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To improve channel throughput and the fairness of random access channels, we propose a new backoff algorithm, namely, the sensing backoff algorithm (SBA). A novel feature of the SBA scheme is the sensing mechanism, in which every node modifies its backoff interval according to the results of the sensed channel activities. In particular, every active node sensing a successful transmission decreases its backoff interval by an additive factor of the transmission time of a packet. In order to find the optimum parameters for the SBA scheme, we have studied the optimum backoff intervals as a function of different numbers of active nodes (N) in a single transmission area with pure ALOHA-type channels. We find that the optimum backoff interval should be 4N times the packet transmission time when the random access channel operates under a pure ALOHA scheme. Based on this result, we have calculated numerically the optimum values of the parameters for SBA, which are independent of N. The SBA scheme operates close to the optimum backoff interval. Furthermore, its operation does not depend on a knowledge of N. The optimum backoff interval and the SBA scheme have been studied also by simulation. It is shown that the SBA scheme out-performs other backoff schemes, such as binary exponential backoff (BEB) and multiplicative increase linear decrease (MILD). As a point of reference, the SBA scheme offers a channel capacity of 0.19 when N is 10, while the MILD scheme can only offer 0.125. The performance gain is about 50%.