This paper investigates linear soft combination schemes for cooperative spectrum sensing in cognitive radio networks. We propose two weight-setting strategies under different basic optimality criteria to improve the overall sensing performance in the network. The corresponding optimal weights are derived, which are determined by the noise power levels and the received primary user signal energies of multiple cooperative secondary users in the network. However, to obtain the instantaneous measurement of these noise power levels and primary user signal energies with high accuracy is extremely challenging. It can even be infeasible in practical implementations under a low signal-to-noise ratio regime. We therefore propose reference data matrices to scavenge the indispensable information of primary user signal energies and noise power levels for setting the proposed combining weights adaptively by keeping records of the most recent spectrum observations. Analyses and simulation results demonstrate that the proposed linear soft combination schemes outperform the conventional maximal ratio combination and equal gain combination schemes and yield significant performance improvements in spectrum sensing.