Network diversity multiple access protocols (NDMA) have been shown to considerably outperform previously proposed algorithms. However, several issues in their analysis remain unsolved, particularly under the assumption of imperfect collision-multiplicity detection in asymmetrical system configurations (i.e., configurations where the users have different channel and queuing statistics). To partially fill this gap, this paper presents a detailed study on stability, throughput and delay properties of asymmetrical nonblind NDMA protocols under such imperfect detection assumption. Additionally, the protocol formulation includes a carrier-sense mechanism which is found to improve system performance under finite-SNR environments and which can be useful in assessing the benefits of retransmission diversity on IEEE 802.11 wireless local area networks (WLANs). New expressions for the parameters and performance metrics of the NDMA protocol under different assumptions are here provided. These include the stability condition of a system without feedback to acknowledge correct packet reception and the derivation of the boundaries of the throughput region using a joint cross-layer optimization with respect to the probabilities of transmission and false alarm. Simulation results are used to further assess the performance of the protocol and to confirm the analytic results.