full load. When successive decoding is viable, rate splitting increases the cognitive rate compared to single-user decoding. Finally, we discuss the control signaling needed to perform spatial shaping in cognitive system with legacy transmission.