In this paper, we investigate a cooperative spectrum sensing scheme in which the local sensors at the secondary users perform an M-level quantization on the local decision statistic, and the quantized data are reported through erroneous channels, to be fused under Neyman-Pearson (N-P) criterion. The local quantization can be as fine as the bandwidth limitations permit; thus, the idea behind our effort is to smooth up the path towards the challenge of cooperative spectrum sensing under bandwidth constraints. We initially aim at formulating the N-P fusion rule with M-level quantization of the decision statistic. In this vein, we derive the required randomized test for the N-P fusion that represents the total performance of our spectrum sensing scheme. We further introduce a tight lower bound for the optimal performance of the primary user signal detection. An analytical procedure towards the bound and its relevant quantization setup at the local sensors are proposed and examined through case studies. The proposed near optimal bound gets closer to the optimal performance as the channel probability of error decreases, such that for ideal channels, it is seen to provide the exact optimal performance.