This paper investigates the use of cooperative spectrum sensing (CSS) to detect primary user (PU) signals during spectrum sharing between the PU and the secondary user (SU). In particular, we employ a variant of CSS (which achieves space diversity), called weighted gain combining CSS (W-CSS), which has the potential to achieve increased diversity gain and enhance detection performance. In a typical W-CSS system, the SU needs to obtain the PU signal power information in order to set the proper weight value. However, as it is hard for the SU to ascertain whether the PU is present or absent, this is difficult to obtain. To address this problem, a PU signal power estimation algorithm is introduced. In addition, we also analyze the statistics of the estimator and derive the detection probability of the W-CSS when the PU signal power estimation algorithm is applied. The analysis and related simulation results reveal that the detection probability of the proposed W-CSS under time-variant Rayleigh fading asymptotically approaches the detection probability in an additive white Gaussian noise channel as the number of antennas is increased. This also follows results from our Monte Carlo simulations, showing that multiple antenna elements could suppress the effect of Rayleigh fading. In short, the accuracy of the estimation algorithm is affected by channel variation (especially in the case of fast Rayleigh fading). Hence, to address this problem, we employ multiple antenna elements with a square-law combining energy detector in the W-CSS.