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Fast proliferation of IEEE 802.11 wireless devices has led to the emergence of High-Density (HD) Wireless Local Area Networks (WLANs), where it is challenging to improve the throughput because each device has to share channel with all the other devices within its carrier sensing range. Although the existing adaptive Physical Carrier Sensing (PCS) techniques can improve the throughput, they result in high frame loss rate. In this paper, we investigate a Multi-AP (MAP) architecture, in which each user can associate with multiple APs according to the network topology and traffic distribution, for adaptive PCS based HD-WLANs. One of important features of the MAP architecture is that it can obtain Multi-AP diversity in both uplink and downlink. In uplink (from users to APs) the frame loss rate can be decreased by combining the reception of all associated APs, and in downlink the throughput can be improved significantly by dynamically selecting one of associated APs for transmissions according to the channel fading and traffic distribution. We first study the uplink and downlink performance of the MAP theoretically, and then propose an AP association algorithm for deciding which APs to associate with, an AP selection algorithm for dynamically selecting an AP for downlink transmissions, and an ACK management solution for avoiding ACK collisions. We build a testbed based on Intel StarEast platform to make real experiments for performance evaluation. In a typical experiment scenario, compared to the scheme with the adaptive PCS only, up to 30% throughput gain can be observed in uplink, and nearly 100% throughput gain can be found in downlink.