In this paper, nonlinear schemes are proposed and analyzed for the spectrum sensing in cooperative cognitive radio networks under the influence of impulsive (heavy-tailed) noise. By jointly employing the order statistics, generalized likelihood ratio test, and counting rule in the framework of spectrum sensing according to the noise environment, the proposed scheme is shown to exhibit a better performance than the conventional counterparts. Through computer simulations, the performance characteristics of the proposed cooperative spectrum sensing scheme are investigated and analyzed in various noise circumstances. It is confirmed from numerical simulation results that the proposed scheme, under various noise circumstances which might be different from one cognitive radio to another, can provide significant improvements of performance over the conventional schemes.