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数学建模 中继器的分布 2011美赛B题
Abstract
Repeater is a network equipment for expanding the distance of the signal transmission. PL can eliminate the impact of repeaters.
With the theory of comb, the distribution of repeater we build spend from the circle in the middle to all directs. From the wireless communication theory, repeater service area is a circle of 18km radius. We determine the minimum number of repeater with gradually approximation method. We obtain the result, and we need 19 repeaters to meet the requirements of 1000 users and circular flat area of radius 40 miles radius, radius of repeater is 11.09 miles. But for the requirement of 10000 users, 19 repeaters can’t meet. We solve this question through increasing the number of repeater. We need to set 37 repeaters after calculating.
As for impact of mountain, we set another repeater on the peak, when peak when this peak hider the transmission of signal. Because the influence of mountain area is the obstacle of peak when signal transmission.
Introduction
Repeater Coordination
The VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by “repeaters,” which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.
In addition to geographical separation, the “continuous tone-coded squelch system” (CTCSS), sometimes nicknamed “private line” (PL), technology can be used to mitigate interference problems. This system associates to each repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the
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