With the rapid development of wireless communication technology, the spectrum resources are increasingly strained which needs optimal solutions. Cognitive radio (CR) is one of the key technologies to solve this problem. Spectrum sensing not only includes the precise detection of the communication signal of the primary user (PU), but also the precise identification of its modulation type, which can then determine the a priori information such as the PU' service category, so as to use this information to make the cognitive user (CU) aware to discover and use the idle spectrum more effectively, and improve the spectrum utilization. Spectrum sensing is the primary feature and core part of CR. Classical sensing algorithms includes energy detection, cyclostationary feature detection, matched filter detection, and so on. The energy detection algorithm has a simple structure and does not require prior knowledge of the PU transmitter signal, but it is easily affected by noise and the threshold is not easy to determine. The combination of multiple-input multiple-output (MIMO) with CR improves the spectral efficiency and multipath fading utilization. To best utilize the PU spectrum while minimizing the overall transmit power, an iterative technique based on semidefinite programming (SDP) and minimum mean squared error (MMSE) is proposed. Also, this article proposed a new method for max-min fairness beamforming. When compared to existing algorithms, the simulation results show that the proposed algorithms perform better in terms of total transmitted power and signal-tointerference plus noise ratio (SINR). Furthermore, the proposed algorithm effectively improved the system performance in terms of number of iterations,