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The mobile outdoor radio environment is challenging for vehicular communications. Although multipath propagation offers diversity and benefits in non-line-of-sight (NLOS) conditions, simultaneous multipath and mobility results in a doubly-selective fading channel. In practice, this means that the channel parameters vary significantly in both time and frequency within the bandwidth and typical packet durations used in 802.11p/WAVE standards for short-range vehicular communications. This paper presents the results of extensive field trial campaigns conducted in several countries, totaling over 1100 km. These field trials are scenario based, focusing on challenging low-latency, high-reliability vehicle-to-vehicle (V2V) safety applications including intersection collision warning, turn across path, emergency electronic brake light, do not pass warning, and precrash sensing. Vehicle-to-infrastructure (V2I) applications are also considered. The field trials compared the performance of off-the-shelf WiFi-based radio equipment with a more advanced 802.11p compliant radio employing more sophisticated channel estimation and tracking. Field trial results demonstrate significantly improved performance using the advanced radio, translating into greatly increased driver warning times and stopping distances. In fact the results show that off-the-shelf WiFi equipment fails to provide sufficient stopping distance to avert accidents in some cases. During the field trials, channel sounding data were also captured. Analysis of these channel measurements reveals the critical importance of accurate channel estimation, tracking the channel in both time and frequency within each packet. Delay spread and Doppler spread statistics computed from the channel measurements validate previously reported results in the literature. The results in this paper, however, provide the first instance of channel measurements performed simultaneously to application performance evaluation. The objective is to- - firmly establish the link between radio channel characteristics and the performance of critical V2V safety applications.