In this paper, we consider the primary user detection problem in cognitive radio systems by using multi antenna at the cognitive radio receiver. An optimal linear combiner multi antenna based spectrum sensing technique is proposed using the multitaper spectrum estimation method. A suboptimal square law combiner multi antenna based technique, using the multitaper method, is also proposed. The decision statistics’ probability density functions of the proposed techniques are derived theoretically. Probabilities of detection and false alarm formulae are presented using the Neyman Pearson criterion. Both proposed techniques are derived when energy detector is used. Based on our results, we found that the general likelihood ratio detector1 (GLRD1) and the blind GLRD that are proposed in the literature, require signal to noise ratios SNRs=7.5 and 9.6 dB, respectively to achieve a probability of detection of 99.99% at false alarm 1% with additive white Gaussian noise (AWGN) using 4 antennas and 16 samples for sensing. In our proposed optimal and suboptimal techniques, the required SNRs are found as 12 and 7.5 dB, respectively to achieve the same probabilities in the same conditions. Of course, this result gives an indication that even GLRD multi antenna based spectrum sensing techniques are blind in their philosophy, but that comes at the expense of their performance. Simulation results that confirm the theoretical work are also presented. An AWGN and Rayleigh flat fading environments are examined in the results. Finally, a new concept of cooperative spectrum sensing, the master node, is introduced.